bassplayer142 said:
... I guess a thought experiment where impossibly you take everything in the universe and smash it together including yourself.
Is The 2nd law flawed in a way we don't know? Note that I don't really care about the plausibility of the big crunch but rather the question of entropy being completely valid.
Your thought experiment suggests a way of defining entropy so that no observer can ever see the law violated.
Suppose you define entropy not as absolute (in the eye of a being outside the universe) but in a way that depends on an observer.
This is fairly common in physics. The momentum of something is defined from the standpoint of a particular observer. It is relative to the observer rather than absolute.
So you might say that the entropy is the log of the ratio of the number of microstates per macrostates (which the particular observer can distinguish).
It depends on this ratio: #microstates/#macrostates
So if the observer dies, that particular measure of entropy becomes ill-defined. Or if all possible observers with the same point of view (this side of the Crunch or Bounce) are destroyed then the
2nd Law cannot be violated.
Because it doesn't matter what microstates and macrostates an observer on the other (re-expansion) side of the bounce detects and enumerates. New observer, new definition of what are distinguishable macrostates, new measure of entropy. Discontinuity. No violation of the 2nd Law (in the eyes of anyone observer.)
The original formulation of the 2nd Law was always from the standpoint of an observer--they just didn't emphasize this. It says that no observer will be able to build a perpetual motion machine. well a Big Crunch wouldn't allow anyone to build a perpetual motion machine or a perfectly efficient heat engine or any suchlike. So one could argue that the Big Crunch is OK.
Just my two cents. People differ about this, but that's my take on it.