Dispatches From Turtle Island

Higgs Prediction Revisited

2012-02-27T09:20:00.002-07:00

Last year, I predicted at this blog that a Standard Model Higgs boson would have been discovered or ruled out by the time that the Academy Awards were awarded in 2012, which happened yesterday. Overall, I give myself credit for being more right than wrong. While we don't have a five sigma "discovery" in hand, the evidence at the end of last year, which when updated early this year approaches 4 sigma, makes the case that a Higgs boson of approproximately 125 GeV exists quite strong, and strongly disfavors a Higgsless model. Moreover, the details of that discovery rather strongly support the notion that this particle lacks a net electromagnetic charge and tends to show rather strongly that it has spin zero.

The discovery to date doesn't definitively rule out the possibility that there may be additional Higgs bosons out there, as in SUSY models, or that the discovered particle is actually composite, but there is no evidence strongly pointing towards the ressonance seen having any characteristics inconsistent with a Standard Model Higgs boson.

W Boson Mass Refined

2012-02-24T13:31:00.000-07:00

One of the parting boons provided by Tevatron experiment (now shut down) to the world is an updated and more precise measurement for the mass of the W boson. The Tevatron result, combined with the past measurements leads us to conluded that "the new world average for the W boson mass is . . . 80390 +/- 16 MeV." Before this result, the accuracy was +/- 23 MeV.

Neutrinos Don't Move Superluminally After All

2012-02-24T13:18:00.000-07:00

Since September, scientists have been scratching their head over results that appear to show neutrinos traveling between Switzerland and Italy faster than light would. . . . there was a good reason the measurements and reality weren't lining up: a loose fiber optic cable was causing one of the atomic clocks used to time the neutrinos' flight to produce spurious results. If the report is confirmed (right now, there's only one source), then it provides a simple explanation for the fascinating-yet-difficult-to-accept results. According to the new report, researchers are preparing to gather new data with the clocks properly hooked into computers, which should definitively indicate whether the loose connection was at fault.

From here via Gauge Connection.

Just to recall the situation, the initial report has shown neutrinos travelling at speeds a detectable, but tiny percentage rate in excess of the best measured values of the speed of light, when special relativity and what we know about the kinetic energy of the neutrinos and their rest masses would have caused us to expect them to travel at speeds below the speed of light by an amount too small to be experimentally detectable.

Everyone in the physics community had suspsected as a most likely explanation experimental error, which appears to have been the cause of the superluminal speeds detected, to be at fault, but until no, no one had been able to point to a source of experimental error that would create a discrepency sufficiently large to explain the result.

A variety of theoretical explanations for variations of the theory of special relativity had been advanced to explain it (I myself viewed the possibility that the measured speed of light is actually slightly lower than the true value of "c" in the equations of general and special relativity due to interactions with electromagnetic phenomena unaccounted for previously in the vicinity of massive bodies of ordinary matter, i.e. an error in past rather than current experiments, as most likely if the experimental result from OPERA were confirmed). But, it turns out that those theoretical explanations will end up being disfavored going forward since their prediction that indeed OPERA could be seeing superluminal neutrinos didn't turn out to be accurate.

Drought Doomed The Mayans

2012-02-23T17:11:00.002-07:00

A prolonged decline in the frequency of summer storms that produced a drought in Central America (and beyond) lead to the demise of Mayan civilization around 800-950 CE. Their demise, in turn, cleared the way for the ascendancy of the subsequent Aztec civilization, that started to develop in what is now Southern Mexico in the late 1200s CE, which was in place when Columbus arrived in the New World (in 1492 CE) until the Aztec empire of Moctezuma II was toppled by Conquistador Hernán Cortés with the empire having collapsed by 1521 CE. In between, in what is known as the "Post Classical" period, the Mayan empire fragmented into successor city-states that gradually recovered and were consolidated into the renewed Aztec empire. The Mayans were successors to the Olmec civilization from ca. 2000 BCE to 400 BCE.

Predictors of Phoneme Inventory

2012-02-21T20:27:00.000-07:00

Why do different languages have different numbers and kinds of vowels and consonants?

The data point to latitude and the number of people who speak a language as having statistically significant impacts on consonant inventories and word length as related to vowel inventories (multiple citations are omitted in the blockquote below without editorial indication):

[C]onsonants are more likely to be found further away from the equator and . . . more vowels are associated with shorter word lengths. . . .

The clustering of a large number of consonants north and south of the equator might be the result of climatic zones. Cold-climate languages, for instance, are found to have a high frequency of consonants at a very low frequency (obstruents). By contrast, languages in warm climatic zones possess sound classes exhibiting moderate to high levels of sonority (rhotic consonants, laterals, nasals and vowels).

As for word length: It is widely acknowledged in the literature that vowels and consonants subtend to different linguistic functions. Consonants are often associated with word identification, whereas vowels contribute to grammar and to prosody. Vowel quality is also implicated in regular sound change, which results in paradigmatic changes, whereas consonants are frequently cited as being changed through lexical diffusion. Lastly, consonant systems expand with “minimum articulatory cost”, whereas vowel systems appear to follow pressure for maximal perceptual differences.

All of this, in turn, is part of a larger slew of recent rebuttals of Atkinson's 2011 paper purporting, quite unconvincingly with statistical tools and a popular online atlas of language features, to show serial founder effects in the global patterns of phoneme inventories, which would suggest that as people moved further from Africa that they lost sounds from their languages without gaining new ones.

Another key point made in the whole post, but not really captured in the quote above, is that the data aren't as independent as they seem, because phonemes are embedded in an interdependent set of language features such that particular language features bias languages towards having many other complementary features, and when one of these features changes, other features typically change in response to them. Put another way, most language features are functional rather than neutral, even though they show great diversity from language to language.

I Come To Praise SUSY, Not To Bury It.

2012-02-21T19:53:00.001-07:00

Another summary of the latest non-detection and expanded exclusion range for stops (supersymmetric partners of top quarks) at Resonaances spells out the situation:

To a casual observer, the seminar presenting the results may have resembled a reenactment of the Saint Valentine's day massacre. Nevertheless I will argue here -- more out of contrariness than conviction -- that SUSY may be battered, bruised, covered in slime, and badly bleeding, but formally she is not yet dead. For most particle theorists, the death will be pronounced scalar partners of the top and bottom quarks are excluded up to ~500 GeV, the precise threshold depending on taste, education, and diet. That's because excluding light stops and sbottoms is going to squash any remaining hopes that supersymmetry can address the naturalness problem of electroweak symmetry breaking, for which purpose it was originally invented. However, the LHC collaborations have yet not presented any robust limits on the stop masses. Instead, here's what the LHC have taught us about SUSY so far:

* Since summer 2011 we know that in a generic case when all colored superpartners including stops have comparable masses and decay to the lightest supersymmetric particle (LSP) producing a considerable amount of missing energy then stops have to be heavier than about 1 TeV.

* Since last Tuesday we know if the only squarks below TeV are those of the 3rd generation then gluinos have to be heavier than about 600-900 GeV, depending on the details of the supersymmetric spectrum. . . .

To summarize, the year 2012 will surely go down in history as the Higgs year. But among more studious future historians of science it may also be remembered as the year when SUSY, at least in its natural form, was finally laid to grave...

Another major report on experimental support for SUSY is due in a couple of weeks.

An experimental exclusion of SUSY entirely is quite a bit more profound than it seems at first glance. Nobody but particle physics geeks knows much about SUSY. But, string theory necessarily implies SUSY, so an experimental exclusion of SUSY is also an experimental exclusion of string theory. And, string theory is a beyond the Standard Model theory with a much better P.R. agent than SUSY.

Let me repeat this simply so that those of you who aren't paying attention can get it:

The Large Hadron Collider is on the verge of experimentally ruling out all of the most plausible versions of string theory.

Why is this huge?

Probably about half of the theoretical physicists in academic positions in the United States right now are string theorists. Most of the beyond the Standard Model theories being tested at the LHC are predictions of SUSY or String Theory. String theory, despite its waning prominence, has far more published work and far more adherents among professional physicists than any other beyond the standard model theory that could unify the three Standard Model forces into a "Grand Unified Theory" (i.e. GUT) or unify these with gravity as well into a "Theory of Everything" (i.e. TOE).

At one point people thought that there were a lot more alternatives to String Theory, but then, somebody figured out that all of the different versions are just different ways of describing what is called "M theory".

Sometimes people talk about Loop Quantum Gravity (LQG) as a competitor to String Theory, and as a quantum gravity theory, it is a competitor. But, LQG doesn't even aspire to be a GUT or a TOE.

Various versions of a beyond the Standard Model theory called "Technicolor" are on life support too, because fundamentally, Technicolor is a theory designed to solve theoretical problems that arise if it turns out that there is Higgs boson at a mass on the same order of magnitude as the W and Z bosons. But, the likely discovery of a 125 GeV +/- Higgs boson pretty much makes Technicolor obsolete. The failure of experiments to reveal magnetic monopoles or proton decay has also culled a lot of naively attractive GUT models other than string theory.

Thus, disproving SUSY, together with other recent developments, basically brings theoretical physicists back to square one in the errand of trying to unify all of the fundamental forces found in physics and explain why we have the particles that we do from a more fundamental basis.

Neanderthal Social Structure Summarized

2012-02-20T15:13:00.000-07:00

A new open access paper summarizes what we can infer about the social structure of the Neanderthals, which looks a lot like the social structure of modern human hunter-gatherers.

I would suggest: 1) that the 5 km radius from which the vast bulk of raw material was obtained corresponds to the normal subsistence exploitation range for bands while they occupied a given site, as is consistent with ethnographic observations of hunter/gatherers' usual foraging ranges of up to 5 km (per Higgs and Vita-Finzi 1972; Hayden 1981, 379–81); 2) I would interpret the tools and blanks (generally without bulk raw lithic material) from the 5–20 km radius (and possibly up to 50 km – as seems to be the pattern in Figure 7) as curated tools carried from site to site by individuals belonging to a single local band and travelling within the full band's normal subsistence territory (i.e. c.1250–2800 sq km); 3) I would view the very small but consistent number of finished lithics derived from more than 50 km, even up to 300+ km, as most likely representing curated tools transported, used and discarded in the course of episodic interactions between bands, e.g. during multi-band aggregations or alliance visits. Band ranges of 1250–2800 sq km within a 13,000 sq km interaction network would result in 5–10 or more small local bands forming a larger ‘macroband’ or mating network as previously discussed. . . . there were linguistically distinctive Neandertal groups of about 200–500 that preferentially interacted and intermarried with each other and maintained some sort of group identity, which also distinguished them from enemies whom they occasionally killed and cannibalized. . . .

A number of sites from Europe, the Near East and the Ukraine all exhibit occupation floor areas and hearth patterns that indicate the existence of local bands as the basic, year-round social units with about 12–25 members, including children and the aged, probably organized into nuclear family groups. The use of some sites by smaller hunting or task groups, or even by occasional individual families foraging temporarily on their own, is probably also represented in the archaeological record. . . .

[V]isiting between bands, fluidity in band membership between allied bands, preferential intermarriage between allied bands, and periodic aggregations of a number of allied bands probably involving ritual sanctifications, all make good sense in the European Middle Palaeolithic. The transport of stone tools beyond 30–50 km from sources appears to reflect periodic visiting with other bands or the aggregation of several allied bands. Kill sites such as Mauran, representing over 1000 tons of meat butchered over a few centuries or millennia, and ritual sites such as Bruniquel may reflect such aggregation and social bonding events between local bands or their representatives.

There is clear evidence of enemy relationships among Neandertals in terms of cannibalism, and it seems most likely that there were conscious social distinctions between allied local bands and enemy bands, probably also expressed in terms of dialectical or linguistic differences, similar to those exhibited among the low-density ethnographic populations in Australia and Boreal North America. Thus, there are compelling reasons to conclude that there were, indeed, ethnic identities among Neandertals. . . .

There are also indications of the elevated status of some individuals in Neandertal communities, including preferential treatment in life of some aged or infirm individuals, preferential burial treatments, skull deformation, skull removal, special clothing or painted body designs, personal adornments or prestige objects, and the use of small exclusive ritual spaces. . . . status was probably . . . linked to one or more other domains such as ritual, war, kinship or intergroup relations.

While some researchers have questioned whether Neandertals had a significant sexual division of labour, there are good reasons for assuming that such divisions were just as strongly developed, if not more so, as those among ethnographic hunter/gatherers.

Cemeteries, although rare, seem to have existed in the most productive environments and may reflect corporate kinship groups that owned specific resource locations, or, more conservatively, may have simply symbolically expressed membership in a consciously recognized social group such as the local band.

Overall, the cognitive and social differences between Neandertals and anatomically modern humans that are highly touted by some researchers seem relatively insignificant, if they existed at all, at the level of basic cognitive and sociopolitical faculties. . . .

The main differences that are apparent between Middle and Upper Palaeolithic groups seem to be related to the development of complex hunter/gatherer social organization and economies in some areas of the Upper Palaeolithic versus the simpler hunter/gatherer economies and societies of the earlier Palaeolithic (aspects of which continued to characterize ethnographic hunter/gatherers in resource-poor environments).

Italians Detect 1.4 MeV solar neutrinos

2012-02-14T16:45:00.002-07:00

Italian scientists have detected solar neutrinos with an energy of 1.4 MeV (i.e. mega-electron-volt) which had been predicted to arise from proton-electron-proton interactions that give rise to deuterium in the sun.

About 1 in 400 solar deuterium atoms are made this way, rather than through the usual proton-proton fusion process that produces much higher energy neutrinos. Neutrinos arising from interactions at particle colliders are likewise much more energetic (on the order of 140 MeV). About three such neutrinos are detected each day at their lab placed deep underground to filter out interference from sources other than neutrinos which interact very weakly with ordinary matter, confirming our understanding the nuclear physics that are going on in the sun.

High energy neutrinos move so close to the speed of light that it is virtually impossible to make meaningful determinations about neutrino rest mass, since their relativistic kinetic energy so profoundly dwarfs their very small mass. In principle, measurements of the speed of low energy solar neutrinos traveling at a speed distinguishably less than that of the Lorentz transform speed limit of special relativity could make it possible to directly infer the rest mass of a neutrino with much greater accuracy.

The energetic equivalent of the mass of an electron is about 0.5 MeV/c^2, and the mass of the up and down quarks respectively are on the order of single digit MeV equivalents. The various varieties of ordinary neutrinos are believed to have rest masses in the KeV to eV range, closer in mass-energy to photons than other fermions.

SUSY Rumors A Bust

2012-02-14T16:30:00.002-07:00

Woit explains at his blog that rumors of a major experimental indication of supersymmetric particles at the Large Hadron Collider, which would have been announced today, turned out to be unfounded. The latest LHC data simply increased the mass threshold below which a couple of types of proposed bosons in supersymmetric theory, stops (the supersymmetric partner of the top quark) and gluinos, have been ruled out experimentally.

South Asian Paleoclimate Documented

2012-02-14T15:37:00.007-07:00

How was the South Asian paleoclimate data gathered?

A new study provides about ten thousand years of continuous climate data for South Asia.

This research, lead by researchers from the Woods Hole Oceanographic Institute, analyzed evidence from a Bay of Bengal sediment core, which captures discharges from the large Godavari river system. The core data comes from carbon isotopes of leaf waxes, reflecting the amount of arid-adapted/savannah vegetation in the Godavari catchment, and oxygen isotopes from a marine microfossil that record salinity. This points to a general aridification trend over the course of the middle and late Holocene, supporting what we already would infer from pollen data in Rajasthan or monsoon proxies in the Arabian Sea, but this time providing more direct evidence from South India.

Given the strong role of seasonal monsoons in the climate of South India that is lacking in the Mediterranean basin and West Eurasia, it wouldn't have been surprising if South India's climate was quite distinct, even at the level of general trends, from the climate of places further to the West.

What does the study tell us about South Asian pre-history?

The two particularly big events in South Asian pre-history that one would like to establish the role of paleoclimate in motivating are the collapse of Harappan civilization in the Indus River Valley that preceded the rise of Indo-Aryan expansion from the same vicinity (ca. 1500 BCE, give or take), and the rise of agriculture in South India (ca. 2500 BCE, give or take), which is likely to be associated with the rise of the culture that led to the expansion of the Dravidian languages. Towards this end, the conclusion of the study states that:

The significant aridification recorded after ca. 4,000 years ago may have spurred the widespread adoption of sedentary agriculture in central and south India capable of providing surplus food in a less secure hydroclimate. Archaeological site numbers and the summed probability distributions of calibrated radiocarbon dates from archaeological sites, which serve as proxies of agricultural population, increase markedly after 4,000 BP in peninsular India. . .

In contrast, the same process of drying elicited the opposite response in the already arid northwestern region of the subcontinent along the Indus River. From 3,900 to 3,200 years BP, the urban Harappan civilization entered a phase of protracted collapse. Late Harrapan rural settlements became instead more numerous in the rainier regions at the foothills of the Himalaya and in the Ganges watershed.

There are some indications supported by Rig Vedic legend, archaeological ruin distribution, and satellite imagery that the event in the Indus River watershed may have concluded more dramatically, with one of the major tributaries to the Indus River shifting to a new course and leaving a huge expanse of the old Hakra river basin that was once at the heart of Harappan civilization suddenly dry in what is now the Cholistan Desert. For example, a recent search of sites in this desert found a Indus Valley Civilization seal from golden age of that culture.

The dates mentioned by the paper (ca. 2000 BCE for the South Indian Neolithic and ca. 1700-1200 BCE for the demise of Harappan civilization) are a bit later than the dates I have seen based on the oldest known remains in each region. I've seen estimates dating the oldest South Indian Neolithic sites to 2500 BCE, and there are traces of Indo-Aryan influence in the Cemetery H culture back to about 2000 BCE in the Northwest India/Northern Pakistan, and 1900 BCE is frequently used as an end point for Harappan civilization. But, the differences aren't huge and seem to be fairly consistent in magnitude and direction. They could simply reflect dates that are trying to capture the very earliest points at which a new civilization appears and the point in time at which it really starts to thrive.

Were there major droughts in South India, or was the trend a gradual one?

One curious point that isn't mentioned in the blog post on this study (but may be hidden in the data) is that in the Fertile Crescent region there were two very distinct severe droughts in the same general time period that punctuated the general trend towards aridity in the Holocene there.

One was happened at roughly 2000 BCE and is associated with the collapse of the Akkadian Empire in Mesopotamia, the First Intermediate Period in Egypt, and the beginning of the rise of Hittite power in Anatolia. The other was around roughly 1200 BCE is associated with the sweep of significant historical events across the ancient West Eurasian world known as Bronze Age Collapse. It remains unclear if these droughts extended as far east as South Asia, and this data set would be the obvious place to look for these punctuated period of drought as opposed to a more gradual trend towards aridity.

We also know from North American pre-historic paleoclimate correlations with archaeology that prolonged droughts are the sorts of things that can cause civilizations to fall and lead to dramatic upheavals in human affairs.

The answer to this question calls for a closer analysis of the data than I can do right now, and may require access to non-open access sources. Insights in the comments on this point would be greatly appreciated.

An Early Human Role In Climate Change?

The data from South India are also relevant to the extent to which Holocene climate change may have been driven by human activity. The new data tend to argue for human activity changes as an effect rather than a cause of early Neolithic era climate change.

The trend towards aridity in the Holocene corresponds with the rise of the Neolithic era when humans started farming and herding, activities that had significant ecological effects locally. But, the question of cause and effect arises.

Did farming and herding arise and start to become more important out of necessity because increased aridity made hunting and gathering lifestyles less viable, and perhaps favored agriculture in other ways, for example, by producing fewer deluge storms that could destroy crops)?

Or, did farming and herding disrupt ecosystems that were critical to maintaining regional homeostasis and stabilizing weather patterns, for example, by preventing soil from turning to dust and entering the atmosphere. This would be early human activity driven climate change, and in West Eurasia, where the prevailing winds can carry Fertile Crescent climate effects across the rest of the region, a causal connection isn't implausible.

But, South India developed agriculture about four or five thousand years after it appeared in the Indus River Valley and five or six thousand years after it arose in the Fertile Crescent, and aridity in South India is mostly driven by monsoon rains from the Southeast, so the human activity in the Fertile Crescent and Indus River Valley shouldn't have much impact on its aridity, and agricultural activity in China (both North and South) would have been sufficiently remote that it would be surprising to see early agriculture there influencing climate in South India whose whether patterns are more tied to conditions in Indonesia and Southeast Asia than to China.

If South India was seeing the same kinds of climate change trend towards aridity as West Eurasia at about the same times, the case that the rising trend towards aridity in West Eurasia was the product of human activity is weakened as a hypothesis.

Note: Minor updates to language and links added on February 20, 2012.

Evidence Mounts For Massive Gluons

2012-02-13T15:52:00.003-07:00

Quantum Chromodynamics (QCD) is the study of how quarks and gluons interact, something about which there is a great deal of experimental evidence and consensus in high energy settings (aka ultraviolet), but about which there is less of a consensus in low energy (aka infrared) where quarks and gluons are confined within composite particles whose internal activity is harder to probe experimentally without increasing the energy of the system to UV levels. We have QCD equations from the Standard Model that make it possible to calculate this behavior in principle, but the math is very, very hard to compute with, even with supercomputers.

Conventionally, we talk about gluons as having a zero rest mass, but that analysis is model dependent (the model assumes a constant mass subject only to Lorentz adjustments) and based on a fit to exclusively UV range data.

The emerging consensus is that faster moving gluons approach zero mass, while slower moving gluons approach a finite mass on the order of 600 MeV +/- about 15%.

The interpretation of the Landau gauge lattice gluon propagator as a massive-type bosonic propagator is investigated. Three different scenarios are discussed: (i) an infrared constant gluon mass; (ii) an ultraviolet constant gluon mass; (iii) a momentum-dependent mass. We find that the infrared data can be associated with a massive propagator up to momenta ~500 MeV, with a constant gluon mass of 723(11) MeV, if one excludes the zero momentum gluon propagator from the analysis, or 648(7) MeV, if the zero momentum gluon propagator is included in the data sets. The ultraviolet lattice data are not compatible with a massive-type propagator with a constant mass.

The scenario of a momentum-dependent gluon mass gives a decreasing mass with the momentum, which vanishes in the deep ultraviolet region. Furthermore, we show that the functional forms used to describe the decoupling-like solution of the Dyson–Schwinger equations are compatible with the lattice data with similar mass scales.

From O Oliveira and P Bicudo, Running gluon mass from a Landau gauge lattice QCD propagator (2011) J. Phys. G: Nucl. Part. Phys. 38 045003 doi:10.1088/0954-3899/38/4/045003.

At any rate, that is my take on what to make from analysis of the current state of research that is often stated in terms that make less direct statements about quantities and properties of QCD entities familiar to non-QCD specialists than the abstract from a 2011 paper cited above.

This "decoupling solution" to the QCD equations appears to yield a stable result which should be confirmed by physical results if they can ever be made, while the alternative, a "scaling solution," in which a zero momentum gluon is massless, is apparently unstable and hence unlikely to have a physical manifestation.

The implications of the decoupling solution are weird. In special relativity, a massive particle gets gains effective mass as it goes faster. In the QCD decoupling solution, a massive particle loses effective mass as it goes faster. Special relativity "feels" a bit like air resistance. QCD "feels" a bit like the relationship betweeen the friction experience by something moving along a snow covered surface and its speed.

But, there are elements of a massive gluon approach that are quite attractive and intuitive in light of the other data and constraints. It helps explain why the mass of ordinary protons and neutrons and also more exotic combinations of quarks seems to come mostly from the gluons and not the quarks. It fits the intuition that massive bosons should be associated with short range forces, while massless bosons should be associated with long range forces. It fits the notion that the strong force (which gets more insurmountable with distance and nearly vanishes at short range) looks a bit like the inverse of gravity (which gets weak at long range and strong at shorter ranges). It provides a way to reconcile disparate data from low energy and high energy contexts that appear to be inconsistent with a constant gluon mass or a massless gluon.

Not every little glitch in the theory has been neatly ironed out and presented definitively, but the trends towards this interpretation becoming dominant seems to be mounting.

Descendants Of Confucius

2012-02-10T21:10:00.002-07:00

Confucius lived in China about 1500 years ago. How many of the 1.2 billion living people in China have him somewhere in their family tree today?

Probably, almost all of them.

A couple of days ago, Victor Mair wrote about some provocative behavior on the part of "Kŏng Qìngdōng 孔庆东, associate professor in the Chinese Department at Peking University, who also just happens to be the 73rd generation descendant of Confucius (Kǒng Fūzǐ 孔夫子 ; Kǒng Qiū 孔丘), or at least he claims to be a descendant of Confucius." . . .

[In numerical geneological models there was] a threshold, let us say Un generations ago, before which ancestry of the present-day population was an all or nothing affair. That is, each individual living at least Un generations ago was either a common ancestor of all of today's humans or an ancestor of no human alive today. Thus, among all individuals living at least Un generations ago, each present-day human has exactly the same set of ancestors. We refer to this point in time as the identical ancestors (IA) point. . . .

Within China, there's been more than enough mixing to ensure that by now, if anyone is a descendent of Confucius, everyone is.

From here.

The date for a most recent common ancestor of all members of a population by any line of descent is generally (and logically) considerably more recent than the identical ancestor point.

Also, realistically, there is enough non-randomness and structure in human reproductive choices that "almost everyone is" to a very high percentage figure (perhaps 99.999%+) is probably quite more likely to be the case than literally "every single person is." There might be only 12,000 people or less in China who are not descended from Confucius at all, but in real life, there are probably some people who are not.

An exploration of the kind of assumptions one has to make to reach these conclusions is explored in the linked post. Suffice it to say that the results are quite robust with range of numerical values for assumptions in population models that is much broader than intuition would suggest producing similar historical points at which all persons in a population have a shared common ancestors and an identical set of ancestors (not necessarily in the same proportions) respectively.

I have not quoted an estimate in the original post regarding the likelihood that someone in China has a least one of their genes derived from Confucius because, as pointed out in the comments to that post, the estimate is profoundly wrong.

The actual probability that a Han Chinese person has a gene derived from Confucius from some ancestor is actually on the order of 2.5% (assuming that there are about 25,000 genes in humans) not "3 chances in a quintillion" as the original post claims, because the original post ignores that fact that most people will have multiple lines of descent to the same historical person. But, the underlying point, that having someone in your geneology does not necessarily mean that you have any genetic descent from them several dozen generations later, is a valid point.

As a footnote, the increasingly strong possibility that most people in a large population will have multiple lines of descent (indeed a great many multiple lines of descent) to most or all of the total set of people who are ancestral to the current population, is very much the same kind of observation that makes it heuristically very likely that Goldbach's Conjecture is true for all very large numbers.

The identical ancestor point has some very practical implications for population genetics. For example, the closed set of ancestors implies that, with the exception of mutations that have happened since the identical ancestor point and managed to remain in the gene pool, that the set of genes present in someone in the population is closed at the IA date.

The way the numbers work out, a population that isn't fully isolated from another population is typically going to have an IA date that is certainly within the Holocene era (i.e. about twelve thousand years ago) and typically somewhere within the historic era (i.e. about six thousand years ago). Of course, sustained periods of complete isolation of different populations from each other pushes the IA date back to sometime before the populations were separated. But even slight amounts of population exchange for a surprisingly small number of generations can dramatically reduce the time frame in which everyone in two populations have a most recent common ancestor or identical ancestors.

Tree Ring Data Underestimates Temperature Declines Due To Volcanos

2012-02-08T14:52:00.001-07:00

You can use tree rings to estimate climate cooling due to volcanic erruptions. But, this method of estimating paleoclimate has limitations, especially in cases of rapid and severe volcanic erruption driven climate change, because all cooling below a given threshold is invisible since tree rings can get no smaller or aren't formed at all in a given year if it is too cold.

Rigor In Quantum Field Theory

2012-02-08T12:51:00.003-07:00

Axiomatic QFT is an attempt to make everything absolutely perfectly mathematically rigorous. It is severely handicapped by the fact that it is nearly impossible to get results in QFT that are both interesting and rigorous. Heuristic QFT, on the other hand, is what the vast majority of working field theorists actually do — putting aside delicate questions of whether series converge and integrals are well defined, and instead leaping forward and attempting to match predictions to the data. Philosophers like things to be well-defined, so it’s not surprising that many of them are sympathetic to the axiomatic QFT program, tangible results be damned.

The question of whether or not the interesting parts of QFT can be made rigorous is a good one, but not one that keeps many physicists awake at night. All of the difficulty in making QFT rigorous can be traced to what happens at very short distances and very high energies. And that’s certainly important to understand. But the great insight of Ken Wilson and the effective field theory approach is that, as far as particle physics is concerned, it just doesn’t matter. Many different things can happen at high energies, and we can still get the same low-energy physics at the end of the day. So putting great intellectual effort into “doing things right” at high energies might be misplaced, at least until we actually have some data about what is going on there.

From Sean Carroll at Cosmic Variance (emphasis added).

The rigor issues axiomatic QFT theorists are concerned about is mostly taught in the upper division undergraduate mathematics course called "Real Analysis", which I skipped in favor of applied subjects myself, betraying my biases on this issue.

Nobel prize winning physicist Richard Feynman publicly worried quite a bit about the rigor of quantum field theory and convergent infinite series in particular, but probably didn't lose much sleep over it. If you don't lose sleep over helping to invent the nuclear bomb, infinite series that might not converge are probably not going to do you in either

The emphasized sentence is really the key one from a practical perspective. This is the line between what we can say that we know as a result of the Standard Model with considerable confidence, and what we recognize that we don't know with current quantum mechanical equations.

The very short distance issue, at its root, boils down to assumptions in quantum mechanics that (1) particles are point-like, (2) space-time is continuous rather than discrete, (3) locality in space-time is always well defined, and (4) the effects of general relativity (as distinct from the effects specific to special relativity that is well accounted for in quantum mechanics) on how systems behave is modest. The tools of "analysis" in mathematics (i.e. advance calculus) are pretty much useless in situations where the first three assumptions do not hold. To do interesting mathematics without those three assumptions, you pretty much have to use "numerical methods" which means that you can basically only do calculations by having computers conduct myriad subcalculations that it would be impracticable to do by hand (which helps explain why research programs that abandoned those assumptions never really got very far until powerful computers were available).

The fourth assumption (the absence of extreme general relativity effects) is different in kind and more fundamental. General relativity inherently gives rise to all sorts of singularities, which mathematicians abhor, in the "classical" (meaning non-quantum mechanical) formulation of these equations, and any mathematically rigorous reformulation of general relativity on a quantum mechanical basis needs some sort of asymptotic limit that instrinically prevents the equations from blowing up in the wrong ways as one comes close to what would be the singularities in the normal formulation of general relativity.

Loop quantum gravity is one fairly successful research program (so far) at developing a way of addressing these issues of rigor in assumptions (2), (3) and (4) are dispensed with in lieu of a discrete space-time in which locality is only an imperfect and emergent implication of the theory at super-Planckian scales, and the effects of general relativity are fully accounted for by the theory. LQG is a work in progress, but hasn't yet hit the kind of seemingly insurmountable theoretical roadblocks to progress that have cropped up in String Theory, the other main approach in theoretical physics that is trying to formulate a rigorous treatment of gravity at a quantum scale.

The high energy issue also implicates the effects of general relativity in quantum systems, and also recognizes that there may be beyond the Standard Model physics that are unified or present new particles or forces at high energies rather than displaying the force specific symmetries observed at experimentally accessible energy scales.

The loop quantum gravity program has very little to say about these issues of high energy physics, but these issues are at the heart of String Theory.

The point about the limited utility of theorizing without sufficient data to provide much guidance is an astute one, and the story of String Theory is one of a theory with so many degrees of freedom that no one can find a unique version of it that can be derived from experimental observable and tested with current technology, or even technology conceivable in the next few decades.

Arcadian Pseudofunctor Ends

2012-02-08T12:15:00.004-07:00

For reasons not disclosed, Kea has discontinued her Arcadian Pseudofunctor blog, a theoretical math and physics blog, which has appeared in the sidebar here for some time. Kea is a female theoretical physicist from New Zealand who has lately been in the frustrating situation have having the appropriate academic training to do the work, but not the academic affiliation necessary to have proposed publications taken seriously, get invited to the relevant academic conferences, and so on. I've appreciated her many interesting posts.

I wish her the best and hope, as seems to be the case, that she will continue to be a presence in the physics blogosphere through comments on blogs and academic paper posting at ViXra, of which she has several, and so on.

Maintaining a blog is a time consuming labor of love that for a physicist can eat time better spent doing research, that doesn't necessarily always reach the intended audience, so I can understand that there are a multitude of good reasons why one might decide to close one.

Since this blog is no longer active, I have removed it from the sidebar.

Pre-Out Of Africa Population Sizes and Densities

2012-02-07T10:11:00.000-07:00

Dienekes notes the latest estimate of the population size of modern humans ca. 130,000 years ago, which would be just prior to the Out of Africa event, citing and quoting from Per Sjödin, Agnès E Sjöstrand, Mattias Jakobsson and Michael G B Blum, "Resequencing data provide no evidence for a human bottleneck in Africa during the penultimate glacial period" Mol Biol Evol (2012)doi: 10.1093/molbev/mss061.

