## Is QM non-local?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: Is QM non-local?

Joy Christian wrote:The overall picture you are presenting is ontologically quite poor.

That's your opinion, but needless to say I disagree with it.
In fact I wonder what remains in your picture, if anything, as ontologically significant. One well known problem with poor ontology is the question: Why do we see the patterns in the world that we do see in the first place. They become mysterious without adequate commitment to ontology.

True, that is a problem for those who deny ontology. But not relevant for what I'm saying. I don't even know what you mean by "ontologically significant". I distinguish "information about nature" from "nature itself". Information about nature is certainly ontologically significant, but it is not ontology by itself. What you describe may apply to those who believe "there is no nature other that information". I'll use the Fermat example again to clarify what I'm saying. There are two possibilities:
a) Fermat's principle is ontological, ie photons in nature actually choose where to go based on now long it will take to get there.
b) Fermat's principle is epistemic, ie we know from observation that the path light takes happens to be the one that takes the shortest time, even though we do not know how nature accomplishes it.

The equations from both cases are identical and will result in the same accurate predictions every time. However, case (a) does not admit any other possible ontology that could account for the observation, it states categorically that there is no other ontology than the one stated -- photons some how query all possible paths, calculate how long it will take and then take the shortest one.
Case (b) on the other hand, simply uses the principle as a way to get the correct answer. In fact, case (b) does not rule out case (a). If nature was in fact doing it as stated in case (a), case (b) would still be a reasonable position to take. But it is not correct to suggest that case (b) is denying ontology or that case (b) is ontologically poor.

But I suppose these issues are now sufficiently removed from the original question posed in this thread to be called "off-topic."

On the contrary, it is very relevant. It is at the core of the Non-locality discussion. We've seen how such things can result in non-locality even in a classical principle like Fermat's. The interpretation of the Shrodinger's equation or the wavefunction is not any different and similar problems arise in the interpretation of the path-integral or pilot waves in the Bohmian interpretation, or even Huygens principle (from which Shrodinger drew inspiration). Of couse anyone is free to interpret them ontologically but paradoxes are bound to result. This is what Ed Jaynes termed the Mind Projection Fallacy.
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### Re: Is QM non-local?

Joy Christian wrote:
FrediFizzx wrote:How do your hidden variables "connect" to the Schrodinger equation?

As yet they don't, but I have some ideas about a possible connection. It is a profound problem, and I have a profound solution in mind.

It is probably not so clear cut as to how your hidden variables connect to the Shrodinger equation but there may be a more easily seen connection to the Dirac equation via the Pauli matrix algebra. The Dirac equation can actually be written two different ways.

$i\hbar\gamma^{\mu}\partial_{\mu}\psi - mc\psi = 0$

$i\hbar\gamma^{\mu}\partial_{\mu}\psi + mc\psi = 0$

So again, we have the sign ambiguity showing up. Can this be traced back to your hidden variable for the sign ambiguity via the Pauli algebra? I think we would have to actually re-arrange like so,

$mc\psi - i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

$mc\psi + i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$
FrediFizzx
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### Re: Is QM non-local?

FrediFizzx wrote:
Joy Christian wrote:
FrediFizzx wrote:How do your hidden variables "connect" to the Schrodinger equation?

As yet they don't, but I have some ideas about a possible connection. It is a profound problem, and I have a profound solution in mind.

It is probably not so clear cut as to how your hidden variables connect to the Shrodinger equation but there may be a more easily seen connection to the Dirac equation via the Pauli matrix algebra. The Dirac equation can actually be written two different ways.

$i\hbar\gamma^{\mu}\partial_{\mu}\psi - mc\psi = 0$

$i\hbar\gamma^{\mu}\partial_{\mu}\psi + mc\psi = 0$

So again, we have the sign ambiguity showing up. Can this be traced back to your hidden variable for the sign ambiguity via the Pauli algebra? I think we would have to actually re-arrange like so,

$mc\psi - i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

$mc\psi + i\hbar\gamma^{\mu}\partial_{\mu}\psi = 0$

I am not sure whether this sign ambiguity is the same as the one in the orientation of the 3-sphere I have used in my framework.

In any case, neither Schrodinger equation nor Dirac equation can be connected directly to my local-realistic framework, because both of them describe evolutions of the amplitudes of the probabilities of obtaining measurement results, not the evolutions of the probabilities themselves. Since my framework is about expectation values of obtaining joint measurement results without relying on the amplitudes like $\psi$, the best way to approach the problem is through the Ehrenfest theorem:

$\frac{d\;}{dt}\left\langle{\cal O} \right\rangle=\frac{1}{i\hbar}\left\langle\left[ {\cal O},\,H\right]\right\rangle+\left\langle{\frac{\partial{\cal O}}{\partial t}}\right\rangle,$

where ${\cal O}$ is a time-dependent operator to be "observed", $H$ is the corresponding Hamiltonion, and $\left\langle{\cal O}\right\rangle$ is the expectation value of ${\cal O}.$

http://libertesphilosophica.info/blog/
Joy Christian
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