Re: Arrow-of-time (3 types) reverse as universe supposedly starts to contract?

Very good question!

Most physicists would say that the cosmological and thermodynamical arrows of time are related, but there's a lot of confusion as to exactly how this happens.

The thermodynamic arrow of time emerges because of Boundary Conditions -- if you force a collection of particles into a low entropy state (or boundary), let it evolve (without another low entropy boundary in its future), then statstically its entropy will tend to increase.

In this picture, the entropy of our universe increases because there is a PAST boundary condition (b.c.) at the Big Bang, which for some unknown reason constrained the early universe to have very low entropy. Entropy naturally increases away from that initial low entropy constraint -- and the universe naturally expands away from that point as well. So it seems the two arrows are linked. (The pyschological arrow is the same as the thermodynamic arrow no matter what.)

But are they always linked? Suppose that the universe recollapses into a big crunch, but there's no FINAL b.c. to correspond to the initial b.c. (Or, alternatively, the final b.c. has a very high entropy, unlike the initial b.c.) Then entropy WON'T change direction when the universe starts to recontract -- entropy will still be increasing away from the initial boundary even though the universe is now collapsing.

But this is very asymmetrical -- if the universe recollapses it would be symmetric to put the same b.c. on the Big Crunch that was present at the Big Bang. So what if there IS a final b.c. on the universe?

Now we start to get outside of known physics. Quantum Mechanics and Field Theory are formulated ASSUMING that there's an initial boundary condition but no final condition which the universe is fated to meet. But there are two theoretical options. Murray Gell-Mann and James Hartle have formulated a theory of quantum mechanics where everything has TWO boundaries -- one in the past and one in the future. In this model, the thermodynamic arrow IS precisely linked to the cosmological arrow -- they both change at the same point. Still, they conclude that this model probably doesn't conform to our own universe.

But a much better idea is getting some new attention these days. Just this week a paper appeared in Physical Review Letters by L.S. Schulman (v.83, p.5419), resurrecting the idea of a two-component universe. In this model, half of the universe has an initial b.c. (but no final b.c.), and the other half has a final b.c. but no initial b.c.! We obviously live in the first component, but Schulman proposes that perhaps the second component makes up the dark matter we observe gravitationally but can't see. He also shows that perhaps it's not possible to make the paradoxes one would think would be inevitable in a universe where half of it had a final boundary.

In this model, our component would NOT change its thermodynamic arrow when the universe starts to recollapse -- our portion of the universe would still have a past boundary, not a future one. But the entropy of the universe as a WHOLE might very well change direction -- if you took into account both the past b.c. component and the future b.c. component.

If you'd like to learn more about this, I suggest the excellent book "Time's Arrow and Archimedes' Point" by Huw Price. (Price calls Schulman's idea the "mixing model") As for how these questions are ever going to be resolved experimentally... If there is a final boundary-component to the universe, presumably there are time-reversed stars or other final-boundary radiation which might be detected. But first someone has to finish the design for the first telescope that can indirectly detect its own emissions! I'm working on that one...