Re: [asa] Fw: Pilot-wave theory

From: Randy Isaac <randyisaac@comcast.net>
Date: Sun Jun 21 2009 - 22:58:52 EDT

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 Sun Jun 21 22:59:28 2009

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