Conjugate variables and the universe

Date: Sun, 12 Nov 1995 01:51:01 -0800
From: Paul Easton <paul@brl4.med.nyu.edu>
Reply to: quantum-d@teleport.com
To: quantum-d@teleport.com
Subject: QUANTUM-D: Conjugate variables and the universe

This is an idea that has been hanging around me for a while.
I studied physics but have not worked in it. The idea seemed
too audacious for me to use. But now I realize that nothing
is too wild for quantum theory. I should hang it on that peg.
 
I am not entirely happy with the paragraph on duality and could
probably do better. I certainly could use feedback. Please
send comments. I am open to collaboration.
 
The idea is primarily cosmological but QM comes up if you hang
in there.
 
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.
 
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.
 
Whether statistical or exact, the idea of symmetrical boundary
conditions implies that there are two streams of entropy,
running in opposite directions. As we understand entropy in
statistical mechanics, things on the whole go from order to
disorder simply because there are many more possible disorderly 
states than orderly ones. The microscopic physical laws have no
relation to orderlyness, which is a macroscopic concept.
So to say that order runs down or entropy goes up is a
probablistic statement, but such a strong one that one can take
it as a law.

So entropy increases only because it is presently at a much
lower value than it could be. As far back as we can see, the
ultimate cause of this state of affairs is the big bang, which
represents a radically improbable state from our present point
of view.
 
By our hypothesis, it is about as improbable to get to the
end state from here. Therefore, just as by the workings of
chance things are getting scrambled in position space,
there should also be occurring, seemingly by chance, the
continual creation of order in momentum space. To put it
another way, if we look at the world in spacial coordinates
energy is being thermalized (although there is also a cooling
effect due to the expansion of the universe). If we could see
things in (non-local) momentum coordinates from our direction
of time, we would see thermal energy being bound into structure.
 
By analogy to position space structures, like us, which
hang together by positional contiguity, momentum space
structures hang together by momentum contiguity. Structure
is a kind of information, which means that free energy is
required to create it, and to maintain it if it is dynamic.
We draw our free energy from the spacial boundary condition,
so it is in our past. A conscious momentum space being would
draw free energy from the future boundary condition, and so
have an opposite sense of time.
 
If our symmetry assumption holds, momentum space locality is
just as good as positional locality for elementary particles.
Thus we can expect to see positionally nonlocal interactions
between particles whose momentum is the same, or close to it.
 
Quantum duality could probably be explained on this basis.
We can see position space structures because that is the domain
that we inhabit. We don't see momentum space structures for
reasons we will mention later. When we get down to the particle
level we go beyond structure. The particles are not associated
with any particular direction in time. They exist equally in
position and momentum space. But to observe them we must employ
position localized detectors, so we can only directly measure
their position. (If we were momentum space structures we could
directly observe momentum but not position.) To justify our
limitations we come up with the probability wave.
 
Why don't we see momentum space structures? We and our
instruments are much better at seeing position than momentum.
Also these structures are probably on a very large scale,
since in the end they merge into one structure which is
universal. Also, maybe we do, indirectly. I am referring to
"dark matter" which we infer from its gravitational effects.
Suppose this is actually the momentum space equivalent of
stars. Since they have the opposite sense of time, they
would suck up photons like vacuum cleaners from our point
of view. About as dark as you can get.
 
Dark matter is estimated to constitute 90 per cent of all matter.
This may imply that we are closer to the end than we think.
Presumably we will make it through the millennium though.