What Physically Causes Time to Progress and Vary in Different Places?

[Demystifier]

Don't you think that it is possible, in principle, to arrange such initial conditions that entropy decreases with (the coordinate) time in a small region of the universe?

 

[masudr]

Don't you think that it is possible, in principle, to arrange such initial conditions that entropy decreases with (the coordinate) time in a small region of the universe?

If you take the belief that time is a result of entropy changes (B1) then yes. But the probability is too small. And in a really, really small bit of the universe, if things momentarily, for a very, very short moment of time, go the other way, does it make a difference?

I have a question too: Assuming the above belief B1 is true, if the universe started off (started off doesn't even make sense in this context, but bear with me) in a state of high entropy, then there would be no noticeable evolution of time. Am I correct?

 

[Chris Hillman]

Entropy, anyone?

Well, any serious discussion of entropy on cosmological scales raises all kinds of issues, not least of which is that there are many things one might mean by "entropy". However, a good place to begin would be the very readable book by Lawrence Sklar, Space, Time, and Spacetime. See in particular the discussion of ergodic theory. Then see Poincare and Kac recurrence theorems, plus the relationship between measure-theoretic and topological entropy in Walters, Introduction to Ergodic Theory. Note that measure-theoretic entropy is related to a purely combinatorial notion, Boltzmann entropy, which can be interpreted in terms of group actions... and so on and on and on. There are many distinct but interesting notions of entropy, which tend to bear specific relationships to each other, and ferreting these out is a fascinating task for mathematicians.

 

[quantum123]

Don't you think that it is possible, in principle, to arrange such initial conditions that entropy decreases with (the coordinate) time in a small region of the universe?

Yes, you are the result.

 

[Demystifier]

I have a question too: Assuming the above belief B1 is true, if the universe started off (started off doesn't even make sense in this context, but bear with me) in a state of high entropy, then there would be no noticeable evolution of time. Am I correct?

Yes you are.

 

[Demystifier]

Yes, you are the result.

Thanks, you too.