On 04-09-2023 01:35, Bruce Kellett wrote:
On Sun, Sep 3, 2023 at 11:37 AM smitra <smi...@zonnet.nl> wrote:
On 31-08-2023 06:08, Bruce Kellett wrote:
That is all very well, but it is not a local account of violations
of
the Bell inequalities. You merely claim that the local theory is
such
an account, but you do not spell it out.
John has addressed this in a subsequent reply where he cites an old
reply giving the detailed account involving polarizers.
I have responded to John in a separate post. He appears to have a very
weak grasp of logic, and his arguments are not valid.
Thing is that in conventional QM we only have the dynamics only
involves
the Schrödinger equation and collapse.
The Schrodinger equation is not necessary for quantum mechanics. The
Heiseberg matrix formulation does not involve the SE. Time evolution
is just a unitary transformation after all. The wave function is not
necessary. Dirac, in his book on quantum mechanics, mentions the wave
function only in an inconsequential footnote.
It's equivalent, so it doesn;t matter that there exists an alternative
formalism.
The time evolution according to
the Schrödinger equation is manifestly local,
But unitary evolution according to the SE cannot account for the
correlation of entangled particles.
It can, just calculate it and don't collapse the wavefunction. If the
parallel worlds are unobservable FAPP, then it shouldn't matter whether
or not you assume they exist or not, at least for these sorts of
practical experiments.
while the collapse is the
only non-local part. So, any version of QM in which there is no
collapse
is guaranteed to be local.
Another important thing to note here is that Bell's theorem only
applies
to hidden variable theories, it does not apply to QM in general.
Where on earth did you get that idea from? As John has pointed out,
Bell's theorem does not require even quantum mechanics. It is just a
piece of mathematics.It applies with complete generality to quantum
mechanics, with or without hidden variables.
Bell's theorem is about local hidden variables theories, it's not a
theorem of QM in the sense of something that follows from the postulates
of QM like e.g Ehrenfest's theorem. It's theorem that follows from he
assumed properties of a general local hidden variables theory and it
derives bounds on correlations. You can then consider the correlations
of certain observables in QM and see that they violate these
inequalities.
What conclusions can we draw? If we assume that QM is not fundamental
and that there exists a hidden variables theory that reproduces QM
either exactly or to a good approximation, then we can conclude that
such a hidden variables theory cannot be local.
Or we can conclude that QM is fundamental and that there is no deeper
hidden variables theory underlying QM. In this case the violation of
Bell's inequality does not imply non-locality. However, collapse is then
still a non-local mechanism.
The MWI
is not a hidden variables theory, so Bell's theorem has nothing
whatsoever to say about this.
Again, As I pointed out to John, even if you assume that Bell's
theorem does not apply to MWI (and of course it does), then it does
not follow that the theory is local. It could be non-local for reasons
unconnected with Bell's theorem.
Yes, but the only source of non-locality is collapse. Once you get rid
of collapse, the theory becomes local, because the Standard Model is a
local theory.
We have had this discussion before, and you couldn't give the
detailed
local account then either.
You disputed the well established fact that all known interactions
are
locaThat is not a well establised fact. Given the violations of the
Bell inequalitiers, the only well established fact is that standard
QM is non-local.
As pointed out above the violation of Bell's inequality only implies
non-locality in hidden variables models. Bell's theorem s a theorem
derived from the general properties of an arbitrary local hidden
variables theory and one then derives bounds for correlations.
You seem to pretend that it's a theorem of QM, in which case one would
start from the postulates of QM and derive bounds on correlations for
any system described by a local Hamiltonian. That's obviously not true.
You would not take a formal answer like
psi(x, t) = Exp(-i H/hbar t) psi(x,0)
where H is the a local Hamiltonian that describes the dynamics for
an
answer.
Of course that is not an answer. It is merely a re-stating of your
contention that QM is always local. Whether or not that Hamiltonian
formulation is able to account for the Bell-type correlations is
precisely the point at issue. Restating that the correlations do
indeed have a local explanation does not take us any further forward.
No non-local interactions have ever been demonstrated to exist.
You wanted me two explicitly write out H for a Bell-type
experiment for H a manifestly local Hamiltonian, and then to compute
the
time evolution. Me not doing that was your argument that something
non-local was going on here.
No. My argument hinges on the applicability and universality of Bell's
theorem. Your failure to provide a counterexample was merely proof
that you don't know what you are talking about.
Bell's theorem only applies to local hidden variables theories. It only
applies to QM in the sense of ruling out that if QM is not fundamental
and has an underlying hidden variables theory, that this hidden
variables theory can be local.
Bell's theorem applies in Everettian
quantum mechanics in exactly the same way as it applies in
one-world
accounts. Bell's theorem proves that the effect is non-local, so
no
local account is possible in any interpretation of QM.
Bell's theorem only applies to hidden variable theories,
Bullshit. We have disposed of that canard already.
Show me any derivation of an inequality of correlations in Bell-type
experiments that follows not from the assumption of an underlying local
hidden variables theory, but directly from only assuming local
interactions and the general postulates of QM.
As you are well aware, QM itself leads to the prediction that certain
correlations actually violate Bell's inequalities.
MWI is not a
hidden variables theory. Bell's theorem does not even prove that
Bell-type correlations are non-local in one-world interpretations of
QM.
Until that time one postulates hidden variables, Bell's theorem has
nothing whatsoever to say about this.
Even if Bell's theorem does not apply, there is no reason to suppose
that the theory is local, since no classical account of the
correlations is possible.
Classical mechanics has been falsified a long time ago. It's irrelevant
that no classical account of correlations is possible.
Saibal
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/b3686f0bfeada1cf4e9fba823d58b8c3%40zonnet.nl.