Using the estimates of autosomal mutation rates derived from actual direct measurement in mother-father-child trios, which I believe to be more accurate than the mutation rate inferred from human-chimpanzee divergence, the effective population size was about 12,000 (95% confidence interval 9,000-15,000), implying a "census" population of about 90,000-150,000 modern humans who are ancestral to people who remain in the gene pool today in Sub-Saharan Africa.

The researchers note that:

Assuming that the range of humans extends over all the 24 millions km2 of Sub-Saharan Africa, the density of humans at that time would have been extremely low between 0.5 and 1.4 individual per 100 km2, which is even lower than the lowest recorded hunter gatherer density of 2 individuals per 100 km2 reported for the !Kung (Kelly 1995) and the density of 3 individuals per 100 km2 estimated for Middle Paleolithic people (Hassan 1981). However, this discrepancy disappears if humans were restricted to an area some 3-6 times smaller than the entire Sub-Saharan Africa.

However, as the modern population densities of Sub-Saharan Africa make clear, an assumption of a uniform population density in Middle Paleolithic Africa makes no sense. Some habitats are better for modern humans hunter-gatherers than others, and the !Kung continue to survive as a hunter-gatherer and herder society precisely because they live someplace with among the worst conditions for modern humans that it is possible to survive upon. In contrast, Middle Paleolithic modern human hunter-gatherers would have lived in the optimal environments for their life style in which they evolved in the first place.

A better estimate of Middle Paleolithic population densities would be to assume that the 120,000 modern humans of 130,000 years ago were distributed in a way roughly proportional to modern population densities (which still have to reflect ecological habitability due to a lack of economic development), with areas that would not have a floor population density of at least the 2 per 100 km2 population density of the !Kung being effectively uninhabitable by sustainable modern human populations in that area, and the population densities of modern humans in prime territory like the African Rift Valley being much greater - approaching peak population densities seen in hunter-gatherer socities based on fishing in places like the Pacific Northwest during the Pre-Columbian era. A population density of 10 per 100km2 with a much smaller percentage of Sub-Saharan Africa within the modern human range at that point (perhaps just 5% to 10% of the total area) seems like a more plausible assumption.

Archaic Homins Had Alzheimer's Disease Risk Genes

2012-02-03T23:29:00.000-07:00

John Hawks notes that both Neanderthals and Denisovians, where ancient DNA provides any sign at all, had genetic markers that are associated with an enhanced risk of Alzheimer's Disease in Europeans today. It isn't clear what to make of this fact as he explains with a few disclaimers, although it isn't terribly surprising that any gene related to inferior intellectual function is less common in modern humans than it was in archaic hominins.

The Roots Of The Na-Dene Languages Are In Alaska

2012-02-03T14:37:00.004-07:00

Alaska is the presumed starting point for (at least) three very important migrations that defined the cultural history of the entire Western Hemisphere, but so far the archaeological record within the state has shed virtually no light on two of them, and relatively little on the third. . . .

The first of these migration is, of course, the initial peopling of the Americas in the Late Pleistocene. . . . Recent research in various places has increasingly indicated that the Clovis culture of around 13,000 years ago was not the direct result of the earliest migration into the Americas, but it is still the case that any migrations during the Pleistocene (and it’s increasingly looking like there were at least two) almost certainly would have had to go through Alaska. Unfortunately, despite several decades of looking, no sites have yet been found in Alaska itself that can plausibly be taken to reflect the first immigrants into North America from Asia. An increasing number of early sites have been identified in the past twenty years, but these are all still too late to represent a population ancestral to Clovis or any of the other early cultures found further south. Part of the problem here is that preservation conditions for archaeological sites in most of Alaska are atrocious, and in many areas even finding early sites is extremely difficult. The fact that the state is huge and sparsely populated also means that very little of it has even been surveyed for sites[.]. . .

The second of the migrations I mentioned above is that of speakers of Athapaskan languages [Ed. also known as the Na-Dene languages] to the south, ultimately as far as the Southwestern US and the extreme north of Mexico. As I’ve mentioned before, it’s long been quite obvious that Navajo and the various Apache languages, as well as several languages of California and Oregon coasts, are closely related to a larger number of languages in Alaska and northwestern Canada. The distribution of the languages, as well as some internal evidence in the southern branch, strongly suggests that the direction of the migration that led to this situation was north-to-south, and similar evidence similarly suggests that the start point was somewhere in what is now Alaska. Despite the enormous distance over which Athapaskan languages are now spread, the greatest diversity of the languages grammatically is actually found within Alaska. That is, some Alaskan languages are more closely related to Navajo than they are to other Athapaskan languages in Alaska. While this is all clear linguistically, tracing the actual migration archaeologically has been enormously difficult at both ends. Athapaskan archaeology in Alaska in particular is remarkably poorly understood compared to the archaeology of Eskimo groups, due in part to the fact that Athapaskans have mostly occupied the interior areas that are harder to investigate than the primarily Eskimo coastal areas. . . .

The third migration, and by far the best understood, is that of so-called Thule peoples from northwestern Alaska eastward across the Arctic as far as Greenland.

From here (emphasis and editorial comment added).

While the genetic distinctiveness of the Na-Dene compared to other Native Americans already favored a distinct Na-Dene migration wave to North America from Siberia, and that fact that the Navajo and Apache languages have their roots in Northwestern North America was widely understood, the evidence that the maximum linguistic diversity is in Alaska rather than the Pacific Northwest of the United States, for example, is still significant.

The linguistic evidence tends to coroborate and enhance the genetic evidence by independently disfavoring the possibility that the Na-Dene have origins in a population expansion within some enclave of the pre-existing Native American population that made some economic breakthrough (perhaps some new fishing or hunting technique) and had rare genes that were lost due to serial founder effects in other parts of the New World. It also tends to validate linguistic connections between the Na-Dene and the Yenesians (e.g. the Ket people of Central Siberia) by putting the source population for the North American Na-Dene people pretty much as close to their Old World origins as they could possibly be.

Linguistic evidence of Alaskan origins for the Na-Dene also tell us that the oldest Na-Dene archaeological remains in the interior of Alaska ought to be older than the oldest Na-Dene arcaheological remains in contexts where the conditions to preserve these relics is better, which accompanied by our knowledge that the Na-Dene were likely post-Clovis, helps pinpoint places in Alaska (and particular sedimentary layers at particular digs within Alaska) where is makes sense to look for early Na-Dene archaeology. Archaeologists need to be looking for cites centuries or even millenia earlier than the earliest known Na-Dene sites anywhere else in North America.

But, perhaps most tempting of all is the observation that "some Alaskan languages are more closely related to Navajo than they are to other Athapaskan languages in Alaska." This suggests that it may be possible in the case of these languages, as it was in the case of the Bantu languages and the languages of the people of Madagascar, and the languages of the European Gypsies (aka Roma), to identify the source of an exceptionally long distance prehistoric migration not just to the place where the source language family as a whole was spoken, but to one very geographical specific place within that region that was the source of the particular group of long distance migrants who were the source of the expansion.

Each of these examples also cross validate each other. They suggests that often a long distance migration is going to involve an isolated, "heroic" journal of a single community of people with their origins in a single place, no doubt lead by some visionary leader (he may have seemed crazy at the time), to a new homeland whose links to the larger linguistic and cultural grouping in which they have their origins is filtered entirely through the way it manifests in this particular community, and stands in opposition to migration models that posit bland, almost random walk, diffusions of peoples who are experiencing population expansions.

Narratives like the Biblical Exodus story, rather than being implausibly far fetched, seem to be almost paradigmatic of how a long distance migration of an ethnically distinct population to the new homeland happens. The push and pull factors that motivated these long range migrations at the time, and the events that were critical in making it possible for the new arrivals to displace or culturally dominate the pre-existing residents of their new homes may be forever lost to history, but these kinds of migrations necessarily must have had those aspects to them.

Actually, it isn't quite that simple. Viewed more closely, the linguistic evidence is suggestive of Eastern Athapaskan languages arising from two distinct waves of migration with origins in or around Southern Alberta, and Western Athapaskan languages including Navajo having roots in a different migration (although, in fairness, the three separate branches of migration seem to have been reasonably close in time).

The same author expands upon his conclusions in a follow up post (which happens to reference a Wikipedia page I've put a great deal of work into developing).

it’s generally thought that the Athapaskan migrations which eventually led to the entrance of the Navajos and Apaches into the Southwest began in Alaska. The northern Athapaskan languages are actually spoken over a very large area of northwestern Canada as well, but the linguistic evidence clearly points to Alaska as the original place where Proto-Athapaskan was spoken at the last point before it splintered into the various Athapaskan languages. That is, the Urheimat of the Athapaskans seems to have been somewhere in Alaska.

There are two main pieces of evidence pointing to this conclusion. One is the fact that it has been quite well established at this point that the Athapaskan language family as a whole is related to the recently-extinct language Eyak, which was spoken in south-central Alaska. Eyak was clearly not an Athapaskan language itself, but it had sufficient similarities to reconstructed Proto-Athapaskan to establish a genetic relationship. Since Eyak was spoken in Alaska, it therefore seems most probable that the most recent common ancestor of both Eyak and the Athapaskan languages (Proto-Athapaskan-Eyak) was also spoken in Alaska. . . .

A stronger piece of evidence is the internal diversity of the Athapaskan languages themselves. A general principle in historical linguistics is that the Urheimat of a language family is likely to be found where there is maximal diversity among the languages in the family. . . . When it comes to Athapaskan, this condition obtains most strongly in Alaska. The languages in Canada and the Lower 48 are all relatively closely related to each other within the family as compared to some of the languages in Alaska. Although interior Alaska is overwhelmingly dominated by Athapaskan groups, the linguistic boundaries among these various groups, even those adjacent to each other, are often extremely sharp.

This is particularly the case when it comes to the most divergent of all the Athapaskan languages: Dena’ina. (. . . in many publications this term is spelled “Tanaina,” . . . ”Dena’ina” is the generally preferred form these days[.] . . .) This is the language traditionally spoken around Cook Inlet in south-central Alaska, including the Anchorage area. While it’s clearly Athapaskan, it’s very weird as Athapaskan languages go. It is not mutually intelligible with any other Athapaskan language, although it borders several of them, and it is in turn divided into several internal dialects that are strikingly diverse. . . . there are two main dialects, Upper Inlet and Lower Inlet, and that Lower Inlet is further subdivided into two or three subdialects: Outer Inlet, Inland, and Iliamna. . . the Lower Inlet dialect is more conservative than the Upper Inlet one, which shows extensive influence from the neighboring Ahtna language, which is also Athapaskan but not very similar to Dena’ina. Within the Lower Inlet dialect, the Inland dialect is the most conservative . . . presumably due to the relative isolation of this dialect, which is spoken in the Lake Clark area and further north in Lime Village. . . . this the most likely homeland of Dena’ina speakers . . . [who] moved from the interior to the coast relatively recently. . . .

Despite the relative conservatism of the Lower Inlet dialect, however, all its subdialects do show a certain amount of influence from Yup’ik Eskimo (particularly in the development of the Proto-Athapaskan vowel system). This is unsurprising, as these dialects lie on the boundary of the Yup’ik area to the west and south, and the Dena’ina groups in these areas show extensive Eskimo influence in many aspects of their traditional culture. . . . the main distinctions among the Dena’ina groups were economic, having to do with their subsistence systems, while other social systems were pretty similar across the various groups. The Lower Inlet groups, especially those in the Seldovia area on Kachemak Bay near the outlet of Cook Inlet, showed a much heavier dependence on hunting sea mammals and a correspondingly heavier influence from nearby Yup’ik Eskimo groups with a similar adaptation than their compatriots further north who had a more typically Athapaskan lifestyle based on salmon fishing and hunting of terrestrial animals.

The fact that Dena’ina, the most divergent of the Athapaskan languages and therefore the one that most likely split earliest from Proto-Athapaskan, is spoken in Alaska makes it very likely that Proto-Athapaskan was spoken in Alaska as well. Indeed, if . . . the Lake Clark area was the original homeland of the Dena’ina, this potentially places Proto-Athapaskan quite far west within Alaska and quite close to areas traditionally occupied by Eskimo-speakers. . . . however. . . it’s still very unclear when the breakup of Proto-Athapaskan occurred and who occupied which parts of Alaska at that time.

Thus, the Urheimat of the Athapaskan aka Na-Dene languages in North America was probably somewhere West of Anchorage in areas that are now occupied by Eskimos, but wouldn't have been prior to the arrival of the Thule, sometime within the last fifteen hundred years, who apparently displaced them to inland locations. Also, while the author doesn't expressly address the point, the arrival of the Thule in North American took place close in time to the Na-Dene migration to the Southeast United States, which suggests that this Navajo and Apache exodus story may have its origins in flight from the ancestors of modern Eskimos who displaced them from their previous homeland. It is also roughly coincident with the rise of the Cahokia based Mississippian culture (which despite its name apparently reached at least as far as the Atlantic Coast of North Carolina) and the Viking Vinland colony in far Northeastern North America, and roughly coincides with the Chaco culture of the American Southwest. The interactions between the basically hunter-gatherer Athapaskan cultures and the agriculturalist Pueblo culture are explored here.

The author of the excerpts above provides further detail in a third post on the subject which he concludes with the following observations:

[I]t definitely seems that the Dena’ina most likely spread from west to east, and the Ahtna may have been spreading in the other direction at approximately the same time. Archaeological evidence suggests that the Dena’ina spread into the Kenai peninsula (across the inlet from their apparent homeland) took place less than a thousand years ago. Since it seems very clear that the Athapaskans had been in Alaska for a very long time before that, certainly long enough for Dena’ina in the southwest to diverge markedly from the various languages that form a large dialect continuum in the Tanana and Yukon valleys, this suggests that the story of Athapaskan prehistory is both very complicated and very long-term.

More Of BSM Parameter Space Ruled Out

2012-02-03T13:14:00.000-07:00

The Large Hadron Collider relentlessly increases the envelope of energy levels where beyond the Standard Model physics can't be lurking. As of January 31, 2012, some of those new limits on beyond the Standard Model physics from LHC include the following:

Fourth Generation Top Quarks

[I]n a large class of little Higgs and composite Higgs models the fermionic partner of the top quark decays as t' → b W about half of the time. The current limit on the t' mass assuming 100% branching fraction for the t' → b W decay is 525 GeV. For little Higgs et al. the limit is slightly weaker, slightly above 400 GeV (due to the smaller branching fraction) but that is also beginning to feel uncomfortable from the point of view of naturalness of these models.

This result is entirely expected, because a fourth generation electron would be strongly expected to be lighter than a fourth generation top quark, just as each of the other three generations of up quarks are heavier than each of the corresponding three generations of charged leptons. And, while neutrinos are almost impossible to see directly in a detector, and heavy quark decay products can form electrically neutral hadrons that are somewhat hard to see, or can create jets of decay products that are hard to distinguish from know heavy particle decays because there are so many particle detections that have to be combined and because there are many possible scenarios that generate heavy particle decay jets, a very heavy fourth generation electron would generate a very distinctive signal in the data. So it would be surprising if a fourth generation top quark were the first fourth generation particle to be detected.

W' Bosons

What about a particle that behaves more or less like a W boson but is heavier? The bounds on this are also getting tighter, but with a twinge of hope, a single outlier event at a TeV scale.

[T]here is no compelling theoretical reasons for such a creature to exist. However they represent a characteristic and clean signature . . . an energetic electron or muon accompanied by missing energy from a neutrino. To tell W' from the ordinary W boson one looks for events with a large transverse mass . . . . Intriguingly, in the muon channel an outlier event with a very large transverse mass of 2.4 TeV is observed in the data. Of course, most likely it's just a fluke[.]

Heavy top-antitop quark pair decays

This search targets heavy (more than 1 TeV) particles decaying to a pair of top quarks, a signature very common in models with a new strongly interacting sector, like composite Higgs or the Randall-Sundrum model. . . . this search relies on fancy modern techniques of studying substructure of jets, in order to identify closely packed jets that could originate from a fast moving top quark. No resonance is observed in the t-tbar spectrum. . . . the LHC sensitivity now reaches the cross sections predicted by popular versions of the Randall-Sundrum model, excluding Kaluza-Klein gluons lighter than about 1.5 TeV.

This is about fifty percent greater than the limits prior to the LHC.

What is a Randall-Sundrum model?

Randall–Sundrum models . . . imagine that the real world is . . . a five-dimensional anti de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes.

The models were proposed in 1999 by Lisa Randall and Raman Sundrum because they were dissatisfied with the universal extra dimensional models then in vogue. Such models require two fine tunings; one for the value of the bulk cosmological constant and the other for the brane tensions. Later, while studying RS models in the context of the AdS/CFT correspondence, they showed how it can be dual to technicolor models.

There are two popular models. The first, called RS1, has a finite size for the extra dimension with two branes, one at each end. The second, RS2, is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model. . . . It involves a finite five-dimensional bulk that is extremely warped and contains two branes: the Planckbrane (where gravity is a relatively strong force; also called "Gravitybrane") and the Tevbrane (our home with the Standard Model particles; also called "Weakbrane"). In this model, the two branes are separated in the not-necessarily large fifth dimension by approximately 16 units (the units based on the brane and bulk energies). The Planckbrane has positive brane energy, and the Tevbrane has negative brane energy. These energies are the cause of the extremely warped spacetime.

A study in 2007 showed that this class of models could be proven or disproven based on searches for "Kaluza-Klein gluons" at LHC.

SUSY

A minimum mass for gluinos, a particle predicted by SUSY, is based on the latest results, "600-900 GeV depending on how squeezed is the SUSY spectrum."

LHC Multilepton Search Unimpressive So Far

2012-01-30T16:37:00.005-07:00

They looked at events with at least four leptons (electrons and muons) and some missing transverse momentum. In the inclusive selection, they observed 4 events while the expectation was 1.7 ± 0.9 events; that's roughly a 2.5-sigma excess although one should include the non-Gaussianity of the distribution to get a more accurate figure.When the Z veto was imposed, they got no events while the expectation was 0.7 ± 0.8 events which is OK within 1-sigma error. So only the veto-free figure is intriguing.

From here.

Material deviations from the Standard Model, of course, tend to support Beyond the Standard Model theories. And, greater than expected numbers of multilepton events, in particular, tend to support Supersymmetry (i.e. SUSY).

Statistical Issues

But, of course, as Motl acknowledges by remarking that the distribution is non-Gaussian, estimating a statistical significance for a discrete variable with a low value, like the predicted number of multilepton events at an experiment at the Large Hadron Collider, as a continous variable, is inaccurate. The probability of a number of events less than zero is zero, which makes a two sided set of error bars problematic. There are specific, probabilities for zero, one, two, three, four, five, etc. events under the Standard Model, and you have to compare a single data point to those probabilities.

Doing the statistical significance calculations correctly is going to reduce the statistical significance of finding 4 multilepton events, when the modal result would be 2 multilepton events, 1 or 3 multilepton events would be quite routine, and neither 0 nor 4 events is wildly improbable.

With a Z veto, which is designed to filter out false positives, you have a barely modal expectation of one event, which zero events and two events being quite likely (and zero being quite a bit more likely than two events).

Of course, when you are looking at two separate measurements that have some independence from each other, the probability that one or the other will be a given amount more than the expected value is greater, also reducing their statistical significance. You expect one 2 sigma event for every twenty trials and the more trials you do, the less notable a 2 sigma or 2.5 sigma event viewed in isolation becomes when the total context of experimental outcomes is considered.

Put another way, done right, the naiive 2.5 sigma event is probably very close to and possibly below a 2 sigma event, if the statistics is done right.

Implications For SUSY Parameter Space

Of course, since there are all sorts of SUSY theories, there is no one SUSY prediction for the number of multilepton events, although the LHC results, like those before it, imply that any deviation from the Standard Model expectation in SUSY, if it exists, must be quite subtle.

To be just a bit more refined, I have never heard anyone claim that SUSY theories for a given expected value of a result, have a materially different standard deviation from that expected value. The expected values are different, but not the variability. Therefore, if you are testing two hypotheses, one that the Standard Model is correct, and the other that a particularly SUSY model is correct, SUSY models that predict, for example, six or more multilepton events (rather than the observed two), or five or more Z vetoed multilepton events (rather than the observed zero), are strongly disfavored by the LHC results. This is potentially a pretty meaningful and precise constraint on the parameter space of SUSY models.

This is not the only constraint on SUSY parameter space. The apparent Higgs boson mass of about 125 GeV imposes real constraints, as do exclusion searches setting minimum masses of the lighest supersymmetrical particle which are fast approaching the TeV mass level. We are entering the era where fine tuning is increasingly necessary to fit SUSY theories to the data, and by implication, to fit string theory vacua to the data. LHC's experimental data won't have enough statistical power to entirely rule out SUSY even if every single one of its results is negative for its entire run, but it will impose every tighter constraints of SUSY parameter space that ties the hands of string theorists trying to fit theories to the observed data.

The simpliest versions of SUSY are already ruled out, but human ingenuity's capacity to come up with more clever versions that fit new constraints abounds.

The M Theory Conspiracy

2012-01-29T20:22:00.000-07:00

I've heard less plausible sociology of science arguments.

The Strategic Aspects Of A Research Agenda

2012-01-29T17:50:00.000-07:00

In designing a research program, it is useful to distinguish between uncanny and mundane predictions. An uncanny prediction is one that is incongruous with both current scientific understanding of the phenomenon and any corresponding folk models, i.e., the prediction specifies aspects of the world that are hitherto unrecognized. In contrast, a mundane prediction is one that is consistent with our current understanding of the world, be it scientific or folk. If supported, uncanny predictions have a large impact on scientific knowledge – they provide substantial prima facie evidence supporting the hypothesis from which they were derived, and they open up new areas of empirical exploration. In contrast, when mundane predictions are supported, they have far less impact on scientific knowledge. Typically, a variety of existing perspectives can account for familiar phenomena, hence supported mundane predictions provide marginal evidence for the hypothesis from which they were derived; likewise, because the given effects are already familiar, such findings do not lead to new areas of empirical exploration. Most uncanny predictions will fail, and most mundane predictions will succeed. This is because existing scientific perspectives, and many folk models, will generally be accurate, hence hypotheses that are incongruent with such knowledge will often be incorrect, while hypotheses that are congruent with it will often be correct. Phrased in cost/benefit terms, uncanny predictions are thus a high-risk, high-yield enterprise, while mundane predictions are a low-risk, low-yield enterprise.

From here.

Altaic Populations Linked Via Uniparental DNA To Native Americans

2012-01-29T16:04:00.000-07:00

The Altai region of southern Siberia has played a critical role in the peopling of northern Asia as an entry point into Siberia and a possible homeland for ancestral Native Americans. It has an old and rich history because humans have inhabited this area since the Paleolithic.

Today, the Altai region is home to numerous Turkic-speaking ethnic groups, which have been divided into northern and southern clusters based on linguistic, cultural, and anthropological traits.

To untangle Altaian genetic histories, we analyzed mtDNA and Y chromosome variation in northern and southern Altaian populations. All mtDNAs were assayed by PCR-RFLP analysis and control region sequencing, and the nonrecombining portion of the Y chromosome was scored for more than 100 biallelic markers and 17 Y-STRs.

Based on these data, we noted differences in the origin and population history of Altaian ethnic groups, with northern Altaians appearing more like Yeniseian, Ugric, and Samoyedic speakers to the north, and southern Altaians having greater affinities to other Turkic speaking populations of southern Siberia and Central Asia.

Moreover, high-resolution analysis of Y chromosome haplogroup Q has allowed us to reshape the phylogeny of this branch, making connections between populations of the New World and Old World more apparent and demonstrating that southern Altaians and Native Americans share a recent common ancestor. These results greatly enhance our understanding of the peopling of Siberia and the Americas.

Source: Matthew C. Dulik, Sergey I. Zhadanov, Ludmila P. Osipova, Ayken Askapuli, Lydia Gau, Omer Gokcumen, Samara Rubinstein, and Theodore G. Schurr, "Mitochondrial DNA and Y Chromosome Variation Provides Evidence for a Recent Common Ancestry between Native Americans and Indigenous Altaians", The American Journal of Human Genetics, 26 January 2012 doi:10.1016/j.ajhg.2011.12.014 via Razib Khan at Gene Expression who provides one of the key tables (breaks added in closed access paper abstract above for ease of reading).

The abstract is about as clear as mud in the context of prior research in this area, because when one says "that southern Altaians and Native Americans share a recent common ancestor", it isn't at all clear which Native Americans you are discussing, and methodological issues make the genetic conclusions seen in isolation unconvincing without a rich context to support them.

Wikipedia summarizes the state of the academic literature Y-DNA of indigeneous Americans prior to the latest paper as follows (citations and some headings and portions unrelated to Y-DNA omitted, emphasis added):

Human settlement of the New World occurred in stages from the Bering sea coast line, with an initial layover on Beringia for the small founding population. The micro-satellite diversity and distributions of the Y lineage specific to South America indicates that certain Amerindian populations have been isolated since the initial colonization of the region. The Na-Dené, Inuit and Indigenous Alaskan populations exhibit haplogroup Q (Y-DNA); however, they are distinct from other indigenous Amerindians with various mtDNA and atDNA mutations. This suggests that the peoples who first settled the northern extremes of North America and Greenland derived from later migrant populations than those who penetrated further south in the Americas. Linguists and biologists have reached a similar conclusion based on analysis of Amerindian language groups and ABO blood group system distributions. . . .

Haplogroup Q . . .

Q-M242 (mutational name) is the defining (SNP) of Haplogroup Q (Y-DNA) (phylogenetic name). Within the Q clade, there are 14 haplogroups marked by 17 SNPs. In Eurasia haplogroup Q is found among Siberian populations, such as the modern Chukchi and Koryak peoples. In particular two populations exhibit large concentrations of the Q-M242 mutation, the Kets (93.8%) and the Selkups (66.4%). The Kets are thought to be the only survivors of ancient nomads living in Siberia. Their population size is very small; there are fewer than 1,500 Kets in Russia. The Selkups have a slightly larger population size than the Kets, with approximately 4,250 individuals. 2002 Starting the Paleo-Indians period, a migration to the Americas across the Bering Strait (Beringia), by a small population carrying the Q-M242 mutation took place. A member of this initial population underwent a mutation, which defines its descendant population, known by the Q-M3 (SNP) mutation. These descendants migrated all over the Americas.

Q subclades Q1a3a and Q1a3a1a . . . .

Haplogroup Q1a3a (Y-DNA) and/or Q-M3 is defined by the presence of the rs3894 (M3) (SNP). The Q-M3 mutation is roughly 15,000 years old as the initial migration of Paleo-Indians into the Americas occurred. Q-M3 is the predominant haplotype in the Americas at a rate of 83% in South American populations, 50% in the Na-Dené populations, and in North American Eskimo-Aleut populations at about 46%. With minimal back-migration of Q-M3 in Eurasia, the mutation likely evolved in east-Beringia, or more specifically the Seward Peninsula or western Alaskan interior. The Beringia land mass began submerging, cutting off land routes.

Since the discovery of Q-M3, several subclades of M3-bearing populations have been discovered. An example is in South America, where some populations have a high prevalence of (SNP) M19 which defines subclade Q1a3a1a. M19 has been detected in (59%) of Amazonian Ticuna men and in (10%) of Wayuu men. Subclade M19 appears to be unique to South American Indigenous peoples, arising 5,000 to 10,000 years ago. This suggests that population isolation and perhaps even the establishment of tribal groups began soon after migration into the South American areas.

Haplogroup R1 . . .

Haplogroup R1 (Y-DNA) is the second most predominant Y haplotype found among indigenous Amerindians after Q (Y-DNA). The distribution of R1 is believed to be associated with the re-settlement of Eurasia following the last glacial maximum. One theory put forth is that it entered the Americas with the initial founding population. A second theory is that it was introduced during European colonization. R1 is very common throughout all of Eurasia except East Asia and Southeast Asia. R1 (M137) is found predominantly in North American groups like the Ojibwe (79%), Chipewyan (62%), Seminole (50%), Cherokee (47%), Dogrib (40%) and Papago (38%). The principal-component analysis suggests a close genetic relatedness between some North American Amerindians (the Chipewyan and the Cheyenne) and certain populations of central/southern Siberia (particularly the Kets, Yakuts, Selkups, and Altays), at the resolution of major Y-chromosome haplogroups. This pattern agrees with the distribution of mtDNA haplogroup X, which is found in North America, is absent from eastern Siberia, but is present in the Altais of southern central Siberia.

Haplogroup C3b . . .

Haplogroup C3 (M217, P44) is mainly found in indigenous Siberians, Mongolians and Oceanic populations. Haplogroup C3 is the most widespread and frequently occurring branch of the greater (Y-DNA) haplogroup C. Haplogroup C3 decedent C3b (P39) is commonly found in today's Na-Dené speakers with the highest frequency found among the Athabaskans at 42%. This distinct and isolated branch C3b (P39) includes almost all the Haplogroup C3 Y-chromosomes found among all indigenous peoples of the Americas. The Na-Dené groups are also unusual among indigenous peoples of the Americas in having a relatively high frequency of Q-M242 (25%). This indicates that the Na-Dené migration occurred from the Russian Far East after the initial Paleo-Indian colonization, but prior to modern Inuit, Inupiat and Yupik expansions.

Analysis of Dating

There are a couple of different methodologies for mutation dating. Pedigree mutation rates support a most recent common ancestor between Native American and South Altaic populations ca. 5,170 to 12,760 years ago (95% confidence interval, median 7,740 years ago), and a most recent common ancestor between North Altaic and South Altaic populations that is only a bit more recent (a 95% confidence interval 3,000 to 11,100 years ago, median 5,490 years ago). Evolutionary mutation rates support a most recent common ancestor of North Altaic and South Altaic of a median 21,890 years ago, and a statistically indistinguishable most recent common ancestor of Native Americans and South Altaic of a median 21,960 years ago.

Of course, all of the interesting inferences from the dates flow from the method you use and its accuracy. The evolutionary mutation rates suggest a split just before the Last Glacial Maximum and is suggestive of a scenario in which part of a population retreats to the South from the glaciers, while the other seeks a refuge in Beringia.

The pedigree date (which usually is closer to the historical corrolates that make sense) would be a decent fit for secondary Na-Dene migration wave that is before the original Native American population of the New World, but is before more recent circumpolar population migrations in and after the Bronze Age. The pedigree date also makes the possibility that there is an authentic Na-Dene to Yenesian linguistic link far more plausible than the older evolutionary date. Linguistic connections ought to be impossible to see at a time depth of 21,000 years, but is conceivable with a link that could be less than a third as old.

The "median split time" using pedigree dates is 4,490 years ago for N. Altaians v. S. Altaians, and 4,950 years ago for Native Americans v. S. Altaians, which would coincide with Uralic language expansion and the first of three major waves of Paleoeskimo migration to the New World. The evolutionary dates give a 19,260 years ago "median split time" for N. v. S. Altaians, and 13,420 years ago for Native American v. S. Altaians, an order reversal from all the other dates apparently driven by a wide and old date biased confidence interval. The very old genetic dates don't make a lot of sense, however, given that megafauna extinction dates in Siberia suggest a modern human arrival there ca. 30,000 years ago, plus or minus.

The indications that the northern Altaians are less strongly genetically connected than the southern Altaians to Native Americans is quite surprising. Linguistically and culturally the Northern Altaic populations would seem closer, but those are things that are more succepible to change over time and the southern populations may have faced stronger cultural pressures than the more remote and isolated northern populations.

The reasoning here matters a great deal, of course, and with a closed access paper isn't easy to evaluate. The abstract seems to indicate that the linkages are being based on the phylogeny of non-recombining Y-DNA haplogroup Q (the dominant one in Native Americans) without necessarily relying much on the mtDNA part of the analysis. In particular, it isn't easy to tell from the abstract how succeptible the data are to a multiple wave, as opposed to a single wave migration model.

There are really no sensible models for the arrivals of modern humans in the New World that can fit with a split between Native Americans and Siberian populations any later than 13,000-14,000 for the predominant haplogroups of Y-DNA haplogroup Q found in South America (Q-M3 and its descendants). But, a link of a secondary subtype of Y-DNA haplogroup Q that is pretty much exclusively found in North America at a later date is quite possible to fit consistently with plausible population models. Evolutionary mutation rate dates would strongly disfavor this scenario, but pedigree mutation rate dates could comfortably accomodate this scenario.

Deep Thoughts From Marco Frasca

2012-01-26T21:28:00.005-07:00

Italian physicist Marco Frasca's latest paper leaves his usual comfort zone of QCD and discusses instead a deep and fundamental relationship between the Schrödinger equation (that describes how the quantum state of a physical system changes in time) and the equations of the observable stochastic (i.e. probablistic) processes of Brownian motion (which describes the dispersion of particles that flows from their random movements) from first principles via some mathematical leaps of insight that have eluded some of the best minds in math and physics for almost nine decades (counting from the publication of Schrödinger equation, which is younger than the equations that describe Brownian motion). Essentially the Schrödinger equation is the square root of the equation that describes Brownian motion, when the equations are properly formulated and the square root if defined in a clever way that gives rise to a complex number valued solution.

