Friday, September 23, 2016

Some Back Of Napkin Observations About The Universe

Selected Facts

The universe is now about 13.8 billion years old and has a volume on the order of 4*10^80 m^3, and a radius of about 46.6 billion light years, which is about 4*10^26 meters.  A light year is about 9* 10^15 meters.

In general, the relationship of a Schwarzschild radius to mass is r=2GM/c^2.

The total ordinary matter of the universe has an estimated mass of 10^53 kg.  The Schwarzschild radius of this mass is 1.485*10^26 meters.

Add in dark matter and dark energy and you are still no more than about 10^55 kg. The Schwarzschild radius of this mass is 1.485*10^28 meters.

The most dense objects in the universe have a density of on the order of 6*10^17 kg/m^3.

The volume of the ordinary matter in the universe at that density is about 10^35 cubic meters, and the volume of the ordinary matter, dark matter and dark energy in the universe at the scale is about 10^37 cubic meters.

This implies a scale of 10^12 meters to 10^13 meters of an object with all of the matter and energy in the universe at neutron star/smallest stellar black hole level densities, which is far smaller than the volume of the universe after inflation, or the universe's Schwarzschild radius.

After cosmological inflation, the universe allegedly had a scale of about 10^24 meters after just 10^-32 of a second. Before inflation, the universe allegedly had a scale smaller than an atom. A hydrogen atom has a volume on the order of 6* 10^-31 cubic meters.


Thus, if the universe is squeezed below the threshold of a radius somewhere in the range of 10^12 m to 10^13 m, protons and neutrons can no longer be the primary source of matter in the universe. And, in a universe that small, it isn't obvious that it is possible for particles to have kinetic energy either, because there is no room for them to move. 

So, at that point there are basically two options. Protons and neutrons can be replaced by more massive hadrons with some second and/or third generation quarks in them, and/or fermions can be replaced by bosons, so that more than one particle can be in the same place at the same time.

The heaviest possible baryon not involving a top quark (which ordinarily decays to a bottom quark before it can hadronize) is one made of three bottom quarks with a mass roughly 15 times that of a proton or neutron, which would allow for a radius about 2.5 times smaller, so as little as 4*10^11 m.

If hadrons made of three top quarks were possible in these extreme circumstances, they would have a density of roughly 520 times that of protons and neutrons, which would allow for a radius about 8 times smaller than a neutron star, so about 1.25*10^11 meters (about one light day).

Below that threshold, the universe could not be made up predominantly of fermionic matter.  Only bosons would be possible below that threshold. This could presumably include gravitons, photons, gluons, weak force bosons, Higgs bosons, and mesons.

The Canonical Chronology of the Universe

Honestly, the first ten seconds or so of the canonical chronology of the universe is all pretty speculative in my opinion. 

These include, in order:

* Planck epoch (10^-43 seconds) (10^19 GeV a.k.a. 10^32 K) Quantum gravity dominates.

* GUT epoch (10^36 seconds) (10^16 GeV) The Standard Model forces are merged.

* Electroweak and Inflationary epoch and Baryogenesis (inflation from 10^-33 seconds to 10^-32 seconds, the rest thought 10^-12 seconds) (10^28 K to 10^22 K a.k.a. 10^15 GeV to 10^9 GeV) The electroweak force grows distinct from the strong force; inflation causes space-time to surge from smaller than an atom to 100 million light years; quarks come into existence, and perhaps leptons too.

* Electroweak symmetry breaking and the Quark Epoch (10^-12 seconds to 10^-6 seconds) (10^12 K).  The electromagnetic force and weak force become distinct, the Higgs mechanism starts to function more or less as it does now, and there are quarks which have not hadronized in a quark-gluon plasma. This is the first era in which the universe was as cool as the highest energies observables that have been seen at the Large Hadron Collider (or any other experiment ever done on Earth), so this era, whenever it occurred, is roughly at the limits of the energies where the Standard Model is experimentally confirmed.

