Time to resurrect stochastic quantum mechanics?

Date: Mon, 18 Dec 1995 01:04:59 -0800
From: Vic Stenger <vjs@uhheph.phys.hawaii.edu>
To: quantum-d list <quantum-d@teleport.com>
Subject: QUANTUM-D: Time to resurrect stochastic quantum mechanics?

I have just re-read Chapter 9 of Jammer's _Philosophy of Quantum 
Mechanics_ which is about stochastic interpretations of QM.  I had not 
appreciated these interpretations in the past, since they are seldom 
mentioned in all the clamor about Copenhagen, quantum consciousness, many 
worlds, and hidden variables.

In turns out that for sixty years people have been making various 
derivations of the Schrodinger equation, and the uncertainty principle, 
based on the simplest assumption that one can make about the deviation of 
a particle's motion from classical behavior, namely that it undergoes 
random Brownian motion.

At the end of the chapter, Jammer presents a very simple derivation 
(although two equations that have errors - I leave that as an 
exercise to the student to find them).  Starting with the Fokker-Planck 
equation, which gives the time rate of change of the probability density 
for any Markov process, that is, any random process where the probability 
for one step does not depend on any of the other steps), and the equation 
of continuity, which is just probability conservation, the Schrodinger 
equation follow in a few lines.  It is just a diffusion equation.

Nevertheless, in the final paragraph Jammer dismisses the stochastic 
interpretations because they require the particles to interact with an 
underlying ether for which no evidence exists.

However, Vigier has pointed out that Dirac showed a long time ago that 
the quantum vacuum forms a covariant (that is, relativistically kosher) 
ether.  And, of course, quantum field theory has for forty years dealt 
with a fluctuating vacuum of photons and particle pairs.  

Vigier also has shown that spacelike jumps in a particle's path can occur
if the particle is allowed to zigzag in spacetime under the action of
these vacuum fluctuations.  This "nonlocality" occurs without
superluminality, showing that the two are not equivalent. 

Thus a stochastic interpretation in which the Brownian motion occurs in 
spacetime, so that steps backward in coordinate time are allowed (proper 
time continues to change monotonically) provides a picture of 
definite particle paths that still gives all the results of quantum 
mechanics.

For related discussions see http://www.phys.hawaii.edu/vjs/www/visual.ps
and other information accessible from my web page.

Vic Stenger
http://www.phys.hawaii.edu/vjs/www/vjs.html

cf. Visualizing the quantum world... http://www.teleport.com/~rhett/quantum-d/posts/vjs_11-8.html