Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
The difficulty with these semi-classical interpretations of quantum phenomena is that they tend to work nicely for a few very simple cases and fall to bits when things get more complex. Bohm's quantum potential works almost perfectly for single electron atoms, in which the quantum potential simply holds the electron still, but falls apart for multi-electron atoms, which require a higher dimensional space for the quantum potential to live.<p>Although Bell did defend pilot wave theory--which is taught in every introductory QM course and covered in every introductory QM text--he himself did not see it as anything more than an inspiration for a more complete interpretation, which would necessarily be non-local in accordance with the theorem that bears his name.<p>My own belief is that pilot waves cannot account for quantum statistics, and therefore cannot account for the heat capacity of solids: <a href="http://www.tjradcliffe.com/?p=470" rel="nofollow">http://www.tjradcliffe.com/?p=470</a> There is a claim that pilot wave theory somehow deals with this, but the argument is focused on the decay of radioactive particles rather than thermodynamics, which seems to be odd, because the thermodynamic argument is the fundamental one: the heat capacity of solids is an unequivocal way of counting available states, and if hidden variables (such as the "true" positions and momenta of the piloted particles) exist then they break the symmetry under exchange that gives rise to the statistics we observe, and create additional states that would... hmmm...<p>OK, having thought about it for a bit I'm no longer <i>entirely</i> convinced it's impossible that pilot waves might preserve the symmetry while also preserving identity. It would require that exchanging the labels on the pilot waves precisely compensate for the labels on the particles. Would that be enough? I'm going to have to think more about this before forming a more firmly held opinion on it.