[T]he square root of Brownian fluctuations of space are responsible for the peculiar behavior observed at quantum level. This kind of stochastic process is a square root of a Brownian motion that boils down to the product of two stochastic processes: A Wiener process [i.e. "the scaling limit of a random walk"] and a Bernoulli process proper to a tossing of a coin. This aspect could be relevant for quantum gravity studies where emergent space-time could be understood once this behavior will be identified in the current scenarios.

Note, however, that there is at least one obvious step that has to be bridged between this conclusion and a rigorous theory of quantum gravity, since the Schrödinger equation is a non-relativistic effective approximation of quantum mechanics.

[T]he solutions to the Schrödinger equation are . . . not Lorentz invariant . . . [and] not consistent with special relativity. . . . Also . . . the Schrödinger equation was constructed from classical energy conservation rather than the relativistic mass–energy relation. . . . Secondly, the equation requires the particles to be the same type, and the number of particles in the system to be constant, since their masses are constants in the equation (kinetic energy terms). This alone means the Schrödinger equation is not compatible with relativity . . . [since quantum mechanics] allows (in high-energy processes) particles of matter to completely transform into energy by particle-antiparticle annihilation, and enough energy can re-create other particle-antiparticle pairs. So the number of particles and types of particles is not necessarily fixed. For all other intrinsic properties of the particles which may enter the potential function, including mass (such as the harmonic oscillator) and charge (such as electrons in atoms), which will also be constants in the equation, the same problem follows.

In order to extend Schrödinger's formalism to include relativity, the physical picture must be transformed. The Klein–Gordon equation and the Dirac equation [which provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity] are built from the relativistic mass–energy relation; so as a result these equations are relativistically invariant, and replace the Schrödinger equation in relativistic quantum mechanics. In attempt to extend the scope of these equations further, other relativistic wave equations have developed. By no means is the Schrödinger equation obsolete: it is still in use for both teaching and research - particularly in physical and quantum chemistry to understand the properties of atoms and molecules, but understood to be an approximation to real behaviour of them, for speeds much less than light.

Presumably, however, it would be possible to square the relativistic versions of the Schrödinger equation (such as Dirac's equation) in an analogous manner to derive are diffusion equations for Brownian motion in relativistic settings that is consistent with special relativity, while still illustrating how complex number valued underlying quantum mechanics can reflect an emergent and fluctuating underlying nature of space-time.

As a footnote, it is also worth noting that his paper was made possible only with the a collaboration with elite mathematicians that would have been much more difficult to facilitate without the crowdsourcing of part of the problem that the Internet made possible.

Monroe, Louisiana As The Source Of New World Civilization

2012-01-26T14:25:00.001-07:00

A series of articles in Science magazine a month ago (cited below), have transformed my understanding of human civilization in the Pre-Columbian New World. Together with some secondary sources like Wikipedia, the World Almanac 2012, Jared Diamond's "Guns, Germs and Steel", and a few other websites, the implication is that the history of civilization in the New World is far more united in space and over millenia, far greater in scale, and far more sophisticated than I had believed as recently as two months ago.

In a nutshell, which will probably take multiple more lengthy posts to explore in the future, here is the conjectural narrative.

Several sites in the general vicinity of Monroe, Louisiana show the emergence of the earliest large scale mounds and earth platforms, which were part of projects on a scale comparable to the earlier Sumerian pyramids, Egyptian pyramids, Mesoamerican pyramids, and megalithic complexes of Atlantic Europe in the period from about 3700 BCE to 2700 BCE. These appear to have provided these people with a means by which to more easily endure the periodic flooding of the Mississippi River, do not show signs of large trade networks, and while they may show indications of transitional proto-agriculture, do not show signs of a full fledged food production system based upon eating domesticated plants and animals as the entire basis for their diet.

A little more than a thousand years later (flourishing 1600 BCE to 1000 BCE), however, a civilization that appears to be derived from this first wave of mound builders appears at Poverty Point, which is within a day's walk of the earlier sites in Louisiana. This urban center is much larger in scale, perhaps comparable to a medium sized archaic era Greek city state, and shows clear signs of a trade network that extends as far as Milwaukee, Wisconsin in the North and the Ozarks in the West. It used copper and engaged in fine stoneworking. Its trade network may have even extended farther still. The way that its structures are aligned with solstices and equinoxes, its burial practices, its pottery, and the arrangement of structures in the complex, appear to strongly echo and to probably be antecedent to the Mesoamerican civilizations of the Olmecs (from ca. 1200 BCE), the Mayans (from ca. 900 BCE), and the Woodlands Hopi of Ohio (from ca. 400 BCE).

The Inca civilization, as a well organized technological large scale civilization as opposed to merely a gorup of people engaged in disconnected hamlet scale agriculture, fishing, hunting and gathering, appears to derive largely from Mesoamerica. For example, pottery appears in Ecuador ca. 3200 BCE, but does not appear in Peru until around 1800 BCE, and the earliest large scale states emerge in the Inca region ca. 0 CE, about a millenium after the Olmecs and the Mayans. At the point of Columbian contact, there were regular trade and communication relationships between the Aztecs who had consolidated political control of Mesoamerica in a civilization clearly derivative of the Olmec and Mayan civilizations, and the Inca civilization.

Timing and broad outlines of the way that their communities were planned also suggest that a couple of large scale village network societies in the Amazon, ca. 0 CE to 1650 CE, may have been influenced or informed to some extent by the Poverty Point culture or by Mesoamerican societies that were influenced at a formative point by the Poverty Point culture.

From the Hopi woodland culture emerged a sprawling urbanized region in the vicinity of Saint Louis, Missouri, over a region about a day's walk across along one of the main confluences of the Mississipi River basin called Chahokia around 1000 CE. This civilization took a major hit around the 1160s and 1170s during a major New World drought, and eventually collapsed as an urban complex around 1350 CE around the time of the Little Ice Age, although much declined remants of this civilization persisted pocketed throughout its prior range up until the point of European contact at which point European diseases dealt a further blow to what was left of this civilization.

Chahokians worked copper, had fine stonework, constructed gigantic earthworks with invisible interior elements (layers of black earth, white gravel and red earth, inside mounds corresponding more or less to the layers of hell, Earth and heaven in their cosmology) on a scale comparable to the Egyptian pyramid at Giza or the largest Mesoamerican pyramids, although no traces of a written language have been uncovered at this point.

The central complex may have housed 10,000 to 20,000 people, and the larger area may have housed 75,000 people, making the complex a bit larger than the largest urbanized complexes of the Amazon (about 50,000), and in the top ten of Mesoamerican cities at their Pre-Columbian peak (the largest urban area in the Pre-Columbian New World, in the vicinity of what is now Mexico City had about 300,000 people). It was by far the largest urbanized area in what is now the United States and Canada.

The Mississippian culture of which Chahokia was a focal point engaged in maize and pumpkin farming, as well as the farming of a few domesticates or semidomesticates later abandoned as food sources, although they may have significantly supplemented their food sources with hunting, gathering and fishing. At one major feast whose remnants were unearthed by archaeologists at Chahokia, those present dined on about 9,000 deer.

Chahokia's trading network, colonies and strong cultural influences extended throughout the entire Mississippi basin from the Rocky Mountains to the Great Lakes to the Appalacian Mountains and also throughout all or most of the American South where Chahokia's culture overlaps heavily with the Southeastern Cultural Complex. For example, trade brought Chahokia Great White shark teeth from the Atlantic, and minerals from Georgia and Alabama. The mythology and rituals of the Osage Indians correspond closely to the Chahokian ceremonial system that we know from archaeology. Indian tribes that speak the Sixouian languages, of which the Osage language is a part, were spoken in a linguistic area ca. 1500 CE that corresponds closely to the core Chahokian aka Mississippian cultural area. Their "national sport" was a game a bit like Bocci ball in which one threw of ring or disk and then tried to throw your spear as close to that point as possible, which attracted large crowds of spectators, was as popular among average people as softball or soccer, and was the subject of high stakes gambling.

Thus, as recently as two or three hundred years before Columbus arrived in the New World, almost all of the United States to the east of the continental divide and to the west of the Appalacians and the South of the Great Lakes and almost all of the American South were all part of a reasonably united cultural complex that had its most direct common origins (admittedly with a couple of intervening "dark ages") in the vicinity of Monroe, Louisiana around 3700 BCE.

It may not have been one centralized megastate, but it could fairly be compared to the kind of balkanized area with a shared culture found in Europe or in the Indian subcontinent. At a time depth of something on the order of 1600 BCE to 900 BCE, the Poverty Point culture heir in the Monroe, Lousiana area was probably one of the formative cultural contributors (together with important local innovations, particularly with the addition of the domesticated plants to the mix) to the earliest sophisticated civilizations of Mesoamerican and those civilizations, in turn were probably formative cultural contributors to the civilizations of South America in the greater Inca geographic region and in the Amazon. The successors to the Poverty Point culture in North America called the Mississippian culture centered at Chahokia, that may have bloomed via a combination of improved climate conditions, the development of a variety of maize that thrived in the North American climate (derived from the Mesoamerican version which was domesticated somewhere in the vicinity of the Pacific Coast of modern Mexico), and high profile astronomical events like Hailey's Comet and a major supernova, reinvigorated that culture.

It is also hardly a stretch to suppose that the Uto-Aztecian language speaking populations of Northern Mexico and the American Southwest (including the Ute's of Colorado) and the Anastazi (whose civilization collapsed in the megadroughts 1160s and 1170s) probably have their origins in the Aztec civilization of Mesoamerica, which may in turn have a deep time depth connection to Poverty Point, Louisiana.

There is a solid argument supported by strongly suggestive evidence that directly or indirectly, almost all of the civilizated cultures in the Americans trace their roots to a significant extent to an ancient civilization of mound builders ca. 3700 BCE in the vicinity of Monroe, Louisiana.

On the other hand, we also know that the Apache and Navajo Indian tribes of the American Southwest a derived from the Na-Dene people of the Pacific Northwest and arrived in the American Southwest as a result of a migration around 1000 CE.

General Implications

This superculture spanning five millenia and providing a source that had dramatic cultural influences on large swaths of both North American and South America probably did not extent quite everywhere in the New World. The indigeneous cultures to the west of the North American continental divide and to the North of the Great Lakes, and possibly also some in the American Northeast, parts of Florida, and "uncivilized" parts of South American were probably not a part of this superculture.

This also means that the vast majority of people in the New World, at the time of European contact, either were part of a Chalolithic culture, or had ancestors within the last few hundred years who had been, even if their own society had reverted to a hunter-gather mode.

The Viking presence in the New World was contemporaneous with the high point of the Mississippian culture (ca. 1000 CE to 1350 CE), which may explain both why the Vinlanders could not dominant the locals and gain sweeping control of North American the way that the Iberians of half a millenium later would further South, and this small Viking civilization collapsed at about the same time that the Chahokia did for basically the same Little Ice Age climate driven reasons.

This archaeological background also suggests that in addition to the "Guns, Germs and Steel," that Jared Diamond notes, that a critical advantage that the Europeans arriving in the New World, at least in North America, had was timing. They encountered the indigeneous North Americans not at their glorious peak of ca. 1000 CE, but two or three centuries into an era of decline, comparable perhaps to the period from 1200 BCE to 900 BCE, following Bronze Age collapse, or from 476 CE to 776 CE that we call the "dark ages" following the collapse of the Roman Empire. Indigeneous North American civilization has just about hit bottom and not had time to meaningfully recover yet, when it was hit anew first by devistating European diseases, and close on the heels of this devistating series of plagues, by a population with guns, swords, and military history that surpassed that of the Native Americans (inclding the experience of fighting distant foreign wars in the Crusades), a written language, horses and other domesticated animals, long distance sea travel, a somewhat more effective social organization.

If the North American population had managed a few hundred more years to reignite their civilization (and probably adopt the written language of the Mesoamericans in some form), they might have been far better able to hold their own, perhaps even more effectively than the Aztecs and Incas did. Yes, they were behind in a relentless march of progress and faced limitations in their domesticated plant and animal options that the European population that they encountered had not. But, the development and dissemination of a flood of new evidence in the couple of decades since Diamond wrote his book, suggests that the lag was closer to hundreds of year than several millenia as he suggested in his book.

This narrative of the emergence of New World civilization is profoundly more unified and cohesive in time and in space than was previously known. This helps to explain the mystery of why there were so few and such geographically expansive language families in North American where there had not previously been known to be such large scale societies (the advanced Inca and Aztec societies and prior existence of the Mayans and Olmecs made the modest number of languages in the geographically smaller anyway areas of Mesoamerica and Pacific South America explainable long ago). It also provides suggestive evidence regarding what kinds of linguistic relationship between known North American language families might exist at what time depths, so that linguists can know what they should expect to be the most fruitful places to look for genetic linguistic connections between known North American language families. And, these narrative suggests that the process of linguistic consolidation in North American may be more similar to that seen in the Old World and at much shallower time depth in North America, than we have previously believed.

The existence of more advanced than previously known civilizations in the Amazon also helps explain why such a seemingly hunter-gatherer dominated, population fragmenting jungle could possibly have any language families that have as much geographic extent as the ones we have observed do (although, of course, vast numbers of South American languages are unclassified isolates or microlanguage families) and gives us a relatively recent event (linguistically speaking) to explain why their connections can have a relatively shallow time depth relating them to each other. Again, this supports the conclusion that linguistic unity really does flow from the same expanding society with a technological edge process we've seen in the Old World, rather than following some different rule, which makes the inferrence that any unexplained large language families is the product of a lost prehistoric culture that will eventually be discovered stronger.

Implications For Population Genetics

Finally, before I make a final conjecture, this unified narrative has implications for efforts to cast light on prehistoric Native American populations from modern population genetic data. The assumption that a person with Native American genes was representative of a stable genetic population at the place where his or her 16th century Native American ancestors are known to have lived for tens of millenia prior to that point in time is manifestly contrary to what our emerging understanding of the archaeological evidence reveals. We know that there were dramatic ebbs and falls of archaeological cultures in particular regions at least for the past six thousand years or so, that were driven by more than random chance factors governing individual hunter-gatherer tribes in an unstructured way. These cultures were large in extent, wide in geographic distribution, engaged in some documented folk wanderings supported by archaeological and oral historical and early explorer historical evidence, and we now have some generalized context within which to know what direction any influence on 16th century population genetics due to Precolumbian migrations would have flowed if the cultural impacts of the known archaeological cultures had a demic component.

Now, as a matter of practicality, the small founding population of the New World, the limited demic impact of the known later waves of migration from Asia in most of the New World, and the serial founder effects applicable to even broad geographic regions that have been a partial cause of genetic distinctions between Latin American indigeneous peoples and certain groups of North American indigeneous peoples, mean that huge swaths of North American Indians in the geographic range of the Mississippian Superculture and its antecedents may have been so genetically homogeneous after seven thousand or so years of a nomadic hunter-gatherer existence in the region of people all derived from the same small founder population, that any subsequent impacts of demic migration and/or replacement may be virtually invisible at all but the most fine grained levels in modern genetic data.

Also, the existence of the Mississippian superculture with its known ups and downs, materially alters the kind of demographic models that are a plausible fit to reality for North American Indians. The most plausible demographic model given current evidence is that in the post-Clovis, pre-Mound Builder United States that there was a rapid early expansion of perhaps three thousand years or less from a small Beringian founding population that filled the continent at a low hunter-gatherer population density, that there was probably a peak as more effective Clovis hunting methods expanded human populations at the expense of prey populations over a thousand years or so, that there was probably a human population crash over a few centuries immediately after the Clovis era when overhunting and ecological collapse related to overhunting reduced the carrying capacity of the environment using a Clovis culture "business model" and didn't stablize until the surviving Native Americans found a new way to surive in harmony with their megafauna free environment, that a quite low effective population baseline of pure hunter-gatherers (which would be mutationally limited due to a small effective population) whose numbers ebbed and flowed meaningfully with medium and long term climate conditions and prey population health for about seven thousand years (providing lots of occasions for minor bottlenecks that could shed low frequency genetic mutations), and that there was a population expansions attributable to Poverty Point from ca. 1600 BCE to 1000 BCE followed by some degree of populatioon decline followed by gradually rebuilding populations until a much more dramatic population expansion ca. 1000 CE to 1160 CE, followed by a population crash across the New World at that point, followed by gradual recovery or gradual slump in population until about 1350 CE, followed by a Little Ice Age and civilization collapse population slump that is only starting to recover at the point of European contact, at which point there is another well documented slump and massive episode of intra-Native American and Native American-European admixture where historically documents and modern population genetics provide solid estimates of population sizes at given points in time, the impact of deadly diseases and admixture percentages. Both Poverty Point era and the Chahokian era provide particularly likely contexts for unusually high admixture, migration and replacement events. We can produce similar big picture, moderately detailed, archaeologically driven demographic histories using the latest available discoveries in Mesoamerica and in differing parts of South America.

This is obviously a much more complex demographic history than one could produce with a simple back of napkin exponential approximation of the kind very often used in actual published papers on prehistoric population genetics, but now that we know quite a bit about what actually happened, oversimplying that demographic history when we try to extrapolate modern population genetic data to prehistory with implicit assumptions about that demographic history that we know not to be true are inexcusable if we want to have the best possible evidence regarding the population genetics of the Americas in prehistory.

Did Asian Ideas Help Trigger New World Civilization?

While none of my sources mention the possibility, I also offer up one conjecture, which I myself don't actually necessary believe is more likely than not, but which is, given the timing of the events in question a far more plausible possibility than would have been at all supportable a couple of decades ago.

This is the possibility that some of the rise in New World civilization that started to emerge at Poverty Point could have been given a critical boost from exposure to Asian ideas.

The case of a cultural influence from Leif Erikson's 1000 CE on the culture centered around Chahokia is still so devoid of evidence, and even more weak in plausibility, since there don't seem to be any recognizable similarity in kinds of ideas or cultural features that could have been transmitted, even though it is possible that an idea could have been passed from person to person from Vinland to Chahokia, and there would have even been established trade routes in the Great Lake basins and Mississippi River basin which would extend to the Saint Lawrence seaway and Upstate New York, to carry those ideas, in a manner akin to the Eurasian Spice Road. Since, there is some evidence to suggest may have brought some Bronze Age technologies (and even simple versions of Tartan weaving patterns) to Mongolia and China from Europe and West Asia. While it could have happened, it didn't seem to have happened.

But, we know that Bronze Age Asian artifacts made it to Alaska from Asia with Paleoeskimos ca. 2500 BCE, and again with another wave of Dorsett Paleoeskimos ca. 1500 BCE, that there was a Thule (i.e. proto-Inuit) wave of migration that was possible an outgrowth of a culture that was also the source of the Uralic language family around 500 CE, and that there is suggestive evidence for a Na-Dene migration to the Pacific Northwest sometime before 1000 CE, but probably many millenia after the first wave of Native American migration to the New World across the Beriginian land bridge around the time of the last glacial maximum when sea levels were lower. A time span for Na-Dene migration of ca. 4000 BCE to 1500 BCE would have been technologically possible in terms of maritime travel technology, and would have been early enough to allow transmission of Asian ideas (probably with minimal demographic impact, if any) to Poverty Point. All of these populations, unlike Leif Erikson's encounter, were substantial enough to give rise to substantial populations, two of which survive to this day in North America (the Na-Dene and the Inuit), and the other two of which each lasted at least a millenium and has left genetic traces of admixture in some of the surviving Arctic and near Arctic North Americans.

Poverty Point is an almost inevitable early destination for anyone exploring North American via the kind of canoe or kayak that Paleoeskimos and the Na-Dene culture had at their disposal. All one needs to do is put your boat in any navigable tributary in the Mississippi River basin that makes up a large share of the entire North American continent and eventually the river will take you there without even having to hazard all that many impassable rapids - these Native American explores lacked nothing that young Huckleberry Finn had. And, a wealth of historical and prehistorical evidence tend to show that exploration and migration frequently run up and down major river systems, be they the Nile, the Danube, the Tigress and Euphrates, the Indus, the Ganges, the Yellow or the Yangtze. Sooner or later, some representative of any exploring new civilization was likely to end up on their shores and carry with him the stories of his travels.

All four of the likely pre-Columbian, post-Clovis waves of migration of new people's to North America were very likely to have happened at a time when someone in Northeastern Siberia who was at least advanced technologically enough to have a boat that could get him to North America from there was likely to be aware to some extent of some of the technological innovations that had taken place in the North Chinese Neolithic of ca. 7,000 BCE - 8,000 BCE that hadn't existed with North American was originally settled by modern humans. Someone even modestly familiar with the ideas associated with that Neolithic cultural complex (or perhaps even a Chalcolithic or Bronze Age cultural complex in North China), while they wouldn't have been able to reproduce the North Chinese civilization in full (just as few people and perhaps no one knows enough individually to reproduce modern American civilization in its entirety), could have provided enough ideas to set the people of Poverty Point on the track towards developing a semi-urbanized, food producing, copper age, stone carving civilization.

As I explained at the start of this conjecture, I'm merely noting that this kind of chain of culture influence is possible, even a plausible possibility that isn't obviously contradicted by what we already know, without actually claiming that it actually happened.

But, the mere possibility that the rise of civilization in the New World might not have been the completely independent innovation that it is widely credited with having been is so paradigm shifting in our understanding of prehistory, and motivated by fact that could not have been known by people investigating this possibility even a couple of decades ago, that it bears further investigation.

Sources (an incomplete list)

Andrew Lawler, "America's Lost City", 334 Science 23 December 2011: 1618-1623 (DOI: 10.1126/science.334.6063.1618).

Andrew Lawler, "Preserving History, One Hill at a Time", 334 Science 23 December 2011: 1623.

Andrew Lawler, "Does North America Hold the Roots of Mesoamerican Civilization?", 334 Science 23 December 2011: 1620-1621.

Jared Diamond, "Guns, Germs and Steel" (1997).

Archaeology Broadway Style

2012-01-22T22:04:00.001-07:00

The linked post has a You Tube video that is the most epic broadway style rock anthem testament to nerdiness (in this case, the kind that is at the root of archaeology), since the musical "Chess" (which was itself composed by a Swedish ex-Abba member). The post is not in English, but the video (which is not entirely safe for work), by a Norwegian singer who has a show a bit like Saturday Night live in Norway, is in English.

Quantum Field Theories Defined

2012-01-22T21:24:00.002-07:00

Lubos helpfully defines various terms which include the words "quantum field theory."

Woit On Symmetry In Physics

2012-01-19T13:17:00.001-07:00

Peter Woit has a really worthwhile answer to this year's Edge Website question of the year, which is "What is your favorite deep, elegant, or beautiful explanation?" He says:

Any first course in physics teaches students that the basic quantities one uses to describe a physical system include energy, momentum, angular momentum and charge. What isn’t explained in such a course is the deep, elegant and beautiful reason why these are important quantities to consider, and why they satisfy conservation laws. It turns out that there’s a general principle at work: for any symmetry of a physical system, you can define an associated observable quantity that comes with a conservation law:

1. The symmetry of time translation gives energy
2. The symmetries of spatial translation give momentum
3. Rotational symmetry gives angular momentum
4. Phase transformation symmetry gives charge

In classical physics, a piece of mathematics known as Noether’s theorem (named after the mathematician Emmy Noether) associates such observable quantities to symmetries. The arguments involved are non-trivial, which is why one doesn’t see them in an elementary physics course. Remarkably, in quantum mechanics the analog of Noether’s theorem follows immediately from the very definition of what a quantum theory is. This definition is subtle and requires some mathematical sophistication, but once one has it in hand, it is obvious that symmetries are behind the basic observables.

Here’s an outline of how this works, (maybe best skipped if you haven’t studied linear algebra…) Quantum mechanics describes the possible states of the world by vectors, and observable quantities by operators that act on these vectors (one can explicitly write these as matrices). A transformation on the state vectors coming from a symmetry of the world has the property of “unitarity”: it preserves lengths. Simple linear algebra shows that a matrix with this length-preserving property must come from exponentiating a matrix with the special property of being “self-adjoint” (the complex conjugate of the matrix is the transposed matrix). So, to any symmetry, one gets a self-adjoint operator called the “infinitesimal generator” of the symmetry and taking its exponential gives a symmetry transformation.

One of the most mysterious basic aspects of quantum mechanics is that observable quantities correspond precisely to such self-adjoint operators, so these infinitesimal generators are observables. Energy is the operator that infinitesimally generates time translations (this is one way of stating Schrodinger’s equation), momentum operators generate spatial translations, angular momentum operators generate rotations, and the charge operator generates phase transformations on the states.

The mathematics at work here is known as “representation theory”, which is a subject that shows up as a unifying principle throughout disparate area of mathematics, from geometry to number theory. This mysterious coherence between fundamental physics and mathematics is a fascinating phenomenon of great elegance and beauty, the depth of which we still have yet to sound.

Most of this is familiar to me, but I had not lodged in my head the deep connection between the notion of energy and the notion of time translation.

More Higgs Boson Mass Numerology

2012-01-19T05:00:00.027-07:00

There are some constants other than the Higgs boson mass in the Standard Model that have been measured that can be combined in very simple formulas to give numbers that are within the margin of error of current Higgs boson mass estimates.

One is that experimental indications for the Higgs boson mass in the vicinity of 123-125 GeV are remarkably close to precisely one half of the Higgs field vaccum expectation value of 246 Gev. The other is that experimental indications for the Higgs boson mass are remarkably close to precisely half of the sum of the masses of the W+ boson, the W- boson and the Z boson (or alternatively, the sum of the masses of the W+ boson, the W- boson, the Z boson and the photon, since the photon mass is zero; or alternatively, the sum of the masses of all of the fundamental fermions, since the gluon rest mass is also zero). The sum of these masses is about 250.3 GeV, half of which would be about 125.15 GeV.

One could get an intermediate value by adding the sum of the relevant boson masses to the Higgs field vev and dividing by four (a result suggestive of a linear combination of the four electroweak bosons, the W+, W-, Z and photon).

Another way to bridge the gap would be to use the "pole masses" of the W and Z bosons, rather than their conventional directly measured masses. This basically adjusts the masses of unstable fundamental particles downward by a factor related to their propensity to decay in an amount proportional to half of their decay width, which at a leading order approximation is about 1.8 for these bosons. This would give us a sum of the three pole masses which is equal to roughly 248 GeV, which would be a fit to a 124 GeV Higgs boson pole mass if there is such a simple relationship, although the match would presumably have to be to the pole mass of the Higgs boson (something not yet possible to estimate with any meaningful accuracy as we have considerable uncertainty in both the Higgs boson mass and its decay width).

These pole mass calculations are approximate, and an exact calculation has significant terms at two loop level and probably beyond, so coming up with an exact pole mass calculation figure is a bear of a calculation. But, the notion that the Higgs field vacuum expectation value might be equal to the double the Higgs boson pole mass, and to exactly the W+ boson pole mass, the W- boson pole mass, the Z boson pole mass, and the possibly the (zero) masses of the photon and/or the eight gluons, is an attractive one. It is also suggestive of the idea that the Higgs boson itself might be understood as a linear combination of four spin one electroweak bosons to get a Higgs boson, whose pairs of opposite sign spins combine to produce an aggregate combined spin of zero, in line with the scalar character of the Higgs boson. One would need some reason to come up with a factor of two, or alternatively, some reason to add in the Higgs vev to the sum of the four electroweak boson masses which would naturally be divided by four since it is derived from a linear combination of four bosons.

The Z boson mass is related exactly to the W boson mass by the Weinberg angle aka weak mixing angle (an angle, for which the sin squared is about 0.25, which Rivero has some interesting numerological speculations in a 2005 paper and whose possible origins are discussed in terms of a heuristic set forth in a 1999 article). So, if there is some simple relationship between the Higgs boson mass, the Higgs field vacuum expectation value, the W boson mass and the Z boson mass, such that the Higgs field vacuum expectation value and Higgs boson mass can be calculated from the W boson and Z boson masses, it ought to be possible to derive all of these constants exactly, in principle at least, from the W boson mass and the Weinberg angle (which is definitionally derived from the relationship between the weak and electromagnetic gauge couplings).

Of course, even if the experimental values come to be known with sufficient precision to rule out such simple relationships, one is still left with the question: why should this simple relationship be such a near miss? For example, does the simple relationship capture the first order terms of an exact relationship whose next to leading order and beyond terms are unknown?

Afterthoughts

This all becomes even more exciting if one can come up with a generalization of the Koide formula to account for all of the charged fermion masses from just a couple of constants. Both the W boson mass and Z boson mass were predicted from other constants known at the time before they were discovered, and one could conceivably get the number of free constants in the Standard Model down to a much smaller number.

While not precisely on point, this is also as good a point as any to ask, why have string theory and SUSY so utterly failed to provide accurate predictions of the mass constants or mixing matrix values in the Standard Model? Isn't that the very least that we should expect of any purported grand unification or theory of everything scheme?

Picture Of Lost Civilization In The Amazon Emerging

2012-01-16T17:31:00.001-07:00

The Amazon is home to more groups of uncontacted hunter-gatherers than anyplace else in the world, with the possible exception of Papua New Guinea. But, it isn't generally known as a center of pre-Columbian advanced civilizations comparable to that of the Aztecs of Mesoamerica and the Incas of the Pacific Coast of South America. The only real traces found among contemporary Amazonians of a possible lost civilization are a few legends and some very geographically broad linguistic groupings that don't fit the usual geographically confined hunter-gatherer mold.

But, new pieces of evidence increasingly show signs of a civilization that did greatly modify its environment in the Amazon.

Alceu Ranzi, a Brazilian scholar who helped discover the squares, octagons, circles, rectangles and ovals that make up the land carvings, said these geoglyphs found on deforested land were as significant as the famous Nazca lines, the enigmatic animal symbols visible from the air in southern Peru. . . . parts of the Amazon may have been home for centuries to large populations numbering well into the thousands and living in dozens of towns connected by road networks, explains the American writer Charles C. Mann. In fact, according to Mr. Mann, the British explorer Percy Fawcett vanished on his 1925 quest to find the lost “City of Z” in the Xingu, one area with such urban settlements. . . . So far, 290 such earthworks have been found in Acre, along with about 70 others in Bolivia and 30 in the Brazilian states of Amazonas and Rondônia.

Researchers first viewed the geoglyphs in the 1970s, after Brazil’s military dictatorship encouraged settlers to move to Acre and other parts of the Amazon, using the nationalist slogan “occupy to avoid surrendering” to justify the settlement that resulted in deforestation.

But little scientific attention was paid to the discovery until Mr. Ranzi, the Brazilian scientist, began his surveys in the late 1990s, and Brazilian, Finnish and American researchers began finding more geoglyphs by using high-resolution satellite imagery and small planes to fly over the Amazon.

Denise Schaan, an archaeologist at the Federal University of Pará in Brazil who now leads research on the geoglyphs, said radiocarbon testing indicated that they were built 1,000 to 2,000 years ago, and might have been rebuilt several times during that period. . . . So far, 290 such earthworks have been found in Acre, along with about 70 others in Bolivia and 30 in the Brazilian states of Amazonas and Rondônia.

Researchers first viewed the geoglyphs in the 1970s, after Brazil’s military dictatorship encouraged settlers to move to Acre and other parts of the Amazon, using the nationalist slogan “occupy to avoid surrendering” to justify the settlement that resulted in deforestation. But little scientific attention was paid to the discovery until Mr. Ranzi, the Brazilian scientist, began his surveys in the late 1990s, and Brazilian, Finnish and American researchers began finding more geoglyphs by using high-resolution satellite imagery and small planes to fly over the Amazon.

Denise Schaan, an archaeologist at the Federal University of Pará in Brazil who now leads research on the geoglyphs, said radiocarbon testing indicated that they were built 1,000 to 2,000 years ago, and might have been rebuilt several times during that period. Researchers now believe that the geoglyphs may have held ceremonial importance, similar, perhaps, to the medieval cathedrals in Europe. This spiritual role, said William Balée, an anthropologist at Tulane University, could have been one that involved “geometry and gigantism.”

In 2008, National Geographic reported on a somewhat similarly developed civilization in a part of the Amazon remote from these geoglyphs.

Dozens of ancient, densely packed, towns, villages, and hamlets arranged in an organized pattern have been mapped in the Brazilian Amazon. . . . In 1993, Heckenberger lived with the Kuikuro near the headwaters of the Xingu River. Within two weeks of his stay, he learned about the ancient settlements and began a 15-year effort to study and map them in detail.

So far he has identified at least two major clusters—or polities—of towns, villages, and hamlets. Each cluster contains a central seat of ritualistic power with wide roads radiating out to other communities.

Each settlement is organized around a central plaza and linked to others via precisely placed roads. In their heyday, some of the settlements were home to perhaps thousands of people and were about 150 acres (61 hectares) in size.

A major road aligned with the summer solstice intersects each central plaza.
The larger towns, placed at cardinal points from the central seat of power, were walled much like a medieval town, noted Heckenberger. Smaller villages and hamlets were less well defined.

Between the settlements, which today are almost completely overgrown, was a patchwork of agricultural fields for crops such as manioc along with dams and ponds likely used for fish farms.

