LishLash

Electromagnetic fields propagate throughout 3D physical space, which makes them inherently relativistic. Pilot Waves do not propagate in 3D physical space, they manifest in complex-valued Configuration Space, which is inherently non-relativistic. Pilot Waves are produced by the evolution of the quantum wave-function, evaluated via Schrodinger's Equation. These solutions are expressed as superposed complex-valued probability amplitudes in Configuration Space. Physically realizable solutions are projected into 3D physical space as probability density fields, according to Born's Law (= the conjugate square of the probability amplitude), which Bohmian Mechanics derives from its Quantum Equilibrium Hypothesis. The probability density field is not a physical entity, it is just a prediction of the likelihood of detecting a particle at any specific point in 3D physical space.

According to Bohmian Mechanics, relativistic particle trajectories do in fact exist, but their sole property is the actual location of the particle in 3D physical space at any point in time. That physical trajectory is the sole "hidden variable" in Bohmian Mechanics, and as shown by Bell's Theorem, can only be a non-local hidden variable (in order to remain consistent with QM). All other properties that can be measured are not those of the particle itself, but of the Pilot Wave that guides the motion of the particle. What BM contends is that in practice, the only things we can actually detect are the 3D positions of particles. If particles did not manifest in 3D physical space, there would be nothing to detect, since the only way we have of detecting e.g. an electromagnetic field is to observe how it deflects particle trajectories.

The non-locality of the Pilot Wave is the inevitable result of it manifesting in Configuration Space, which like the quantum wave-function itself, is inherently non-relativistic. This means that unlike the relativistic propagation of electromagnetic waves in 3D space, Pilot Waves propagate instantaneously throughout Configuration Space. This non-local (i.e. non-relativistic) property of Pilot Waves is what is misinterpreted as "faster-than-light information transfer" by those who mistakenly assume Pilot Waves propagate in 3D physical space.