On 27-11-2024 04:48, Bruce Kellett wrote:
On Wed, Nov 27, 2024 at 2:21 PM smitra <[email protected]> wrote:
On 26-11-2024 23:27, Bruce Kellett wrote:
You are talking a lot of nonsense. I refer you to a paper by
Brunner
_et al._, Rev Mod. Phys. 86 (2014) pp.419-478.
This is also available at arxiv.org/abs/1303.2849 [1] [1]
The abstract states "Bell's 1964 theorem, which states that the
predictions of quantum theory cannot be accounted for by any local
theory, represents one of the most profound developments in the
foundations of physics."
Brunner _et al._ go on to derive the CHSH
(Clauer-Horne-Shimony-Holt)
inequality using only local dynamics, and prove that this
inequality
is violated in conventional QM, as well as in many experiments.
This
proves that quantum mechanics is intrinsically nonlocal. (If you
like,
it demonstrates that nonlocal states are intrinsic to the theory.)
And b.t.w. if there is a Bell's theorem purely about unitary QM
that
doesn't invoke hidden variables, you could just state it right
here.
I don't prove Bell's theorem here, but I have referred you to
Bell's
original papers, and also to the review article by Brunner et al.,
above. If you actually do the research for yourself, you can see
that
many authors agree with what I have been saying. You are the one
that
is out on a limb.
I have given you references here, and I have referred you to
Bell's
original papers before.. But you do talk an awful lot of nonsense.
Quote from Brunner's paper:
"To avoid any misunderstanding from the start, by “locality” we
do not mean the notion used within quantum mechanics and
quantum field theory that operators defined in spacelike separated
regions commute. Bell’s notion of locality is different and
is clarified below"
They define locality in terms of factorizability, as in their equation
3.
And if I read on to see what Bell’s notion of locality is, then,
as
expected, it involves local hidden variables.
"Let us formalize the idea of a local theory more precisely.
The assumption of locality implies that we should
be able to identify a set of past factors, described by
some variables λ, having a joint causal influence on both
outcomes, and which fully account for the dependence
between a and b. Once all such factors have been taken
into account, the residual indeterminacies about the outcomes
must now be decoupled, that is, the probabilities
for a and b should factorize:"
So, basically the standard local hidden variables framework.
Read a little more carefully. "Once all such factors have been taken
into account ....
the probabilities for a and b should factorize."
They take into account hidden variables and then it should factorize.
They only generalize a bit, the theory does not need to be
deterministic, you have a probability distribution that then expresses
the correlations as an integral over the hidden variables, which is eq,
(3).
If it were a hidden variable theory, then the probabilities for a and
b would depend on those hidden variables, and that is what is
explicitly ruled out.
No, it's not ruled out, it expicitely depends on the probability
distribution over huidden variables.
So Brunner is not using a hidden variable
theory.
It's a hidden variable theory, but not necessarily a classical
deterministic theory.
The main point is that, even taking unknown joint causal
factors into account, the probabilities at the remote ends factorize.
In other words, what happens at A does not affect what happens at B,
and vice versa. This is the notion of locality that they use to derive
the CHSH inequality -- nothing to do with hidden variables.
It's a hidden variable theory that's not equivalent to QM (when the
correlations factorize). Locality in these theories does not correspond
to locality in QM.
QM is what it is, it's a manifestly local theory when we use a local
Hamiltonian, but the theory is of a different structure than the class
of theories that correspond to our intuitions. Imposing locality in
those theories makes them unable account for correlations within QM, we
need to invoke non-local behaviors in these theories to be able to
reproduce QM. Does that mean that QM is non-local. No, because what we
did here was to replace QM by a different theory and then interpret QM
using that different theory. The proper conclusion should be that QM is
a fundamentally different theory than the class of theories in that
paper, so stochastic vatriants of classical deterministic theories don't
fit the bill either.
At the end of the day entanglement is a real phenomenon that QM has no
problems describing via only local interactions. This then naturally
leads to a Many Worlds picture, because when measuring z-components of a
singlet state, if everything is manifestly local and Alice finds spin
up, how can Bob's result now been determined to be spin down, given than
if Bob's outcome is not pre-determined before Alcie found spin up (we
know this from Bell's theorem, you don't need a violation of a Bell's
inequality in a particular experiment to conclude this for any
particular experiment), unless the two possible outcomes for Bob both
physically exist?
If you dispute that QM is local, then you still have a big problem,
because when measuring z-components of a singlet state, Alice measuring
spin up still means that Bob will find spin down, and you cannot point
to any known non-local interactions capable of explaining how Alice's
measurement instantaneously makes Bob's result physically determined.
So, your general opposition to a many worlds picture is far more your
own problem than it is for the proponents of such theories. The
proponents of MWI do face other problems, but non-locality isn't one of
them.
Saibal
Bruce
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[2].
Links:
------
[1] http://arxiv.org/abs/1303.2849
[2]
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