Re: [asa] Fw: Pilot-wave theory

 George, I don't see how this 2nd solution can be compatible with the experimental violation of Bell's inequality, since it involves a localized singularity corresponding to the position of a classical particle.? Hasn't that been soundly disproven over the past 2 decades?

Phil

-----Original Message-----

From: George Murphy <GMURPHY10@neo.rr.com>

To: Randy Isaac <randyisaac@comcast.net>; asa@calvin.edu

Sent: Mon, Jun 22, 2009 11:51 am

Subject: Re: [asa] Fw: Pilot-wave theory

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 18:55:55 2009