The late bird also sometimes catches the worm

As the white rabbit said, I'm late! But I claim time reversal invariance. It's too bad that my mammoth post is right after Hannah's short and sweet description of reading things "right". Read hers first -- mine stands to no comparison.

First, here's my version of how the blog was named: The ends of the universe needed for our apartment to have a blog and it was to be called "mirror mortals". It took a couple of tries for Yasha and Hannah to arrive at this name, and there was a close call where Yasha was led astray for a moment and the universe had to momentarily create the blog mirrorthoughts@blogspot.com and fill it with some spur-of-the-moment inanity to prevent him from turning down the wrong path. In the end the idea dawned on Hannah and took root, and so the blog was named.
 A blog is a place for all of us to write down our random (and in some cases useful) thoughts, mostly, it seems, for the benefit other wannabe bloggers who for some reason want to name their blog "mirrormortals". It might be because I'm a fatalist that the first thing I thought of when I saw the name of this blog was the mirror of death -- which, after all, is birth, something very different that also happens to mortals. So I'll open with a very extended pun on the title (of whose origin I wash my hands), and write about the physics of time reversal.

I've wondered for a while why time goes forward. We experience the future as different from the past, but all the noticeable laws of the universe are invariant under the "temporal" mirror. If you suddenly reversed the momentum and spin of every particle in the universe, time would start to go backwards and recreate our past (there are some questions about chirality of certain atomic reactions, but it's doubtful if we'd notice notice much if only these were switched -- time, for one, would still go "forward"). After asking a bunch of physicists, the explanation I've come to believe is that the "arrow of time", as it's called, is an accident of where we are in the evolution of the universe. I'll give my layman's version of events, and let people who know more explain why I got it all wrong.

The universe (or at least one time-end of it) started with the big bang, where space was infinitesimally small and everything that there was in it -- really close together. The universe then expanded very quickly in the forward time direction, and for reasons of its own that physicists still have a hard time explaining, the stuff that there was in it didn't expand quite as quickly and uniformly as the space in the universe. We live pretty close to the big bang (in an appropriately grandiose time frame), still during the time of the "housing boom" where there's a lot of room, but matter and energy are still clumped in a more organized manner, residual from a time when the universe was small. Notice that this isn't the same as claiming that time goes forward because the universe is expanding -- it's going forward because it expanded a lot recently, and isn't about to contract a lot that near in the future. (Such a point of view would imply in particular that if the universe ends in a time-reversal opposite of a big bang -- something physicists today usually doubt -- then we're probably much closer to the beginning than to the end). And with this point of view, the characterizing property of the asymmetry of time is that stuff tends to spread apart (if time were reversed, it would tend to clump together -- which would be, after all, different). If you made some measurement of the "clumpiness" of the universe -- say, integral of density of matter squared (maybe with some relativistic correction for energy), then it would tend to decrease as you move your slice of space forward in time. The word "tend" here describing dead matter is somewhat suspicious, but can be given rigorous meaning. If you take any configuration of matter with a high level of clumpiness and allow it to develop for a second according to the laws of physics in a universe of our fixed size and energy, then with overwhelmingly high probability if you measure clumpiness again the second measurement will come out smaller than the first. The physical notion of "entropy" gives a way to quantify this tendency. Any measure of order -- including our "clumpiness" -- has an associated entropy. (Without qualification, "entropy" means something different -- in particular, it doesn't change with time in a closed system. This terminological imprecision confuses a lot of people.)

But what I've always wanted to see is a series of explanatory steps linking the big bang's introduction of time asymmetry into the world and our day-to-day perceptions of this asymmetry which are much more nuanced, and in many cases counter to the general tendency towards disorder, to quote Achebe, that "things fall apart". Say, how do you explain the fact that we remember the past farther than we can predict the future, or the fact that we process food into energy and not the other way around? The first step in any such explanation is the sun -- a "clump" of matter and energy from early in the universe, thinning itself out by releasing light into space. The sun's rays that reach Earth are reflected in a more disorderly fashion, and as lower-energy photons than they arrive, and if I'm not mistaken, this provides the initial push for all the time-asymmetric processes associated with life, including us. But how exactly does this explain our ability to remember? Why are we so much more concerned with being mortals than with the mirror property of having been born? I think there's a lot here to think about, and I wonder whether physicists have done so.