Re: A Treatise On Quantum Theory II (was: Textbook on quantum mechanics)

whopkins_at_csd.uwm.edu
Date: 02/19/05 

Date: 18 Feb 2005 16:07:40 -0800

[On the notion that a universe with a Big Crunch has time flowing the
other way]

Uncle Al wrote:
> I disagree. Entropy is only a statistical arrow of time. Angular
> momentum is an absolute arrow of time.

Yes, but the *universe*, itself, is a thermal state at positive
temperature. That, in itself, gives you an arrow of time!

Consider the consequences of that. A system at negative energy (as
explained in the s.p.r. article on the Mass Gap & 3rd Law) would have a
number of states that increases with decreasing energy, so that its
temperature would be negative.

Immersed in a heat bath of positive temperature, it will continue to
absorb energy from it until it reaches equilibrium.

This imposes an assymmetry on any quantum field theory, whereby all the
negative energy states are effectively filtered out (as well as those
of positive, but low energy, like soft photons; thus also avoiding the
Infrared divergence!); while those at positive energy remain.

Instead of postulating this property (as is done in the usual,
Wightmann formalism), it appears it can be derived. In turn, this
imposes an arrow of time on the vacuum state. Further, since this
by-passes the naive folk-argument about "negative energy particles
cascading to negative infinite energy", it , in turn, it opens back up
the ability to deal with negative energy states for particles and to
consistently treat the bosons and fermions in a particle-based setting.

But back to the other issue:
In an expanding universe, all the correlations in a system will tend to
disperse out to the environment, resulting, classically, in an increase
of entropy; and (for quantum degrees of freedom), decoherence. This is
part of how the Decoherence approach explains away the emergence of
classicality (and, also as a result) irreversibility.

In contrast, in a contracting universe, these correlations are squeezed
into tighter and tighter spaces, so that one starts to see the
spontaneous appearance of macroscopic order out of them. So, you
should expect to see all the depictions of backwards running films play
out in such a universe, as described. A quantum theorist in this
universe would then be posing an irreversible theory of "recoherence"
(the Spin Echo experiment and Quantum Eraser, writ large!)

> Feynman's rotary water sprinkler is another example. Angular
momentum
> is not symmetric to time reversal.

But there is no corresponding assymmetry of angular momentum states in
the universe reflecting the assymmetry of time. Tops don't all spin
one way. [Okay, maybe you can argue the assymmetry for neutrinos, but
I don't think this really changes the conclusion, since this is more a
product of left-right assymmetry than temporal assymmetry].

Angular momentum assymmetry is a reflection of P, not T. (For instance
in 4-D, no such assymmetry exists, but a temporal assymmetry can still
be contemplated -- thus showing that the two concepts are independent).

There's 3 factors in CPT. If you keep one constant, the result is
you'll confuse the other two. But P != T.

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