The problem with pilot wave is it’s non-local, and so it contradicts with special relativity and cannot be made directly compatible with the predictions of quantum field theory. The only way to make it compatible would be to throw out special relativity and rewrite a whole new theory of spacetime with a preferred foliation built in that could reproduce the same predictions as special relativity, and so you end up basically having to rewrite all of physics from the ground-up.
I also disagree that it’s intuitive. It’s intuitive when we’re talking about the trajectories of particles, but all its intuition disappears when we talk about any other property at all, like spin. You don’t even get a visualization of what’s going on at all when dealing with quantum circuits. Since my focus is largely on quantum computing, I tend to find pilot wave theory very unhelpful.
Personally, I find the most intuitive interpretation a modification of the Two-State Vector Formalism where you replace the two state vectors with two vectors of expectation values. This gives you a very unambiguous and concrete picture of what’s going on. Due to the uncertainty principle, you always start with limited information on the system, you build out a list of expectation values assigned to each observable, and then take into account how those will swap around as the system evolves (for example, if you know X=+1 but don’t know Y, and an interaction has the effect of swapping X with Y, then now you know Y=+1 and don’t know X).
This alone is sufficient to reproduce all of quantum mechanics, but it still doesn’t explain violations of Bell inequalities. You explain that by just introducing a second vector of expectation values to describe the final state of the system and evolve it backwards in time. This applies sufficient constraints on the system to explain violations of Bell inequalities in local realist terms, without having to introduce anything to the theory and with a mostly classical picture.
The problem with pilot wave is it’s non-local, and so it contradicts with special relativity and cannot be made directly compatible with the predictions of quantum field theory. The only way to make it compatible would be to throw out special relativity and rewrite a whole new theory of spacetime with a preferred foliation built in that could reproduce the same predictions as special relativity, and so you end up basically having to rewrite all of physics from the ground-up.
I also disagree that it’s intuitive. It’s intuitive when we’re talking about the trajectories of particles, but all its intuition disappears when we talk about any other property at all, like spin. You don’t even get a visualization of what’s going on at all when dealing with quantum circuits. Since my focus is largely on quantum computing, I tend to find pilot wave theory very unhelpful.
Personally, I find the most intuitive interpretation a modification of the Two-State Vector Formalism where you replace the two state vectors with two vectors of expectation values. This gives you a very unambiguous and concrete picture of what’s going on. Due to the uncertainty principle, you always start with limited information on the system, you build out a list of expectation values assigned to each observable, and then take into account how those will swap around as the system evolves (for example, if you know X=+1 but don’t know Y, and an interaction has the effect of swapping X with Y, then now you know Y=+1 and don’t know X).
This alone is sufficient to reproduce all of quantum mechanics, but it still doesn’t explain violations of Bell inequalities. You explain that by just introducing a second vector of expectation values to describe the final state of the system and evolve it backwards in time. This applies sufficient constraints on the system to explain violations of Bell inequalities in local realist terms, without having to introduce anything to the theory and with a mostly classical picture.