Collapse of the Wave Function?

I'm not sure if this question has been answered before, but I didn't find it in the long list of already-answered questions. Maybe I just missed it. If it has already been answered, then just send me a link to the answer. Thanks. Here's the question:In the Afterword of David Griffith's "Introduction to quantum mechanics" (1994), it is mentionned that Bell's theorem proved that "no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics". According to Griffith, this pretty much put an end to local realism.Now, in special relativity, Einstein proved that the kinetic energy K of an object of mass m at velocity v was (not easy to write this without Math ML, but you know what I'm talking about):K = (m*c^2 / (1-v^2/c^2)^.5 ) - m*c^2which was drastically different from Newton's K = m*v^2/2. However, the Taylor series expansion of Einstein equation shows that the first term of the expanded series is indeed m*v^2/2, showing that the 2 equations converge at v = 0 and diverge as v increases.The difference between the 2 equations didn't add any new local or non-local variables (c being a constant, not a variable), so my question is: is it possible that Schrodinger's equation is not only incomplete, but simply wrong, and a revised equation could predict, for example, the wave function collapse without adding any hidden variable, just like Einstein did with special and general relativity versus Newton's equations.After all, Schrodinger partial differential equation can only be solved using various approximations, so these approximations could also be wrong (even though they've been proven right most of the time, but then again Newton's equation were also "right" most of the time).My guess is that Im not the first person to raise that question. Has there been any research in the subject?Thank you.
- Simon (age 44)
British Columbia, Canada

Great question. FIrst, let's clarify the implications of the Bell Inequalities. They actually make no mention whatsoever of any form of quantum mechanics. They purely concern the necessary consequences of non-conspiratorial local realism. Nature consistently violates those necessary consequences. Therefore any form of non-conspiratorial local realism must be false.

Now we're ready to turn to quantum mechanics. The sort of modifications of the Schrödinger equation (or, more properly, of relativistic quantum field theory) that you are wondering about have been considered for a long time. The go by the name of "macro-realism." Some of the best known ideas are due to Ghirardi, Rimini, and Webwer and to Phillip Pearle. Since the first versions of these were local realist ideas, they cannot succeed. Pearle in particular has been working on ideas that are non-local, but I think he would agree that they have not yet succeeded either. I once published another toy idea for modifying QFT in a non-linear way, but it too has problems.  

So it remains conceivable that some modification of QFT will solve the measurement problem. The sorts of ideas that you're thinking about, however, are local in our ordinary spacetime, and they cannot work.

Mike W.

(published on 12/22/2015)