All of the events in above purportedly take place in the first 10^-6 seconds (i.e. one millionth of a second) of the universe.

The remainder of the first second of the universe in this chronology (starting at 10^-6 seconds after the Big Bang) is called the Hadron epoch (10^11 K to 10^9 K) during which quarks transform from a quark-gluon plasma to ordinary hadrons, and anti-hadrons are annihilated in collisions with ordinary matter hadrons, giving rise to the existing matter-antimatter asymmetry in quarks.

At the commencement of the next era, called the Lepton epoch, when the temperature of the universe is about 10 billion kelvins which translates into energy scales of 1 MeV, neutrinos "decouple" and cease to interact with ordinary matter.  The Lepton epoch allegedly lasts nine seconds and during this era new lepton-antilepton pairs are created in abundance, but ultimately energy levels fall to a point where new pairs are not created and redundant lepton-antilepton pairs annihilate.

At 10 seconds to 1000 seconds after the Big Bang, the connection with reality starts to kick in as this is when Big Bang Nucleosynthesis allegedly occurs at energies from 10 MeV to 100 keV (temperatures of 10^11 K to 10^9 K).  This is when protons and neutrons bind themselves into primordial atomic nuclei. And, the Big Bang Nucleosynthesis hypothesis is quite precisely supported empirically by the relative frequencies of chemical elements in the universe.

10 seconds after the Big Bang in this chronology is also the start of the Photon Epoch during which the temperature of the universe falls from 10^9 K to 10^3 K that lasts until 10^13 seconds (about 380,000 years). During this time period "a plasma of nuclei, electrons and photon; temperatures remain too high for the binding of electrons to nuclei."

Starting during the Photon Epoch, at 47,000 years after the Big Bang in the chronology (starting at a 10,000 K temperature of the universe) is the Matter Dominated Era when the energy density of matter dominates both the energy density of radiation and dark energy, slowing the expansion of space, which continues until 10 billion years after the Big Bang.

At a moment about 380,000 years after the Big Bang in this chronology, is a moment called Recombination (4,000 K) when "Electrons and atomic nuclei first become bound to form neutral atoms. Photons are no longer in thermal equilibrium with matter and the universe first becomes transparent. The photons of the cosmic microwave background radiation originate at this time."

This is followed by the Dark Ages from about 380,000 years after the Big Bang until 150,000,000 years after the Big Bang (a.k.a. redshift 20) during which the temperature of the universe falls from 4,000 K to 60 K and "The time between recombination and the formation of the first stars. During this time, the only radiation emitted was the hydrogen line." At the end of the Dark Ages, called Reionization around 150,000,00, the first stars form.  The oldest observed object in space is galaxy GN-z11 at a red shift of 11.09.  By 1,000,000 years after the Big Bang (redshift 6) the temperature of the universe has fallen to 19 K and galaxies and the first "proto-clusters" start to form in earnest.

The temperature of the universe falls to 4 K and Dark Energy begins to dominate at 10,000,000 years after the Big Bang (red shift 0.4) which causes the expansion of the universe to accelerate.

The temperature of the universe is now 2.7 K at 13.8 billion years after the Big Bang.

Commentary on The Chronology

The canonical chronology of the universe is pretty well supported, in sequence and our understanding of the physical laws that applied when the events at that part of the sequence were happening at least, around the time of the Quark Era and after Electroweak Symmetry Breaking canonically commencing 10^-12 seconds after the beginning of the universe.

Everything happening before then in the canonical chronology of the universe has not been experimentally probed and is rather speculative. There is no solid evidence that at some energy scale above the Large Hadron Collider's scope but below the GUT scale, that electromagnetism and the weak force were really unified, or that at the GUT scale, all three Standard Model forces were unified. While the phenomena attributed to cosmic inflation are definitely real, there is no solid evidence that these were actually caused by cosmic inflation of the nature of the inflation phenomena, if it did occur. I am hardly a voice alone in the wilderness in being skeptical of a cosmic inflation hypothesis when it takes a book length physics article just to describe the variations on that hypothesis that have been seriously proposed.  And, nobody really knows what physics looks like at the Planck scale and beyond.

