Equilibrium and approximation in Bohm's theory

Date: Thu, 22 Feb 1996 01:21:27 -0800
From: Brian Josephson <bdj10@cus.cam.ac.uk>
To: quantum-d@teleport.com
Subject: Equilibrium and approximation in Bohm's theory

Rhett Savage writes:

> Questions of consciousness aside, consideration of "back-action" as 
> a dynamical fact nourishes a suspicion that linear quantum theory is 
> fundamentally an approximation...
> 
> On 1/28, Stanley Jeffers wrote:
> 
> >    I would like to offer the following comments on Jack Sarfatti's
> > recent post (Jan 25,1996) of his abstract "Is Consciousness a 
> > Violation of Quantum Mechanics?"
> > 
> > > Bohm showed that the Schroedinger equation and the Born 
> > > probability interpretation of orthodox quantum  mechanics 
> > > depend upon the approximation that there is a new kind of 
> > > "organic" or "wholisitc" non-local and context-dependant 
> > > "quantum force" that the wave function exerts on matter 
> > > in addition to the electro-weak, strong and gravitational 
> > > forces...
> > 
> > There is no such approximation involved in Bohm's analysis.  Starting 
> > with a real wave given by psi=R exp(iS/h), the Schroedinger equation
> > separates into two equations, one of which is a continuity equation in 
> > R squared. The other looks, for all the world, like a Hamilton-Jacobi
> > equation but includes a quantum potential term which is independent of 
> > the amplitude of psi and distance. The analysis is exact  and does not 
> > depend on any approximations.
> 

(BDJ) As I understand it, Jeffers' assertion is incorrect.  The 'exact
analysis' does assume an equilibrium state whereby the Bohmian probability
density has settled down to the square of the wave function.  Only in that
case does Bohm reduce to Schroedinger.  Various people have noted that the
possibility of deviations of the actuality from the equilibrium value may
make a difference.  

  [ For example, Valentini's papers entitled "Signal-locality, 
    uncertainty and the Subquantum H-theorem" parts 1 and 2,  
    published in Physics Letters A (1991):

       Physics Letters A, Vol.156 No.1-2 pp.5-11
       Physics Letters A, Vol.158 No.1-2 pp.1-8 
                                                  - rs ]

You will even find this in the writings of John Bell
(and so it must be true!): 

"That the theory is supposed to apply fundamentally to the world as a
whole requires ultimately that any 'observers' be included in the system. 
This raises no particular problem as long as they are conceived as not
essentially different from computers, equipped perhaps with 'random'
number generators ... To include creatures with genuine free will would
require some development, and here the de Broglie-Bohm version might
develop differently from the usual approach.  To make the issue
experimental would require identification of situations in which the
differences between computers and free agents were essential" (p. 115 
of 'Speakable and Unspeakable in quantum mechanics').

The context was delayed-choice experiments but the theme was the same - 
that it may not always be permissible to replace wave functions by 
density matrices.

But fundamentally where the arguments in quantum-d are going astray is 
the fact that below the level of a statistical theory there may be a 
different kind of physics where the details, i.e. the deviations from the 
average, are important.  When this is so, incorrect results come from 
taking the statistical version as gospel truth.

Brian


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