On 24-03-2022 22:57, Bruce Kellett wrote:
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.
One can indeed write down non-local effective Hamiltonians, but the
fundamental laws of physics are strictly 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.
The fundamental Hamiltonian that also describes how the entangled state
was created, is local. It's only when you put in the entangled spinor
state in by hand that you get an effective 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.
This is wrong. The Hamiltonian is always local if it gives a full
description of all the physical degrees of freedom of a system. If you
choose to describe the dynamics of only part of a system while keeping
other degrees of freedom frozen in some state, then you'll end up with
an effective Hamiltonian that depends on that state, and that can yield
a non-local effective Hamiltonian.
Bell's theorem then serves to prove that these non-local quantum
systems cannot have a local hidden variable underpinning.
Local hidden variable theories are ruled out in general.
Saibal
Bruce
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