Towards a new interpretation of quantum theory?
"Euclidean Quantum Mechanics"

Date:Sat, 16 Mar 1996 20:00:11 -0800
From: Mitchell Porter <qix@desire.apana.org.au>
To: quantum-d@teleport.com
Subject: Towards a new interpretation?

Here are a few papers which I will no doubt be posting more about,
but which I am already convinced are worth reading:


"From Quantum Physics to Probability Theory and Back", J.C. Zambrini.
p393-431, in: _Chaos - The Interplay Between Stochastic and Deterministic
Behavior_. Proceedings of the XXXIst Winter School of Theoretical Physics,
Karpacz, Poland, February 1995. ed. Pietr Garbaczewski, Marek Wolf,
Aleksander Weron. Springer-Verlag, 1995. (Lecture Notes in Physics series,
No. 457.)

This paper describes an attempt to get something like quantum mechanics
out of something like ordinary stochastic processes (i.e. no complex
amplitudes, only probabilities between 0 and 1). This hasn't yet been
done, but it's very interesting. What Zambrini does describe is a way
to get something that looks a little like the Born Interpretation (his
equation 3.10), by specifying initial _and final_ probability 
distributions for a particle undergoing Brownian diffusion. The 
probability that the particle should then be found somewhere at an 
intermediate time depends on the product of the initial probability 
distribution, evolved according to the diffusion equation, and the final 
probability distribution, evolved backward according to a time-reversed 
diffusion equation. (This is discussed in section 3.)

J.C. Zambrini's homepage: 
http://ptmat.lmc.fc.ul.pt/matematica/docentes/prof-assoc/jcz.html


Huw Price, 'A neglected route to realism about Quantum Mechanics', 
_Mind_, 103 (1994), 303-36; "to be reprinted in Grim, P., Mar, G. & 
Williams, P. (eds.) _The Philosopher's Annual_, Vol. XVII, a selection 
of 'the ten best philosophy articles to appear in print in 1994'".
On the web at http://xxx.lanl.gov/abs/gr-qc/9406028

Huw Price, 'Locality, independence and the pro-liberty Bell'
http://xxx.lanl.gov/abs/quant-ph/9602020

These two papers argue, in effect, that Bell's theorem does not
disprove local realism, if one allows that future measurements may
tell you something about prior states, via what you might call
retro-correlation, rather than retro-causation; or "zigzag conditional 
probability", rather than Costa de Beauregard's "zigzag causality"
(my terms, not Price's).

Huw Price's homepage:
http://plato.stanford.edu/price/index.html


What remains to be done is to find a way to interpret quantum states
as ensembles in "Euclidean quantum mechanics", and to derive quantum
transition probabilities, probably using information about the
experimental setup in the form of prior conditional probabilities.

There's a definite similarity here to John Cramer's Transactional
Interpretation, although I find the TI obscure on a number of points
(are there particles following definite trajectories, or just emitter
and absorber waves? if only the latter, what does the emitting and
the absorbing? how does TI deal with entangled states - are the 
offer waves traveling in configuration space?).

To conclude with a quote from Arthur Eddington (Gifford lectures, 
Cambridge 1928, p216) which is cited by Zambrini:

  The whole interpretation [of quantum mechanics] is very obscure,
  but it seems to depend on whether you are considering the probability
  after you know what has happened or the probability for the purpose
  of prediction. The psi.psibar is obtained by introducing two
  symmetrical systems of psi waves traveling in opposite directions
  in time; one of these must presumably correspond to probable
  inference from what is known (or is stated) to have been the
  condition at a later time.

-mitch
http://desire.apana.org.au/~qix