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 mustgivecorrelations that satisfy the inequalities. Whereas QM, and experiment, show that these inequalities are violated.Determinism is also assumedIt is not. Bell made no such assumption. I require textual proofofsuch 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 alocalsystem 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 superveningonisolated local point-like objects, is local by construction. Ithas nonon-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

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