system
Given the following post, respond as if you're commenting on Reddit:
human
What "physically" is the wave described in Pilot-wave Theory/Bohmiam mechanics?

In Pilot-wave Theory (de Broglie–Bohm theory), what **is** the wave that the particle is interacting with? Is it like a quantum field theory wave, one for every particle or type of particle in the universe? Some sort of interaction with space-time? Or some sort of emergent property of the particle itself - in which case how does that differ from wave-particle duality?
gpt
The pilot wave in dBB is not much more than a variation on a standard wavefunction. It's simply part, alongside the hidden classical trajectory, of the dBB description of the quantum state. There's nothing much to it - the state is simply a description of the information you have about the system. As long as there's something happening and someone caring about it, there's going to be a state.

I throw a ball and you watch it. The state you assign to the system includes a position vector pointing from origin to ball. What is "physically" this vector? Is it emergent? An interaction with spacetime? What **is** it? Nothing, it's just an arrow you drew in your head to make sense of it.

Now another point about the dBB pilot wave, just because you mentioned it. It's way, way, way, way, way bigger than this

> Is it like a quantum field theory wave, one for every particle or type of particle in the universe?

the pilot wave (though this also applies to normal Copenhagen wavefunctions) is a single wave for the whole Universe, but it does not lie in our physical 3D space, but in the space of all configurations. For a field theory like the standard model, this is a terrifyingly large space. Imagine all possible combinations of waves you could have of all fields of the SM throughout all of space, and each possible combination you think of as a point, and all of these points together make up a gigantic space, and the pilot wave /  wavefunction is a wave on *that*. It's really, really, really big of a concept, another reason not to worry too much about its physicality or any similar stuff. Sometimes (always) physics is just about measurement results; philosophical problems such as this are not a main concern (if a concern at all).

p.s.: We don't all believe field theory is fundamental though. If string theory / holography are correct, this space actually has a finite number of points, and wavefunctions are not that big. Still big however.