"The whole landscape is almost like a latticework, the way it is gridded off," Heckenberger said. "The individual centers themselves are much less constructed. It is more patterned at the regional level."

At their height between A.D. 1250 and 1650, the clusters may have housed around 50,000 people, the scientists noted.

According to Heckenberger, the planned structure of these settlements is indicative of the regional planning and political organization that are hallmarks of urban society.

"These are far more planned at the regional level than your average medieval town," he said, noting that rural landscapes in medieval settlements were randomly oriented.

"Here things are oriented at the same angles and distances across the entire landscape."

Charles C. Mann, in his book 1491, argued that these civilizations collapsed because they came into contact with old world diseases despite limited direct contact with Europeans, and that there was a rewilding of the Americans in response to this population collapse.

This is a possibility that shouldn't be ruled out. But, I'm not necessarily sold on that as the only possible cause, because we have other examples of relatively advanced societies like the irrigation agriculture based societies of the Four Corners area of Colorado that rose and fell due to climate conditions in the Pre-Columbian era, and civilizations like the Mayans and Olmecs that preceded the Aztecs that were interrupted by successor civilizations that were more successful. We have have old world examples like the Harappans of the Indus River Valley and the Western Roman Empire, who apparently managed to experience the collapse of their societies without the assistance of an influx of superlethal Old World diseases.

Still, clearly these civilization did collapse, and clearly they did have some level of urban organization and agriculture in the pre-Columbian era in the Amazon.

Lubos v. Koide

2012-01-16T13:56:00.002-07:00

Lubos, at his blog, makes the case for Koide's formula for the lepton masses, which has been expanded by later investigators, being mere numerology. While he is pretty out of the mainstream when it comes to climate change and cultral sensitivity, he is quite mainstream and credible in his specialty of theoretical physics from a SUSY/String Theory perspective and his post makes the argument against Koide's formula being deeply significant about as well as it is possible to do so in a blog post sized exposition. His argument is not a straw man and deserves serious consideration.

Koide's Formula, recall, is the observation that the sum of the masses of the three charged leptons, divided by the square of the sum of the positive square roots of the charged leptons, is equal to two-thirds. It has been confirmed to five signficant digits which is consistent with experimental evidence, predicts a tau mass to a couple of significant digits more than the currently most precise value, has held up even though it was quite a bit off the most precise values at the time it was formulated several decades ago, and is interestingly exactly at the midpoint of the highest possible value for that ratio (1) and the lowest possible value for that ratio (1/3).

His main points are as follows:

(1) It is much easier to find approximate, but surprisingly close, mathematical coincidences than you would think but manipulating a handful of constants in every conceivable way.

(2) Since the formulation is dimensionless, it is actually a function of two lepton mass ratios, rather than three independent mass values, which makes it somewhat less remarkable.

(3) If the ratio 2/3rd is conceptualized as a 45 degree angle, rather than a ratio, it is not at the midpoint of the possible values, making it less special.

(4) Koide's formula uses the real valued numbers for charged lepton masses, rather than the complex valued charged lepton masses, called "pole masses" that include an adjustment for the decay width of unstable particles (basically, their half lives, converted into mass units), and when Koide's formula is applied to pole masses, the 0.79 ratio that results don't seem as special. Lubos thinks it is unnatural to use something other than pole masses in anything that expresses a fundamental relationship of charge lepton masses.

(5)

In the Standard Model, the masses of charged leptons arise from the Yukawa interaction term in the Lagrangian, [which is a simple function of] y . . . a dimensionless (in d=4 and classically) coupling constant; h . . . the real Higgs field; [and] Ψ,Ψ ¯ . . . the Dirac field describing the charged lepton or its complex conjugate, respectively. To preserve the electroweak symmetry – which is needed for a peaceful behavior of the W-bosons and Z-bosons – one can't just add the electron or muon or tau mass by hand. After all, the electroweak symmetry says that the left-handed electron is fundamentally the same particle as the electron neutrino. Instead, we must add the Yukawa cubic vertex – with two fermionic external lines and one Higgs external line – and hope that Mr Higgs or Ms God will break the electroweak symmetry which also means that he will break the symmetry between electrons and their neutrinos. . . . [In turn] In the vacuum, the Higgs field may be written as h=v+Δh. Here, v is a purely numerical (c -number-valued) dimensionful constant whose value 246 GeV was known before we knew that the Higgs boson mass is 125 GeV. The value of v is related to the W-boson and Z-boson masses and other things that were measured a long time ago. The term Δh contains the rest of the dynamical Higgs field (which is operator-valued) but its expectation value is already zero. . . . [And,] m e is just a shortcut for m e =y e v where the Yukawa coupling y e for the electron and the Higgs vev v= 246 GeV are more fundamental than m e. If you write the masses in this way, v will simply cancel and you get the same formula for Q where m is replaced by y everywhere. However, this is not quite accurate because the physical masses are equal to yv up to the leading order (tree level diagrams i.e. classical physics) only. There are (quantum) loop corrections and many other corrections. Moreover, the values of y that produce Q=2/3 are the low-energy values of the Yukawa couplings. Even though the Yukawa couplings are more fundamental than the masses themselves, their low-energy values are less fundamental than some other values, their high-energy values.

In other words, both arguments (4) and (5) are arguments that in the ordinary formulation of the Standard Model, the charged lepton mass inputs into Koide's formula are not fundamental and therefore have no business exhibiting profound and mysterious relationships to each other that have any basis in fundamental physics and hence are probably just numerological coincidences.

I'm not sold on the argument Lubos makes, for a few reasons, that I'll note with Roman numerals to avoid confusion with his reasons:

(I) Koide's formula has come into closer alignment with the experimentally measured values of the charged lepton values as they have been discovered more precisely, while most numerical coincidences (e.g. efforts to describe the electromagnetic coupling constant as a simple integer valued number) fall apart as the experimentally valued number becomes known with more precision. A five significant digit match to a simple, dimensionless, rational number shouldn't be dismissed lightly.

(II) Lots of well motivated Standard Model derived constant predictions (e.g. the W and Z masses, the proton and neutron masses) are not know to any more precision than Koide's formula, so judged by its fit to empirical evidence, Koide's formula is holding its own.

(III) Almost everyone who understands particle physics well enough to be a professional in the field intuitively agrees that the many constants of the Standard Model are not simply random and have deeper interrelationships to each other than we have yet come up with well formulates laws of physics to explicate. Put another way, there is clearly some formula out there that if discovered would derive particle masses, particle decay widths, CKM/PMNS matrix phases, coupling constants of the fundamental forces, and the constants of the running of the fundamental force coupling constants, from a much smaller set of more fundamental constants, and there is no a priori reason that we aren't capable of discovering that relationship.

If you start from the assumption that there is some deeper relationship between these constants, then the question is which are the proposed relationships between these constants has proven most fruitful so far and has tended to become more rather than less accurate as more empirical evidence has become available.

Put another way, if you assume that these constants do have a deeper relationship, then any other empircially relationship between them that is observed necessarily derives in some way from the deep relationship and hints at its nature. The empirical validity of the dimensionless Koide's formula to great precision, at the very least, is proof of a no go theorem for other proposed deeper relationship between charged lepton masses that does not observe that relationship. It fairly tightly constrains the universe of potentially valid deeper theories.

At the very least, Koide's formula poses an unsolved problem in physics akin to the Strong CP problem, i.e. "why is no there observable CP violation in the physics of the strong force?"

In the same vein, the phenomenological and predictive success of the modified gravity theory "MOND" as originally formulated by Milgrom in describing galactic rotation curves with a single numerical constant, doesn't necessarily mean that this phenomena is really caused by the law of gravity being misformulated rather than dark matter. But, it also necessarily implies that any dark matter theory that takes multiple unconstrained numerical constants to produce results that MOND can match with one numerical constant with similar accuracy is missing some very important factors that cause real galaxies to have far more tightly constrained structures than their formulation permits. The fact that a strong phenomenological relationship exists doesn't tell you its cause, but it does generally establish that there is some cause for it.

(IV) Lots of phenomenological relationships in physics that aren't fundamental at the deepest sense and can be derived from mere approximations of theoretical physics formulas which are known to be more accurate are still remarkably accurate and simple in practice.

For example, the phenomenological fact that planets follow orbits around the sun that are ellipses with foci at the planet in question and the sun, turns out to be extremely accurate, and possible to express with high school algebra and derive with elementary first year calculus, even though it ignores all sorts of more accurate physics such as the corrections between general relativity and Newtonian gravity for objects that are in motion, and the fact that planetary orbits are actually determined via supremely difficult to calculate many bodied problems that include the gravitational effects of every little bit of matter in the solar system and beyond, not just a two body problem and a formula in the form F=GmM/r^2. Before Kepler figured out that the orbits were ellipses, Copernicus came up with a simpler approximation of the orbits as spheres around the sun (which are degenerate forms of the equations for ellipses), which while also wrong, was still an immense leap relative to the prior formulations.

Similarly, the classical ideal gas law, PV=NkT, involves physics that aren't fundamental (it can be derived from first principles from statistical mechanics and a few simplifying assumptions, and statistical mechanics, in turn, relies on classical mechanics that have to be derived at a fundamental level in far from obvious way from quantum mechanics). Yet, we still teach high school and lower division physics and chemistry students the ideal gas law because it, and non-ideal gas variants of it that use empirically determined physical constants to fit real gases, turn out to be useful ways to develop quantitative intuition about how gases behave and approximate that behavior with accuracy sufficient for a wealth of applications. The ideal gas law, in turn, was derived from even simpler observations about two variable proportionality or inverse proportionality relationships (e.g. V=cT for a gas of a constant volume) that were observed phenomenologically, long before all of the pieces were put together.

Thus, the fact that Koide's formula doesn't naturally and obviously correspond in form to current physically well motivated electroweak unification models doesn't necessarily count as a strike against it. It may be that the terms in more complex formulations of fundamental sources of charged lepton masses, either cancel out or have insignificant physical values that are swamped by other terms. For example, I suspect that a more exact formulation of Koide's formula for leptons may require the inclusion of all six lepton masses. But, the neutrino masses are so negligible relative to the charged lepton masses that their impact on Koide's formula may be invisible at the currently level of precision with which we know the charged lepton masses.

Odds are that a some level of precision, Koide's formula will cease to hold. But, for example, if the amount by which it is off is at an order of magnitude that could be accounted for via the inclusion of neutrino masses and tweaking the sign of electron neutrino mass term (a Brannen suggested possibility), then Koide's formula starts looking like an incomplete approximation of more exact theory that holds for reasons considerably deeper than coincidence, rather than merely a fluke.

(V) A notion of what is fundamental and what is derived, with a set of constants that are all tightly constrained to be related to each other mathematically, is to some extent a matter of perception. The notion that inferred Yukawa coupling constants, or pole masses of particles must be more fundamental than observed particle rest masses without adjustment for rates of decay, is not at all obvious. There is nothing illogical or irrational about described Yukawa coupling constants and pole masses as derived values, and charged lepton rest masses as fundamental.

My strong suspicion, for example, given the strong patterns that are observed in decay widths, is that the decay width of a particle is a derived constant that is the product in some manner or other of rest masses and some other quantum numbers, rather than having a truly independent value for each particle. Pole mass may be a more useful description of a particle's mass in some equations, just as a wind-chill adjusted temperature may be a more useful description of the ambient temperature in a location for some purposes. But, that doesn't necessarily mean that it is truly more fundamental.

And, reliance upon Standard Model formulations of particle masses as a source of the "true" nature of particle mass is also questionable when one of the deepest problems of the Standard Model is that its formulations can't provide particle masses from first principles for fermions or the Higgs boson (although the photon, W and Z boson rest masses can be derived from it).

(VI) Lubos ignores the relatively productive recent efforts that have been made recently to express other Standard Model particle mases (where the true values are often known to just one or two signficant digits) in Koide-like triples or other Koide-like formulations, an apparent three to one relationship between Koide-like formulations for quarks and for leptons (that fits the three to one relationship betweeen quarks and leptons seen in precision electroweak decay products), possible derivations of fermion mass relationships from CKM/PMNS matrix elements and visa versa (often finding links via the square root of fermion masses to be more natural), the phenomenological observation of quark-lepton complementarity in CKM/PMNS matrix elements, and so on. If there was just one Koide triple in the fermion mass matrix, it might just be a fluke. When there are multiple Koide triples in the fermion mass matrix that all seem to take on some kind of integer value to well within the range of empirically measured masses, dismissing the result as a fluke is problematic.

The implied angle of forty-five degrees from Koide's formula, for example, also comes up in quark-lepton complementarity, which relates to CKM/PMNS matrix element relationships.

(VII) Lubos also puts on blinders to the potential relevance of the square root of fermion mass as a potentially fundamental matter having some relationship to emerging evidence in his own string theoretic field of the similarity between gravity (which is a force that acts on mass-energy) and a squared QCD type gauge group, in which color charge is replaced with kinematic terms.

Dim Matter Strikes Again

2012-01-12T14:04:00.000-07:00

More accurate observations of globular clusters have turned up low luminosity stars, with masses of about 0.18 times that of the sun, that account for a large proportion of the globular cluster's previously estimated dark matter which was based on brighter observed stars and lensing observations for the entire cluster.

These clusters are considerably more rich in dark matter than individual galaxies and the phenomenological predictions of modified gravity theories derived from an early version called MOND consistently underestimate the amount of dark matter in these clusters. But, this new result finding that there is considerable luminous ordinary matter in these clusters that had not previously been seen by astronomers because their instruments weren't powerful enough to see them suggests that MOND's shortcoming in its estimates of the magnitude of effects due to something other than Newtonian gravity acting on observable luminous matter may be much smaller than previously believed.

This result should be considered together observations in late 2010 that revealed that the amount of low luminosity ordinary matter in elliptical galaxies had been grossly underestimated. The more accurate ellipical galaxy census suggested that the true amount of dark matter in the universe due to that revision in the estimate amount of normal matter in ellipical galaxies alone was closer to 50% of all ordinary and dark matter combined, rather than the frequently quoted 80% figure.

Other recent theoretical studies have shown that some portion of the effects attributed to dark matter in spinning galaxies is actually attributable to general relativistic corrections to models that estimate the effects of gravity with a Newtonian approximation, although different theorists have reached dramatically different estimates of the magnitude of these effects by using different methods to simplify the description of a spinning galaxy to which the equations of general relativity are applied.

This new result on globular clusters, combined with the prior work on dim matter in ellipical galaxies and general relativistic effects, suggests that the actual percentage of matter in the universe which is dark matter may be considerably less than 50%. Dark matter may actually end up being one third or less of all of the matter in the universe.

If one takes the position that a cosmological constant is a perfectly acceptable and respectable alternative to a hypothesis that 80% of the universe is made out of "dark energy" observed in no other way, and that it represents a property of space-time itself, and that the actual proportion of matter which is dark is much smaller than previous estimates, then dark matter candidates like neutrinos (perhaps in condensate form) that don't require the discovery of new fundamental particles, begins to look more plausible.

Pinning Down Archaic Admixture Population Models

2012-01-12T12:49:00.003-07:00

There are many outstanding disputes, critical to understand the demographic history of Eurasian modern humans in the Upper Paleolithic era, related to the population models that are used to describe how Neanderthal genes could have ended up in almost all modern Eurasians at frequencies on the order of 2%-4% of our autosomal genome in a sample made up of many thousands or tens of thousands of individuals, despite a complete absence of Neanderthal mtDNA or Y-DNA in any genetically tested modern human, from a large sample of tens or hundreds of thousands of individuals, including hundreds of ancient DNA samples. This population genetic data has been accumulated in a collective scientific enterprise that has deliberately oversampled populations that are likely to be genetically diverse outliers in both data sets, although there are far more outlier populations and ancient DNA populations that are undersampled for autosomal genetics than there are that have been undersampled for mtDNA.

One of the confounds in estimating what kind of process gave rise to the introgression of Neanderthal DNA into modern humans is the question of how much of the Neanderthal DNA originally present in hybrid individuals has been purged over time from modern humans, either due to random genetic drift in admixed modern human populations, or due to selective disadvantage associated with particular Neanderthal genes.

It helps, in comparing possibilities that we have significant shares of the Neanderthal genome from ancient DNA to compare against modern genomes.

Neanderthal genes that could have introgressed into modern humans can be broken into one of four categories: (1) genes in which the Neanderthal genome and modern human genome are indistiguishable (which is a very substantial share of the total, probably on the order of 95% or more), (2) Neanderthal genes with a positive selective advantage (there is some early indication that this may mostly consist of HLA genes which are related to the immune system, (3) Neanderthal genes that have a selective disadvantage relative to modern human genes, which statistically should have been removed from the human genome over the relevant time spam of at least 30,000 years or so, and quite possible two to four times as long as that, even if the selective disadvantage is very modest, particularly as disadvantageous genes slowly become separated from nearby genes that may have selective advantage through the recombination process over many generations, and (4) Neanderthal genes that are selectively neutral.

One can determine in modern populations which Nenderthal genes are present at elevated frequencies indicative of selective advantage and which are only present at a baseline level, in order to both estimate the true selectively neutral baseline level of admixture before selection started to act on the genes in modern humans with Neanderthal ancestry, and to estimate the magnitude of the advantage associated with those genes present at elevated frequency. This task is somewhat harder than it seems because one has to address statistical noise that elevates the frequency of some random genes for reasons unrelated to selective advantage, but is well within the capabilities of well established statistical methods.

One can also search, by direct comparison, for distinguishably Neanderthal genes that have not ended up in any modern human at all. There are basically three ways that this could happen: (1) the genes were never transferred in an admixture event because there were a finite number of admixture events and only an approximately random half of the Neanderthal genome was transferred in each event, so some genes may never have been transferred in any of the events, (2) the genes were transferred in an admixture event and left the modern human genome via random genetic drift, (3) the genes were transferred in an admixture event but due to selective disadvantage associated with the genes, they were culled from the modern human genome. The percentage of Neanderthal specific genes known to exist which are found in no modern human populations can provide a very accurate estimate of the combined impact of these three factors, although by itself, it doesn't do much to tell you how much of each factor plays a part.

It is mathematically trivial to relate the impact of the first factor to the number of admixture events that took place, and the relationship between the percentage of genes never transferred in admixture events and the number of admixture events is highly non-linear. For one admixture event, the percentage of 50%. For two it is 25%. In general, the never transmitted proportion of the genome is 1/(2^n) where n is the number of admixture events. In any scenario where there are seven or more admixture events in all of human history, the percentage of Neanderthal specific genes never transmitted in admixture events is below 1% and at somewhere on the order of twelve to fourteen admixture events ever in all of modern human history, the impact of this factor would be completely undetectable with any level of statistical significance in an autosomal genome data set as large as the one that is currently in existence.

If the effective population size of the modern human populations that admixed with Neanderthals was on the order of four hundred to seven hundred and fifty individuals, the effect of non-transmission of specific genes in any admixture event should be negligable, and even at an effective population size as low as two hundred, the impact of this factor should be a very small proportion of the total number of Neanderthal genes not observed in any modern human population. Yet, most estimates of the effective population size of the founder population of modern human Eurasians are at least in the single digit thousands, and archaic admixture itself, while it would inflate the apparent effective population size of the founder population of modern human Eurasians, at the 2.5%-4% of the total population size would not have an effect so significant that it would bring the effective population size of the founding population of modern human Eurasians to the low three digits, particularly to the extent that the estimates are corroborated by mtDNA and Y-DNA based estimates that have on archaic component.

This means that essentially all of the "missing" Neanderthal DNA (at least outside the sex chromosomes where there are clearly population structure and demographic history factors that are non-random at play) must statistically derive from either genetic drift or selective disadvantage.

We can then work to estimate both components separately using a variety of population genetic parameters, and work to look at the parameter space of assumptions that can produce outcomes consistent with the percentage of missing Neanderthal DNA that we observe.

Random drift of selectively neutral genes is easy to model with very accurate results using just a handful of parameters, either analytically, or numerically with Monte Carlo methods. Some of the key parameters are generation length, effective modern human population size at the time of admixture, number of admixture events, spacing of admixture events, boom and bust variability in effective modern human population size, and population growth (which can be quite accurately estimated in the long run from a variety of evidence, even if fine grained variability in this rate is hard to determine).

For populations that experience growth in the long run (as modern humans in Eurasia obvious did), where the number of generations is very large, it turns out that generation length doesn't actually matter very much, because when you have a number of generations in excess of one thousand with a population that reaches the many millions sometime in the Upper Paleolithic, and an overall percentage of admixture that is at least on the order of the 2.5%-4% it has reached at long term fixation, which has apparently been reached for all Eurasian given the supercontinental uniformity present in that percentage, the amount of genomic loss that takes place due to random drift bceomes insensitive to the number of generations because random drift is much more powerful an effect, in a non-linear manner, when populations are small. At a leading order estimate, the likelihood of losing a gene entirely from a population in any given span of generations is a non-linear function of the absolute number of individuals in the population who carry that gene. Basically, the percentage likelihood that a gene will leave the population by random drift is roughly proportional to the probability that a random sample from the effective population equal to the absolute number of gene carriers in the population would be zero. Once the absolute number of carriers and zero is several sample error standard deviations apart from a sample of that size, the probability of loss of a gene entirely due to random drift approachees zero.

Complicating this is a factor that also looks like random drift, which is mutation. While not listed as a separate factor, another way that a gene can be removed from the gene pool is through a mutation at that locus. The probability of this happening is a function of the number of generations involved and the effective population size of each generation, divided by the number of carriers of a particular gene, and discounted for the fact that lots of mutations are lethal and never enter the gene pool. This is the method used to make estimates of the age of mtDNA and Y-DNA haplogroups and it isn't very accurate, but there is a considerable body of empirical evidence that put order of magnitude bounds on the size of this effect. So, whlle the error bars on this component of the random loss of selectively neutral genes from the population might have extremes that vary by as much as a factor of two to ten if we were really being realistic about who precise our methods of mutation dating have proven to be in practice (perhaps more, given that the timing of the admixture event has something on the order of a factor of two uncertainty in it to begin with and that our estimates of generation length in Upper Paleolithic modern humans aren't terribly accurate and our effective population chart also has a pretty fuzzy line), if the effect is at an order of magnitude lower than other sources of removals of genes from the population's genome, we can safely ignore it, even if the precise magnitude of the effect is not known with a great deal of certainty.

From the other direction, there have been a number of reasonably useful estimates of the proportion of genes in the human genome, and the proportion of genes in a variety of other species, which do, or do not, show indications of having a selective effect at any given time (which basically consists of genes that have not reached fixation in the species for which there is no good reason to believe that selection produces multiple varieties in stable proportions as it does for HLA genes). In general, these studies have shown that the proportion of genes that are currently experiencing active selective pressures at any given time appear to be fairly modest, but not negligable either.

There is no really good way to estimate the relative numbers of selectively advantageous archaic genes to selectively disadvantageous archaic genes. There argument for more good genes than bad is that Neanderthals had more time to adapt to the new environment that modern humans were entering. The argument for more bad genes than good is that Neanderthals went extinct while modern humans didn't, so overall, modern humans had a selective advantage of some form over Neanderthals. But, it isn't unreasonable to infer that there should be an order of magnitude similar number of each. There is also no particularly good reason to think that the proportion of the genome that is selectively neutral at any given point in time has changed very much or was much different from Neanderthals than it is for modern humans. So, an examination of the number of Neanderthal genome genes present in elevated levels that hence show signs of selective advantage could cast some light, at least, on the proportion of Neanderthal genes that gave rise to selective disadvantages and were purged from the modern human genome. The early indications from this kind of analysis are that the proportion of Neanderthal genes still in the modern human genome which show signs of having been positively selected for is small relative to the total number of Neanderthal genes in the modern human genome.

Despite the fuzziness of all of these reasoning, from a quantitative perspective, the bottom line in all of this analysis is that we would expect a significantly disproportionate share of the proportion of missing genes from Neanderthal genome to have been lost due to selectively neutral random drift rather than natural selection, and that even this crude bound allows us to make fairly specific numerical estimates of the proportion of Neanderthal specific genes that were lost because they were selectively disadvantageous and the proportion of Neanderthal specific genes that were lost due to one of a couple of forms of random genetic drift.

Placing numerical bounds and maximum likelihood estimates on the proportion of Neanderthal specific genes that were lost due to random genetic drift with this kind of analysis, in turn, allows us to significantly narrow the parameter space of population model assumptions that could produce the observed amount of random genetic drift. The observed proportion of random genetic drift in the Neanderthal genome would be particularly relevant in placing bounds on the paramater space for assumptions about effective modern human population size at the time of admixture, number of admixture events, spacing of admixture events, and the boom and bust variability in effective modern human population size. And, there are independent ways to provide additional bounds on many of these parameters from other lines of population genetic data and anthropology and the physical anthropology of Neanderthal remains, so the flexibility in one paramater doesn't inject too much flexibility into other paramaters.

Also, a reasonably tightly bound overall estimate of the magnitude of random genetic drift from the proportion of the Neanderthal genome that has been purged from modern humans provides a robust, and fairly direct estimate, from the longest time period for which ancient DNA is available for hominins, that can be used to inform estimates of the rate at which selectively neutral genes are purged by genetic drift in modern humans that is relatively population model independent for use in analysis of non-Neanderthal admixture population genetics (e.g. in estimates related to Denisovian admixture, putative African archaic admixture, admixtures of modern human populations in the Upper Paleolithic era, and the accuracy of estimates of the probability that a chance in the proportion of a particular gene in a population was due to random genetic drift or selection), since the error bars on this direct measure of random genetic drift in autosomal genes over that time period would be much smaller than the error bars around estimates of any of the specific parameters in parameter space that could be used to estimate it from first principles using population models alone. Thus, making this estimate in the Neanderthal case would materially improve the statistical power of all of our long term population genetic estimates, a contribution that may be unique and may not be available with greater precision from any other set of data for the foreseeable future.

Explicitly estimating the impact of selective effects and the loss of genes due to random genetic drift is also likely to establish that the total number of archaic admixture events was larger than an estimate that ignores these effects, because, on balance, these effects tend to reduce the number of Neanderthal genes in the modern human genome. Thus, the process of estimating these numbers of likely to reveal that Neanderthals and modern humans had sex more often that a crude back of napkin estimate would suggest. And, if the kind of process assumptions (Haldane's rule which also impacts fertility assumptions, and predominantly female modern human mothers for hybrid children born into modern human tribes that averted extinction, which implies that there are large numbers of uncounted cases where Neanderthal mothers that were erased from modern human populations in the present) that most naturally explain the disconnect between autosomal genetic data and uniparental genetic data are also incorporated into the analysis, the amount of cross species sexual activity between Neanderthals and modern humans may have been quite a bit higher indeed than the current percentage of our autosomal genome attributable to Neanderthal genes would suggest, probably on the order of a factor of two to five, which would be roughly the difference between a once in a generation event (a crude estimate without these considerations) and something like a once every few years event.

My intuition is that the amount of allele loss due to random genetic drift acting on selectively neutral genes that is actually observed in the Neanderthal case would suggest that the magnitude of the impact of random genetic drift in purging selectively neutral genes from modern human populations is quite a bit smaller than could safely be inferred by a naiive estimate based on other existing data and pure population modeling not supported by this kind of empirical calibration. Thus, I suspect that this data will, generally, favor findings that it is more likely that a given chance in gene frequency was a selective effect rather than a random one, and that populations not subject to selective pressures are more genetically stable than one might naiively expect even with a fairly careful theoretical analysis.

The Population Genetics Of Mutts

2012-01-12T09:02:00.000-07:00

Population genetic studies that are designed to capture pre-historic genetic diversity and the origins of modern "peoples" focuses on "pure blooded" individuals whose ancestors (typically at least back to four grandparents) have known and identical origins in the locale to which the sample is assigned. There are studies of admixed populations (e.g. mestizos and African-Americans, the people of Madagascar and "colored" Anglo-Caribbeans and South Africans), but those studies usually focus on populations where the admixture was population-wide, took place half a dozen generations or more ago, and may have involved considerably less of a choice element than is found in modern mixed couples.

For the purpose of discerning pre-historic population structure, this kind of selection makes sense.

But, it would be interesting to see, from a genetic diversity and heredity perspective, if there are systemic differences between monoancestral people and multiancestral people, in general.

For example, are there genetic trades related to psychological makeup (e.g. traits linked to the Big Five personality trait of openness to experience, or traits linked to novelty seeking) that are found at markedly different frequencies in monoancestral and multiancestral people?

Does "Denisovian Admixture" Come From Homo Erectus?

2012-01-10T15:47:00.000-07:00

Papuans and Australian Aborigines (and to a lesser extent populations admixed with them, unadmixed Southeast Asians and Negrito populations in the Philippines) have in their autosomal genomes a significant low single digit percentage overlap with the ancient Denisovian genome extracted from an archaic hominin tooth in Siberia. This is absent in other global populations of the world.

What ancient hominins did they admix with and acquire these genes from?

A new paper that Maju has called attention to as his anthropology oriented blog makes the case for what I have long believed to be the most plausible scenario, that "Denisovian admixture" really represents admixture with Asian Homo Erectus individuals, encountered by the first significant wave of modern humans to reach Asia via a coastal route, who promptly went extinct as a separate species (as opposed to a minor contributor to the resulting population's genetic diversity) following this contact with modern humans and before the next wave of modern humans arrived. Hence, the Denisovians (whose remains date to something on the order of forty thousand years or more after the last traces of archaic hominins in archaeology or from genetic traces anywhere else in the historic Asian Homo Erectus range), to the extent that they have the genes found in modern Melanesians and Australian aborigines, were either a relict Asian Homo Erectus population, or a population that was admixed with Asian Homo Erectus individuals.

Here are some excerpts from the paper linked at his post:

Findings include some evidence of a male biased gene flow from the Denisova lineage to Papuan ancestors and possibly even more archaic gene flow. It is unclear if there is evidence for more than one Neanderthal interbreeding . . . . Papuan could have a unique split with the Denisovan (as Reich et al. 2010 suggest the Papuan lineage received ~5% of its genes from that lineage). As we will see later, the apparent reason for this would seem to be that the distance from Denisova to Chimp is more strongly underestimated than that from Denisova to Papuan. The underestimation of the Denisova to Chimp distance could be due to Denisova harboring some very archaic alleles. . . The decrease in frequency of the DP pattern on X, particularly when compared to the NP pattern (which is near autosomal average frequency on X) suggests the possibility of asymmetric gene flow in this introgression event. If so, it would seem that this might be most readily explained by greater survival and reproduction of the offspring of Denisova males impregnating the modern human female ancestors of Papuans rather than the other way around.... Note the high frequency of the DNP pattern, which may be due to the Denisovan relatives that mixed not being closely related to the Denisovan sampled. . . . a hierarchical structured coalescent model with at least two introgression events between archaic humans and out of Africa Moderns leads to a substantial increase in fit. Overall fit however, is still far far worse than could be expected. It seems that to improve the fit a number of factors may come into play. Firstly, there are too many private NH, NF and NP [Neanderthal-Han, -French and -Papuan] patterns. Secondly, the latter of these, NP, seems markedly less than the former two. . . . One model that may do a better job of describing the data with fewer parameters is independent mixing of Neanderthal genes with Han and French, but to a nearly identical total degree. Also, lesser mixing of Neanderthal genes into Papuan, made up for by a larger proportion of archaic alleles in Papuans coming from the mixing with an archaic that is only slightly closer to Denisova than to Neanderthal. This would in turn suggest that the mixing with Neanderthals was not purely right out of Africa and it was not a single event. Instead, there may have been opportunity for European ancestors to pick up Neanderthal alleles, in the unknown part of Eurasia they existed in prior to moving into Europe, ditto and independently for the ancestors of the East Asians, while Papuan ancestors moved fairly rapidly through the zone of classical Neanderthals and picked up most of their archaic genes in the Indonesian region. The form of this ancestral population may have been about equally related to Neanderthals and Denisovans, but may also have had an appreciable proportion of even earlier (e.g., Homo erectus genes) in its genome.

Maju questions the independent but identical Neanderthal admixture scenario for East Eurasians and West Eurasians based on the absence of Neanderthals in East Asia. However, the Neanderthal admixtures could take place anywhere between the Levant and South Asia and Europe (the Neanderthal range, more or less) so long as it took after the proto-West Eurasian and proto-East Eurasian populations had split and begun their migrations.

I'd started to think something along the same lines after looking at data from John Hawks at his blog on the distribution of private v. shared Neanderthal allelles in West Eurasian v. East Eurasian populations, which is very had to obtain if the admixture happens and reaches anything approaching fixation before the two branches of Eurasians split into separate populations as the migrate out of Southwest Asia and into the rest of Eurasia. There are good reasons to think that very similar population dynamics would produce very similar overall admixture percentages for out of Africa modern humans in this scenario, but this would explain the differences in the particular archaic genes found in each population which don't overlap as much as they should for other scenarios to be more likely.

Of couse, from a genetic perpsective, a highly structured population in which different clans admix with different Neanderthals in the same geographic area is effectively a split of the populations in place, even though it could happen pre-migration.

The male to female dominance in the source of archaic admixture that this paper describes based on technical ancient DNA in X chromosomes is also something that I have advocated strong for on other grounds (the lack of Neanderthal mtDNA and Y-DNA lineages in modern humans) in prior posts.

