Physics questions

Date: Tue, 7 Nov 1995 12:10:45 -0800
From: Ellis Cooper <xtalv1@delphi.com>
Reply to: quantum-d@teleport.com
To: quantum-d@teleport.com
Subject: QUANTUM-D: Physics questions

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Editor's note: here are a series of somewhat interconnected questions
               posted by Ellis Cooper - replies of very general interest
               are welcome to this list. as always, more specific replies
               should be directed to Ellis Cooper  
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I learned about QUANTUM-D from the "Welcome Information" posted to
PSYCHE-D. I have been trying to learn physics most of my life, but
due to neuronal limitations I am still stuck on a number of basics which
it seems to me everyone else has long overcome. Anyhow, I have a number
of questions on which I hope you may help me. Even though I started
out wanting to be a theoretical physicist, my Ph.D. is in pure
mathematics (category theory, 1973), but professionally I am now an
embedded systems engineer. So I have this slightly weird combination
of extreme abstraction (I have a fair idea of what a fibre bundle is)
and a very hands-on engineering and software experience. Note that I
am deeply interested in physics independently of my interest in how
physics might relate to a possible science of consciousness. The
questions are as follows:

1.	In Feynman's paper, "Space-Time Approach to Non-Relativistic
Quantum Mechanics," I am stuck to provide a rigorous explanation of
the key to understanding the "the classical limit" as h goes to 0,
where he writes, "If h is very small, the exponent will be a very
rapidly varying function of any of its variables xi. As xi varies,
the positive and negative contributions of the exponent nearly
cancel. The region at which xi contributes most strongly is that at
which the phase of the exponent varies least rapidly with xi (method
of stationary phase)." What I want, ideally, is the carefully
stated and proved little "obvious" lemma that justifies this
intuitively obvious assertion. When I look at the explanation of the
"method of stationary phase" in Choquet-Bruhat - DeWitt-Morette,
things get more confusing, not less. It is also confusing to read in
Hartle-Hawking "Wave Function of the Universe" that "the oscillatory
integral in Eq. (1.2) is not well defined but can be made so by
rotating the time to imaginary values."

2.	Referring again to Feynman's paper, I do not see where it is
proved, and again, this must be obvious to everyone but me, that if
phi(R) is a probability amplitude, as in his Equ. (12) on p.372, then
its square by definition is a probability, so if R is the whole of
spacetime, then the probability should be equal to 1.

3.	What is the relation of perturbation theory to Taylor's
Theorem in undergraduate calculus?

4.	I am at almost a complete loss at understanding the EPR and
Bell Theorem arguments. What I would like to know is whether it makes
any sense at all to ask, look, if two particles start together at the
same place and fly away from each other, can't we say that the "real"
object is a "V" shape in spacetime, ONE SINGLE THING, not two things
flying apart?

5.	I gather that one of the important points about the Heaviside
Operation Calculus is that "When solving a differential equation for
an unknown function, y, by classical methods, it is customary to give
one or more "initial conditions" - values of y, y', y'', etc., at t =
0 - and ignore the values of y prior to t = 0. In solving
differential equations with Heaviside calculus, we may specify _jump
function parts_ of y, y', and y'', etc. instead of giving initial
conditions." [D. H. Moore:"Heaviside Operational Calculus, an
Elementary Foundation": p.82: American Elsevier: 1971]. What I want
to know is whether there is anything at all like the HOC for
Schroedinger's Equation, in other words, isn't there a way to bring
the complete statement of the physical situation - initial and
boundary conditions - INTO THE EQUATION? I would like to know whether
this is possible, and if so, whether it might have some bearing on
The Measurement Problem.

6.	In [S. Y. Auyang: "How is Quantum Field Theory Possible?":
p.220: Figure B.3], caption "A dynamical system of interacting fields
in the fiber bundle formulation," I have a number of questions, some
of which may already be answered in her book elsewhere, but I get
lost and need help. First of all, where in this picture should I find
the idea of "wave function in a Hilbert space of wave functions"?
Where, in this picture, should I imagine the "collapse of the wave
function"? Where, in this picture, is the Equation of Motion? What
does Equation of Motion have to do with "Yang-Mills Equation"? How
does this picture relate to Feynman's path integral?

7.	Please provide any information about a review of S. K. Auyang's 
book.

8.	How does the concept of "renormalizability" - whatever it is
- relate to "laws of physics"? Is it a law, a model, a calculation
technique, or what?

9.	Has anyone published a respectable account of how a FINITE
data structure, "the human genome", manages to become capable of
NON-COMPUTABLE creativity, as in Penrose's work?

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 |    Ellis D. Cooper                          http://www.ec3.com |
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