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 16:53:35 -0800

whopkins@csd.uwm.edu wrote:
> > Not to plug new or upcoming books, but [oops too late],

I'm only putting out the Prologue here, to try and lay out the general
direction I'm heading in, not an entire treatise itself! The rest of
the Prologue explains, in part, what I'd like to cover.

> The basic point of departure (and there are many) is
> to firmly cast the foundation in the realm of finite
> temperature physics; and closely integrate it with
> statistical mechanics and classical physics, itself;
[...]
> The Big Picture
> ===============
[... explanation showing that the observable universe (i.e.
the past light cone) is a hypersphere with the Big Bang on
the other end...]

Finite Temperature
==================
Of course, it is entirely possible that both a Big Bang and Big Crunch
exist, that both the Past and Future have such events, but that the one
with the Future is as of yet far more remotely situated. Then one may
see a very faint and partial illumination of the Future, along with
sporadic snippets of memories of events postdating the memories
themselves. Or it may still be the case that, despite the apparent
assymmetry in the sky, and the assymmetry in time that seems consequent
upon it, that memories of the future are still possible, but simply
more sporadic, rarely ever registering beyond the noise of the
background noise within a person's head (or within other physical
systems, such as computers).

it's almost a folk cliche' nowadays, that some of the snow seen on a TV
set, when attuned to a channel that has nobody on it, is actually
background radiation of the Big Bang, itself straight out of the CMB.
This, then, should make a key point all the more clear: no large-scale
physical system can be completely isolated from its environment. It is
an axiom, then, that the Universe is a heat bath, at the present time
at a temperature of about 3 degrees Kelvin above absolute zero, and
that everything is immersed in it. The only proper foundation of
Quantum Theory, therefore, is one at finite, non-zero temperature.
This distinction will make itself readily apparent when we find
ourselves back at the question of the Big Picture, when discussion of
negative energy particles and the 'vacuum state' of a quantum field.
It will also make itself felt, even more acutely in fact, when
discussing the question of what meanings ought to be given to the
various objects appearing in a formalism of quantum theory. In
particular, the question of where the probabilistic behavior of a
quantum system arises from must, at some point, be addressed;
particularly since there really is nothing at the bottommost level of a
formalism of quantum theory that calls forth this property.

This latter question will, in fact, assume a central importance here.
The classical foundation of quantum mechanics has, in essence, two
postulates. The first is the Evolution Postulate, which states that
the "observables" of a system and its "states" evolve in accordance,
respectively, with the Heisenberg equation of motion and the
Schroedinger equation. [Which yields, in turn, respectively, the
Heisenberg and Schroedinger pictures.] The other -- however -- runs
antithetically to this, asserting in effect that despite this
progression in time, there are instances (called "Measurements") where
information is extracted from a system. The information is
probabilistic -- it may be one outcome or another, each with set
probabilities of occurring, and the state the system is in immediately
afterwards is one that is known cannot be described by anything arising
from the first postulate. It's entirely from the second postulate that
the notion of probability enters into play. Without it, quantum theory
would involve probabilities in any way.

Yet, there is a serious incongruity. The second postulate lies totally
at odds with the first, and there is no clearly delineated set of rules
indicating at which instances it may be applied (i.e., which events in
space and time actually comprise what are called "measurements"?) The
picture painted is of a system running along normally minding its own
business, when suddenly and sporadically it suffers "measurements"
inflicted upon it that causes it to spew out random information (more
so than a treatise does) and jump at random into another state
completely unrelated to anything that would have arisen by the first
postulate alone. Yet, without the second postulate, you're no longer
able to account for the fact that quantum systems *do*, in fact, behave
as if they did this very thing.

So, it is almost universally accepted that the second postulate is in
no way fundamental. This shifts the burden of explanation onto the
shouldners of the fhirst, which has already shown its incapacity to
handle the weight. Various approaches have been adopted to try and
remedy the defect or "explain it away" -- Consistent Histories,
Decoherence, Everett, Deutsch's Multiple Universes, etc. Indeed, all
have had a measure of success in crossing at least part way and even
bringing up new issues and perspectives. But all have failed to close
the deal. For, no matter how you look at it: There. Are. No.
Probabilities. In. The. First. Postulate. They can NOT come from
there, nor from ANYTHING -- no matter how argued -- that uses only this
postulate. They may bring us close to the deal, but cannot close the
deal and get in bed with it.

