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?
Thursday, January 12, 2012
Tuesday, January 10, 2012
Does "Denisovian Admixture" Come From Homo Erectus?
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:
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.
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.
Monday, January 9, 2012
Note on Contributors
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
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."
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
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 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:
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.
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.
Thursday, January 5, 2012
New Finding Hints At Common Mechanism in Alzheimer's And Autism
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
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
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.
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
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):
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.
[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.
Tuesday, January 3, 2012
Have Goldbach's Conjecture Or The Riemann Hypothesis Been Proved?
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."
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."
Saturday, December 31, 2011
The Smartest Mathematican I Know (Under 50)
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).
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).
Thursday, December 29, 2011
Looking Back At 2011 and Forward To 2012
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.
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
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.
Wednesday, December 28, 2011
Feynman's IQ
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.
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.
Thursday, December 22, 2011
Is the Wavefunction of Quantum Mechanics Real?
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.
Monday, December 19, 2011
The Case For The Massless Up Quark
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.
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
One of the pivotal questions in fundamental physics is the nature of neutrino mass.
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).
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).
Friday, December 16, 2011
Musings On Mass In A Higgsful World
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):
(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.
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.
Thursday, December 15, 2011
Higgs Announcement Reactions In The Physics Blogosphere
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.
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.
Wednesday, December 14, 2011
Musings On Gluon Speed, Mass and Charge
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.
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.
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