by jostylr | 2025-08-03 03:09:49+00:00
You are correct that the pilot wave theory (Bohmian mechanics) says that instead of wave OR particle, it is wave AND particle.

But the particle does not generate the wave. There is one wave function governing the whole universe. It is a function on the 3n-dimensional configuration space of all of the particle positions. To find the velocity of a given particle at a given time, one needs to put in the position of all of the particles of the universe. Practically speaking, in an experimental setup, the macro state of the environment is sufficient to create an effective wave function of the particle which is how we can effectively use quantum mechanics on a subsystem of the universe. The collapse of the wave function in measurements is a reflection that once the little system interacts enough with the environment, then the separate environmental configurations have separated out the behavior of the wave relative to the one particle so that an effective collapse wave function can be used.

This plugging in the configuration of all the particles is a gross violation of a relativistic outlook (what is the universal now?). Bell after seeing Bohm's theory immediately grasped the implications and wanted to know if that nonlocality could be removed. His work, along with EPR, was to demonstrate that there was no theory of any kind that could avoid the non locality if results of experiments actually happen when we think they do.

The double slit experiment is perfectly explained by the approximate wave function of the 1 particle system going through both slits and interfering with itself while the particle is guided by that wave which is why there is an interference pattern that builds up out of particular particle dots. There is nothing other than practical difficulties to make the wave separation happen later but have outcomes as if it didn't; it is all about what the wave function is doing as the particle is most likely to be where |psi|^2 dictates it to be. That is what the law of motion assures. One could theoretically simulate the paths conforming to make this happen though the paths themselves could have quite unexpected behavior.

There are various extensions to Bohmian mechanics to deal with particle creation, annihiliation, quantum field theory, and relativistic versions. None are as complete as non-relativistic quantum mechanics in having a mathematically proven existence, but a large part of that is quantum field theory being unsound; the Bohmian part is not a problem. There are avenues being pursued to solve the quantum field theory infinite divergences using Bohmian insights (basically use wave functions that respect probability flowing along with particle creation and annihilation). The work is promising but difficult.

For the relativistic versions, it is easy enough to create a foliation of space-time to create a "now". There are even versions where the foliation is created out of what is already existing structure. Mathematically it seems fine as far as I know. But philosophically, it is weird to have an invisible fundamental structure existing that seemingly contradicts the main lesson of relativity.