by **Joy Christian** » Sat Jan 18, 2020 3:13 pm

Joy Christian wrote:***

Quite independently of my above comments, let me explain why I think Bell's "theorem" is a con and the demand by the Bell-believers from a local-realistic theory is a swindle.

Consider a pair of biased coins, with some magnets inside them. They are loaded with magnets in such a way that, out of 100 tosses of the pair, both coins land on their heads 43 times and on their tails 43 times. On the other hand, the first coin lands on its head and the second coin on its tail 7 times, and the first coin lands on its tail and the second coin on its head 7 times.

In fact, we can perform an actual experiment by tossing the pair of coins 100 times and make the following table of outcomes by denoting a head as plus and a tail as minus:

First coin | Second coin

1) + | +

2) + | +

3) + | -

4) - | +

5) - | -

... etc.

This table is clearly analogous to the table of results that are supposed to have been observed by the experimentalists in Bell-test experiments. There is nothing mysterious about this table.

But does that mean that we can predict the outcomes of an individual toss of the pair, say those listed in the 4th entry above? The answer is: Yes, in principle, because, after all, the pair of coins, biased or not, is a classical deterministic system and nothing prevents us from working out the exact outcome of a toss if we knew all the variables and dynamics involved in the toss.

So far so good. But here is the swindle, or sleight of hand, that enters in the demand by the Bell-believers from a local-realistic theory. Even though it is possible in principle to predict the outcomes of the toss of the pair of coins, it is impossible in practice to predict the outcomes of a given toss despite the fact that we are dealing with a simple classical system. All we can do is predict the probabilities for the outcomes to turn out ++, --, +-, and -+ as being 43%, 43%, 7%, and 7%, respectively. It is impossible in practice to do any better than this.

Ignoring this elementary fact, among other things, is what makes Bell's "theorem" a con and a swindle.

So, just to summarize my view, the correct and legitimate demands from a local-realistic model for the singlet correlations are the following:

The measurement outcomes observed by Alice and Bob must be of the form A(

a, h) = +1 or -1 and B(

b, h) = +1 or -1, where

a and

b are the measurement directions freely chosen by Alice and Bob and "h" is a set of hidden variables or an initial state of the singlet state. Moreover, these measurement outcomes must respect the averages < A > = 0, < B > = 0, and < AB > = -

a.

b.

That is all. An example of a model that satisfies the above requirements is, of course, my quaternionic 3-sphere model:

https://arxiv.org/abs/1911.11578. It has existed since March 2007.

Note that A(a, h) = +1 or -1 and B(b, h) = +1 or -1 does not mean that we must predict whether A(

a, h) = +1 or A(

a, h) = -1 for a given run of a Bell-test experiment [and likewise for B(

b, h)]. It would be illegitimate to demand such an event-by-event prediction from a local-realistic theory for the reasons I have explained in the quoted text above.

Note also that this does not contradict what Fred is trying to do. All I am saying is that Bell-believers have no right to demand an event-by-event prediction from a local-realistic theory.

***

[quote="Joy Christian"]***

Quite independently of my above comments, let me explain why I think Bell's "theorem" is a con and the demand by the Bell-believers from a local-realistic theory is a swindle.

Consider a pair of biased coins, with some magnets inside them. They are loaded with magnets in such a way that, out of 100 tosses of the pair, both coins land on their heads 43 times and on their tails 43 times. On the other hand, the first coin lands on its head and the second coin on its tail 7 times, and the first coin lands on its tail and the second coin on its head 7 times.

In fact, we can perform an actual experiment by tossing the pair of coins 100 times and make the following table of outcomes by denoting a head as plus and a tail as minus:

First coin | Second coin

1) + | +

2) + | +

3) + | -

4) - | +

5) - | -

... etc.

This table is clearly analogous to the table of results that are supposed to have been observed by the experimentalists in Bell-test experiments. There is nothing mysterious about this table.

But does that mean that we can predict the outcomes of an individual toss of the pair, say those listed in the 4th entry above? The answer is: Yes, in principle, because, after all, the pair of coins, biased or not, is a classical deterministic system and nothing prevents us from working out the exact outcome of a toss if we knew all the variables and dynamics involved in the toss.

So far so good. But here is the swindle, or sleight of hand, that enters in the demand by the Bell-believers from a local-realistic theory. Even though it is possible in principle to predict the outcomes of the toss of the pair of coins, it is [b][i]impossible[/i][/b] in practice to predict the outcomes of a given toss despite the fact that we are dealing with a simple classical system. All we can do is predict the [b][i]probabilities[/i][/b] for the outcomes to turn out ++, --, +-, and -+ as being 43%, 43%, 7%, and 7%, respectively. It is [b][i]impossible[/i][/b] in practice to do any better than this.

Ignoring this elementary fact, among other things, is what makes Bell's "theorem" a con and a swindle.

[/quote]

So, just to summarize my view, the correct and legitimate demands from a local-realistic model for the singlet correlations are the following:

The measurement outcomes observed by Alice and Bob must be of the form A([b]a[/b], h) = +1 or -1 and B([b]b[/b], h) = +1 or -1, where [b]a[/b] and [b]b[/b] are the measurement directions freely chosen by Alice and Bob and "h" is a set of hidden variables or an initial state of the singlet state. Moreover, these measurement outcomes must respect the averages < A > = 0, < B > = 0, and < AB > = -[b]a[/b].[b]b[/b].

That is all. An example of a model that satisfies the above requirements is, of course, my quaternionic 3-sphere model: https://arxiv.org/abs/1911.11578. It has existed since March 2007.

Note that A(a, h) = +1 or -1 and B(b, h) = +1 or -1 does not mean that we must predict whether A([b]a[/b], h) = +1 or A([b]a[/b], h) = -1 for a given run of a Bell-test experiment [and likewise for B([b]b[/b], h)]. It would be illegitimate to demand such an event-by-event prediction from a local-realistic theory for the reasons I have explained in the quoted text above.

Note also that this does not contradict what Fred is trying to do. All I am saying is that Bell-believers have no right to demand an event-by-event prediction from a local-realistic theory.

***