Some people, notable Heisenberg, have thrown their hands up in the air
and simply admitted defeat, even going as far as to assert (like
Deutsch and Everett) that the quantum world does NOT, in fact, exhibit
any probabilistic behaviour at all. It's all in the head. Even your
consciousness is under the umbrella of quantum theory, so it too
exhibits all the weirdities of quantum theory (superposition of states,
etc.) so that the notion of You in the singular is rejected.

That can never be empirical, and (to say the same thing twice) nothing
in the physical world can ever single out this precept as its sole
explanation.

In all these deliberations, it somehow failed to dawn on just about
everyone that there already is a source of randomness in the universe
at large. Indeed, the approach of Decoherence nearly hits the nail on
the head, calling it the "Environment". But which environment?

When we postulate that the Universe is immersed in a heat bath at
positive temperature, we also mean to assert this with all the modern,
technical, connotations that these terms have accrued. To assert the
Universe is in a thermal state at a set temperature IS a hypothesis on
the fundamental existence of probability in the Universe. For a
thermal state is, itself, probabilistic. What we are assuming is that
were a physical system to settle down into equilibrium with outer
space, it would be at a temperature of 3 degrees Kelvin, and would be
in such a state that the probabilities of it being at an energy E would
be proportional to exp(-beta E) where beta = 1/(k T), k is on the order
of 10^{-23} Joules/degree Kelvin, and T is the 3 degree Kelvin
temperature. That's a probabilistic combination of pure energy states
-- a mixed state.

When a quantum system is immersed in a heat bath, or in any large
system in a probabilistic state, it will exhibit the very states and
probabilistic properties that one associates with quantum systems. The
Second Postulate is not needed, for we have another more fundamental
one that subsumes it: the Universe is, in effect, an open system -- a
heat bath of positive temperature. This is what closes the remaining
10% of the deal that Decoherence only brought us part way along.

The significance of such expectations cannot be underscored. It is
common practice, in Quantum Cosmology, to assume the Universe is in a
PURE quantum state, which flies directly in the face of the
overwhelming reality, just described here. Someone forgot about the
CBE. If it were truly in a pure state, then -- at least going by the
account given in Canonical Quantum Gravity -- there would be absolutely
no concept of any such thing as time flow: not in reality, not even in
perception by those subsystems (including humans) contained in this
universe. The state would be eternally the same. Literally, nothing
would ever be seen to happen. Reality would be completely timeless.

The rather obvious paradox -- the Problem of Time -- should make it
clear that the Universe is in anything BUT a pure state. It is in a
mixed, thermal, state. And a mixed state, being the probabilistic sum
of pure states, automatically entails the omnipresent reality of
probability.

To the degree one commits to the notion of a mixed state, one is
reintroducing a measure of classical physics back into the world. The
reason for the traditional insistence on pure states is one wants to
assert the universality of the quantum hypothesis. This states that
all systems, in all the degrees of freedom they exhibit, accord with
quantum theory. Everything, both large and small, is equally subject
to the laws of quantum physics: even the Universe, in its entirety.

Now, I don't know about you, but that assertion -- especially that last
part -- is a little brash. While there is clear evidence that systems
with quantum degrees of freedom EXIST, there's no evidence -- nor can
there ever by any -- that ALL degrees of freedom, even of the Universe
in the large, are quantum! In particular, to the extent that the
structure of a large system, such as the Universe, deviates from this
hypothesis of universality, it may indeed show mixed states -- such as
the one the Universe is actually in!

We assert, in contrast, that the Universe at large exhibits both
classical and quantum degrees, and that in the neighborhood of
infinity, it is classical. More specifically: the CMB is a classical
thermal state.

Among other things, this means that a proper foundation of Quantum
Theory must not only include some notion of thermodynamics or
statistical physics at its foundation -- putting these branches of
Physics on par with General Relativity and Quantum Field Theory as
fully equal pillars of foundation -- but that it must bridge the gap
between classical and quantum physics, transcending the distinction
between the two, into an enveloping formalism that has both pure
quantum and pure classical physics as subsets.

[... to be continued ...]

[Note: all 3 parts were copied from 2 sides of a page of a 6" by 9"
notebook. Feynmann, eat your heart out.]

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