On Wed, Apr 6, 2022 at 9:47 AM smitra <smi...@zonnet.nl> wrote:
> On 05-04-2022 01:24, Bruce Kellett wrote:
>
> >>> The central assumption that Bell makes is that of locality, or
> >>> separability. He shows that any local (separable) theory must give
> >>> correlations that satisfy the inequalities. Whereas QM, and
> >>> experiment, show that these inequalities are violated.
> >>
> >> Determinism is also assumed
> >
> > It is not. Bell made no such assumption. I require textual proof of
> > such a claim.
>
> Local hidden variables determine the measurement results ----> Bell's
> inequalities are satisfied.
>
You don't assume determinism to reach this conclusion. Deterministic HVs
are one possibility, and these are ruled out by the experimental results
violating the inequalities. So indeterminism remains intact. Assuming
determinism at the start would be self-defeating, and Bell was not a fool.
>> QM is not deterministic. And locality is
> >> not the same as separability.
> >
> > It is. You show me a separable system that is not local, or a local
> > system that is not separable.
>
> Locality = The dynamics if a system is local. We don't call classical
> physics non-local just because you can creater a system that exhibits
> non-local effects.
> >
> > Humean supervenience, which regards all of physics as supervening on
> > isolated local point-like objects, is local by construction. It has no
> > non-separable states by definition. The argument is simple:
> >
> > All local states are separable (By definition of locality and
> > separability).
> > Therefore non-separable states are not local. (Modus tollens)
> > Quantum mechanics embodies non-separable states.
> > Therefore quantum mechanics contains non-local states.
> >
>
You have not responded to this direct argument. I should point out that I
did not make it clear in the original presentation that I am talking about
states that are defined at two or more distinct spacetime points. If you
have everything at a single point, the distinction between locality and
separability becomes blurred. So, in more detail. We have a state defined
at two distinct spacetime points, x and y: C(x,y). If we assume Humeanism,
each spacetime point is complete and independent of all other spacetime
points. This is locality, and it means that the function C(x,y) can be
written in terms of functions at x and y separately:
C(x,y) = A(x)*B(y) or A(x) + B(y).
In other words, locality for this function means that it is separable into
distinct functions that refer only to either x or y, but not both.
This is my first premise: All local states are separable.
If the function C(x,y) cannot be split into two parts, one referring to the
point x, and one referring to the point y, it is known as non-separable. An
example is the singlet state of two spin 1/2 particles:
C(x,y) = (|+_x>|-_y> - |-_x>|+_y)/sqrt(2)
in what I hope is an obvious notation. This state is entangled and cannot
be written as a product or sum of parts referring separately to x and y.
This state is non-separable.
The modus tollens then follows directly. Showing that non-separable states
are necessarily not local.
Bruce
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