Re: [asa] Fw: Pilot-wave theory

From: George Murphy <GMURPHY10@neo.rr.com>
Date: Mon Jun 22 2009 - 11:51:59 EDT

Randy -

It depends on what level of metaphysics you're talking about. For the big questions - free will, determinism, divine action - de Broglie's theory wouldn't be significantly different from any other causal interpretation of QM. On what I would call the meta-theoretical level it would suggest possible connections with the attempts to develop classical unified field theories that were popular among some physicists through the 50s. (In fact that's one reason I was interested in deB's approach.) But those attempts haven't turned out to produce much of value. One of the things that they have in common with deB's "theory of the double solution" is the idea that particles could be represented as small regions in which values of the fields & hence energy density are very high but not infinite - i.e., nonsingular. But it's been shown that under fairly general conditions such "particle like" solutions can't exist.

Interestingly, that isn't the type of thing Einstein was looking for in his attempts to develop a unified field theory. He had a more subtle idea, that field equations might "overdetermine" solutions in such a way that they would be defined only along certain worldlines. That may be one reason why he wasn't too impressed with Bohm's approach, even though it restored causality. On that Einstein said something like "He got his results too cheaply."

Shalom
George
http://home.roadrunner.com/~scitheologyglm

  ----- Original Message -----
  From: Randy Isaac
  To: asa@calvin.edu
  Sent: Sunday, June 21, 2009 10:58 PM
  Subject: Re: [asa] Fw: Pilot-wave theory

  Very helpful, George. In the highly speculative possibility that this is right and the Copenhagan interpretation fades, what would be some of the possible metaphysical implications?

  Randy
    ----- Original Message -----
    From: George Murphy
    To: wjp@swcp.com ; randyisaac@comcast.net ; philtill@aol.com
    Cc: asa@calvin.edu
    Sent: Sunday, June 21, 2009 10:12 PM
    Subject: Re: [asa] Fw: Pilot-wave theory

    Purely on the history - & that pre-Bohm.

    De Broglie discussed these ideas in Non-Linear Wave Mechanics: A Causal Interpretation (Elsevier, 1960) - which, in spite of the date of publication, picks up on ideas he'd been developing ~ 35 years later. He discusses some of the history in this book. The basic idea is that the linear Schroedinger eqn is an approximation to a non-linear eqn in which particles would be represented by regions of very high concentrations of field amplitudes, similar to the way in which Einstein & co-workers later worked out the equations of motion for a particle in general relativity. As de Broglie describes the history, he did not feel prepared at the 1927 Solvay Conference to present this theory in any detail, and so offered there a truncated version in which the non-linear region of such a future theory is described simply by a particle which is "guided" by the solutions of the linear equation - this a "pilot wave" theory. This wave never intended to be anything more than a provisional suggestion. Since his ideas didn't receive much suppport, & since he didn't see how to develop the more complete theory, he went along with, & taught, the consensus Copenhagen intepretation for some years. In the 1950s, partly because of Bohm's related ideas, he returned to the earlier concept.

    De Broglie discusses this here in connection with the "second solution" of the Schrodinger equation. Here's what that means for a free particle. The usual wave function in such a case is simply a plane wave, psi = exp [i(p.x-Et)/2*pi*h]. But it's easy to show that U = psi/sqrt[x - Vt], with V = p/m the velocity of the corresponding classical particle, is also a solution, albeit a singular one that blows up at the location of the particle (r = Vt).

    Shalom
    George
    http://home.roadrunner.com/~scitheologyglm

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Received on Mon Jun 22 11:53:50 2009

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