On 12/17/2024 3:18 PM, Bruce Kellett wrote:
On Wed, Dec 18, 2024 at 9:57 AM Russell Standish
<[email protected]> wrote:
On Tue, Dec 17, 2024 at 05:48:02PM +1100, Bruce Kellett wrote:
> The proof is fairly straightforward. Informally,
locality means
> that if we have two disjoint points, A and B,
separated by some
> distance , either spacelike or timelike, then what
happens at point
> A cannot affect what happens at point B, and what
happens at point
> B cannot affect what happens at point A. This
informal notion can
> be formalized by saying that the joint probability
for outcomes a
> at point A , and b at point B, must factorize, so
that the joint
> probability can be written as a product of two
terms, one dependent
> only on factors local to point A, and the other
dependent only on
> factors local to point B:
>
> Pr(a,b) = p(a)*p(b),
>
> once all common causal factors have been taken into
account.
>
-
>
> Thank you. That's what I thought. AG
>
>
> How is non-local defined? Does it imply instantaneous, or
faster than light
> transference of information? AG
>
>
> I defined non-local above: whatever happens at A does not affect
B and vice
> versa. It has nothing to do with faster-than-light transfer of
information. If
> there was some FTL transfer between A and B, then the effect
would be local.
> The idea that non-locality means FTL effects is a common
confusion. That idea
> is totally wrong.
>
> Bruce
It strikes me that for Bruce, "local" means factorisability of the
joint probability distribution. Which for most other people is what
"locally real" means, IIUC, ie the conjunction of a measurement
outcome depends only on physical things (reality) in the past light
cone (locality).
I thought it had been made clear that the factorization holds after
all such common causal factors had been taken into account.
Reality does not enter into it. "Reality" is usually taken to refer to
Einstein's idea of realism - namely that a state has a definite value
before any measurement.
Which is almost never the case in QM. Except for prepared eigenstates
of the measurement, states have some probabilities of values.
That idea of realism plays no role in the Brunner proof of non-locality.
I'm not saying Bruce is wrong with his definitions, but he is in
the minority AFAICT.
BTW - I'm not claiming that MWI is a locally unreal theory, but it has
been claimed by eg Deutsch. But now I see why Bruce would say that any
"locally unreal" theory is "non-local", as his definitions are
different.
I think the fact that the CHSH inequality can be derived by assuming
only factorizability as Brunner has defined it is sufficient for one
to claim that quantum mechanics is non-local in the required sense. So
any theory that reproduces the results of quantum mechanics must be
non-local. Claims by Deutsch and others that MWI is local are,
therefore, spurious. Either MWI is not a full implementation of
quantum mechanics, or it, also, is non-local.
Bruce
There's a good explication of the clash between MWI and the Born rule:
arXiv:1110.0549 On the origin of probability in quantum mechanics by
Stephen D. H. Hsu
Brent
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