What Is Loschmidt's Paradox and Its Implications for Quantum Mechanics?

[Jimster41]

i hate to start a new thread.

Is it correct to say there is nothing in the current SM (or SUSY?) that resolves Loschmidt's puzzle of where irreversibility comes from. Or is it (non-commutativity?) a basic feature feature of all QM? If it is a basic feature of all QM, is it thought to require an explanation or root cause? Is that why there is so much about deriving non-commutative algebra's and geometries from theories of QG?

http://en.m.wikipedia.org/wiki/Loschmidt's_paradox

 

[stevendaryl]

As far as I understand it, irreversibility in physics is assumed not to be due to asymmetry in the laws of physics, but due to the fact that the initial universe was very low in entropy. Of course, explaining WHY the initial universe was so low in entropy might very well involve new physics.

 

[wabbit]

My layman speculative view of this is that our arrow of time is defined by the direction in which entropy is increasing. In other words the second law doesn't say "entropy increases with time" but "time increases with entropy".

And this must flow some way - the equations are symmetric but a given solution always has locally a direction of increasing entropy, and thus an arrow of time.

What the second law forbids is the coexistence of a breaking glass and a self-assembling one. I believe this is related to information exchange between interacting systems leading to collective synchronisation - roughly, if a lot of information is flowing into a system, this information must be flowing to its parts as well, so generally, for complex systems, (largish) subsystem share the same direction of entropy increase, hence the same time arrow. Microscopic subsystem can have small entropy fluctuations corresponding to time arrow reversal, but this is a rare/minority occurence.

This may of course be hopelessly misguided, it is just how I try to deal with this to not worry about the time arrow too much:)

 

[atyy]

QM does provide new possibilities for an arrow of time.

http://arxiv.org/abs/1007.3957
http://arxiv.org/abs/1402.3380

However, within the Copenhagen interpretation of QM, one still has to impose some notion of an "irreversible macorscopic outcome" from the outside.

 

[wabbit]

I like the argument in the second paper - even non QM, an out of equilibrium system will approach equilibrium.
This is time reversible. The evolution from non equilibrium starting point is towards equilibrium with overwhelming probability in either time direction, i.e. knowing that it is in that state now, it is far more likely to have reached it as a fluctuation out from equilibrium than as a relaxation from an even bigger past fluctuation. I think this must be true when the evolution equation is probabilistic and time symmetric, like an Orstein-Uhlenbeck process or a time-symmetric Markov process with an invariant distribution.

 

[Jimster41]

The second paper is a... trip. Very interesting. Gotta look up what the Hadamard Product. Also I wish I understood their statement on page 5 "It has been well established by now that, in a normal macroscopic quantum system, the overwhelming majority of states in the energy shell H correspond to the thermal equilibrium state". seems important w/respect to expectation and it sounds a bit like the SLOT already in play?

[Edit] they explain right after, but then I also don't quite get why the non-eq states are of lower dimension?