Note on Contributors

2012-01-09T10:36:00.000-07:00

There are two contributors listed for Wash Park Prophet and this blog. Both are me, Andrew Oh-Willeke. My main blogger account and gmail account are different and having two contributors facilitates not having to log out of one account and log into the other to post at this blog or to make comments at Blogger authenticated sites.

The Origins Of "c" As The Speed Of Light Constant

2012-01-09T10:31:00.002-07:00

An in depth examination of the convention of using the letter "c" to represent the speed of light is found here.

In the same vein, it is worth observing that the origins of the word "quark" and the specific letters for the quarks (u, d, s, c, b, and t) is much better known and that in the case of the c and b quarks that the letter have represented more than one word. For example, the b quark has been described as both a "bottom quark" (the current mainstream designation) and a "beauty quark."

New Koide-Like Formula For Quark Masses

2012-01-09T10:27:00.000-07:00

Arivero at Physics Forums notes that there is a short new preprint out by A. Kartavtsev at the Max-Planck Institute in Germany on Koide triples generalized to the quark sector that provides a phenomological prediction of quark mass for the six quarks. The abstact reads:

The charged lepton masses obey to high precision the so-called Koide relation. We propose a generalization of this relation to quarks. It includes up and down quarks of the three generations and is numerically reasonably close to the Koide limit.

The paper suggests that it may make sense to include all six leptons in the Koide formula (which has no impact on the relationship within the range of experimental accuracy because neutrino masses are so small), and in turn to include all six quark masses in the generalization of the Koide formula to quarks. In this generalization, the arccosine of the Koide formula for leptons implies an angle theta lepton, of pi/3 and the arccosine of the Koide forumla for quarks implies an angle theta quark of pi/4.

Between Koide's original formula, developing analysis of the idea of quark-lepton complementarity and the most recent paper, Arivero notes that:

Werner Rodejohann and He Zhang, from the MPI in Heidelberg, proposed that the quark sector did not need to match triplets following weak isospin, and then empirically found that it was possible to build triplets choosing either the massive or the massless quarks. This was preprint http://arxiv.org/abs/1101.5525 and it is already published in Physics Letters B. . . .

Then myself, answering to a question here in PF, checked that there was also a Koide triplet for the quarks of intermediate mass. I have not tried to find a link between this and the whole six quarks generalisation, but I found other interesting thing: that the mass constant AND the phase for the intermediate quarks is three times the one of the charged leptons. This seems to be a reflect of the limit when the mass of electron is zero, jointly with an orthogonality between the triplets of quarks and leptons in this limit: it implies a phase of 15 degrees for leptons and 45 degrees for quarks, so that 45+120+15=280. If besides orthogonality of Koide-Foot vectors we ask for equality of the masses (charm equal to tau, strange equal muon), the mass constant needs to be three too.

So,

with the premises
1. Top, Bottom, Charm have a Koide sum rule
2. Strange, Charm, Bottom have a Koide sum rule
3. Electron, Muon, Tau have a Koide sum rule
4. phase and mass of S-C-B are three times the phase and mass of e-mu-tau

All of this continues to add to the appearance of some method to the madness of the many constants of the Standard Model, although it isn't quite yet clear precisely why this arises and precisely how the reliationship should be stated.

New Finding Hints At Common Mechanism in Alzheimer's And Autism

2012-01-05T15:19:00.002-07:00

The amyloid precursor protein is typically the focus of research related to Alzheimer's disease. However, recent scientific reports have identified elevated levels of the particular protein fragment, called, sAPP-α, in the blood of autistic children. The fragment is a well-known growth factor for nerves, and studies imply that it plays a role in T-cell immune responses as well.

From here.

Abnormal immune function has been noted in children with autism before, but no cause had previously been identified. The new study suggests that this protein that is already a biomarker for Alzheimer's disease may also be a biomarker for autism. Alzheimer's disease is the most well known form of geriatric dementia, although pre-clinical signs of it may start to manifest as early as young adulthood.

Autism is typically first diagnosed in preschool children and narrow definition autism is a characteristic subtype of developmental disability found in 1 in 110 children that disproportionately affects boys that is part of an "Autism spectrum" that is found in more children and at the milder end is sometimes described as a form of mere neurodiversity.

The research suggest that it may be possible in a few years to do a blood test for autism, allowing for earlier diagnosis, which could be helpful if earlier treatments have a better chance of being effective, and could also reduce the risk of misdiagnosis leading to inappropriate treatment.

Jester Predicts A Bad Year For BSM Physics

2012-01-05T14:50:00.000-07:00

According to Jester, the LHC and efforts to uncover sources of experimental error at OPERA are likely to conclude the year 2012 with the door closed to many past experimental hints of beyond the standard model physics. Superluminal neutrinos, excess top-antiquark asymmetries, excess CP violations in B meson decays, sub-TeV SUSY, and more are likely to be ruled out in the coming year. He sees the medium term future dominated by precision Higgs boson physics calculated to determine the coupling constants of, and confirm the properties of this boson that probably exists at a mass of about 125 GeV and will probably be officially "discovered" in 2012.

The Best Case So Far For OPERA Experimental Error

2012-01-05T14:39:00.000-07:00

A recent pre-print argues that the apparent superluminal speed of neutrinos observed at the OPERA experiment arises from a subtle miscalibration of the clocks at CERN and OPERA via GPS satellites (due to a relativistic correction proportional to the distance between the two clocks on Earth), with a calculated effect size of 58 nanoseconds which is basically consistent with a 62+/-3 nanosecond difference between the observed time to cover the distance in question and the expected time at the canonical value of the speed of light.

This leaves us with the rather boring conclusion (because it entails no new physics) that the OPERA neutrinos produced at CERN were simply going at their expected speed, given their known total combined kinetic and rest mass energies (deducted from "missing energy" in collider experiments), of approximately the speed of light minus one part per 10^9, rather than their originally announced speed of the speed of light plus one part per 10^5.

The Case For the Cosmological Constant

2012-01-05T14:13:00.003-07:00

One way of describing the universe is to describe it as having a uniform distribution of dark energy. Another is to simply conclude that the correct statement of the equations of general relativity include a cosmological constant. They aren't equivalent, although current evidence provides no means to distinguish the two theories. Marcus, at the Physics Forums, sums up the arguments for a cosmological constant (for which I have a great deal of sympathy) rather than a "substance" that is dark energy having physical reality (formatting revised to better fit this blog's style conventions):

[Loop quantum gravity physicists Bianchi and Rovelli's] "constant prejudices" paper which is the topic of this thread opens by quoting the first sentence of an article in Physics World co-authored by cosmologist Ofer Lahav (prof Astro. at University College, London). This is the kind of hype B&R are targeting (quoting Calder and Lahav in Physics World 23 (June 2010), 32–37):

Arguably the greatest mystery of humanity today is the prospect that 75% of the universe is made up of a substance known as "dark energy" about which we have almost no knowledge at all.

Earlier I quoted an excerpt from the version that Bianchi and Rovelli published in Nature journal "News and Views" section, the 15 July issue. Anyone who has read the piece in Nature carefully will realize that the operative word is "substance". They argue that it is misleading to talk about Λ (a small constant curvature) as a "substance". Quoting B&R's piece in Nature:

But it is a conceptual mistake to confuse Λ with QFT’s vacuum energy. Λ cannot be reduced to the ill-understood effect of QFT’s vacuum energy — or that of any other mysterious substance. Λ is a sort of ‘zero-point curvature’; it is a repulsive force caused by the intrinsic dynamics of space-time.

Efforts are under way to understand how this "zero point curvature" arises from the underlying quantum dynamics of space-time.

As quantum relativists the authors are naturally interested in how the zero point curvature relates to QG degrees of freedom: "the intrinsic [quantum] dynamics of space-time". There have been several articles about this. For a recent examples see page 41 of the 2010 paper by Meusburger and Fairbairn--also the paper by Han (a member of the Marseille group who has co-authored with B&R.) Continuing the B&R excerpt:

Tests on the ΛCDM model must continue and alternative ideas must be explored. But it is our opinion — and that of many relativists — that saying dark energy is a ‘great mystery’, for a force explained by current theory, is misleading. It is especially wrong to talk about a ‘substance’. It is like attributing the force that pushes us out of a turning merry-go-round to a ‘mysterious substance’...

For the full Nature article see:
http://www.astro.uu.nl/~vinkj/LSS/Na...10_Bianchi.pdf
The Bianchi, Rovelli, Kolb piece has a link to B&R's Arxiv article
"Why all these prejudices against a constant?"
http://arxiv.org/abs/1002.3966

If you accept that the cosmological constant is not a substance and is not mysterious and may very well be as fully understood as it will ever be, in terms of an accurate mathematical expression of it, and in terms of mechanism, then only dark matter and not "dark matter" is mysterious.

As I've repeatedly noted in this space, new data on the amount of ordinary matter in ellipical galaxies based on astronomy observations (which have not yet been widely assimilated) also indicates that the amount of dark matter is closer to 50% of all matter in the universe, not 80%. And, there are credible arguments that some significant part of that dark matter is due to general relativistic effects that were ignored in making the estimates, that are present in spiral galaxies and indeed, in an galactic structure with angular momentum.

After accounting for all those factors, and probably some slight remaining undercount of ordinary matter in the universe due to an inadequate ability to detect dim matter in certain kinds of distant galaxies and galactic clusters, this still leaves significant dark matter. My own best guess is that this is probably nothing more than fancy than plain old left handed neutrinos, possibly in a condensate, with little kinetic energy, and that standard leptogenesis scenarios have greatly underestimated how many neutrinos can plausibly be generated by standard weak force processes.

If that is true, than the lure of beyond the standard model physics motivated by the need for a dark matter candidate to account for 80% of the matter in the universe is not well founded.

Have Goldbach's Conjecture Or The Riemann Hypothesis Been Proved?

2012-01-03T11:52:00.014-07:00

The Big Picture In Modern Number Theory

Goldbach's Conjecture is one of the oldest unsolved problems in all of mathematics and has not been rigorously proved. My attention is focused on it because I'm currently reading, the novel "Uncle Petros and Goldbach's Conjecture" by Apostolos Doxiadis, which on its surface is about a man who devotes his entire adult life to proving it without success.

Goldbach's Conjecture, the unsolved Riemann's Hypothesis, the recently proved Fermat's Last Theorem, and a variety of similar proven and unsolved problems in number theory, collectively imply that there is far more structure to the properties of whole numbers (like their status as prime or non-prime numbers) than the process by which they are defined would necessarily imply, and that as a result, the realm of the possible results of mathematical problems that involve these numbers are considerably more narrow than one would naively believe them to be if their subtle properties were not known.

Number theory is currently in a state where there are a whole panoply of highly interrelated and highly constrained conclusions about the properties of numbers that appear to be true to an extremely great level of certainty based upon brute force numerical approximations and intermediate results towards proofs that have almost proved many of these theories but the efforts to prove these theories to date have holes.

Mathematicians have been unable to ground this body of mathematical theorems in a way that establishes that they are really correct, because nobody has had the half a dozen or so insights that would be necessary to make the conceptual leaps necessary to prove that these theorems definitively correct, and it is even theoretically possible that these theorems could be impossible to prove logically even if they are actually true in all cases.

These half a dozen or so missing insights are a Holy Grail that keeps number theorists going for long hours on obscure work year after year, because anyone who spends some seriously time studying these unsolved problems, looking at the overwhelming evidence that almost all of them must be true or very nearly true with a very narrow class of exceptions, and making a stab at trying to solve them, comes away with a deep conviction that the insights that we are missing as we try to piece together proofs could be profound insights of wide application on a par with notions like the germ theory of disease in medicine, or the unification of space and time in general relativity. The unsolved problems in the field are well enough defined and sufficiently interrelated that one could imagine a single modern day Leonhard Euler solving all of them in a few years of a single career, even if that genius mathematican ended up dying young as so many mathematical geniuses have historically.

In particular, one of the insights that is strongly hinted at, although it has not been proved, is that the prime numbers can be used as a basis set to very simply generate all other numbers through addition in much the same way that they can be used to generate all other numbers through multiplication, even though nothing used to define addition and multiplication and the set of all numbers makes this necessarily true in any obvious or trivial way.

Goldbach's Conjecture

One common way of stating Goldbach's Conjecture, actually stated by Leonhard Euler in 1742 in response to a letter from Christian Goldbach, which is maddening because this profoundly challenging unsolved problem of mathematics is so simply stated is that:

"Every even integer greater than two can be expressed as the sum of exactly two prime numbers."

Note that the prime numbers in question may be identical, that the number one does not count as a prime number for this purpose, and that there may be more than one pair of prime numbers that meet this condition for a given even integer.

A set of integers whose sum is equal to a number is called a "partition" of that number, so Goldbach's Conjecture and some related ideas explored here all involve mathematical theorem about various kinds of partitions of various kinds of numbers.

Fermat's Last Theorem (that there are no sets of three integers, a, b, c and n greater than zero, for which a^n+b^n=c^n for any value of n other than two), which was proposed in 1637 by Pierre de Fermat, and proved by Andrew Wiles (with the assistance of Richard Taylor and many mathematical predecessors who proved steps intermediate to the final result) in 1995, is also a mathematical theorem about partitions.

So is a similar theorem, which was proved by Lagrange in 1770 that "any natural number can be represented as the sum of four integer squares" (a set that includes zero).

Corollaries

The conjecture has a number of corollaries (i.e. theorems that are implied if the conjecture is true, although not necessarily visa versa).

For example, Goldbach's Conjecture implies that:

"Every odd integer greater than five can be expressed as the sum of exactly three prime numbers." The prime numbers in question may be identical, the number one does not count as a prime number for this purpose, and there may be more than one triple of prime numbers that meet this condition for a given odd integer. This theorem is actually the theorem originally formulated by Christian Goldbach sometimes called the weak Goldbach conjecture and it directly implies that every even number n ≥ 4 is the sum of at most four primes (likewise, a determination that every even number is the sum of at most four primes is sufficient to establish this conjecture).

and

"Every odd integer greater than seven can be expressed as the sum of exactly three odd prime numbers." (i.e. it is not necessary to all three prime partitions that include the number two).

and

"Every even integer greater than ten can be expressed as the sum of exactly six prime numbers."

and

"Every even integer greater than eighteen can be expressed as the sum of exactly six odd prime numbers."

and

"Every odd number greater than twenty-one can be expressed as the sum of exactly seven odd prime numbers."

A similar hypothesis, which is another conjecture, is that "Every large odd number (n > 5) is the sum of a prime and the double of a prime."

Progress Towards A Proof

A single even number greater than two that could not be expressed as a sum of exactly two primes, or a single odd number greater than five that could not be expressed as a sum of exactly three primes, would falsify these conjectures. But, no such number has been found in replicated computer searches up to 10^17.

Chen Jingrun proved "in 1973 . . . that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime (the product of two primes)[14]—e.g., 100 = 23 + 7·11."

Olivier Ramaré, in 1995 proved that every even number n ≥ 4 can be expressed the sum of at most six primes.

The Riemann Hypothesis

Another great unsolved problem in mathematics (i.e. a hypothesis that has neither been proved nor disproved), and in particular, in number theory, is the Riemann Hypothesis, and it too has interesting intermediate results and connections to the Goldbach Conjecture.

The Riemann Hypothesis is not obviously related to Goldbach's Conjecture, although it turns out there the two are related to each other. The Riemann Hypothesis concern the zeros of the Riemann zeta function.

The Riemann zeta function and a generalized version of it called the Dirichlet L-functions, are a based on special kinds of of infinite sequences of fractions that get generally smaller as the series progress. Since the fractions get smaller, the sum of these series often have finite value, and the Riemann zeta function and the various kinds of Dirichlet L-functions are equal to the sum of infinite series related to that particular function for a given complex number s.

The Riemann zeta function is the sum of an infinite series for terms 1/n^s where n in the series takes on each value from 1 to infinity, and s is permitted to be any complex number (i.e. a number with a real and imaginary component, either or both of which may be zero, where the imaginary component is equal to a real number times the square root of negative one sometimes called the "imaginary number"), rather than merely a natural number. Values of the zeta function for values of s equal to 3/2 (quantum theory), 2 (prime number frequency), 3 (physics and number theory) and 4 (physics) all have importance as physical or mathematical constants; the value of s equal to 1 is called the "harmonic series" with wide mathematical applications, and the value of s equal to 0 is -1/2.

The Riemann Hypothesis, which has neither been proven nor disproven, hypothesizes that all zero values of the Riemann zeta function are complex numbers of the form 1/2+it where i is the imaginary number and t is a real numbered variable multiplied by the imaginary number in the overall complex number put into the Riemann zeta function. Godfred Harold Hardy proved that there are infinitely many zeros of the Riemann zeta function on the line 1/2+it in the complex plane (although not all such values are zero) in 1914, but his proof didn't rule out the possibility that the Riemann zeta function might have other zeros.

The prime number theorem, imprecisely stated, provides that "the average gap between consecutive prime numbers near N is roughly ln(N)." The prime number theorem, in turn, is equivalent to a statement that there are no zeros of the Riemann zeta function of the form 1+it.

The generalized Riemann Hypothesis, conceived in 1859 by Bernhard Riemann with reference to work done by Johann Peter Gustav Lejeune Dirichlet in 1831, applies to generalized Riemann zeta functions called Dirichlet L-functions. Dirichlet L-functions which are sums of series of fractions with denominators identical to the Riemann zeta function, but for which the Riemann zeta function's numerator of "1" is only the simplest of cases. The generalized version also allows numerators that are functions of the "n" value for the term in question that can cycle through values such as 0, 1, -1, i, -i, w, w^2, and -w, -w^2 (where w equals e^(pi*i/3)), for successive terms of the series in various sequences defined in a particular way.

If the complex numbers s that are zeros of all Dirichlet L-functions, and not just Riemann zeta functions, are also all on the line 1/2+it in the complex plane, than the generalized Riemann hypothesis is true and a great many particularly strong conclusions in number theory can be reached, including conclusions related to the distributions of prime numbers, conclusions related to Goldbach's Conjecture, and conclusions related to how fast computing algorithms will work that are tighter than conclusions that can be made without proving this hypothesis.

Implications For Goldbach's Conjecture and Related Conjectures

The Riemann Hypothesis is important in number theory because Euler proved the product of the term 1/((1-p)^-s) for each prime number p and a given complex number s is equal to the Riemann zeta function for a given complex number s. Thus, the Riemann zeta function turns out to have a relationship of the proportion of numbers that are prime numbers, and that probability that a number of any given magnitude is a prime number.

The Riemann Hypothesis implies if true that every odd integer can be expressed a sum of not more than five primes, a result proven by Leszek Kaniecki in 1995, which limits violations of Goldbach's Conjecture to odd integers which can be expressed as a sum of one, two, four or five primes, but not three primes.

In 1997, Deshouillers, Effinger, te Riele and Zinoviev proved that the generalized Riemann hypothesis implies that "Every odd integer greater than seven can be expressed as the sum of exactly three odd prime numbers."

The Smartest Mathematican I Know (Under 50)

2011-12-31T20:16:00.001-07:00

The smartest mathematican I know personally is Susan J. Sierra, who was a fellow math major with me at Oberlin College. After earning her PhD from the University of Michigan (Go Blue!) and some post-doc positions (ever heard of a place called "Princeton" where folks like a guy called Einstein used to be on the faculty), she is now on the faculty at the University of Edinburgh where she is working in the fields of noncommunitive algebric geometry, noncommunitive algebra, algebric geometry.

Hopefully, local fashion will not cause her to develop an affinity for tartan, however. The Carnegie Mellon Tartans are one of Oberlin's athletic rivals (and yes, they do generally crush us, as a quick Google search would make clear).

In other words, she's doing work in the areas of math that are the underpinnings of Yang-Mills theory (e.g. in the fundamental physics of the Standard Model that underlies nuclear physics which has been confirmed by every experiment in the last 40 years is a non-communitive algebra, in loop quantum gravity, in string theory, in higher dimensional physics (not just fundamental physics but also fields like condensed matter physics where higher dimensional formulations of problems can be easier to solve when transformed into algebric transformation of problems too hard to solve in their natural form), and a surprising number of practical problems that are more mundane.

A mundane example of noncommunitive geometry is the kind of math you need if you are a program like mapquest trying to determine the optimal route to get from point A to point B in a city with one way streets and rush hours. The time it takes to get from point A to point B in one direction and the shortest path between them may be different from the time it takes to get from point B to point A due to traffic loads, stop lights, one way streets and so on. While basic Newtonian mechanics assumes a communitive geometry, in general, any system with an arrow of time induced by CP violation, friction, or the second law of thermodynamics implies a noncommunitive geometry.

Noncommunitive algebra also has mundane as well as ordinary applications. For example, the mathematics behind tax planning is noncommunitive, because the tax code treats losses (i.e. negative numbers) very differently from profits (i.e. positive numbers) and is also asymmetric in time, for example, with different treatments of carryforwards of losses and carrybacks of losses. Any set of functions that operate differently forward and backward is noncommunitive. Noncommunitive algebras are also sometime called "non-Abelian", as Mr. Abel's name has become synonymous with communitive algebras (some odd associations and footnotes related to him can be found here).

At its most basic, algebric geometry is the study of equations that can translate into shapes, like the analytic geometry that you studied in pre-algebra or trig in high school, which have been widely known since Alexander the Great studied them as part of his education (although the conic sections weren't as neatly tied to equations then as they are now, something we owe to Descartes and his peers). But, geometries in more than our ordinary four dimensions are much harder to express in any way other than equations, and since fields like string theory call for more than four dimensions, one really can't make sense of any of it without a firm command of algebric geometry. It is also critical to fundamental issues in relativity and gravity such as the still unresolved question of whether it is conceptually possible for the geometric formulation of gravity in general relativity to have an equivalent formulation in the nature of a force exchanged by particles such a graviton, or whether there exists some proveable "no go theorem" that could establish that it is impossible to have a formulation of general relativity in a Minkowski space-time.

Also, if you had the impression that there are no unsolved problems remaining in mathematics, you are incorrect. Susan Colley, one of my math professors at Oberlin College, explains in a recent article just how many open questions remain in mathematics and provides some current examples such as the outstanding Millenium Prize questions (some of which, like the question in Yang-Mills theory, readers of this blog in academia are actively working in their own research to solve).

Looking Back At 2011 and Forward To 2012

2011-12-29T13:12:00.001-07:00

This blog started in May as an effort to focus my Wash Park Prophet blog by breaking it into a science blog and a general blog more heavily concentrated on law and politics, on the theory that the two sets of posts are more or less independent. After a brief transition period, the total output on the two blogs combined has turned out to be very similar to that of the separate blogs and the split was just about perfect in capturing close to half of the total in each blog.

The traffic and comments have taken a hit at this blog, but the quality of the comments has been good. There have been multiple comments from anthropologists and physicists in the fields covered and from some of the best bloggers in their fields, and this blog is starting to show up in more google searches of scientific subjects.

Posts with strong policy implications, like most of my posts on IQ and mental health, I've kept on the Wash Park Prophet side.

This blog has given me a space to think more deeply about the subjects covered and to explore them at a conceptual level that plays out their implications and corollaries. Enough of those insights have been plausible enough to make the enterprise interesting, whether or not they turn out to be correct. I've also learned and resolved several misunderstandings I've had about physics and anthropological data in the process, and filled many gaps in my understanding. For example, I have a much more solid understanding of how the Standard Model weak force works.

This year has had a bumper crop of new developments in physics, mostly related to the search of the Higgs boson, and several notable developments in neutrino physics, such as evidence for slightly superluminal neutrinos, evidence for more than three generations of neutrinos, and advances in pinning down their masses and PMNS transition matrix entries for neutrinos.

Hints of beyond the Standard Model CP violation and of mass differences between particles and antiparticles have been quashed. A Higgs boson has probably been detected. No other new particles not predicted by the Standard Model have been detected. The multiple exclusions of dark matter candidates in both particle physics, direct detection efforts, and astronomy constraints on dark matter properties have made within the Standard Model options, like neutrino condensates, look more attractive. Definitive evidence of hypothetical quantum physical behavior, like neutrinoless double beta decay, flavor changing neutral currents, magnetic monopoles, proton decay, evidence of extra dimensions, evidence of discrete structure in space time, and evidence of compositness in fundamental particles has remained elusive. The inconsistency between the radius of ordinary hydrogen and muonic hydrogen, perhaps due to inaccurate measurements of the former is one of the few laboratory scale anomalies that has lasted. The prospect of a particle physics desert now that a Higgs boson has been identified looms. The Higgs boson doesn't destroy SUSY, although it makes technicolor a historical curiousity. But, SUSY supporters are getting discouraged as more and more models in its parameter space are excluded, including the MSSM, the minimal supersymmetric standard model, and most R-parity conserving version of the theory.

In the area of anthropology, archaeology and pre-history, the big stories have been ancient DNA, evidence of admixture with archaic hominins, archaeological evidence of modern humans at very early Out of Africa dates in India and Arabia, the discrediting of mutation rate dating particularly for Y-DNA, and much more widely available whole genomes that are being collected and analyzed by bloggers outside the academy. Increased data make it possible to develop increasingly complex and constrained outlines of pre-history, although Jared Diamond's notion that technologically driven (often food producing technology driven) waves of migration with varying degrees of admixture have had a profound impact on population structure does seem to continue to be a major theme. Some legends and origin myths are being confirmed, others are being flatly rejected as counterfactual.

In 2012, the prospect for more ground breaking fundamental physics developments seems modest. Beyond the Standard Model theories are falling by the day. Majorana masses for neutrinos continue to be more and more disfavored by the evidence despite their theoretical attractiveness. The Higgs boson discovery profoundly increases the energy scale at which the Standard Model equations start to become pathological. The prospects of new physics at the TeV scale look ever more dim. The number of plausible fundamental dark matter candidates gets slimmer and slimmer -- direct detection experiments and astronomy constraints seem to disfavor the heavier candidates, while particle physics have closed the door on any light fundamental particles that interact with the weak force. Sterile neutrinos aren't ruled out experimentally, but the absence of evidence for Majorana mass in neutrinos weakens the case for them.

The prospects for new breakthroughs in pre-history in 2012 seems greater. The quantity of whole genome data and the quality of our ability to analyze it has grown, we are likely to get some new ancient DNA samples to add to a very limited data set, and new understandings of pre-history coupled with relatively low levels of armed conflict and fewer autarkic regimes are making it easier to identify and study archaeology in places where it is most likely to bear fruit relevant to the remaining open questions in the field. It is too much to hope that we might find a Rosetta stone to illuminate the Harappan language or some similar hotly debated pre-historic linguistic question, but simply pinning down more accurately the timeline of plant and animal domestication in Africa (particularly in the Sahel and Ethiopia), for example, could add a great deal of certainty and corroboration to models of pre-history and lingustics there that tell us more about sequencing and relative relatedness than they do about the historical moments at which key events happened and the technological and social forces that drove those events.

LHC detects long predicted b-anti-b meson

2011-12-29T11:06:00.002-07:00

In further proof that the Standard Model works, the Large Hadron Collider has found a heavy and quickly decaying meson made of a bottom quark and anti-bottom quark that had long been predicted by QCD but had never been observed. There are about a dozen dozen hadrons predicted by the Standard Model, and most have been observed already, but a few of the heavier ones remain well characterized but undiscovered. This finding narrows the ranks of the missing hadrons. Analysis of the importance of the new find can be found here.

Feynman's IQ

2011-12-28T11:44:00.002-07:00

Nobel prize winning physicist and science popularizer Richard Feynman, whose graphic novel biography by Ottaviani and Myrick I recently finished, claimed himself to have an IQ of about 125 on a school test, although he was off the charts in mathematical ability.

The cover of the graphic novel, by the way, features this quote, "If that's the world's smartest man, God help us.", from Lucille Feynman, his mother.

You can also read about his thesis at a recent blog post.

Is the Wavefunction of Quantum Mechanics Real?

2011-12-22T17:00:00.000-07:00

Steve Hsu has a nice post on that extent to which different ways of thinking about quantum mechanics, sometimes called "interpretations" can be distinguished in thought experiments and real experiments, with the strong implication that the wavefunction of quantum mechanics has a physical reality, although I will leave the subtlties of wording of this delicate matter to him and the blog post that he in turn is quoting.

The Case For The Massless Up Quark

2011-12-19T22:11:00.000-07:00

A generalization of Koide's formula suggests a nearly massless up quark, contrary to model dependent estimates that suggest an up quark mass of about 40%-60% of the down quark mass (e.g. here), while the formula accurately estimates the conventional value of the d quark mass. There is a case for this in supersymmetric theories as a solution to the "strong CP problem.", although this approach has been questioned. Early lattice QCD simulations in the Standard Model also suggested that the massless up quark solves the strong CP problem.

A masslesss or nearly massless up quark can also be brought to bear to account for neutrino mass.

There is somewhat similar interesting inquiry into massless QCD vacuum energy and its relationship to gravity.

It isn't unusual to model QCD with masses for all the light quarks set at zero for calculational convenience and still have the model produce meaningful results.

Neutrinoless Double Beta Decay

2011-12-19T20:23:00.002-07:00

One of the pivotal questions in fundamental physics is the nature of neutrino mass.

The observation of the neutrino oscillations in experiments with atmospheric, solar, reactor and accelerator neutrinos proves that neutrino masses are different from zero and that the states of flavor neutrinos e, μ, tau are mixtures of states of neutrinos with different masses. There are two general possibilities for neutrinos with definite masses: they can be 4-component Dirac particles, possessing conserved total lepton number which distinguish neutrinos and antineutrinos or purely neutral 2-component Majorana particles with identical neutrinos and antineutrinos. . . .

Neutrino masses are many orders of magnitude smaller than masses of their family partners, leptons and quarks. . . . The most natural possibility of the explanation of the smallness of the neutrino masses gives us the seesaw mechanism of the neutrino mass generation. This beyond the Standard Model mechanism connects smallness of neutrino masses with the violation of the total lepton number at a large scale and Majorana nature of neutrino masses. If it will be established that neutrinos with definite masses are Majorana particles it will be strong argument in favor of the seesaw origin of neutrino masses.

Investigation of the neutrinoless double beta-decay of nuclei is the only practical way which could allow to proof that neutrinos are Majorana particles.

From here.

Theorists tend to prefer the assumption that the neutrino and anti-neutrino are identicial, and hence that a process known as neutrinoless double beta decay is possible.

The Experimental Constraints On Neutrinoless Double Beta Decay

One experiment by H. V. Klapdor-Kleingrothaus (Heidelberg-Moscow) published in 2001 claimed to see neutrinoless double beta decay experimentally, and claimed six sigma support for that conclusion by 2006, but the experiment has not been successfully replicated in three other completed attempts to do so, and has been subject to considerable criticism in the discipline.

More than a dozen current or proposed experiments that are already under construction or will commence construction in the next few years, are looking for signs of neutrinoless double beta decay.

The predicted frequency of neutrinoless double beta decay in a simple Majorana mass scenario is a product of the three neutrino mass eignenstates and the correspoding PMNS matrix elements. A 2010 recap of the theory is found here. The key number that is produced using these estimates is on the order of 0.2-0.6 eV according to H. V. Klapdor-Kleingrothaus which corresponds to effective Majorana masses. A larger number would yield a higher (and presumably easier to observe) decay rate, while a smaller number would yield a lower (and presumably hard to observe) decay rate.

An effective Majorana mass of this scale would imply absolute neutrino masses that are much greater than the experimentally established values for the differences in mass between the three neutrino mass eigenstates by a couple of orders of magnitude, and hence, a nearly degenerate set of neutrino mass eigenstates, a result that seems like a poor fit to a measured value of theta 12 in the PMNS matrix that is about ten times as large as theta 13 in the PMNS matrix - since big differences in transition matrix values seem to have some association with big differences in mass between the particles in question.

Experiments that are underway would increase the sensitivity of the experiments to Majorana masses more than ten times as small as that of Klapdor-Kleingrothaus, making is possible to rule out or confirm that finding. Direct neutrino detection experiments, such as Ice Cube, which just went on line in Antarctica, also provide measurements of neutrino properties that can constrain the theoretically expected values for neutrinoless double beta decay in Majorana mass neutrino models. (See also here setting out the experimental agenda for neutrino research in 2004 through about 2014).

While current experiments establish only the relative mass differences between neutrino eigenstates, rather than absolute masses, if the absolute values are on the same order of magnitude as those differences (on the order of 0.003 eV for the first and second mass eigenstate gaps and 0.05 eV for the second and third mass eigenstate gap), then they are much lower than the Klapdor-Kleingrothaus effective Majorana neutrino mass estimate, and would seem to be inconsistent with a Majorana neutrino mass in anything but a normal mass hierarchy (a first generation neutrino mass lighter than a second generation neutrino mass which is lighter in turn than a third generation neutrino mass). Astronomy data also place significant minimum values on neutrinoless double beta decay rates (the linked article also remarks on the very strict current experimental limitations on the magnetic moment of neutrinos which disfavors the possibility that they may be composed of charged preons).

