Note local hidden variables is impossible. The pilot wave theory is the theory of "hidden variables" that led Bell to his theorem. Basically, EPR shows that either nature is nonlocal or there were hidden variables. Bell showed that hidden variables had to have something nonlocal about them. So Einstein created relativity and helped to highlight how nature has an aspect that seems incompatible with it (basically, there is a "now" which, however, may be undetectable and is not our "now").
For those curious, the nonlocal hidden variables are the positions of the particles. Very hidden. So hidden, they are the only thing we see in experiments!
The particles are guided by the wave function. This resolves all the weird paradoxes such as Schrodinger's cat. It provides a great way to understand and investigate nonlocality, spin, identical particles, etc. in a very precise theory that even has broadly applying existence and uniqueness of solution theorems, unlike classical mechanics.
Hi! I'm a mathematician, I've always been curious about physics, but I've never understood some of the concepts of QM, such as what is "observation" in the Schrodinger's cat paradox, why QM means the universe is not deterministic, why hidden variables cannot exist, ... mostly because every physicist that I was able to talk to has been unable to properly explain these concepts. Do you know any books/articles/sources about QM that could understand these concepts, without going in unnecessary mathematical and physical details (i.e. using the least physics and mathematics necessary to explain the paradoxes of QM)?
Tough question. The reason you probably did not understand them is that there are reasons are faulty.
The textbook QM says that when experiments happen, the continuous wave function evolution stops and a new wave function is used in its place, chosen randomly based on a prescription using probabilities coming from the original wave function's decomposition in terms of an operator's (matrix) eigenvalues. This is a postulate in their view and that's that.
It makes no sense since what is an observation? They don't explain. They just know it. They use it when doing their experiments and it works well enough. Attempting to formalize it leads to wrong conclusions.
Bohmian mechanics/pilot wave theory is a deterministic, hidden variable theory that works. Within that context, you can understand the rise of operators as observables and the entire collapse rule which turns out to be a convenient approximation to reality in this theory; no actual collapse occurs. There is just one wave function on configuration space (3n dimensional space, n being the number of particles in the universe) evolving continuously via Schrodinger's equation and the particles themselves being guided by the wave function. It is the configuration space for the wave function where nonlocality arises from. Understanding its role in relation to relativity is the key question to understand.
The wave function evolves with lots of its branches being irrelevant which is why we can effectively get rid of them, i.e., collapse the wave function.
I have read it and I must have missed the part you refer to. He was a strong proponent of pilot-wave theory though towards the end he also started to like GRW which itself consists of two distinct ontological possibilities.
In as much as QM makes predictions, pilot wave theory makes the same predictions. But pilot wave theory has the advantage of being an honest theory that actually does make predictions. QM suffers from needing an external agent to collapse the system, an agent that is never specified, particularly on the universal level. Bell puts it very eloquently about whether one needed to wait for the first form of life to do it or perhaps one with a PhD to collapse the universe. He concludes it must be happening more or less all the time and that the mechanism needs to be explained in the theory. We can either change Schrodinger's equation as in GRW or we can add additional variables such as positions of particles as in pilot wave theory. Or we need to accept that most of reality is unlike our actual experience of a single reality such as in many worlds.
For those curious, the nonlocal hidden variables are the positions of the particles. Very hidden. So hidden, they are the only thing we see in experiments!
The particles are guided by the wave function. This resolves all the weird paradoxes such as Schrodinger's cat. It provides a great way to understand and investigate nonlocality, spin, identical particles, etc. in a very precise theory that even has broadly applying existence and uniqueness of solution theorems, unlike classical mechanics.
http://plato.stanford.edu/entries/qm-bohm/