Pilot-wave hydrodynamics - John W. M. Bush
thales.mit.edu
  • pcalau12i@lemmygrad.mlEnglish
    1·
    3 days ago

    imo it is very misleading to think of pilot wave theory as a literal wave propagating through space. The issue is that if there is an actual physical wave propagating through space per particle, that implies one field per particle, and fields need a set of numbers in every location in space, and so for N particles that can be in M possible locations, that would be MN total sets of numbers. But the wavefunction grows at a rate of M^N, not MN.

    I see in many papers a trivial error where people conclude there must be a wave propagating through space because they look at single particle experiments, and when N=1, then MN=M^N, so you can map the wavefunction directly to positions in space, as if it represents a wavefront propagating through physical space.

    But this cannot possibly be the right explanation because if you have an experiment of let’s say three particles that can be in two possible places, then you MN≠M^N. You end up with no mathematically consistent way to assign the wavefunction to positions in physical space, and if you cannot do that, then it cannot meaningfully be thought of as a wavefront propagating through space at all.

    This is because the wavefunction is not an element of 3D space but of 3N configuration space. The two only look the same if you have just one particle.

    There’s many other issues with thinking that the wavefunction represents a physical wave as well. A physical wave has physical properties: amplitude and phase. Both the global and relative phase of the wavefunction can be arbitrarily shifted around with a mere change of convention, so it doesn’t have a well-defined, objective phase value, so it seems weird to think of it as physical at all, and a wave without a physical phase is not meaningfully a wave at all.

    The wavefunction is better understood as a hidden Markov memory, comparable to one of Isaac Newton’s fluxions, which are not physical things at all, but merely a mathematical device used to make the calculations easier, but not even necessary for correct predictions. People really need to abandon this nonviable idea that there are actually invisible quantum waves floating throughout space.