Neutrinoless Double Beta Decay In SUSY Models

Neutrinoless double beta decay experiments also constrain SUSY models which need to have a characteristic SUSY scale on the order of 1 TeV to fit that Klapdor-Kleingrothaus measurement, or smaller if that measurement is not replicated. (Larger decay values have been pretty well ruled out, and by implication, characteristic SUSY scales in SUSY models with Majorana mass of more than 1 TeV, which should be within the power of the LHC to detect, are also disfavored.)

If neutrinoless double beta decay is ten times more rare than that measurement, this would imply a characteristic SUSY scale on the order of 630 GeV, which is a scale that is likely to be ruled out or confirmed at LHC around the same time that that neutrinoless double beta decay experiment results with that precision are available. Neutrinoless double beta decay rates that were thirty or forty times as small as the claimed Klapdor-Kleingrothaus measurement in a SUSY matter would bring the characteristic SUSY scale so low that it would be inconsistent with current LHC bounds.

Of course, nimble theorists can always come up with some variant theory that would escape these bounds (see, e.g. this paper from 2007 with Dirac neutrino masses in a SUSY variant). Indeed, the sheer number of beyond the Standard Model proposals to deal with neutrino properties are immense, although the many are simply slight variants on the same themes. But, the bound on SUSY theories from neutrinoless double beta decay is notable because it is experimentally independent of the particle accelerator driven bounds on the masses of the lighest supersymmetric particles, and because non-detection of neutrinoless double beta decay favors smaller SUSY scales, while non-detection of supersymmetric particles at particle accelerators favor larger characteristic SUSY scales. Taken together, neutrinoless double beta decay experiments and the LHC operate as a vice squeezing SUSY parameter space in opposite directions.

Predictions

Neutrinos Lack Majorana Mass

My personal prediction is that we will eventually establish bounds on absolute neutrino eigenstate mass and bounds on Majorana mass from a failure to detect neutrinoless double beta decay that will together establish definitively that neutrinos have Dirac masses, just like all other Standard Model fermions and as a result of the same mechanism despite the fact that neutrino masses are much smaller than other Dirac masses, that neutrinos and antineutrinos are not the same thing.

This prediction is driven mostly by the pivotal role that the distinction between a neutrino and antineutrino plays in maintaining lepton number conservation (which has never been observed to be violated experimentally and produced large numbers of valid predictions about decay patterns) that motivated their predicted existence in the first place.

A fortiori, this prediction also assumes that SUSY models with Majorana neutrino masses are also wrong. There are other reasons to find the remaining range of SUSY parameter space to be implausible, but this is another one which is quite strict.

There Are No Sterile Neutrinos or Fourth Generation Fermions

A finding that neutrinos lack Majorana mass would not necessarily rule out the possibility that there are right handed neutrinos (aka sterile neutrios) with Dirac mass that give rise to left handed neutrino mass via a seesaw mechanism. The Standard Model assumed that neutrinos had no mass at all, so it is indeterminate as to how this issue is resolved, and its other predictions are largely decoupled from it.

Precision electroweak measurements suggest that fourth generation left handed neutrinos of less than 45 GeV are ruled out, which would be so far in excess of the other three neutrino masses that it makes the entire notion of a fourth generation of Standard model fermions seem implausible. But, because right handed neutrinos would not interact with the weak force, precision electroweak measurements can't rule them out or say much of anything about what masses they might have, although seesaw models tend to favor right handed neutrinos that are much heavier than left handed neutrinos.

Theories with heavy sterile neutrinos draw succor from the perceived need for a fairly heavy dark matter candidate, although direct dark matter searches and astronomy data are incresingly narrowing the experimental window in which such heavy dark matter particles could exist. They also find support from the fact that there are four permutations at each generation of every charged fermion in the Standard Model (LH particle, LH antiparticle, RH particle, RH antiparticle), so the existence of only a LH particle and RH antiparticle seems to leave the neutrino column of the chart of Standard Model particles with gaps, and it is hard to rule out the presence of something in those gaps because a right handed neutrino would be so inherently weakly interacting apart from its gravitational interactions, just as hypothesized dark matter.

But, heavy right handed neutrinos would also contradict the pattern for all of the charged fermions of the Standard Model in which the right handed and left handed versions of the particle and the right handed and left handed version of the antiparticle all had the same mass.

Very heavy right handed neutrinos also seem out of line with the example of the Z boson, which is its own antiparticle, which has a mass only marginally greater than that of the W+ boson which has the W- boson as an antiparticle, with all three being intimately intertwined, and the Higgs boson having a mass on the order of the sum of the three weak force boson masses. Similarly, neutrons are not dramatically heavier than protons, and electromagnetically neutral hadrons generally are not so much different in mass from electrically charged hadrons. If charge or its lack has in impact on mass, it does not seem to be a dramatic influence.

Also, since baryogenesis and leptogenesis scenarios generally assume that quarks and leptons have their origins in weak force decays, any hypothesis with right handed neutrinos must also come up with a leptogenesis scenario specific to them.

My personal prediction, although I make it with far less confidence than I do when predicting that neutrinos lack Majorana mass, is that there are no right handed neutrinos.

The PMNS Matrix has a CP violating phase

There are good reasons from quark-lepton complementarity to suspect that that PMNS matrix has a CP violating phase complementary to the CP violating phase in the CKM matrix.

There also seems to be preliminary evidence for the existence of such a phase at the MINOS experiment where the profiles of neutrinos and antineutrinos seem to be different. (Incidentally, CP violation would also seem to disfavor Majorana neutrino theories, since if the particle and antiparticle are identical, they shouldn't exhibit different behavior.)

I expect that CP violations will be confirmed in the PMNS matrix, in W boson mediated interactions, but not Z boson mediated interactions, with a phase complementary in some way to that of the CKM matrix CP violating phase.

Conclusion Regarding Predictions

My predictions are generically "dull" from a theorist's perspective. They leave the mass generation mechanism for neutrinos in a "black box", they predict no new particles to serve as dark matter candidates (neutrino condensates or perhaps stable glueballs begin to look attractive as dark matter candidates in this scenario), and they predict no new kinds of particle interactions.

They also throw the vast majority of the theoretical output on neutrino physics and models that call for right handed neutrinos, Majorana neutrinos, or seesaw mechanisms into the dustbin. Basically, tens of thousands of fundamental physics papers over the last decade are counterfactual flights of fancy in this scenario.

This approach would seem generically to leave conventional grand unified theories and theories of everything overconstrained. Most predict something more than the Standard Model or are inconsistent with experiment. A nice summary of the data points these models try to fit can be found here. (Footnote, I hadn't noticed before that the not quite running coupling constant scale of the Standard Model is a couple of orders of magnitude lower than the SUSY GUT scale, which would make concerns about very high energy scale breakdowns of the Standard Model with a Higgs boson of the experimentally suggested mass less intense).

Musings On Mass In A Higgsful World

2011-12-16T13:31:00.003-07:00

The lay description of the Higgs boson typically describes it as critical primarily in giving rise to intertial mass by creating a field that is frequently described, essentially, as the viscosity of free space.

Every experiment to date has determined that interial mass and gravitational mass are the same thing. Indeed, the equivalence of these two things is a bedrock foundation of general relativity.

Fundamental fermions each have one of twelve non-zero rest masses. Fundamental bosons each have one of four rest masses, with zero as one of the allowed values (belonging to photons, gluons and the hypothetical graviton, if there is one). We don't have any fundamental theory to explain the relationship of all of the fifteen non-zero rest masses of the Standard Model of Particle Physics to each other (we do have theoretical reasons for photons, gluons and gravitons to have zero rest masses), although we do have a formula that relates the mass of the W bosons to the mass of the Z boson, we know that there are some almost certainly non-random relationships between the fermion masses (such as Koide's formula for the charged lepton masses) although we aren't precisely sure who these numerical relationships arise, and there naiively appears to be a simple formula from which the Higgs boson mass can be derived from the W and Z boson masses (one half of two times the W boson mass plus the Z boson mass)that is a very close match to the tenatatively measured amount, although there is no consensus concerning why this relationship exists either.

It also seems to be the case, that there is an intimate relationship between the fundamental particle masses, the four parameters of the CKM matrix that governs the relative likelihood of particular flavor transitions via W bosons for quarks (including CP violating phases), and the four parameters of the PMNS matrix which codes the same relative likelihoods for leptons. The matrixes also seem to show some sort of relationship between the magnitude of the coupling constants for the three Standard Model forces (electromagnetism mediated by photons, the weak force mediated by W and Z bosons, and the strong force mediated by gluons) each of which is itself a function via equations and constants determined phenomenologically (rather than from first principles) of the energy level of the interaction in question which brings us back to the mystery of mass-energy all over again.

But, mass turns out to be a slippery thing. Mass is not simply additive in composite particles. Each of the couple hundred different possible hadrons has a very precise rest mass, but in composite particles bound by the nuclear strong force, the rest mass of the whole is generally not simply the sum of the rest masses of the component parts. Likewise, while total mass-energy in any system is conserved (with an E=mc^2 conversion factor), interactions via the nuclear weak force routinely do not conserve mass alone.

General relativity and special relativity add further complications. The relationship between mass and acceleration is a simple linear one at low velocities, but must be modified by a Lorentz transform at velocities approaching the speed of light. The relationship between mass and acceleration runs with a particle's kinetic energy levels.

Even more confounding, in general relativity, is the fact that forms of energy other than mass give rise to gravitational effects and are subject to the effects of gravity, even if they don't have any mass at all. A photon will follow the geodesic created by a gravitational field, even though it has no mass, and the flux of photons through a volume of space is part of the stress-energy tensor that gives rise to gravity in general relativity.

A mass field's linear momentum (in three dimensions) including its Lorentz boost factors, its angular momentum (in three dimensions), and the pressure it is experiencing (in three dimensions), in addition to its rest mass and the electromagnetic flux (more accurately four current) of energy in that volume of space also add to the stress-energy tensor.

The conventional stress-energy tensor of general relativity doesn't have terms for strong force flux and weak force flux, neither of which were known at the time it was formulated, but I don't think that anyone seriously doubts that fluxes of these forces contribute to the stress-energy tensor in the precisely the same way that fluxes of photons do.

Convention and personal preference dictates whether observed dark energy effects are modeled as a constant of integration in cosmological equations derived from the equations of general relativity, or as a real, uniform energy field that fills all of space-time and as energy which is a subset of mass-energy, gravitates. Physics already provides several fields which are present at nearly uniform levels throughout the universe - the physically observed and electromagnetic cosmic background radiation, the Higgs vacuum expectation value of the Higgs field, and the energy field implied by zero point energy (i.e. the amplitude in quantum mechanics for a particle-antiparticle pair to arise seemingly out of nothing in empty space), although none of these is a good match for the observed cosmological constant, or the observed overall flatness of space-time away from dense mass fields (as opposed to a strongly convex or concave structure of space time). Additional proposals are also out there, and as I understand the matter, the extent to which graviational fields (aka the background flux of gravitons in the universe) themselves, because they carry energy, give rise to gravitational effects isn't a question that I have seen a consensus answer to in the educated layman's and generalist physicist oriented literature (the question is subtle because "in general relativity the gravitational field alone has no well-defined stress-energy tensor, only the pseudotensor one.")

The standard description of the reason that efforts to describe gravity with a Standard Model plus graviton model is that the quantum mechanical equations of the graviton are not renormalizable, but given what I understand to be general relativity's BRST symmetry, (see, e.g. Castellana and Montani (2008)) it isn't obvious to me that this proposition is really true in a theoretical sense or in the sense that the equations actually break down in the UV limit, even if they may be impracticable to do calculations with by any non-numerical method we known outside special cases where simplifying ssumptions make an analytical solution possible. Castellana's abstract states (preprint here):

Quantization of systems with constraints can be carried out with several methods. In the Dirac formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, different from the Dirac method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of the BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. This derivation is based on the general results on the dependence of the effective action used in path integrals and consequently of Green's functions on the gauge-fixing functionals used in the DeWitt–Faddeev–Popov method. The condition we gain differs from the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge-fixing functionals. Finally we discuss how it should be possible to obtain all of the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.

(Abhay Ashtekar's reformulation of the equations of general relativity in the 1980s has been privotal to the field of quantum gravity.)

The concern that it might be necessary to retain background independence in an extension of the Standard Model with a graviton, see, e.g. here (although not necessarily discrete background independence, at least other than as part of a strategy to formulate the theory in a discrete setting and then use calculus to take the limit of that formulation as the minimal distance became infinitessimal) which is something that a naive quantization of a spin-2 particle on a Minkoski background modeled on other Standard Model quantizations can't capture that effect is a more serious concern. The fact that there is only a pseudotensor, rather than a stress-energy tensor for the gravitional field alone might also be a clue that general relativity's equation has a subtle defect in its formulation.

While the magnitude of Newtonian gravity is a function of rest mass only (and would imply a massless, color charge neutral, electromagnetic charge neutral, scalar spin-0 graviton), in general relativity, the overall magnitude of the effective gravitational force, as I understand it, is a function of total mass-energy in the volume of spacetime where it is being evaluated. Likewise, rather than being the simple radial attractive force of Newtonian gravity, in general relativity the direction in which gravity directs massive and massless particles alike, is modified from its radical attractive direction by a vector that incorporates the directionality of all of the particle motion, energy fluxes and pressure that are acting on volume of space-time in question.

The fact that both ordinary linear acceleration, and the acceleration induced by the force of gravity, which are identical in effect, also induces space and time dialation according to a Lorentz factor, further complicates the affair, which helps explain why the mathematics of general relativity is so challenging.

It has been hypothesized that the whole of general relativity and special relativity can be reproduced by simply quantum mechanical rules for a massless, electromagnetically neutral, color charge neutral spin-2 graviton (a tensor particle) that couples to everything with mass or energy, and the spin-0, CP-even, 125 GeV +/- 2 GeV, electromagnetically neutral, color charge neutral Higgs boson (a scalar particle), although to my knowledge, no one has ever successfully proposed an operational realization of this hypothesis that has been rigorously shown to be equivalent to the equations of general relativity or some variant of those equations that is empirically indistinguishable through some slight technical tweak to the theory (such as Einstein–Cartan theory which adds torsion to the metric which allows gravity to respond to spin angular momentum in a way that the original formulation does not, or the Brans–Dicke theory of gravitation, which is a scalar-tensor theory and hence naively more directly parallel to a Higgs boson-graviton formulation in quantum mechanics).

Modified gravity theories attempting to explain dark matter effects which are consistent with general relativity in all domains where dark matter effects are negligable, are generically scalar-vector-tensor theories (the Bekenstein direct derivation of Milgrom's theory is dubbed TVS, while many versions of Moffat's theory that attempts to do something very similar in a slightly different way, prefers the order SVT), and were these theories to be quantitized, would presumably require, in addition to a spin-2 graviton, a spin-1 gravitovector (presumably massless, color charge neutral, and electromagnetically neutral), and perhaps also a massless spin-0 scalar graviton if the Higgs field couldn't be appropriated for that purpose.

Loop quantum gravity proposes a discrete space-time structure from which the four dimensionality of space-time and locality are merely emergent properties that are ill defined at the quantum level. Rigorous, but theory dependent tests have the discreteness of space-time have so far demonstrated a continous space-time structure at scales that would appear to be well below the Planck scale below which many direct measurements of distance and time associated with particles becomes inherently uncertain. Quantum mechanics exhibits a phenomena called entanglement which fit some definitions of non-locality, although entangled particles must share of speed of light space-time cone from a common point of origin in space-time bound and there are theoretical questions over what this bounded form of non-locality means and what can be achieved with it in terms of information transfer.

LQG tends to envision mass as someting sort of like clumping of nodes of adjacent points in space-time together. Some versions of it have a graviton that emerges from the equations and propogages.

Supersymmetry models, like the Standard Model, does not include gravity and are formulated in Minkowski space. The gravitational extention of supersymmetry models is generally called supergravity (SUGRA) and string theory/M-theory generally attempts to embed supergravity theories within its overarching substructure and naturally predicts the existence of a spin-2 particle associated with a graviton. String theory uses extra-dimensions, in which gravity interacts more easily than the four observable dimensions, as a mechanism by which to turn a force which is much weaker than the other three fundamental forces in the context of systems with small numbers of particles interacting with each other into just another manifestation of the an underlying fundamental force whose symmetries are broken by branes, dimensional compactifcation and other mechanisms that are not always well defined.

Neither general relativity nor special relativity nor Newtonian mechanics and gravity, contemplate a physical, aether-like Higgs field that gives rise to interia. Newtonian mechanics employs the low velocity limit of special relativity relating force and acceleration of F=ma as a low of motion rather than a substance, and takes the fact that matter has mass in amounts to be empirically determined as axiomatic. The equivalence of gravitational mass to inertial mass, and of gravitationally induced accelerations to other accelerations is a core axiom from which that theory is derived, and while general relativity does conceptualize mass as a sort of crystalized energy that factors into the Lorentz equations in a manner different than energy not in the form of mass does, general relativity does not address the question of what process causes energy to crystalize into mass. None of the classical theories of gravity and mechanics has an aether-like field that gives rise to inertia like the Higgs field.

The Standard Model is formulates in Minkowski space, where special relativity applies, but there is no gravity and no curvature of space-time that flows from gravity, although ad hoc applications of classical general relativity in a non-systemic way to the equations of general relativity in circumstances where general relativity effects are intense, for example to understand Hawking radiation from black holes, has been attempted with success. Among other problems with this approach, wave-like field theories do not naturally transform into particle-like theories in curved spacetime, and the acceleration of the observer influences the observed temperature of the vacuum.

It also is worth pointing out that despite the new development of the Higgs boson, parallels between the QCD equations and gravity seem strong than parallels between electroweak equations and gravity, even though the electroweak equations seem to be what is imparting rest mass to the fundamental particles in the Standard Model. The QCD connection is particularly notable given that 99% of baryonic mass arises from gluon exchange in hadrons. One could imagine, for example, a quantum gravity Lagrangian equation that was somehow related to the square of the QCD Lagrangian plus the square of the electroweak Lagrangian, weighted relative to the contribution of each set of equations to the source of the gravitational mass. A 1% contribution to gravity from electroweak sources which frequently were proportional to QCD sources, since weak force decay at any given moment in low energy systems isn't much of a flux and the proportion of particular kinds of fundamental particles (up and down quarks, electrons, neutrinos and unstable fundamental prticles) ought to be relatively uniform everywhere, might make that component of a true law of gravity invisible.

Higgs Announcement Reactions In The Physics Blogosphere

2011-12-15T16:41:00.001-07:00

Lubos explains why he thinks the finding is real and notes alleged consistency with a four generation of fermions Standard Model (SM4) as well as SUSY in his view.

He is convinced (not entirely unreasonably) that the Standard Model with a 125 GeV-126 GeV Higgs boson implies vaccum instability below the Planck scale which is 1.22*10^19 GeV (perhaps as low as 10^9 to 10^13 GeV, but perhaps actually as high as 10^20 GeV), and hence the existence of new physics at some scale above the electroweak energy scale and possibly beyond the range of the ability of the LHC to detect it. FWIW, I think it is very plausible that the vacuum instability threshold is precisely the Planck scale, eliminating the need for all new physics, but there is plenty of room for disagreement both due to uncertainty concerning the values for masses that are close to the threshold of critical threshold in the relevant Standard Model equations and the difficulty involved in using perturbative approximations of the Standard Model equations in energy ranges so far from the energy scale that those approximations were designed to provide accurate calculations in. For example, the coupling constants of the Standard Model are "running constants" that depend upon the energy level of interaction involved and a slight tweak in how those constants run could become very material as such extremely high energy levels in a manner similar to the way that the Lorentz factors in special relativity become much more important in a non-linear way as one approaches the upper bound of the velocity "c" (the speed of light). Assuming that a running formula and running constant values calibrated on energies of less than 10^3 GeV will still be valid at energies more than a million times as great is not a safe assumption. In his view, "One may say that the apparently observed Higgs mass favors squarks in the multi-dozen TeV scale. . . . "garden variety" supersymmetric models with light squarks and "gauge mediation" of the supersymmetry breaking have become almost hopelessly contrived and fine-tuned, and have been nearly euthanized. The apparently observed SUSY-compatible but not-too-low value of the Higgs mass favors scenarios with heavy scalars (especially heavy stop squark); or extensions of MSSM with additional particle species. See another new paper by Carena et al. trying to obtain new possibilities with various hierarchies between slepton and squark masses." In particular, the Minimally Supersymmetric Standard Model (MSSM) is pretty much dead. One paper he cites also concludes that the "gravity mediated constrained MSSM would still be viable, provided the scalar top quarks are heavy and their trilinear coupling large. Significant areas of the parameter space of models with heavy supersymmetric particles, such as split or high-scale supersymmetry, could also be excluded as, in turn, they generally predict a too heavy Higgs particle."

Matt Strassler is more skeptical about the data supporting a Higgs boson discovery at all.

Kea at Arcadian Pseudofactor, after months of diatribes against the existence of a Higgs boson is pretty much convinced and is now looking for big picture contexts that could have the Standard Model with that kind of Higgs boson in it that parallel her previous theoretical lines of inquiry.

For my druthers, I think that a whole variety of constraints are going to make beyond the Standard Model physics for the next decade or two much more timid than they have been in the last few decades. Among the features of models that are going to be increasingly disfavored are:

1. Single digit TeV or lighter new particles.
2. Boson number or lepton number violations at less than extremely high energies.
3. Proton decay (the minimal period just gets longer and longer).
4. Magnetic monopoles.
5. CPT violations.
6. Additional generations of bosons.
7. Additional large scale dimensions.
8. Technicolor.
9. Simpler SUSY models.
10. New gauge symmetries that operate outside the neutrino sector.

I personally seriously doubt that we will find right handed neutrinos or Majorana mass in neutrinos (something that would be shown, for example, by neutrinoless double beta decay, which I doubt will be discovered), although neutrino physics are one of the least experimentally constrained area of fundamental physics today. I doubt that we will find a fourth generation of Standard Model particles, sterile neutrinos outside the three generations observed and outside a fourth generation, scalar or vector gravitons, or other fundamental particles that could be WIMPs like a lightest supersymmetric particle. I doubt that we will find when the dusts settles, anomalous CP violations that hold up after having seen so many disappointments.

I personally think that dark matter effects will turn out to be some combination of (1) a neutrino condensate (or something similar that is a composite effect of non-quarks), (2) undercounted ordinary matter that is "dim", (3) underestimated general relativistic effects in large complex systems, (4) glueballs, and (5) quantum gravity modifications of the equations of general relativity that are only relevant in very weak gravitational fields. In other words, I think that the only particle potentially missing from the list of fundamental particles with any meaningful probability is a plain vanilla, spin-2, zero mass graviton although we could discover that space-time is discrete or that the number of space-time dimensions is ill defined at tiny scales and is only an emergent property of the universe.

Another hot area will be firming up the calculations under the existing Standard Model equations in more extreme and complicated scenarios (e.g. meson molecules, or extremely rare and ephemeral top quark hadrons).

I also think that there is considerable room for exploration of non-locality in fundamental physics.

Some interesting new papers about BSM physics phenomonology include:

An argument that sterile neutrinos may be less experimentally constrained than they seem.

A conclusion based on the apparent Higgs boson mass that "current data, in particular from the XENON experiment, essentially exclude fermionic dark matter as well as light, i.e. with masses below 50 GeV, scalar and vector dark matter particles."

A paper looking at two Higgs-doublet extensions of the Standard Model in light of the new information on the Higgs boson mass, which finds that some versions of possible while others are not.

A look at experimental bounds on lepton number violating models, since: "In the Standard Model (SM), the lepton L and baryon B numbers are conserved due to the accidental U(1)L × U(1)B symmetry. But the L and B nonconservation is a generic feature of various extensions of the SM. That is why lepton-number violating processes are sensitive tools for testing theories beyond the SM." Indirect bounds on branching ratios for lepton number violations from experiments as incorporated into popular lepton number violating theories are extremely stringent.

Superluminal neutrinos could be applied to explain CP violations.

The LHC may be able to see supersymmetric particles of less than 1 to 1.6 TeV when it has acquired a particular volume of data.

Musings On Gluon Speed, Mass and Charge

2011-12-14T13:13:00.003-07:00

We assume, for some very good reasons, that gluons have no mass and move at a uniform speed equal to the speed of light. But, we've never directly measured a gluon's speed or mass.

Confinement, the principle of quantum chromodynamics that particles with strong force color charge do not persist in non-color neutral systems more than momentarily, prevents us from observing free gluons and free quarks with very few exceptions - top quarks can come into being only to immediately decay via a W boson before forming a color neutral hadron, and in theory, multiple gluons could combine into a color neutral "glueball." Otherwise, quarks and gluons remain confined in hadrons - three quark varieties called baryons and two quark varieties called mesons. One could imagine four or five or more quark hadrons, but they are not observed. The only composite structures with more than three quarks which have been observed have subcomponents which are mesons or baryons.

The strong force interactions we see in mesons and baryons, with protons and neutrons constituting the only two varieties of hadrons that are ever stable, take place overwhelmingly at very short distances. A hadron is on the order of a femtometer. Strong force interactions sometime extend beyond an individual hadron, but I'm not aware of any circumstance where the strong force has ever been observed to act at a distance greater than that of several nuceli, something that follows from the nature of the strong force itself that peaks at a short, characteristic distance, but is vanishingly weak at shorter distances or distances even as large as the diameter of a large atom.

At the tiny distances involved, it would be impossible to distinguish experimentally between gluons that move at the speed of light and gluons that move, for example, at (1+1*10^-5) times the speed of light (the OPERA estimate of the speed of high energy neutrinos). Definitively ruling out a mass for gluons is even more fraught and theory dependent, because on one hand, gluons are conceptualized in the relevant equations as having a "rest mass" of zero, but on the other hand, QCD attributes very little of the mass of hadrons (on the order of 1%) to the rest mass of the constituent quarks and almost all of the mass to the gluonic color force fields that bind them, in effect, to the glue which is embodied in gluons. The mass of a hadron is vastly greater than the sum of the rest masses of its parts, and the equations of QCD impart considerable dynamical masses to gluons. Moreover, given that gluons are never actually at rest, the concept of a "rest mass" of a gluon is as much a parameter in an equation as it is something that is "real" in the sense that it could be directly measured, at least in principle.

We can make some rough boundary estimates on the speed of a gluon based upon the size of the proton and neutron, our knowledge from experiment and lattice simulations about the internal structure of protons and neutrons (the gluon field is strongest in the middle and the three light quarks basically orbit around the edges) and the characteristic time period in which strong force interactions take place (which is shorter than the time frame of bottom quark decay, but longer than the time frame of top quark, W boson or Z boson decay). But, there is far too much uncertainty in these estimates to make a very precise estimate and a naive diameter of the nucleon divided by hadronization time estimate could easily be too fast because it would omit information about indirect paths from one quark to another and the frequency with which gluons are emitted by quarks. We have models that can fill in some of these blanks (although the theory doesn't necessary break down the components of the process that add up to the overall hadronization time one by one), but the estimates that would be made are theory dependent, including the assumption that massless gluons travel at the speed of light, which isn't helpful when that is the parameter of the equation that you are interested in testing at great precision.

The OPERA experiment reopens this line of inquiry. Quarks and charged leptons whose speeds have been directly measured (in the case of quarks indirectly in hadrons), couple to photons which, by definition, move at the speed of light. Neutrinos, whose Lorentz speed limit might conceivably be slightly different, at least in the vicinity of Earth, don't couple to photons. Neither do gluons. Neither do Z bosons or Higgs bosons. Z bosons and Higgs bosons, unlike gluons and photons have mass, so they must always travel at some speed less than their Lorentz speed limit related to their kinetic energy.

The Z boson has the shortest lifetime of any of the fundamental particle, even shorter than a top quark, so it is virtually impossible to simultaneous measure their speed and energy with sufficient precision to distinguish its Lorentz speed limit from the speed of light.

We just barely received a non-conclusive determination that the Higgs boson exists. It appears to be extremely unstable, just like the other massive bosons, the W boson and the Z boson. So, there is no way that we can directly measure the Lorentz speed limit of the Higgs boson any time soon.

The way that we first derived the speed of light in a rigorous scientific way was from Maxwell's equation, which set the speed of light, "c", equal to the inverse of the square root of the product of the permittivity of free space and the permeability of free space, which are measures related to the properties of electric and magnetic fields respectively in a vacuum. The current formulation of special and general relativity insists that the Lorentz speed limit for all kinds of particles is the same, but it wouldn't be inconceivable that the speed of a photon and Lorentz speed limit of charged particles, might be different from the Lorentz speed limit for particles that don't interact with photons.

We can get pretty precise relative speed estimates for neutrinos v. photons from a few supernova that we have caught in the act allowing us to measure the arrival time of a wave of neutrinos relative to the photons, and can make a pretty decent one or two significant digit estimate of how far away the source supernova was in that event based on red shift (and perhaps other methods). But, this method cannot measure absolute distances to five significant digits, and we don't have a perfect understanding of the underlying supernova dynamics so we can't be sure, for example, in what sequence the neutrinos and photons were emitted in that event.

Because the strong nuclear force and weak nuclear force operate only at short range, it isn't obvious to me that a revised theory of special relativity and general relativity in which there was one "c" for particles that couple to photons or are photons, and another slightly different "c'" for particles that don't couple to photons and aren't photons, would have any phenomenological impact that would be observable apart from neutrinos travelling a little bit faster than photons.

A theory with more than one Lorentz speed limit for different kinds of particles would be an ugly theory, but so far as I can tell, not one that would necessarily lead to any paradoxes or theoretical inconsistencies.

As a related aside, I don't think that we have found any way to confirm that gluons don't have a magnetic dipole that would be sufficient to indicate that they were composite, rather than being truly fundamental particles with no inherent electromagnetic charge at all. The determination that there are eight different kinds of gluons itself and the way that Feynman diagrams for QCD interactions are handled is almost itself a preon theory, further complicated by linear combinations, as is, for that matter, the derivation of the weak force bosons in electroweak unification theory. We don't call gluons or quarks composite, but the way they exchange color charges comes very close to that kind of description.

Parameterization Independent Q-L Complementarity

2011-12-13T12:48:00.000-07:00

The relationship between the parameters of the CKM matrix and PMNS matrix called quark-lepton complementarity that seems to be only observed in one particular parameterization of these matrixes (of nine possible parameterizations) has been observed. A new study finds a way to achieve essentially the same relationship in any parameterization of the two matrixes.

Bose-Einstein Condensate Dark Matter

2011-12-13T12:02:00.002-07:00

A recent preprint sketches out the notion of a Bose-Einstein condensate as a dark matter candidate and finds that it is a better fit to the data than traditional cold dark matter models because it produces a mass distribution closer to that of observed rotation curves as opposed to the cuspy mass distributions found in cold dark matter models. The alignment of the quantum states of Bose-Einstein condensate matter creates an effectively repulsive force between the particles that counteracts the clumpiness one would see with gravity alone, allowing for a spread out mass distribution, as a result of the fundamental property of fermions that fermions of the same quantum state cannot co-exist at the same point in space. Settled physics describes these properties of Bose-Einstein condensates, and the low temperature environment of deep space is a natural place for this state of matter of persist.

The pre-print finds that the temperatures in deep space are cold enough for condensates to have arisen in the process of the formation process of the universe, and determines that only negligable error is introduced by approximating the behavior of a Bose-Einstein condensate in thermal equilibrium with the cosmic background radiation temperature of about 2.73 degrees kelvin as a zero temperature Bose-Einstein condensate at observationally viable scales.

The study concludes (although only somewhat obliquely) that the masses of the dark matter particles within this condensate, constrained by factors such as the data from the bullet cluster collision, should have about the same order of magnitude as neutrinos (10^-3 eV to 1 eV), which would conveniently dispense with the need to discover some new fundamental particle or type of interaction to explain dark matter effects at the galactic scale, while providing a non-baryonic dark matter candidate (since it is quark free) consistent with prior data.

The pre-print addresses earlier criticisms of Bose-Einstein condensate dark matter by claiming that the critics have not done a good job of modeling the way that Bose-Einstein condensates would behave.

Of course, this implies a univers with a whole lot of neutrinos in it, and through the notion of this dark matter as a relic of the early universe that experiences Bose-Einstein condensation when the universe finally gets cool enough, escapes the usual assumption that neutrino dark matter should be "hot" (i.e. move at relativistic speeds), which would eliminate galactic structure. The pre-print refrains from suggesting a leptogenesis mechanism that could create that many neutrinos, and likewise refrains from even making a definitive association between the predicted Bose-Einstein condensate dark matter and massive neutrinos.

If improved census estimates of the amount of baryonic matter in the universe are accurate and the ordinary matter to dark matter ratio is about 1-1, it suggests a baryogenesis/leptogenesis model in which the total mass of all of the leptons in the universe and the total mass of all the hadrons in the universe is equal.

A similar idea with right handed composite neutrinos with keV masses is explored here. Another similar theory is explored here. A beta decay test of the viability of this kind of scenario has been proposed. Another discussion of experimental evidence in astronomy for non-relativistic neutrinos as dark matter can be found here.

This paper is notable for being one of the few to address how leptogenesis could arise without violatig B-L symmetry or resorting the Majorana mass related methods, although it still requires "new physics."

