On 06-04-2022 09:01, Bruce Kellett wrote:
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,
his is a far stronger constraint than locality, it's only satisfied in
classical models with local interactions.
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.
Only true in classical physics. And this is actually going ton be used
in an experiment to demonstrate quantum gravity in an experiment. By
using gravity to create an entangled state one can prove the quantum
nature of gravity because a local classical force cannot cause
entanglement. The fact that QM is local and yet can lead to non-local
states is a crucial part of that argument.
Saibal
Bruce
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