Tuesday, March 25, 2014

Limits To Experimental Evidence For A Big Bang Singularity

Matt Strassler, rightly, takes a moment to breath and to acknowledge that using general relativity and the Standard Model to extrapolate from the existing universe backward in time only as far as those theories have been validated experimentally, or at least by a consensus very well motivated theoretical argument to extend those theories from the region where they have been validated experimentally, does not take you all of the way back to a Big Bang singularity.

It doesn't get you past the inflation barrier.  It doesn't get you to baryogenesis and leptogenesis.  It doesn't get you to matter-antimatter symmetry.  It doesn't get you back to time periods when the mean energy density of the universe was much above the TeV scale.  But, it really is remarkable how little of the history of the universe all of those processes that we don't understand well actually consume.

The known laws of physics do get you to nucleosynthesis from primordial protons and neutrons (ca. 0.01 to 0.00001 seconds after the Big Bang in conventional cosmologies), and maybe even to a quark epoch ca. 10^-12 seconds after the Big Bang in a conventional cosmology when there is a quark-gluon plasma in the universe that has not settled into hadrons yet.  This is a very long way to work back from a universe that is about 13.7 billion years old, plus or minus 170,000 years or so, but it isn't quite the singularity ether.

This is roughly the point at which you have to plug in the baryon number of the universe, the lepton number of the universe, the size of the universe, the total mass-energy of the universe, the matter-antimatter balance of the universe, the value of the cosmological constant, and the value of all of the parameters of the Standard Model and general relativity, and can get it to extrapolate from there pretty neatly all of the rest of the way to the present using known laws of physics (with a bare bones toy model of dark matter filling in the only bits we don't understand too well yet).

Working back to the size of the universe at the end of the inflationary epoch reputedly squeezes the universe into the size of a grain of sand (about 0.9 millimeters) at a time that ends at about 10^-32 seconds after the Big Bang.  Without inflation (proposed in 1980 by Alan Guth) it would have taken about 10^-11 second instead of 10^-34 seconds for a Big Bang that started at time zero and expanded at the speed of light to reach that size.  Essentially, the increased speed of inflation provides is greater homogeneity at the start of the quark epoch relative to what would have been expected naively, at a lower than naively expected temperature for that proper time, at the cost of wildly violating the speed of light speed limit that is a bedrock of general and special relativity.

Another philosophically problematic aspect of inflation is that it elevates ad hoc assumptions about the nature of the time zero Big Bang state about which we have no supportive direct observational evidence to an unreasonably high priority in choosing a hypothesis.  A neutral charge, neutral color charge, pure energy, zero size starting point may be pretty, but there is nothing terribly sacred about it that actual empirical data forces us to assume.  It may be a natural starting point, but we do not at all known that it is Nature's starting point.

Assuming expansion at the speed of light after inflation, at the start of the quark epoch the universe has a radius of about 10 centimeters (i.e. 0.1 meters), and at the start of hadronization the universe has a radius of about 100 kilometers (an approximately spherical object with dimensions of about the size of a largish U.S. county).  It isn't hard, although I probably won't do it today, to calculate the total mass-energy density of the universe.

So, until you get all the way back to the first microsecond or even a bit less, in a big U.S. county sized universe, the laws of physics as we know them seem to work just fine and we can extrapolate to some "initial conditions" at that point.  But, before that point, we have extrapolated to a point before what we can explain with the laws of physics as we know them and how the initial conditions at that point came to be are much more speculative.

Now, laws of physics that appear to hold for a 22 order of magnitude span of time and space is pretty impressive.  Yet, we still have to sacrifice less than a microsecond from a hypothetical singularity with pure energy initial conditions to a point in the history of the universe that we really and truly understand and aren't just guessing at (even if those guesses make a certain amount of reasonable sense).  It is easy to focus on the controversy in cosmology over what allegedly happened in the first fraction of a microsecond after the Big Bang, while ignoring the consensus over the remaining 99.99999999999999999999% about which there is profound agreement regarding the cosmological history of the universe among physicists.

These initial conditions aren't a singularity, but they an extremely basic point of beginning that we can all have considerable confidence in that is backed up by a lot of available data (except for dark matter which is a bit fuzzy).

Beyond that is something more than entertainment and fancy, but less than utterly reliable science.  Call it the legendary history of the universe, after the earliest periods of written history where fact and fantasy blend into each other.

As much as a scientist as I am, I don't find it terribly pressing to try to go back further before these initial conditions, although I keep my eyes and ears open against the possibility that something sufficiently solid or interesting in this earlier era may turn up.  I'm not much of a mystic, but I can tolerate a sort of stochastic clockwork Creator-God who sets into place a set of initial conditions and laws of physics that prevail at that point and plays no further role in the universe once it is set in motion, or at least I can be content to be agnostic about what happens before the quark epoch or hadron epoch.

Put another way, the beginning of the quark epoch is very close to the point at which we may very well cross over from that which is knowable to that which is unknowable.  But, I prefer to accentuate the positive and think about how big the knowable part is and how small the unknowable parts is in space-time.

I have some theories, and I'm familiar with other theories.  Maybe some insight well get us further.  I certainly recognize how there is a natural link between the pre-quark epoch part of the history of the universe, and the physics of energies far in excess of the LHC,and hence to the deepest layer of the laws of nature.

But, for example, it is generically true that any cosmological inflation theory, in which the universe expands at vastly more than the speed of light, creates problems as well as solving them.  Is time even actually well defined in a tachyonic universe?  Why should the speed of light limit on the speed of the universe's expansion, rather than some other law of nature break down at that point?  Where do physicists get off calling anything that happens (hypothetically) in less than 10^-31 seconds "slow roll inflation"?  What the hell is slow about that?  There is just too much that we don't know.

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