It isn't obvious to me, however, that leptogenesis needs beyond the Standard Model physics to produce an excess of neutrinos over charged leptons and quarks. For example, if you have a Z boson that decays to a W+ and W- boson which in turn decay to a positron, a neutrino, an electron and an antineutrino, and if the positron and electron then annihilate into a photon or Z boson, but the neutrino and antineutrino do not (since they can couple to a Z boson, but not to a photon and could be prevented by matter-energy conservation from creating a final state with anything but neutrinos in it). Moreover, the photon or Z boson can repeat the cycle by creating a W+ and W- boson again until there isn't sufficient matter-energy in the system for the cycle to repeat itself. Charge conservation limits the number of charged leptons and is suggestive of a close link between net charged lepton number and baryon number, and the instability of systems with a lepton and its antilepton in the same vicinity prevents the actual number of charged leptons from being much greater than total baryon number in the long term. But, no similar bound impacts neutrino number,

Dead Sea Once Dry

2011-12-13T10:20:00.000-07:00

The Dead Sea was completed dried out about 120,000 years ago, during an arid period in the region. The earliest evidence for anatomically modern humans outside Africa is from around 100,000 years ago. The study took sediment cores from the Dead Sea to depths sufficient to provide a decent continous paleo-climate record from the region for the entire duration of the time that humans have been outside Africa and at least some of the time period during which it was occupied by Neanderthals (who were present in the Near East until about 50,000 years ago give or take a few thousand years, cohabiting the region with modern humans for many thousands of years).

Higgs Day!

2011-12-13T09:47:00.009-07:00

Philip Gibbs has a great live blog account of today's announcements about the LHC Higgs boson results. Some highlights:

CMS . . . exclusion from 130 GeV up. Excess seen at about 123 GeV of 2.5 Sigma.

The 123 GeV peak is heavier than the 119-121 GeV peak that had been rumored in the past week, and is close enough, once rounding error and statistical uncertainty are considered, relative to the ATLAS result.

Both the CMS and ATLAS results show surprising wide decay widths in their diphoton results, about 6 GeV (which is about three times that of the top quark), which are overlapping but shifted from each other, although this may partially be an artifact of thin data sets rather than an accurate measure of the true decay width of the Higgs boson.

The 2.5 Sigma excess is accompanied by another not quite 2 sigma excess at 137 GeV but given the much better resolution of the data there, a real Higgs boson at that mass ought to have a much stronger signal than sub-two sigma by now, so it is still in the 95% confidence interval exclusion range. "The CMS ZZ->4l clearly rules out the 140 GeV possibility, but has an excess at lower mass."

The ATLAS experiment has about a 2.8 sigma Higgs boson signal at about 126 GeV. ATLAS sees a potential signal, not quite 2 sigma, driven by data from the ZZ->4l channel at roughly 240 GeV, but is within the Brazil bands everywhere heavier than that up to 500 GeV and in that channel at all lower masses. There are results in excess of 1 sigma in the 120-130ish GeV range from ATLAS in this channel but nothing that by itself confirms the diphoton result that ATLAS is seeing (pre-announcement rumors states that the diphoton result involves just three events but is significant because there is nothing else that can create that signal). The combined ATLAS data is outside the two sigma Brazil bands from about 123 GeV to 129 GeV with a peak at 126 GeV. Thus, the results from ATLAS are just barely consistent with those from CMS. (These are the two main experiments at LHC looking for a Higgs boson; the only other place doing high energy physics Higgs boson searches finished its work earlier this year when Tevatron was shut down for lack of Congressional funding due to its inability to add much to LHC findings with its less powerful experiment.) CMS doesn't see much significant in the WW channel which has far more background noise making a signficant observation harder to obtain.

The viXra combined plot from the diphoton channel is significant in mid-120s GeV range, with no other SM light Higgs boson masses in the running. "[T]he CMS combined plot . . . gives a clean indication for no Higgs about 130 GeV [and up] and the right size signal for a Higgs at about 125 GeV, but there is still noise at lower mass so chance that it could be moved."

Per Lubos: "In ATLAS combination with 2.1 sigma (locally) from ZZ and 1.4 sigma (locally) from WW, the combined excess near 126 GeV is 3.6 sigma locally and 2.3 sigma globally (with the look-elsewhere effect correction)[.]"

Resonnances reports: "CMS excludes Higgs down to 127 GeV. ATLAS also excludes the 112.7-115.5 GeV range" and that in the diphoton and quadlepton channels that there is a "mass resolution of order 2 GeV."

The excess is seen by both experiments and in each of these channels. The excess in H→γγ peaks around 124 GeV it CMS, and around 126 GeV in ATLAS, which I guess is perfectly consistent within resolution. In the 4-lepton channel, ATLAS has 3 events just below 125 GeV, while CMS has 2 events just above 125 GeV. It's is precisely this overall consistency that makes the signal so tantalizing.

In sum, the announcement seems to show a Higgs boson in the mid-120 GeV mass range, with a significance on the order of between 3 and 4 sigma for the combined results, but the coincidence between the CMS and ATLAS results isn't quite as precise as one might hope in either estimated mass or signal significance, and confidence in the result is also reduced by the fact that the signals in some of the other channels at this mass range are not as strong as one might wish to see, although there do seem to be some individually insignificant but collectively notable excesses over expected background in the noiser channels.

There are a few other fairly weak bumps in the data, but they are not terribly consistent with each other, so they are probably just flukes. Low experimental accuracy at the low end of the mass range (ca. 115 GeV-121 GeV) leaves the data there particularly inconclusive and uninformative.

From a numerology perspective, the results a consistent with a Higgs boson mass equal to the W+ + W- + Z boson masses divided by two, which is about 125 GeV, but are probably a tad heavy to be equal to half of the Higgs field vacuum expectation value, which would be 123 GeV.

Generally, in physics, two sigma results routinely disappear with more data and rarely amount to anything, three sigmas results pan out about half the time, and five sigma results are considered lasting and permanent discoveries. Today's announcement nudges the likelihood that a light Standard Model Higgs boson exists to somewhat better than 50-50, but as promised, is inconclusive at this point. The fact that there are strong thoeretical reasons to expect that a light Standard Model Higgs boson (or an indistinguishable light SUSY Higgs boson) exists nudges the odds against a Higgsless or heavy Higgs only model being correct a little higher.

Of course, this is only the first year of what will be more than a decade of experiments at LHC. A year from now, the inconclusive results that we received today will almost surely be confirmed or denied and the LHC will move on to looking for other kinds of new physics.

I've been fortunate enough to be alive while quite a few of the fundamental particles of particle physics were first observed (and even while a few of the higher atomic number atoms in the period table were first synthesized and some of the key equations of the Standard Model were developed). A Higg boson could very well be the last one discovered ever, or at least, during my lifetime. Assuming that a Higgs boson is discovered at this mass, the Standard Model of Particle Physics will have no missing pieces, although the masses and transition matrix for neutrinos will still be somewhat indefinite and the question of whether neutrino masses are Majorana masses or Dirac masses will remain unresolved (my sense is that the later is more likely, but see-saw mechanisms are very popular in theoretical circles).

Quote of the day:

Kea said... Wow! Fairies exist! Amazing work from ATLAS and CERN, and thanks for the early report.

FWIW, I rather like Kea's mocking terminology that calls Higgs bosons "fairies" and the Higgs boson, "the fairy field." It certainly beats calling it the "God particle" hands down.

UPDATE: Gibbs has his combined plot estimates out and they are very convincing, particularly after LEP and Tevatron data are included and one looks at the signal to not signal probability charts. I'm pretty comfortable that the Higgs boson find that is currently a 3 sigma result at about 125 GeV +/- a couple GeV is real. The combined data also reinforce the conclusion that this will be the only Higgs boson detected in the under 500 GeV mass range (at least) based upon the data in the combined plots from all four experiments, despite modest "bumps" in specific channels at certain other mass ranges - in the overall picture they fade to become mere statistical noise.

This is a huge triumph for the scientists who predicted this discovery back in the 1970s. It completes the Standard Model. No particle predicted by it is missing, no particle (or force, other than gravity which is beyonds stated scope) which is not predicted by it, has been discovered. There is no replicated high energy physics experiment that is significantly at odds with its predictions (the lone significant deviation at the moment is OPERA's superluminal neutrino result).

At the end of the 1800s, scientists thought that they had conquered all of the fundamental rules of nature, although there were physical constants to be honed and applications of those rules that had not been worked out. Five generations later, we may very well have actually achieved that result.

I am increasingly inclined to conclude we will find no supersymmetry, and that we will ultimately be able to explain dark matter with the physics that we already have in hand. When we someday find a way to integrate general relativity and the Standard Model that it will turn out to be a dotting of i's and crossing of t's moment rather than a discovery that provides any meaningful new phenomenological insight. With all of the underlying pieces having pretty much come together, we may just a mathematical trick or two away from the day when that formulation of quantum gravity becomes possible and the job of theoretical physicists becomes merely a matter of making it all look as pretty as possible.

Higgs Data May Be More Complicated Than Expected

2011-12-12T18:14:00.000-07:00

A compliation of the huge repository of rumors concerning tomorrow's big announcement regarding the ATLAS and CMS Higgs boson searches at the LHC, suggests that the announced results may form a far less coherent picture than expected with indications of possible signals at more than one mass (which, if true, would be the clearest experimental sign ever of supersymmetry, which generically predicts more than one Higgs boson).

BSTR Symmetry

2011-12-12T18:07:00.002-07:00

BRST symmetry is a property present in various kinds of quantum mechanical equations (which is quite mathematically and geometrically challenging), in which one kind of a non-physical output of the equations cancels out another kind of non-physical output of the equations, making the equations "renormalizable" (i.e. possible in principle to calculate without blowing up into infinities). In the context of QCD, another way to put this is that "all the UV [i.e. high energy] divergences of the theory can be cancelled by the counterterms[.]" This symmetry appears to be present even in the non-abelian gauge fields of the weak force and strong force equations, although this reality may need footnotes for exceptions in certain special cases. This was described theoretically in the 1970s, but apparently, since then this insight hasn't done much besides assuaging concerns that renormalization didn't have a mathematically rigorous basis.

The theoretical program involved in working with the BSTR symmetry also provides a theoretically sound alternative to the Feynman path integral conceptualization of quantum mechanics, that is rather more conceptually challenging to grok, but generalizes to cases more complex than QED in Minkoski spacetime more naturally.

Europe's Genetic History Is Complex

2011-12-12T17:53:00.000-07:00

One doesn't have to adopt Dienekes' theory regarding how West Eurasians came to be in full to recognize that his data necessarily implies a complex population genetic history for West Eurasia, because in "the Old World . . . distantly located populations are often more similar to each other than to their more immediate geographic neighbors."

Mixing Angle and Coupling Constant Numerology

2011-12-12T07:59:00.000-07:00

Quantum Diaries Survivor revisits some interesting phenomenological relationships of the quark and lepton mixing angles, that is also died into a way to use fundamental constants to derive the electromagnetic coupling constant. On the two-do list is a check to see how the proposal fits with quark-lepton complementarity ideas which seem more soundly theoreticallly motivated.

Another B Meson Excess CP Violation Bites The Dust

2011-12-09T14:03:00.002-07:00

A 2008 result showing more than Standard Model CP violations in B meson decays at Tevatron has turned out to be a statistical fluke after the collection of more data and a little more precise analysis of the experiment.

New Study Supports ANI/ASI Description of South Asian Whole Genomes

2011-12-09T01:01:00.003-07:00

Indian populations are characterized by two major ancestry components, one of which is spread at comparable frequency and haplotype diversity in populations of South and West Asia and the Caucasus. The second component is more restricted to South Asia and accounts for more than 50% of the ancestry in Indian populations. Haplotype diversity associated with these South Asian ancestry components is significantly higher than that of the components dominating the West Eurasian ancestry palette.

Modeling of the observed haplotype diversities suggests that both Indian ancestry components are older than the purported Indo-Aryan invasion 3,500 YBP.

Consistent with the results of pairwise genetic distances among world regions, Indians share more ancestry signals with West than with East Eurasians.

From here (open access) via here.

The paper itself goes on to state in some portions that I excerpt below (greater than and less than signs transliterated with words because of their impact on html formating in a blog post; internal references to sources and figures omitted):

Reich et al. have also made an argument for a sizeable contribution from West Eurasia to a putative ancestral north Indian (ANI) gene pool. Through admixture between an ancestral south Indian (ASI) gene pool, this ANI variation was found to have contributed significantly to the extant makeup of not only north (50%–70%) but also south Indian populations (greater than 40%). This is in contrast with the results from mtDNA studies, where the percentage of West Eurasian maternal lineages is substantial (up to 50%) in Indus Valley populations but marginal (less than 10%) in the south of the subcontinent. . . .

[W]e used the model-based structure-like algorithm ADMIXTURE that computes quantitative estimates for individual ancestry in constructed hypothetical ancestral populations. Most South Asians bear membership in only two of the constructed ancestral populations at K = 8. These two main ancestry components—k5 and k6, colored light and dark green—are observed at all K values between K = 6 and K = 17. These correlate (r > 0.9; p < 0.00001) perfectly with PC4 and PC2 in West Eurasia, respectively. Looking at the Pakistani populations (0.51) and Baluchistan (Balochi, Brahui, and Makrani) in particular (0.59), the proportion of the light green component (k5) is significantly higher than in the Indian populations, (on average 0.26). Importantly, the share of this ancestry component in the Caucasus populations (0.50) is comparable to the Pakistani populations.

There are a few populations in India who lack this ancestry signal altogether. These are the thus-far sampled Austroasiatic tribes from east India, who originated in Southeast Asia and represent an admixture of Indian and East Asian ancestry components, and two small Dravidian-speaking tribes from Tamil Nadu and Kerala. However, considering the geographic spread of this component within India, there is only a very weak correlation (r = 0.4) between probability of membership in this cluster and distance from its closest core area in Baluchistan. Instead, a more steady cline (correlation r = 0.7 with distance from Baluchistan) of decrease of probability for ancestry in the k5 light green ancestral population can be observed as one moves from Baluchistan toward north (north Pakistan and Central Asia) and west (Iran, the Caucasus, and, finally, the Near East and Europe).

If the k5 light green ancestry component originated from a recent gene flow event (for example by a demic diffusion model) with a single center of dispersal where the underlying alleles emerged, then one would expect different levels of associated haplotypic diversity to suggest the point of origin of the migration. . . . Our simulations show that differences in haplotype diversity between source and recipient populations can be detected even for migration events that occurred 500 generations ago (∼12,500 years ago assuming one generation to be 25 years). For alleles associated with k5, haplotype diversity is comparable among all studied populations across West Eurasia and the Indus basin. However, we found that haplotypic diversity of this ancestry component is much greater than that of those dominating in Europe (k4, depicted in dark blue) and the Near East (k3, depicted in light blue), thus pointing to an older age of the component and/or long-term higher effective population size. Haplotype diversity flanking Asian alleles (k7) is twice greater than that of European alleles—this is probably because the k7 ancestry component is a composite of two Asian components ([at] K > 10).

In contrast to widespread light green ancestry, the dark green ancestry component, k6 is primarily restricted to the Indian subcontinent with modest presence in Central Asia and Iran. Haplotype diversity associated with dark green ancestry is greatest in the south of the Indian subcontinent, indicating that the alleles underlying it most likely arose there and spread northwards. It is notable that this ancestry component also exhibits greater haplotype diversity than European or Near Eastern components[.] . . .

[G]enetic diversity among Pakistani populations (average pairwise FST 0.0056, although this measure excludes the Hazara, who show substantial admixture with Central Asian populations) is less than one third of the diversity observed among all South Asian populations (0.0184), even when excluding the most divergent Austroasiatic and Tibeto-Burman speaking groups of east India. . . . all South Asian populations, except for Indian Tibeto-Burman speakers, show lower FST distances to Europe than to East Asia. This could be either because of Indian populations sharing a common ancestry with West Eurasian populations because of recent gene flow or because East Asian populations have relatively high pairwise FST with other non-African populations, probably because of their history of genetic bottlenecks.

Similarly, the clines we detect between India and Europe (e.g., PC1 and PC2) might not necessarily reflect one major episode of gene flow but be rather a reflection of complex demographic processes involving drift and isolation by distance. Nevertheless, the correlation of PC1 with longitude within India might be interpreted as a signal of moderate introgression of West Eurasian genes into western India, which is consistent with previous studies on uniparental and autosomal markers.

Overall, the contrasting spread patterns of PC2 and PC4, and of k5 and k6 in the ADMIXTURE analysis, could be seen as consistent with the recently advocated model where admixture between two inferred ancestral gene pools (ancestral northern Indians [ANI] and ancestral southern Indians [ASI]) gave rise to the extant South Asian populace. The geographic spread of the Indian-specific PC2 (or k6) could at least partly correspond to the genetic signal from the ASI and PC4 (or k5), distributed across the Indus Valley, Central Asia, and the Caucasus, might represent the genetic vestige of the ANI. However, within India the geographic cline (the distance from Baluchistan) of the Indus/Caucasus signal (PC4 or k5) is very weak, which is unexpected under the ASI-ANI model, according to which the ANI contribution should decrease as one moves to the south of the subcontinent. This can be interpreted as prehistorical migratory complexity within India that has perturbed the geographic signal of admixture.

Overall, the locations of the Indian populations on the PC1/PC2 plot reflect the correlated interplay of geography and language. In concordance with the geographic spread of the respective language groups, the Indian Indo-European- and Dravidic-speaking populations are placed on a north to south cline. The Indian Austroasiatic-speaking populations are, in turn, in agreement with their suggested origin in Southeast Asia drawn away from their Indo-European speaking neighbors toward East Asian populations. In this respect, it is interesting to note that, although represented by only one sample each, the positions of Indo-European-speaking Bhunjia and Dhurwa amidst the Austroasiatic speakers probably corroborates the proposed language change for these populations.

[I]t was first suggested by the German orientalist Max Müller that ca. 3,500 years ago a dramatic migration of Indo-European speakers from Central Asia (the putative Indo Aryan migration) played a key role in shaping contemporary South Asian populations and was responsible for the introduction of the Indo-European language family and the caste system in India. A few studies on mtDNA and Y-chromosome variation have interpreted their results in favor of the hypothesis, whereas others have found no genetic evidence to support it.

However, any nonmarginal migration from Central Asia to South Asia should have also introduced readily apparent signals of East Asian ancestry into India. Because this ancestry component is absent from the region, we have to conclude that if such a dispersal event nevertheless took place, it occurred before the East Asian ancestry component reached Central Asia. The demographic history of Central Asia is, however, complex, and although it has been shown that demic diffusion coupled with influx of Turkic speakers during historical times has shaped the genetic makeup of Uzbeks (see also the double share of k7 yellow component in Uzbeks as compared to Turkmens and Tajiks), it is not clear what was the extent of East Asian ancestry in Central Asian populations prior to these events.

Another example of an heuristic interpretation appears when we look at the two blue ancestry components that explain most of the genetic diversity observed in West Eurasian populations (at K = 8), we see that only the k4 dark blue component is present in India and northern Pakistani populations, whereas, in contrast, the k3 light blue component dominates in southern Pakistan and Iran. This patterning suggests additional complexity of gene flow between geographically adjacent populations because it would be difficult to explain the western ancestry component in Indian populations by simple and recent admixture from the Middle East.

Several aspects of the nature of continuity and discontinuity of the genetic landscape of South Asia and West Eurasia still elude our understanding. Whereas the maternal gene pool of South Asia is dominated by autochthonous lineages, Y chromosome variants of the R1a clade are spread from India (ca 50%) to eastern Europe and their precise origin in space or time is still not well understood. In our analysis we find genetic ancestry signals in the autosomal genes with somewhat similar spread patterns. Both PC2 and k5 light green at K = 8 extend from South Asia to Central Asia and the Caucasus (but not into eastern Europe).

In an attempt to explore diversity gradients within this signal, we investigated the haplotypic diversity associated with the ancestry components revealed by ADMIXTURE. . . our current results indicate that the often debated episode of South Asian prehistory, the putative Indo-Aryan migration 3,500 years ago falls well within the limits of our haplotype-based approach. We found no regional diversity differences associated with k5 at K = 8. Thus, regardless of where this component was from (the Caucasus, Near East, Indus Valley, or Central Asia), its spread to other regions must have occurred well before our detection limits at 12,500 years. Accordingly, the introduction of k5 to South Asia cannot be explained by recent gene flow, such as the hypothetical Indo-Aryan migration. The admixture of the k5 and k6 components within India, however, could have happened more recently—our haplotype diversity estimates are not informative about the timing of local admixture.

Both k5 and k6 ancestry components that dominate genetic variation in South Asia at K = 8 demonstrate much greater haplotype diversity than those that predominate in West Eurasia. This pattern is indicative of a more ancient demographic history and/or a higher long-term effective population size underlying South Asian genome variation compared to that of West Eurasia. Given the close genetic relationships between South Asian and West Eurasian populations, as evidenced by both shared ancestry and shared selection signals, this raises the question of whether such a relationship can be explained by a deep common evolutionary history or secondary contacts between two distinct populations. Namely, did genetic variation in West Eurasia and South Asia accumulate separately after the out-of-Africa migration; do the observed instances of shared ancestry component and selection signals reflect secondary gene flow between two regions, or do the populations living in these two regions have a common population history, in which case it is likely that West Eurasian diversity is derived from the more diverse South Asian gene pool.

Most of this analysis makes sense (although it is extremely equivocal). But, I disagree with the conclusion that a lack of regional differences in genetic diversity between regions implies a time depth of more than 12,500 years. It is more plausible, in my view, given Indo-European historical and pre-historical evidence from multiple other sources to assume a recent and simultaneous dispersal of a large population to many different regions, with the size of the population entering South Asia being somewhat larger than elsewhere, thus sustaining simmilar levels of diversity in different regions with South Asia. In part, their conclusion seems driven by probably inaccurate assumptions about the time depth of the principle European and Near Eastern autosomal components (k3 and k4). Further, if k5 is Indo-Aryan and it had a significant Caucusian source, it may have had considerable age prior to Indo-Aryan expansion during which it could have accumulated its diversity. The weak geographic pattern in k5 within India may reflect a fairly complete subcontinental imposition of a high caste ANI ruling class.

I am also inclined to think that the West Asian/ANI components (k3, k4 and k5) probably represent at least two waves of migration, at least one of which is Harappan (probably k3), and at least one of which is Indo-Aryan (probably k5 with a minority component of k4).

The observation that Central Asia has East Asian components now that it may not have earlier (the current component appears from historical evidence and ancient DNA to have its origins in the last 2,000 years), because they did not enter the South Asian gene pool from Central Asia, is notable and probably correct.

The study also confirms prior studies in finding that Tibeto-Burman populations are more distinct genetically (and hence probably more recent arrivals) than other South Asian populations.

The autosomal profiles show significant instances of African origins in Pakistani populations (and a Dravidian speaking Brahui population no different genetically from its Indo-European language speaking neighbors) but strong ASI components and no discernable African components in Dravidian speakers, even in Andhra Pradesh where Y-DNA haplogroup T frequencies are highest. Andhra Pradesh also has very low percentages of Near Eastern (k3) or European (k4) components in this breakdown, although the sample is small enough that it may not be representative for relatively recently appearing, relatively moderate frequency genetic types that have not reached fixation in the area.

Genus Homo Anatomy May Explain Speech

2011-12-08T23:53:00.000-07:00

Most of the effort to explain the superior speech abilities of humans have focused on cognitive abilities, but a new study finds that the loss of air sacs that are part of the anatomy of Great Apes and missing link genus Afarensis, but not part of members of the genus Homo (at least 600,000 years ago), may also have been important in the development of speech in humans. The study doesn't resolve the presence of this feature in Homo Eragaster or Homo Erectus, ca. 2,500,000 to 600,000 years ago, although it suggests that it makes sense to study those remains with this feature in mind.

GUT Intuitions

2011-12-08T23:17:00.001-07:00

If as loop quantum gravity theorists suggest, gravity truly is a function of the geometry of space-time that is different in kind from the particle basis of the other three fundamental forces in physics, then a grand unified theory (GUT) of the other three forces formulated with a version of the particle propagators of the Standard Model particles in a discrete rather than continuous across a quantum space-time grid is a theory of everything. This would have the virtue of eliminating the need for extra dimensions found in string theory/M theory, but not in mere supersymmetry.

Indeed, simply formulating the Standard Model particles and forces in a not precisely local discrete space-time like loop quantum gravity would itself be a grand accomplishment, finally providing a way to unify the Standard Model and general relativity at all.

It also wouldn't surprise me if the pathologies such as magnetic monopoles and proton decay found in many GUTs, for example, the earliest minimal non-supersymmetric SU(5) theories, could be cured if they were embedded in a discrete, general relativistic rather than a continuous Minkowski space-time.

Another particularly nifty speculative stab at unification by Cohl Furey at the Perimeter Institute (flagged by Kea at Arcadian Pseudofactor) suggests that an algebra arising from the combination of the real numbers, R, the complex numbers, C, the quaternions, H, and the octonions, O, might very well be capable of reproducing the Standard Model, with the algebraic limitations of octonions proving particularly useful in inducing non-physical combinations (hence an RxCxHxO model). As the abstract explains:

Unified Theory of Ideals (2010)

Unified field theories try to merge the gauge groups of the Standard Model into a single group. Here we lay out something different. We give evidence that the Standard Model can be reformulated simply in terms of numbers in the algebra RxCxHxO, as with the earlier work of Dixon. Gauge bosons and the fermions they act on are unified together in the same algebra, as are the Lorentz transformations and the objects they act on. The theory aims to unify everything into the algebra RxCxHxO. To set the foundation, we show this to be the case for a single generation of left-handed particles. In writing the theory down, we are not building a vector space structure, and then placing RxCxHxO numbers in as the components. On the contrary, it is the vector spaces which come out of RxCxHxO.

The paper gives just on incomplete example of the process (for left handed first generation particles), but doesn't follow the concept to completion. But, it does show promise.

Force Interaction Categories In Particle Physics

2011-12-08T22:07:00.003-07:00

The Standard Model has three fundamental forces, the electromagnetic force, the weak force, and the strong force. I outline the categories of particle interactions with these forces below, with the most plausible missing particle categories to explore in bold.

* Standard Model quarks which are fermions interact with all three of these forces. They have weak force interactions (in beta decay) mediated by W and Z bosons, they have strong force interactions mediated by gluons, and they have electromagnetic interactions mediated by photons. There are no known bosons that interact with all three of these forces (if there were, they would presumably be charged gluons with some rest mass and might be hard to distinguish experimentally from light charged mesons like charged pions and charged kaons, for example, perhaps either the short kaon or the long kaon is really a charged gluon with rest mass and not a composite particle).

* Charged leptons (which are fermions) and W+/W- bosons interact with two of these forces, the electromagnetic force and the weak force, but not with the strong force.

* Neutrinos (which are fermions), Z bosons and hypothetical Higgs bosons interact with one of these forces, the weak force, but not with the electromagnetic force or the strong force.

* Gluons (which are bosons) also only interact with one of these forces, the strong force, but not with the electromagnetic or the weak forces. No fermions are known that interact with the strong force, but do not interact with the weak force or the electromagnetic force. Such fermions would presumably have no charge and no rest mass, but would have a color charge.

* Photons (which are bosons) interact with one of these forces, the electromagnetic force, but not with the strong force or the weak force. No fermions are know that interact only with the electromagnetic force. Such fermions would presumably have charge, but no rest mass.

* Hypothetical gravitons (which are bosons) interact with none of these three forces. They have no charge, no rest mass, and color charge. There are no fermions that have no charge, no rest mass, and no color charge, although until recently the neutrinos were believed to be particles of this type and right handed neutrinos, if they existed would fit in this category. A scalar gravitational boson that interacted with no force but gravity could also have no rest mass, but without a force to carry, could be the prototypical dark energy carrier, making it a natural complement to the graviton as the implementation of the cosmological constant component of general relativity. Its absence of non-gravitational effects and constant speed of light movement would probably make the direct detection of such bosons impossible even if they did exist. This might be equivalent to the hypothetical graviscalar.

Three of the four gaps in these categories could be resolved if there was a law of physics that provided that there could be no massless fermions (a gap the might also explain the non-existence of right handed neutrinos, which would interact with nothing but gravity and might not even interact with gravity as rest mass seems to be linked to weak force interactions). There are several other conceivable combinations of interactions and fermion/boson status that have no particles associated with them.

* There are no fermions or bosons that interact with the two forces that are the weak force and the strong force, but not the electromagnetic force. The fermions would be electrically neutral quarks. The bosons would be gluons with rest mass.

* There are no fermions or bosons that interact with the two forces that are the electromagnetic force and the strong force. The fermions would be quarks with no rest mass, almost like up quarks except that nothing would ever decay into them. A no massless fermion rule would exclude them. The bosons would be electrically charged gluons.

Thus, to recap, the missing particle categories that would make sense if there was a no massless fermion rule would be as follows:

Fermions:
1. electrically neutral quarks

Bosons:
1. charged gluons with some rest mass
2. gluons with rest mass
3. electrically charged gluons
4. a scalar gravitational boson (perhaps associated with dark energy)

It is worth observing that there are composite analogs to three of the four strong force interacting missing categories.

* There aren't any electrically neutral quarks (basically neutrinos with color charge), but there are quite a few electrically neutral baryons that are fermions, most famously, the neutron.

Electrically neutral quarks, if they existed, might be good dark matter candidates, since their stable hadrons might be lighter than ordinary baryonic matter for deep reasons that somehow match the reality that neutrinos are lighter than charged leptons. Since they would have mass, they would have weak force interactions, at least through Z bosons. To have W+ or W- interactions, there would have to be quarks with an electrical charge of +/- 1 as well (basically electrons with color charge), to mimic neutrino-charged lepton couplings. But, their absence from the Z boson decay spectrum argues against their existence.

* There are electrically charged mesons (e.g. charged pions and charged kaons) that are electrically charged bosons with rest mass that have color charges that can lead to strong force interactions within them.

* There are electrically neutral mesons (e.g. neutral pions and neutral kaons) that are bosons and have rest mass that have color charges that can lead to strong force interactions within them. Glueballs are also hypothetical bosons that have rest mass and color charges that can lead to strong force interactions within them, even though isolated gluons lack mass.

One could imagine that Nature lacks fundamental particles that simply do what composite particles could out of some sort of cosmic avoidance of superfluous particles rule. Alternately, one could imagine that some of the so called fundamental particles are themselves composite particles made out of preons, so that all of the available categories (or at least many of them) are actually filled by composite particles.

There are no electrically charged gluons without rest mass. Indeed, there are no electrically charged particles of any kind without rest mass; all massless particles lack electromagnetic charge. Perhaps, as a consequence of the deep links associated with electroweak unification and the apparent role of the weak force in giving rise to fundamental particle mass (since all massive particles have weak force interactions and no massless particles have weak force interactions), it is impossible for charged particles to lack rest mass entirely.

The converse proposition, that massive particles must have electromagnetic charges, is not true, unless neutrinos and Z bosons and Higgs bosons are actually all composite particles (a not completely absurd possibility).

The Higgs boson mass is remarkably close to the sum of the W+, W- and Z boson masses divided by two (or perhaps more generally, the sum of all four electroweak boson masses including the massless photon), suggesting some sort of linear combination of them, which has a composite character to it.

It is not hard to imagine a scenario in which the Z boson is a composite of the W+ and W- bosons although it doesn't fit the story of electroweak unification very well, indeed, electroweak unification imagines the Z boson and photons as non-trival linear combinations of a B boson and a neutral W boson via Higgs boson interactions, which makes both Z bosons and photons, in some sense, quasi-composite even in the Standard Model.

Composite neutrinos are a harder pill to swallow, but the neutron certainly provides an analogy, and if light particles can turn energy into mass to emit W and Z bosons, while W and Z bosons can turn mass into energy to emit particles lighter than themselves (or at higher energies, particles heavier than themselves), it certainly doesn't defy nature to imagine that composite neutrinos could have masses less than their component parts.

This isn't to say that any of these particles are actually composite, although they might all be varying manifestations of a single fundamental particle in different configurations a la string theory. The notions of democratic Z boson decay and quark-lepton complementarity, for example, discourages the idea of thinking about any fermions as composite. They all seem to be on a equal footing (or at least 3-1 proportionality due to color charge distinctions) in some sense.

How Do We Know A 125 GeV Signal Is A Spin Zero Higgs Boson?

2011-12-08T20:20:00.004-07:00

Suppose that we learn that there is evidence of a 125 GeV mass particle at LHC. How do we know that it is a spin zero particle, as the Higgs boson is hypothesized to be? It turns out that this isn't too difficult, as comments in response to a question from Doug Sweetser at this blog post disclose.

Q: "Let's say there is a signal around 125 GeV. What kind of work is then required to show that the signal has a particular spin? The Higgs must be spin 0, but if this was some really odd process that was not in the selection code, and it had a spin different from 0, then one see a real signal that was not the Higgs boson. The analysis of this huge amount of data must presume our understanding of what can happen is almost perfectly complete. Doug Sweetser | 12/08/11 | 14:04 PM"

Answer 1: "'What kind of work is then required to show that the signal has a particular spin?'

