Re: Physics questions

Date: Tue, 7 Nov 1995 17:39:17 -0800
From: Stanley Klein <klein@adage.Berkeley.EDU>
Reply to: quantum-d@teleport.com
To: quantum-d@teleport.com
Subject: QUANTUM-D: Re: Physics questions

I will not attempt to answer all of Ellis Cooper's interesting questions, 
but here is a start:

1. I am not sure why you question the cancellation of oscillating phases. 
Just try doing it numerically and you will see how it works. This is not just 
in quantum theory, but also in classical wave optics. My main 
recommendation on Feynman's stationary paths is to read his very readable 
book with Al Hibbs titled "Quantum Mechanics and Path Integrals". McGraw 
Hill,1965. On using imaginary time. That is an often used trick to make all 
the exponentials damp out. But I thought one just gave it a small imaginary 
part. I know the full 90 deg rotation to imaginary time is common in 
statistical mechanics for people who do Feynman path integral in imaginary 
time to do ensemble averaging (or something). If Paul Easton is "listening" 
to this he could do a much better job of explaining it. I am not familiar with 
how it is used in Hartle-Hawking quantum cosmology.

2. I'm not sure what your question is here. That the square of the amplitude 
is the probability is I believe one of the basic axioms of QM. It is well 
motivated by intensity of prequantum electric fields. If you were asking 
why the integral of probablility equals unity (the UNITARITY constraint of 
bootstrappers - that's what I did my thesis on in the good-old-days). The 
best discussion I know of is in one of the best books on quantum mechanics 
ever written (in my opinion). It is the book QED by Feynman. With not a 
single equation in the whole book, he spend a very large part of the book on 
the unitarity constraint. He shows how you have to keep adding lots of 
Feynmen diagrams (light reflecting from a thin film in his main example) to 
get the unity sum. It is a beautiful book.

3. Taylor's expansion can be thought of as a perturbation expansion. But I 
don't know why you want to see it that way. Much better is to read QED, 
where the perturbation expansion is discussed in detail.

4. For the EPR, your notion of the spacetime V isn't too nice because it 
doesn't seem to allow for locality. And locality is one of the hallowed of all 
concepts.

5. This one didn't make sense to me. In QM one calculates the amplitude to 
go from an initial state to a final state. Relevance of Heaviside calculus 
isn't obvious to me. Does that have something to do with step functions? 

6 and 7 I'll plead ignorance on these two also.

8. You ask whether renormalizability is a law, a model, a calculation, or 
what. The best answer I know if is on p. 128 of Feynman's QED:  "But no 
matter how clever the word [renormalization], it is what I call a dippy 
process! Having to resort to such hocus-pocus has prevented us from 
proving that the theory of quantum electrodynamics is mathematically 
self-consistent. ...  Feynman goes on a bit more but this gives you a flavor.

9. You ask how a finite, digital instruction set (our DNA) is capable of NON-
COMPUTABLE creativity, as in Penrose's work. Ahhh, this is quite close to 
the analog vs. digital arguments we've been having on Psyche-D. I have 
gotten overstaturated with that discussion but let me try again. I see a big 
distinction between the scientific and the metaphysical aspects. On the 
scientific aspects (anything that you can carry out an experiment to test) 
you can always convert an analog device (like the brain) to digital as long 
as you make the spatio-temporal mesh fine enough. On the metaphysical 
level there can be differences since one can play around with definitions of 
things like creativity. As to Penrose. There have been volumes and volumes 
and volumes of articles written against Penrose. But I am sure he thinks 
that everyone else is wrong. It is to tricky for me to follow Penrose's 
arguments. My own feeling is very clear. I have never seen any example of 
creativity or perception or mathematical insight or any other aspect of 
human behaviour that can't be done by a digital computer. (But for that 
computer to have consciousness it will require some special digital 
circuitry that nobody understands yet).

Hope that helps. Your questions were quite interesting.
Stan Klein