Re: Entropy, Objectivity, and Timescales

[Leigh Palmer <palmer@sfu.ca>]

> James says:
>
> > Take the initial quantum state, and propagate it with the Schrodinger
> > eq. until there is a non-zero probability of finding the system in each
> > state considered to be accessible.  Does that work for everyone?
>
> No, doesn't work for me.  Let's assume that our system is isolated,
> and use a basis of stationary (definite-energy) states.  Then the
> Schrodinger equation predicts that only those states that appear
> in the initial wavefunction (decomposed in this basis) will ever appear
> in the wavefunction in the future.  Thus, you can wait as long as you
> like, but the number of "accessible" states (counted in this way) will
> never increase.

For heaven's sake! Eigenstates do not persist for long times in dense
systems; they never even occur. Why do you assume an isolated system?
We are talking about entropy, an attribute of a real system. Unphysical
assumptions do not help clarify what is a conceptual problem.

What James means is that we express our microstate as a combination of
single system states (e.g. particles in a box of gas) and allow them to
interact. The propagation of the interaction then proceeds at some
finite speed near sound speed.

Leigh