Re: Conjugate variables and the universe

Date: Wed, 15 Nov 1995 04:26:18 -0800
From: Rhett Savage <rhetorical@nonlocal.com>
To: quantum-d@teleport.com
Subject: QUANTUM-D: Re: Conjugate variables and the universe

The recent posting of Paul Easton, available at 

  http://www.teleport.com/~rhett/quantum-d/posts/easton_11-12.html   

                         ...stimulated various follow ups and comments.
Particularly relevant were two technical remarks:

Paul Easton himself wrote that

> I regret making such a bad blunder right at the start of the text. 
> However I don't feel it is fatal to the text as a whole.
>
>> Hamiltonian dynamics (which as far as I know can express all
>> physical laws) is symmetric under the following transformation:
>> interchange canonical position and momentum coordinates and
>> reverse time. Let us postulate that this symmetry also applies
>> to the macroscopic universe.
>
> I would like to strike that and substitute: Let us assume that both the
> physical laws and the macrostructure of the universe are unchanged
> if we interchange canonical position and momentum coordinates and
> reverse time. (It is better to say that we reflect time around
> the midpoint of the duration of the universe.)
>
> The latter form is the original one. At some point later I got the
> notion that the form of Hamiltonian dynamics proved the hypothesis
> with respect to physical laws, but this was a mistake. The symmetry
> applies to Hamiltons equations, dx/dt = )H/)p etc, but it does not
> necessarily apply to the Hamiltonian. 
>
> I am looking at this and hope to have something further to say...

And along the same lines David Finkelstein commented:

> The transformation you mention is not a symmetry of the Hamiltonian.
> Therefore there is no reason to expect it to be a symmetry of the universe.
>
> (To be sure, Born and Green proposed a theory that was supposed to
> have that symmetry.)

My own view is that Paul Easton's generalized notion of cosmic entropy 
is just crazy enough to possibly be a little bit true...

Paul had written: 

> The primary conclusion is that the universe is bounded in time
> by two extreme states. At the beginning it was very dense in
> position space and very diffuse in momentum space (meaning hot).
> In the end it will be diffuse in position space and concentrated
> in momentum space, like a cold crystal.

Sometimes i wonder how & in what sense our physical concepts have meaning
at earlier or later times? Generally in quantum theory physical concepts
have meaning according to their operational context; the concepts which
are physical observables, represented as operators in Hilbert space, have
a meaning exactly equal to the possibilities of measuring them. General 
concepts like macroscopic space derive their stability from the fact that
a web of implicit distinctions are in place which effectively "decohere"
(measure) them. 

In the early universe there was no place to stand to draw distinctions -
in what sense did space exist when no possible structure giving it an
operational significance existed? 

Later on if the cosmos approaches thermal equilibrium then gradually the 
operational possibilities will change... Continuing with the example of 
space, in the limit of complete equilibrium the possibility of surveying 
accurately will fade away as all distinction fades - what is the proper 
quantum mechanical meaning of physical space in that case?

Entropy (also a physical observable) depends on counting states - if no
distinction is possible then there is only one state. The big-bang was
one such unique state (normally known for its low entropy). Because the 
universe is its own environment, this monostate is also asymptotically 
approached at thermal equilibrium!

Rhett