Indeed, while we can comfortably say that the universe expanded from a size of about 100 million light years radius at which point it was extremely homogeneous and had temperatures not less than 10^12 K to its present size over about 13.8 billion years and temperature of 2.7 K, during which the mass-energy of the universe has been conserved, in a manner consistent with the Standard Model of Particle Physics and more or less consistent with general relativity and the predictions of the lamdaCDM Standard Model of Cosmology, we can't really with any confidence extrapolate much further back to a true Big Bang singularity before that point. We have no way to confirm that the classical formulation of General Relativity or the Standard Model are reliable in those circumstances, or the nature of any "new physics" that might arise at such high energies.

The largest particle masses that the LHC can probe are in the 100s of GeVs (i.e. about 10^11 Gev). This is a factor of 100,000 smaller than the GUT scale and a factor of 100,000,000 smaller than the Planck scale.

An ability to probe the physics of the Quark Epoch experimentally is impressive. But, no colliders that humans will ever be able to construct, and not even the most epic astrophysical events like large supernova and colliding large black holes give rise to any material number of interactions at energies at the GUT scale or beyond. The most energetic gamma rays or cosmic rays emitted from the biggest supernovas have energies on the order of 1.6 TeV, roughly comparable to the highest energies that will be probed at the LHC by the time it is complete or if not at the LHC at the very next generation of higher energy colliders, which could take place in my lifetime.

Fortunately, beyond intellectual curiosity and hints that it might provide about the deeper structure of he laws of physics which we have observed and confirmed, it is not terribly important to know how the laws of physics act in circumstances that we will never be able to observe by any but the most indirect and inconclusive means, and that we will certainly never encounter.

We can, however, say with some confidence that Standard Model physics as we have experimentally tested it prevailed until roughly 13.8 billion years ago, and that the era during which physics at energies higher than we have tested prevailed were present only comparatively briefly, a mere 10^-12 of a second in the canonical chronology of the universe and not more than 0.1 billion years even in the absence of inflation (the temperature of the universe is largely a function of energy density per volume, so the volume of the universe is a more robust measure of when "new physics" might appear than the time elapsed since the Big Bang).

The absolute amounts of time elapsed after the Big Bang are also speculative, and I am skeptical of the accuracy of the duration of all of the Epochs through at least Big Bang Nucleosynthesis. Fortunately, in practice, neither the absolute ages after the Big Bang for any of the Epochs, or the duration of the earliest Epochs, is very material to what we observe today.

For the most part, it really makes no great difference if Big Bang Nucleosynthesis took 990 seconds or 99,900 years, and it makes no great difference if Big Bang Nucleosynthesis started 10 seconds after the Big Bang or 100,000,000 years after the Big Bang (about the length of time that it would take the universe to reach the size it is at that point in the chronology in the absence of cosmic inflation which would make the universe about 1% older than in the canonical chronology of the universe). As long as the initial conditions at the time that Big Bang Nucleosynthesis begins are the same and Big Bang Nucleosynthesis has run its course before the Photon Epoch (a.k.a. Radiation Era) is over, and the outcome of Big Bang Nucleosynthesis however long it occurs is the same, it really doesn't matter.

We have exhaustively studied the cosmic background radiation which we believe derives from about 13.42 billion years ago, long before the first star was born, when the average temperature in the universe was an intolerably hot 4000 degrees Kelvin. Indeed, the Planck experiment was so impressive that it pretty much captured all information about the cosmic background radiation that it is even theoretically possible to obtain with solar system based instruments. There is basically nothing for telescopes to see from before this era, so the best we can do is rule out phenomena that would have left a detectable signature if it had occurred before then and did not.

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