A simple way is the measurement of the angular distribution of the Higgs particles. Higgs boson is a scalar, and so we have to expect a spherical angular distribution. Nick (not verified) | 12/08/11 | 14:57 PM"

Answer 2: "If it decays into two photons you are almost done. There is no angular momentum of the two particles in the centre of mass frame so the spin of the original particle is the sum of the spins on the particles it decayed into. A photon has spin +1 or -1 so you already know the source was spin 0 or 2. If they can get the polarization of the two photons they would know which. PhilG (not verified) | 12/08/11 | 18:07 PM."

The rumors have it that much of the evidence for a Higgs boson to be announced on December 13 is from the diphoton channel, so this makes Answer 2 immediately applicable. Also, while neither of the answers above mentions the fact, due to charge conservation, any diphoton signal (as well as any other electrically neutral set of decay products) must also have an electrically neutral source.

The data should be consistent with either a Standard Model Higgs boson or lightest SUSY Higgs boson

Both of these features (spin zero, electromagnetic charge zero), in a particle with 125 GeV rest mass, would be identical to those of the hypothetical Standard Model Higgs boson and unlike any other previously observed particle, although the lightest neutral SUSY Higgs boson of the supersymmetric set of five Higgs bosons would be, so far as I know, indistinguishable from a Standard Model Higgs boson in all respects. SUSY differs from the Standard Model in the Higgs sector by having more of them, not by having a lightest Higgs boson any different from the Standard Model one.

Per Wikipedia: "the Higgs boson has no spin, hence no intrinsic angular momentum. The Higgs boson is also its own antiparticle and is CP-even." The main distinction between CP-even and CP-odd particles observed experimentally is the distinction between the short kaon (CP-even that decays into two pions) and the long kaon (CP-odd that decays into three pions). Presumably, examination of the number of decay products in the presumed Higgs boson signals (which are probably already part of the screening process looking for a Higgs boson signal) would reveal its CP-odd v. CP-even character as soon as a signal is detected.

The already observed and measureable Higgs field vacuum expectation value also supports the existence of a Higgs boson to create it, and as discussed in previous posts at this blog, both much lower mass Higgs bosons, and much higher mass Higgs bosons over a wide mass range have been experimentally ruled out. So, if there is a Higgs boson, to give rise to a Higgs field vev it must be at approximately this mass range, which also conveniently makes the vacuum stable, or at least metastable, up to or almost up to Planck scale energies.

Known Particles Considered As Alternative Signal Sources

All of the Standard Model particles are either spin 1/2 or spin 1, so diphoton signals effectively rule out any Standard Model fundamental particles or higher mass versions of them.

No Standard Model baryons have spin 0 or 2, so they are ruled out.

There are experimentally known peudoscalar mesons with spin 0, but all of them are far too light. All of the possible pseudoscalar mesons in the Standard Model have been observed experimentally, and all of them have a rest mass of under 6 GeV. The most common pseudoscalar mesons have only about 0.1% of the rumored Higgs boson mass. There are no Standard Model mesons with spin 2.

Hypothetical Particles Considered As Alternative Signal Sources

Since we are looking for something never before observed, it is appropriate to consider hypothetical particles other than the Higgs boson to see if those particles could also match the signal that has apparently been seen. The other possibilities, with one exception, are inconsistent with the rumored signal, and in the last case, the hypothetical supersymmetric particle called the sneutrino seems to have been experimentally ruled out in the relevant mass range by other means.

The only predicted hypothetical particle with spin 2 of which I am aware is the graviton (not even supersymmetry predicts any other spin 2 particles), which is also predicted to have a zero rest mass, which would be inconsistent with a 125 GeV rest mass signal. Thus, if the commentator above is correct on conservation of spin, and the particle is a hypothetical particle other than a Higgs boson, a diphoton signal at a 125 GeV rest mass much must still presumably be some other kind of previously unobserved spin 0 particle aka a scalar particle.

There are hypothetical supersymmetric particles with spin 0 in addition to a lightest Higgs boson with a neutral electrical charge called sneutrinos, but they are predicted to have masses in the tens of TeV by most versions of these theories which have a supersymmetric boson mass multiple that is very large. But, those mass estimates are particularly speculative in the case of sneutrinos since we have only a dim idea of the mass of the neutrinos themselves and those masses are many orders of magnitude lower than the masses of other fermions which have bosonic superpartners in SUSY models. It wouldn't be absolutely inconceivable that an electrically neutral, spin zero signal at 125 GeV could be produced by an electron or muon sneutrino, but it would be very surprising. Recent LHC searches for the sneutrino in other channels distinctive to the sneutrino appear to have ruled it out at the 125 GeV mass, although not absolutely definitively. One non-standard supersymmetric theory proposed in a preprint this summer even hypothesizes that the Higgs boson is an sneutrino.

The hypothetical spin zero, electrically neutral axion is far too light (about the mass of a neutrino or less) to fit this signal and has been ruled out experimentally by other means. Supersymmetric and extradimensional theories also offer up the saxion aka dilaton as an electrically neutral, spin zero hypothetical superpartner of the axion with an expected relatively low mass, but the fact that the neutral axion has been effectively ruled out experimentally makes the existence of a supersymmetric partner to it implausible as well. Not everyone is convinced that the "strong CP problem" that it was proposed to solve is really a problem with QCD physics at all, and the strong CP problem can be solved, mechanically in the Standard Model equations, simply by setting one of the possible constants in those equations to zero.

A spin zero graviscalar, which is predicted in theories to explain the weakness of gravity by assuming that there are five or more dimesions to time-space, would be expected to have no mass, since gravity is an infinite range force, and also would not be expected to not arise in LHC conditions where gravitational fields are not particularly strong.

The spin zero, charge zero Majoron (predicted to play a part in some versions of a hypothetical seesaw mechanism of neutrino mass generation) would look very much like a Standard Model Higgs boson, but given the strong theoretical motivation for a Higgs boson and the weak theoretical necessity of a Majoron, this interpretation of the LHC results, if they are as rumored, would be disfavored. Majorons would have to have masses in the KeV range to be consistent with the already low in 1996 upper bounds on neutrinoless double beta decay rates, and would be even more constrained by the current experimental bounds of this never experimentally seen form of decay (at least at statistically significant levels reliable enough to constitute a reliable observation) as of 2011. So, this signal cannot be a Majoron either.

Conclusion

The decision tree in evaluating this result, in theory, has multiple steps:

1. Is there a new particle of any kind? If not, examine Higgless models.
2. If there is a particle, is it consistent with the Standard Model Higgs? If not, look for new physics.

And, some people have imagined that it could take a decade to answer the second question.

But, because the Standard Model Higgs boson is so distinctive and simple in its spin zero, charge zero, CP-even properties, and is necessary in both the Standard Model and SUSY models in identical forms, this isn't nearly as daunting a task as it seems. It should be possible to confirm the nature of the newly discovered particle simultaneously with, or very shortly after (a matter of months, not years) a "discovery" class five sigma signal of a Higgs boson is detected, if it is there at all.

Of course, a Higgs boson discovery isn't the immediate end of the road for high energy physics. Particles that no one expected theoretically, most famously, the muon in 1937, which spawned the aphorism "who ordered that?" from 1944 Nobel laureate Isidor Isaac Rabi, have been discovered before through brute force experimentation where nothing in particular was expected in advance, in experiments conducted simply to see what was there in the never before seen world of high energy physics. But, experimental results and theory have given us a much better informed sense of what we should be expecting and what is within the realm of logical possibility, than we had in the 1930s.

If the Standard Model Higgs boson has indeed been found, then confirmation of a hint next week should both reach a five sigma "discovery" threshold and be confirmed to be the predicted Standard Model Higgs boson rather than something else unexpected, within months or perhaps a year of the announcement.

What next?

At that point, assuming that a Higgs boson discovery is confirmed (and the lack of a clear signal in many previous search channels makes that anything but certain), the main tasks left for the LHC will be to confirm or falisfy phenomenological predictions of various supersymmetry theories up to the low to middle single digit TeV scale, and to look for beyond the standard model physics that no one has ordered.

If no BSM physics are observed at the LHC scale, there will still be room to tweak other models that propose new forces or particles or equation terms with just a little more powerful experiment, but all of the fair weather friends of SUSY and String theory will desert it in favor of messier fields like nuclear physics or less mature fields like neutrino physics, leaving only the diehard true believers, if the physics "desert" of the Standard Model at those energy levels in fundamental high energy physics turns out to be a reality. (If supersymmetric physics are found, or something else unexpected is discovered, that will be a whole new adventure.)

The most compelling open question in particle physics if a Higgs boson has been found, but there are no other new physics discoveries in particle physics in the near future, will be the quest to directly observe a particle that can explain the phenomenologically constrained dark matter effects observed by astronomers. This is the only major area in physics where there is experimental data exists that needs to be explained by a theory, and there is not a consensus on what theory fits that data, or experimental confirmation that a particular theory, rather than another one, is the right answer to the problem. (There are many areas of physics where existing theories are unsatisfying or even theoretically unsound at a sufficient level of rigor, or where it is not yet possible to calculate a theoretical prediction accurately, but none of these problems have implied theoretical predictions that are contradicted by experiment.)

No particle fitting the bill of a dark matter candidate has been observed, although many have been ruled out. No force or force carrier that could explain dark matter candidates has been observed directly, although several have been proposed and many of those proposed have been definitively ruled out. Indeed, some direct dark matter searches have seemingly ruled out the existence of particles fitting the parameters that many versions of dark matter explanations of the phenomena observed in astronomy require. Standard Model neutrinos should be too light to fit the bill. No stable Standard Model fundamental particle is heavier than a down quark, and the heaviest electrically neutral Standard Model fundamental particles are the three neutrinos. No stable Standard Model composite particle is heavier than a bound neutron, which is not stable in isolation, there are no stable Standard Model mesons, and the dark matter data from astronomy is apparently inconsistent with hydrogen atoms or other baryonic matter as dark matter. Precision electroweak measurements have ruled out the possibility of weak force interacting particles over almost all of the applicable mass range needed for dark matter models.

Dark matter models consistent with the data that would be best fit by particles that are effectively equivalent to sterile neutrinos with masses in the KeV mass range, but there is no experimental data from particle physics to support the claim that they exist and no direct dark matter searches that have been replicated have found signals that are consistent with each other at any mass range so far. Needless to say, efforts are under way to design better experiments in the appropriate mass ranges to directly search for dark matter, but those experiments won't happen at LHC, which is mostly designed to observe weak force mediated particle decays that don't happen when you have stable particles that don't interact with the weak force by decaying into something familiar. Personally, I expect the answer to be some combination (in approximate order of likelihood) of (1) previously undercounted "dim matter" of the ordinary variety, (2) general relativistic effects attributable to the angular momentum of matter in galaxies and photons and gravitons in transit that simplistic approximations have overlooked, (3) free glueballs (which might be unstable in the vicinity of quarks outside of deep space), (4) neutrino condensates, (5) quantum gravity corrections related to the discreteness or non-locality of space-time or to uncertain principle effects in the graviton propogation equations that manifest at a detectable level only in weak gravitational fields that modify the classical equations of general relativity (perhaps resulting in something like Moffat's gravitational equation modifications), (6) right handed neutrinos that are stable unlike left handed neutrinos that interact with the weak force, (7) composite leptons interacting via weak force bosons) that are only weakly bound to each other, (8) heavy sterile neutrinos, (9) the lighest supersymmetric particles, or (10) something like an electrically neutral up quark that doesn't interact with the weak force either, with the mass predicted by Koide's formula for the up quark, that is somehow stable without confinement or doesn't require nearly so strong a gluon mediated strong force field to bind it into color charge neutral hadrons due to its lack of electroweak interactions.

Every hint of new physics beyond the Standard Model in the last three decades or so (except the discovery that neutrinos have mass) has been a disappointment. Excessive CP violations, particle-antiparticle matter asymmetries, and more have turned out to be false alarms. But, there always seems to be some surprise or another around the corner in a new venue (such as the apparent superluminal neutrino results from OPERA that everybody doubts but nobody has found a way to contradict yet).

Sea Monster From Half A Billion Years Ago Described

2011-12-08T15:08:00.000-07:00

About 515 million years ago, an early three foot long arthropod (i.e. bug), from a category ancestral to the various subtypes of arthropods that exist today looked like the picture above, and according to an article in the journal Nature, it was a top level predator roaming the seas. This was determined on the basis of a rare well preserved fossil from Australia. Its compound eyes, which were exceptionally well preserved, were three centimeters long and had a resolution similar to that of a modern dragonfly, one of the sharpest eyed arthropods alive today. It predates many of the distinguishing features used to distinguish taxa such as insects, spiders and crabs, from each other (and predates some distinguishing features that all of them share).

This just goes to show that some of the monsters imagined in science fiction aren't really so unrealistic.

SUSY and the Higgs Boson

2011-12-08T14:45:00.001-07:00

Lubos Motl has a guest post from Gordon Kane, the author of a SUSY theorist who stated based with reasoning restated this December 6, 2011 preprint that 127 GeV was the preferred Higgs boson mass in his view in SUSY theories before the recent rumors that suggest that CERN will announce on December 13, 2011 that there is a 4.3 sigma 127 GeV Higgs boson signal in the combined data of the two LHC experiements searching for a Higgs boson. As previously noted at this blog, his predictions put most of the supersymmetric particles at an undetectable with current or near term experiments 30 TeV masses, but leave a few in the sub-TeV mass range, including one Higgs boson similar to the Higgs boson of the Standard Model. The detection or non-detection of the ligher particles in Kane's SUSY landscape is most notable, as they leave open the possibility that there are BSM physics within the range of the LHC and the possibility that SUSY can be falisfied.

Motl expands on the implications of a Higgs boson of this mass in this post. A money quote:

One may say that 125 GeV is exactly the borderline between the "visible SUSY" for very low masses and the "SUSY in the closet" for somewhat heavier Higgs masses.

If the Higgs mass is above 125 GeV, models with a high energy supersymmetry breaking scale become favored. They include many natural E 6 grand unified theories and extensions of the minimal supersymmetric standard model (MSSM) with extra multiplets (when we add a single scalar field, we get the so-called NMSSM, where N stands for "next to"). . . .

Quite generally, these models – much like Kane-led M-theory phenomenology – assume that most of the scalar superpartners (superpartners of known fermions) have masses between 20 and 100 TeV or so. The fermionic superpartners (gauginos and Higgsinos) may be much lighter and some of them are often (predicted to be) accessible at the LHC. The third generation of squarks (and sometimes sleptons) is usually somewhat (or much) lighter than the first two generations, exactly in the opposite way than for the known quarks and leptons.

Some of these models try to promote different philosophies and personal twists but a big part of their message is overlapping. The LHC should see a Higgs most likely in the 120-135 GeV window and there could be new physics, most likely some fermionic superpartners of the known gauge bosons (or the Higgs) that should still be accessible. Many of the details remain unknown. It's not guaranteed that the LHC will see something beyond the 125 GeV Higgs boson but I think it's rather likely and so does my Princeton source.

FWIW, I think it is rather likely that the LHC will see no new physics whatsoever beyond the Higgs boson, although it will almost surely refine the values we have for various constants of the Standard Model, may refine the beta functions used to describe the running of the coupling constants of the three Standard Model forces, and may expose one or two bad assumptions that are currently widely used in approximating the predictions of the Standard Model from its current equation set. In my view, the Higgs boson find that is widely anticipated greatly reduces the experimental motivation and theoretical imperative to solve "naturalness" concerns about the Standard Model, related to vacuum instability at high energy levels, with SUSY. Post-Higgs, the biggest piece of uncharted Standard Model territory left is in neutrino physics and it isn't obvious that the main two collaborations at the LHC are doing the kind of work that will answer those questions.

Motl also notes a not very impressive rebuttal to String Theory/M Theory critics that says many nice things about unexpected benefits of String Theory methods outside fundamental physics, and positions String Theory as a theory at least as plausible as any alternative theoretical program, but fails to rebut the key point of the critics which is the absence of an experimental justification for String Theory's dominance as a BSM theory taken seriously in academic faculties and in matters like analysis of big dollar collider results against that theory's predictions.

While I'm add it, I will also note one of those other BSM theories,

here with a link in particular to a November 2011 pre-print. I've been following the online discussions leading up to it, which starts at the open access Physics Forums and had industry engineer Carl Brannen as an important contributor, from its inception.

The desirability of a way to determine quark masses other than via direct experimental measurement is quite real, in part, because it illuminates "within the Standard Model" relationship that shed light on deeper relationships between its parameters, and in part, because the accuracy with which we know the ligher quark masses (up, down, strange) is only about one significant digit, and only about two significant digits for intermediate quark masses (charm, bottom).

The uncertainty in the values of the fundamental quark masses is something that injects meaningful uncertainty into QCD background estimates looking for new physics, and since the same values for quark masses are used by almost everyone doing QCD calculations, the bias is systemmic. Experimentally measured QED and electroweak constants are known to far greater precision.

The paper's post-dictions, which include an interesting 3-1 relationship between quarks and leptons that parallels that 3-1 relationship in the weak force frequencies of the two types of particles attributable to the fact that there are three colors of quarks, while only one lepton color, are as follows:

Inputs
me = 0.510998910 MeV ± 0.000000013
mμ = 105.6583668 MeV ± 0.0000038
Mq = 3Ml
q = 3 l

Outputs
m = 1776.96894(7) MeV (Tau)
mt = 173.263947(6) GeV (top)
mb = 4197.57589(15) MeV
mc = 1359.56428(5) MeV (charm)
ms = 92.274758(3) MeV (strange)
md = 5.32 MeV (down)
mu = 0.0356 MeV (up)

The results are within the two sigma error bars of experimental determinations in the case of the tau, top, bottom, charm, strange (80-130 MeV) and down quarks (4.1-5.7 MeV), but has a much lower value than one within the error bars for the up quark mass than the canonical estimate of 1.7-3.1 MeV (mean 2.5 MeV) in a +/- one sigma confidence interval.

The experimental mass values of the heavy quarks cited in the article are:
mt = 172.9 GeV +/- 0.60 +/-.9
mb = 4.19 GeV +0.18−0.06
mc = 1.29 GeV +0.05−0.11 GeV

There have been suggestions by Brannen that one of the neutrinos needs to have a negative sign in the formula to fit the data for that series of masses, and a similar sign adjustment for the up quark (a nice parallel of one reversed sign for the quarks and one for the leptons) would produce a more conventional up quark mass.

Another way to deal with up quark mass is to acknowledge the theoretical issues posed in defining it in terms of observables. There are theoretical virtues to thinking of the fundamental "bare" rest mass of the up quark as zero, which would not be inconsistent with the result achieved from a Koide's mass approximation.

Suffice it to say that I think that this is far more than numerology and that there really is a fundamental physics basis for Koide's formula and its variants that explains the mass matrix.

Taken together with the quark-lepton complementarity principal that relates the parameters of the CKM matrix to those of the PMNS matrix, in a manner that follows a similar ansatz to the extended Koide's formula, there is a mechanism for making very precise phenomenological predictions of Standard Model physical constants that are hard to obtain accurate measurements of experimentally, and for reducing significantly the number of free physical constants in the Standard Model. These precise predictions ought to be possible to confirm continuously over time as experimental data refines the estimated value of these constants.

The predicted low value for the up quark mass, if correct, would also push the total amount of mass in the universe attributable to hadronic glue, as opposed to fundamental particles, to more than 99.6% of the total.

As a footnote, what would be the mass of a b' and t' quarks under the formula used (derived from the top and bottom quark masses and iterated)? It would be approximately 3,555 GeV (i.e. about 3.6 TeV) for the b' and 82,917 GeV (i.e. about 83 TeV) for the t' and 42.96 GeV for the fourth generation charged lepton tau prime (a little less than half of the Z boson mass), barring any sign issues by my back of envelope (literally) calculations. The quark masses implied by this formula for fourth generation quarks would probably be beyond anything that could be discovered at the LHC in the next few years, and the charged lepton mass is experimentally excluded. It would have otherwise been observed in Z boson decays long ago. This, of course, disfavors the notion that there is a fourth generation of fermions at all, something already disfavored by the 45 GeV minimum mass for a fourth generation "fertile" neutrino, which is much, much heavier than the best estimates for the mass of the third generation neutrino without any clear justification or precedent.

The author of some of these papers, Alejandro Rivero, also has the interesting idea, although not stated as clear in his papers as might be hoped, that supersymmetric particles are not fundamental, but are instead composite versions of Standard Model fundamental particles that have the same loop cancellation effects of SUSY particles.

Generic Limits On Fundamental Particle Mass

2011-12-07T11:45:00.000-07:00

The muon has a mean lifetime of about 10^-6 seconds. No other quark or charged lepton has a mean lifetime of more than about 10^-8 seconds, and the half life of a top quark is on the order of magnitude of 10^-25 seconds. W boson are slightly less long lived than top quarks at 3*10^-25 s, and Planck time is on the order of 5*10^-44 seconds. Thus, there is a nineteen order of magnitude difference in decay rate between the longest lived second generation particle, and the shortest lived quark. There is a similar nineteen order of magnitude gap between the top quark/W boson decay time and Planck time.

Generally speaking, the heavier a fundamental particle is, the faster it decays. A muon is about 0.1 GeV. A top quark is about 173 GeV. The implication is that it may be that no particle can have a mass much more than 1700 times the top quark mass (about 294 TeV) without having a decay time of less than Planck time.

One could also related the decay rates to particle generation and note that the nineteen order of magnitude gap is between the longest lived second generation particle and the shortest lived third generation particle. This wouldn't rule out a fourth generation of fermions, but would rule out a fifth generation of fermions.

It is also conceivable that the decay rate of the W boson, which is the means by which fundamental particles can decay, is an absolute limit upon particle decay rates, in which case the top quark is the heaviest possible particle.

Given that all know massive particles decay via the weak force, the mass limitation inferred from decay rates are quite model independent. This kind of reasoning should apply, for example to massive technifermions, massive supersymmetric particles, and hypothetical higher generation bosons.

Now, this isn't necessarily a very strong bound. Some of the models consistent with a lightest Higgs boson of 127 GeV estimate that many of the supersymmetric particles would have masses on the order of 30 TeV, although several would have masses of less than 1 TeV, and experimental bounds on supersymmetric particle are similar to those on next generation quarks discussed below (but under 1 TeV).

Another possible bound on fourth generation Standard Model particles is in the CKM and PMNS matrixes; the absence of detectable amplitudes for transitions to more than three generations suggests that fourth generation Standard Model particles would have to be much heavier than a top quark, and that the decay chain would likely be dominated by a single possibility as the top quark decay is dominated by the decays to bottom quarks.

As I've noted elsewhere, the absence of hadrons made of top quarks also implies, a fortiori, that hadrons made of fourth generation quarks would also not exist. More generally, unless a supersymmetric analog to the strong force had a much more rapid time frame than the Standard Model strong force, supersymmetric hadrons of anything but lowest generation supersymmetric particles would be ruled out, since all supersymmetric particles are heavier than a top quark.

Experimental Bounds on Fourth Generation Particles

Fourth generation quarks (conventionally labeled t' and b') are experimentally excluded for the b' below 199 Gev and for the t' below 256 GeV. These values are not updated for the latest 2011 LHC bounds, which put a lower bound on the b' mass of 385 GeV, and the puts a reasonably expected t' mass values, if there is a t' quark, higher.

If the t' to t quark mass ratio were similar to the t quark to c quark mass ratio, one would expect the t' quark to have a mass of 20 TeV; the b quark to s quark ratio would imply a t' quark mass of 7 Tev; the s quark to u quark mass ratio would imply a t' quark mass of about 3.5 Tev; the tau to muon mass ratio would imply a t' mass of about 3 TeV. The ratio of c quark mass to u quark mass, or of muon to electron mass would suggest an even greater t' mass. Of the b/c, c/s, and s/d mass ratios, none are smaller than a factor of about 3, so one would expect a b' mass of not less than about 522 GeV and much heavier masses on the order of 1 TeV or more would be plausible given expectations for the t' mass.

The lower experimental bound on a tau prime (i.e. fourth generation lepton) mass is about 100 GeV, which is about 55 times the tau mass, and d/s/b type mesons appear to tend to be within an order of magnitude of mass of their same generation charged lepton, so a mass in the high hundreds of GeV would not be particularly unexpected. We know that a Z boson can give rise to a top/antitop pair with a combined mass of 348 GeV which far exceeds the 90 GeV of the Z boson rest mass. But, perhaps at some point there is a limit, and if that limitation is less than the correct mass for fourth generation fermion if there was one, then that limit would prevent fourth generation fermions from arising. The conventional statement of the experimental limitation on fourth generation neutrino mass from precision electroweak measurements is 45 GeV.

Experimental bounds on Z' bosons are in the high hundreds of GeVs.

Implications of a 126 GeV Higgs Boson For Various BSM Physics

2011-12-05T13:28:00.003-07:00

A 126 GeV Higgs Boson, which is rumored to have been seen (at a 4.3 sigma, not quite "discovery" standard), has major implications for beyond the Standard Model physics. It destroys the motivation for technicolor or a composite Higgs boson. It tends to disfavor a fourth generation of fundamental particles.

It undermines, without dealing a death blow to, supersymmetry (i.e. SUSY), and by implication, string theory, both because those models favor lighter Higgs bosons and because the justification for their existence is reduced if the Standard Model is stable at high energy levels.

It disfavors any introduction of new fundamental forces with any phenomenological impact.

It seems to be relatively neutral in its impact of extensions of the Standard Model with right handed or otherwise "sterile" neutrinos. It doesn't really have any strong implications for the notion of quark-lepton complementarity.

It leaves a void in the realm of fundamental dark matter candidates, which tends to make heavy stertile neutrino models and composite dark matter candidates attractive.

It doesn't necessarily have much impact on loop quantum gravity inquiries, or on the possibility of a spin-2 graviton stripped from a string theory context.

UPDATE: An exhaustive compilation of 81 recent published Higgs boson mass predictions as of June 2010, including 23 supersymmetric ones, shows what a parlor game this has become. Sixty-six of the predictions would be falsified by a 126 GeV Higgs boson, and many of the rest would be correct only by virtue of wide error bars. One of the many upper bounds would be invalidated, but only by a few GeV which would probably be within the error bars of the announcement a week from today. Fifteen predictions were consistent with this mass, although many of those predictions were consistent only by virtue of their wide error bars and were not particularly close to a 126 GeV predicted value.

In the supersymmetric theories, one of the effects of finding a "lightest Higgs boson mass" (generically, SUSY models tend to have more than one Higgs boson), is that it fixes one of two key constants from which supersymmetric particle masses are derived in these models, dramatically constraining the mass spectrum of the other particles and as a result, making falsification of the models from failure to find other supersymmetric particles in the expected mass ranges much easier.

The Minimal Supersymmetric Standard Model (MSSM), originally proposed in 1981 as the first supersymmetric model, predicted the exitence of new particles in the 100 GeV to 1000 GeV range, and is already a stretch considering experimental bounds already in existence on the existence of such particles and its need for a light Higgs boson mass, but less minimal SUSY theories aren't ruled out at this point. In addition to providing high lower bounds on the masses of the lightest supersymmetric particles, the LHC has also largely ruled out "R-party conserving" models of supersymmetry.

At the very least, the LHC has established that all supersymmetric particles are heavier than than all non-supersymmetric particles by a considerable margin.

Higgs Rumors Getting More Specific and More Credible

2011-12-05T11:45:00.001-07:00

The latest Higgs rumor (via Not Even Wrong), as of Saturday, regarding a December 13, 2011 announcement of LHC results is as follows:

December 3, 2011:

ATLAS has a 3 sigma excess at 126 GeV while CMS has a smaller excess at 126 GeV, perhaps 2 sigma, both in diphoton channels. These are close enough to combine to give a 3.5 sigma. That would be enough to claim an “observation” but is well short of “discovery”. There will be interest in whether other channels such as ZZ or WW add anything to the result. By the end of 2012 they will have up to four times the data which is enough to multiply the significance by two if the signal holds up. ( I am assuming that the results to be shown on the 13th will use the full 5/fb collected this year. It could be less.) . . . [updated later to] 3.5 sigma in ATLAS and 2.5 sigma in CMS which amounts to about 4.3 sigma combined for the 10/fb. This is about right for the expected significance at this mass.

A 4.3 sigma signal supporting the last particle predicted by the Standard Model (and required for it to work properly) would be a triumph for the Standard Model and will eliminate the need for a large class of theories developed to address the possibility that a light Higgs boson wouldn't be found.

This result, if the rumor is true, also leaves open the very serious possibility that this will be the very last bit of new particle physics discovered experimentally in the foreseeable future. No new non-composite particles or new fundamental forces are needed to make the Standard Model work up to all energy levels that can be probed directly for the foreseeable future.

The implications of a Higgs boson at that mass are explored in this post, which notes that:

Certainly the central topic of the debate will be the stability of the vacuum and whether it implies new physics, and if so, at what scale? . . . It has been known for about twenty years that for a low Higgs mass relative to the top quark mass, the quartic Higgs self-coupling runs at high energy towards lower values. At some point it would turn negative indicating that the vacuum is unstable. In other words the universe could in theory spontaneously explode at some point releasing huge amounts of energy as it fell into a more stable lower energy vacuum state. This catastrophe would spread across the universe at the speed of light in an unstoppable wave of heat that would destroy everything in its path. Happily the universe has survived a very long time without such mishaps so this can’t be part of reality, or can it? As it turns out a Higgs mass of 125 GeV is quite a borderline case. . . . It is also possible that some amount of vacuum instability could really be present. If there is meta-stability the vacuum could remain in its normal state. There would be the possibility of disaster at any moment but the half-life for the decay of the vacuum would have to be more than about the 13 billion years that it has survived so far. . . . At 126 GeV the vacuum might remain stable up to Plank energies (see e.g. Shaposhnikov and Wetterich [2010]). If this is the case then there is nothing to worry about, but depending on the precise values of the standard model parameters, instability could also set in at energies around a million TeV. This is well above anything we can explore at the LHC but such energies are found in the more extreme parts of the universe and nothing bad has happened. The most likely explanation would be that some new unknown physics changes the running of the coupling to avert it from going negative. . . . if the mass of the Higgs turns out to be 120 GeV despite present rumours to the contrary then the stability problem would be a big deal. This would be a big boost for SUSY models that stabilize the vacuum and mostly prefer the light Higgs mass. If on the other hand the Higgs mass was found at 130 GeV or more, then the stability problem would be no issue. 125 GeV leaves us in the uncertain region where more research and better measurements of the top mass will be required.

The abstract for the referenced paper states:

There are indications that gravity is asymptotically safe. The Standard Model (SM) plus gravity could be valid up to arbitrarily high energies. Supposing that this is indeed the case and assuming that there are no intermediate energy scales between the Fermi and Planck scales we address the question of whether the mass of the Higgs boson m_H can be predicted.

For a positive gravity induced anomalous dimension A_lambda is greater than zero the running of the quartic scalar self interaction lambda at scales beyond the Planck mass is determined by a fixed point at zero. This results in m_H=m_{rm min}=126 GeV, with only a few GeV uncertainty.

This prediction is independent of the details of the short distance running and holds for a wide class of extensions of the SM as well. For A_lambda is less than zero one finds m_H in the interval m_{\rm min}< m_H < m_{\rm max}=174 GeV, now sensitive to A_lambda and other properties of the short distance running. The case A_lambda is greater than zero is favored by explicit computations existing in the literature.

They sum up their findings in the conclusion of the article itself:

Detecting the Higgs scalar with mass around 126 GeV at the LHC could give a strong hint for the absence of new physics influencing the running of the SM couplings between the Fermi and Planck/unification scales.

The Planck scale is 2.4*10^18 GeV. The Fermi scale aka the electroweak scale is ca. 246 GeV (aka the Higgs vacuum expectation value).

As another treatment of some of these issues from 2007 explains, when there is a Higgs boson mass in a range that includes 126 GeV:

[T]he SM can be extrapolated, in a fully consistent way, to extremely high-energy scales with a “big desert” picture up to MGUT or even MPl. The presence of right-handed neutrinos at some intermediate scale does not significantly change this conclusion, unless their Majorana masses are very large and we insist to extrapolate the theory at scales even beyond MGUT

In other words, the experimentally favored result appears to dovetail neatly with a Higgs boson mass predicted on the basis that it would eliminate the need for any new physics all the way up to the Planck scale.

The Large Hadron Collider experiments are reaching the tens of TeV energy scale. If there is a Standard Model Higgs boson at 126 GeV, then new physics associated with vacuum instability don't crop up until the millions of TeV energy scale in the Standard Model, and it doesn't take much to tweak the appearance of new physics to even higher energy levels, or even to conclude that this is the critical value at which any need for Beyond the Standard Model physics is eliminated.

We might be able to see the pattern that drives the entire Standard Model and produces all of its parameters in a far more constrained manner, once we finally determine what all of its parameters and equations are, but this could well be the moment when we determine that we have the complete set of rules for the universe except in the circumstances where General Relativity and the Standard Model are inconsistent (e.g. the truly point-like nature of fundamental particles).