What is the fundamental theory of quantum mechanics?

[Demystifier]

And because Decoherence is trying to clarify the process of wave function collapse,

The point is that it doesn't. Decoherence is a completely DETERMINISTIC process, which attempts to explain the ILLUSION of collapse (not a real collapse). But it cannot explain it without assuming something additional, which is not contained in the deterministic Schrödinger equation. There is no consensus about what that additional thing should be, but one possibility is that these are Bohmian particle trajectories.

 

[stevendaryl]

Bohmian Mechanics assigns a wave function of the universe (that is actually not completely true) which evolves unitarily. Since all we need for decoherence is a unitarily evolving wave function of the universe, there is decoherence in Bohmian Mechanics.

OK, let me explain why it is not completely true that Bohmain Mechanics assigns a wave function of the universe. In Bohmian Mechanics, the probability is shifted to the hidden variables, and an initial probability distribution. If we treat the initial distribution as modelling a physical ensemble, then Bohmian Mechanics has a cut, just like quantum mechanics and statistical mechanics. So the true achievement of Bohmian Mechanics is not to remove the cut, but to show the cut in a way that makes it look like the cut in statistical mechanics. Because we don't consider the cut in statistical mechanics "fundamentally mysterious", even though we still don't understand it very well, Bohmian mechanics shows that there is nothing necessarily "fundamentally mysterious" about the cut in quantum mechanics.

Here's what strikes me as weird about Bohmian mechanics (well, one of several things). You can prove that if particle positions are randomly distributed according to the Born rule, then the Bohmian dynamics implies that this connection will continue to be true.

But now consider the case of a SINGLE particle. In that case, the true distribution of particle positions is a delta-function: the particle is definitely in some particular location (you just don't know what that is). But obviously, a single particle can have a wave function that isn't a delta-function. So in this case, there is no connection between particle positions and the square of the wave function.

Maybe the answer is that in Bohm, while the wave function is objectively real, its interpretation (when squared) as a probability involves a subjective notion of probability?

 

[Demystifier]

Maybe the answer is that in Bohm, while the wave function is objectively real, its interpretation (when squared) as a probability involves a subjective notion of probability?

Yes.

 

[bhobba]

I can't see how Bohm's theory can be compatible with decoherence.

It must be, because BM is indistinguishable from the formalism of QM.

The modern version of collapse, which strictly only applies to filtering observations, is how an improper mixture becomes a proper one, which is the issue 3 mentioned previously ie the problem of definite outcomes. Since in BM particles have a definite position and trajectory it's easy to see the improper mixture is a proper one.

Thanks
Bill

 

[Demystifier]

It's not only that BM is compatible with decoherence, but decoherence is actually ESSENTIAL for BM to work. In fact, in his famous paper Bohm actually anticipated the main ingredients of decoherence, before the notion of "decoherence" in quantum physics even existed.

 

[bhobba]

It's not only that BM is compatible with decoherence, but decoherence is actually ESSENTIAL for BM to work. In fact, in his famous paper Bohm actually anticipated the main ingredients of decoherence, before the notion of "decoherence" in quantum physics even existed.

I bow to your superior knowledge of it.

Thanks
Bill

 

[stevendaryl]

It must be, because BM is indistinguishable from the formalism of QM.

The modern version of collapse, which strictly only applies to filtering observations, is how an improper mixture becomes a proper one, which is the issue 3 mentioned previously ie the problem of definite outcomes. Since in BM particles have a definite position and trajectory it's easy to see the improper mixture is a proper one.

Thanks
Bill

I'm not convinced that it's the same (BM and standard QM). In BM, the mixture is always proper, while in standard QM, measurement (or decoherence) is needed to change a pure state into a mixed state.