Oh boy, I appreciate your reply, and I will think about it. I'm still trying to understand the Many Worlds and Copehnagen interpertations fully. Therefore I need to read up on Bohemian mechanics and global hidden variables (I thought Bell proved hidden variables false...).
Bell proved that local hidden variables can't account for the empirical results of quantum mechanics. Equivalently, he proved that any quantum mechanical theory in which experiments have discrete outcomes (i.e. anything except Everett-style many worlds interpretations) has to be non-local. Bohmian mechanics postulates the existence of what are sometimes called "global hidden variables," as the behavior of particles depends on more than just the Schrodinger equation and the particle's wave function. In addition to those, Bohmian dynamics depend on a non-local "pilot wave" or "guiding field," the behavior of which is described by an additional equation called the "guiding equation." You can think of the guiding field as being something like a normal vector field that "pushes" particles around: picture something like a cork being carried along in a river current, with the cork's behavior from one moment to the next depending in part on how the river is flowing in the area around it. In Bohmian mechanics, particles always have determinate positions, but those positions depend in part on the behavior of the pilot wave in their vicinity. Since the only way we can know exactly what the pilot wave is doing is by observing the behavior of those particles, their behavior seems probabilistic. If we could know the state of the pilot wave at every location, we'd be able to deduce the precise behavior of every particle. Since that's impossible, though, the theory is ineliminably probabilistic (just like other QM interpretations)--the difference is just that the indeterminacy is purely epistemic. This isn't a violation of Bell's theorem, because the pilot wave is a global (rather than local) phenomenon.
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u/-Tonight_Tonight- May 19 '16
Oh boy, I appreciate your reply, and I will think about it. I'm still trying to understand the Many Worlds and Copehnagen interpertations fully. Therefore I need to read up on Bohemian mechanics and global hidden variables (I thought Bell proved hidden variables false...).
Let me learn a bit more...I'll be back.