Posted: Nov 10, 2016 9:50 am
by newolder
Some of the problems associated with the de Broglie/Bohm “pilot wave” idea include the inability to treat spin correctly (for a component of spin in, say, the z direction would break the rotational symmetry of pilot waves) and the fact that the pilot waves must act superluminally and therefore contradict special relativity in order to yield an interference pattern.

Our old friend and blogger Lubos Motl has posted a few times on issues with “pilot wave” mechanics, e.g. Bohmian mechanics is incompatible with loop corrections and Droplets and pilot waves vs quantum mechanics The second is a bit of a rant but does contain enough of the mathematics to show the differences between classical objects guided by pilot waves and the Schrödinger wave function.

So even if you forget about the completely different interpretations of the wave function and the shape of droplets, there is a difference (well, many differences, but I chose this one) at the purely mathematical level. The equations governing the evolution of the wave function must be exactly linear and there can't be any debate about it because it's a matter of consistency. The equations governing the evolution of the shape of droplets are almost certainly nonlinear because there is no general constraint that would ban the nonlinearity, and they are therefore 99.999...% likely to occur. You may find situations and approximations in which the nonlinearities are small or the nonlinear equations emulate some linear ones for other reasons, but fundamentally they are very different.

ETA From May of this year, someone is really getting his goat up now...: Anti-quantum zealots.... :lol: