On Fri, Mar 25, 2022 at 7:33 AM smitra <smi...@zonnet.nl> wrote:

> On 23-03-2022 02:11, Bruce Kellett wrote:
> >
> > Well, these results certainly show that some work needs to be done if
> > you are to recover a completely local theory.
> >
> The unitary time evolution in QM is local. There is only an issue with
> collapse, as the mechanism for this is usually left unspecified. But
> apart form the issues with collapse QM is a local theory.

OK. I see now that your insistence that QM is local is based on dogma,
rather than logic. Your claim is that the unitary time evolution in QM is
local, therefore QM is a local theory, regardless of anything else. But
that position relies on another hidden assumption. The unitary time
evolution of QM depends on the Hamiltonian. The Hamiltonian is not given by
the theory; it is constructed according to the details of the system one is
attempting to model. Generally, one is modelling local systems, so one uses
a local Hamiltonian and the time evolution is local. But this is by no
means necessary. One could always use a non-local Hamiltonian, then the
time evolution would not be local.

This is the situation with the entangled spinor case. The state vector is
non-separable and does not specify any particular separation for the two
entangled particles. If one wants to continue to treat this as a single
system even when the particles are far apart, one must use a non-local
Hamiltonian. That is, a Hamiltonian that has a component for each of the
particles. Since these particles are, in general, spacelike separated, the
requisite Hamiltonian is non-local.

So your assertion that quantum mechanics is local because unitary time
evolution is local is false. Unitary time evolution can be local or
non-local, depending on the circumstances. Non-separable entangled states
are one of those circumstances in which QM is necessarily non-local.

Bell's theorem then serves to prove that these non-local quantum systems
cannot have a local hidden variable underpinning.


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