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De Broglie-Bohm and the uncertainty principle

  1. Apr 24, 2012 #1
    According to the De Broglie-Bohm theory, is the universe, in its current state, the only one that could have evolved from its early conditions?

    In other words, because in the theory, each particle actually possesses well-defined position/momentum/trajectory, does the theory imply that the universe we inhabit, to the very finest detail, is inevitable from the initial conditions?
     
  2. jcsd
  3. Apr 24, 2012 #2
    yes Goodison_lad.....Inevitable but not completely predictable....:) (or inevitable to the point where life evolved enough to have free will)

    One of the reasons (that it cannot be totally predictable), and there are many more, would be that:

    when measuring/determining the conditions (at any point in time) you effect the conditions so it can never be totally predictable

    All this is, of course, per De Broglie-Bohm hypothesis/interpretation....

    however I would say that there is (human and to a lesser extent animal) free will and that we can change the course (of our lives) to some extent....

    Whether the universe is inherently random or totally "inevitable" is not of much use...in my opinion.....it's what we do with it?...
     
    Last edited: Apr 24, 2012
  4. Apr 24, 2012 #3
    Thanks, San K. I'd forgotten about the free will element (there's a bunch of threads in the Philosophy section where they're slugging that one out!) but if we accept its existence, I can see how my free choices in setting up an experiment in a particular way could affect the outcomes and set my corner of the universe on a different course.

    So, assuming for the sake of argument, a part of the universe where no life has evolved, would that part of the universe develop inexorably along exactly the same lines as it already has? You hinted at other sources of unpredictability - but would these just represent a limit on our knowledge (according to De Broglie-Bohm) rather than some intrinsic 'anything could happen next' type of uncertainty, as present in other QM interpretetations?
     
  5. Apr 24, 2012 #4
    I think yes, like a balls on a billiard table......per De Broglie-Bohm hypothesis/assumption

    The De Brogile interpretation is deterministic

    and also, of course, the assumption that --- the experimental part of the universe is insulated from the rest of the universe for the duration of the experiment/observation

    yes....per De Broglie-Bohm theory.....the De Brogile interpretation is deterministic.

    however the initial position of the particle is not controllable by the experimenter.......see below:


    In de Broglie–Bohm theory, the wavefunction travels through both slits, but each particle has a well-defined trajectory and passes through exactly one of the slits. The final position of the particle on the detector screen and the slit through which the particle passes by is determined by the initial position of the particle. Such initial position is not controllable by the experimenter, so there is an appearance of randomness in the pattern of detection.
     
    Last edited: Apr 24, 2012
  6. Apr 25, 2012 #5

    Demystifier

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    Yes, that's correct.
     
  7. Apr 25, 2012 #6
    Thank you both.
     
  8. May 7, 2012 #7
    Yes I think what San K said regarding initial condition distributions is the key issue here. Once you have stipulated the values for initial dynamical variables, you get actual well defined trajectories (non classical though). There are no uncertainty relations that arise in an individual process once these conditions have been specified, no commutation relations. Because you are not interpreting the wave function statistically, the whole formalism of linear operators on Hilbert space becomes irrelevant; instead of solving for observables on hilbert space, you generally end up solving non linear differential equations.
    In a sense uncertainty relations are only retrieved due to a chaotic distribution of initial conditions, similar in manner to how probability enters in statistical thermodynamics. So it's the probability of a particle "being" in a certain place and not simply of "finding" the particle at a certain place.
     
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