Bell's theorem refuted via elementary probability theory

[Gordon Watson]

I just looked at Bell 1964. He explicitly gives the analytical solution for your functions. It is a linear function of theta (difference of the settings angles), just as my simulation shows.

Would you like to try again with a new set of functions?

Sure.



and

.

Gordon
.

[local]

I suggest you try to get your work published. Good luck!

[Gordon Watson]

I suggest you try to get your work published. Good luck!

You said that before.

Then you integrated Bell's well-known failed attempt to find A(a,λ) and B(b,λ).

Then you asked: Would I like to try again with a new set of functions?

So I said, "Sure." And gave you two functions that do not fail.

Me, of course, hoping that their similarity to Bell's failed functions might be of interest.

So, for the record, here they all are again:

Bell's failed functions: A(a,λ) = sgn and B(b,λ) = -sgn.

My successful functions, which equate to the functions , etc., previously provided:

and

with .

Hint: Here's the expectation that I derive: , which is (under β) the weighted average of the possible results, weighted according to their probabilities.

HTH; Gordon

[local]

Please let us know when your analysis passes peer review and is published. Your new mathematical technique of integrating an equivalence relation will surely cement your place in history.

[Austin Fearnley]

Gordon Watson » Mon Nov 16, 2020 4:13 pm

I do not program

You could use a spreadsheet or, failing that, a calculator? Just use a= 0 and b= pi/4.

Gordon Watson » Mon Nov 16, 2020 7:58 pm

3. So you can get to one-half the QM result? Malus (C1810) could do that experiment and the calculation: if requested.

[He could also, in a related experiment, simulate the QM result: if he'd been asked!]

So if Malus can readily get one-half the QM result, how come you cannot see that a better source [beyond the then available technology] gives a better correlation today?

Malus's Law depends on the incoming beam to be already polarised. Polarised particles are not assumed in a Bell experiment.
In my model the Bell correlation is caused by polarised particles which are in turn are caused by retrocausality. IMO you need both retrocausality and polarisation in order to get the Bell correlation in a Bell experiment.

Unpolarised particles have a random distribution of spin directions so that (as in local's computer run) a= 0 and b= pi/4 gives correlation 0.5 (rather than the Bell correlation of 0.707).

[local]

The photon based experiments use polarized photons.

[Austin Fearnley]

Aha.

Well, I did say that the retrocausality was needed as well as polarisation.
Polarisation on its own is not enough.
The retrocausality in my model ensures that the particles (note, not the antiparticles) are polarised in the appropriate directions.
So Alice measures electrons which have previously been polarised in the direction of Bob's setting. That is the setting Bob used when the paired positron was measured. (Tenses are strange as Alice and Bob are measuring the particle-antiparticle pair simultaneously yet retrocausality means that the positron has had an eventful time in between the two simultaneous measurements.)
And, just to avoid Richard criticising lack of symmetry, Bob measures electrons polarised in the direction of Alice's detector settings.

So it has to be a specially-guided polarisation and not any random polarisation.

[Gordon Watson]

The photon based experiments use polarized photons.

Which experiments are you referring to?

Gordon
.

[Gordon Watson]

Gordon Watson » Mon Nov 16, 2020 4:13 pm

I do not program

You could use a spreadsheet or, failing that, a calculator? Just use a= 0 and b= pi/4.

Gordon Watson » Mon Nov 16, 2020 7:58 pm

3. So you can get to one-half the QM result? Malus (C1810) could do that experiment and the calculation: if requested.

[He could also, in a related experiment, simulate the QM result: if he'd been asked!]

So if Malus can readily get one-half the QM result, how come you cannot see that a better source [beyond the then available technology] gives a better correlation today?

Malus's Law depends on the incoming beam to be already polarised. Polarised particles are not assumed in a Bell experiment.
In my model the Bell correlation is caused by polarised particles which are in turn are caused by retrocausality. IMO you need both retrocausality and polarisation in order to get the Bell correlation in a Bell experiment.

Unpolarised particles have a random distribution of spin directions so that (as in local's computer run) a= 0 and b= pi/4 gives correlation 0.5 (rather than the Bell correlation of 0.707).

1. Thanks Austin, re the spreadsheet suggestion. If you are interested in simulating the EPRB experiment, etc., get in touch.

2. You are right; I should have been clearer. I left it understood that Malus' work relied on polarised light-beams.

3. Re your model. I see no need for retrocausality.

4. As for the need for polarisation to get the Bell correlation: I trust you realise that the detectors are polariser-analyzers.

Thus the unpolarised particles are polarised via the polariser and detected by the analyser (which publishes the result ±1).

So I suggest that your model needs to reflect this 2-step process. Further: In my view, NO hidden parameters, other the natural physical quantities of the experiment, are needed.

See my definition of true local realism; also, the schematics in eqns (7)-(9) in my last draft.

HTH. Thanks again; Gordon

[local]

Which experiments are you referring to?

When people ask me basic questions that they could easily answer for themselves using available resources, I quote my consulting rate of $300 per hour. Send a PM if you are interested. It's also stunning, but not surprising, that you know so little about the field.

Maybe Richard or another member will indulge you.

[Austin Fearnley]

Gordon Watson » Thu Nov 19, 2020 2:57 pm
...
4. As for the need for polarisation to get the Bell correlation: I trust you realise that the detectors are polariser-analyzers.

Thus the unpolarised particles are polarised via the polariser and detected by the analyser (which publishes the result ±1).
...

Not clear why you think I have it wrong.
Start with a Malus experiment using two polaroid sunglasses filters.
Let Alice have the first polarised filter.
She pre-polarises the beam along angle alpha and it travels on to Bob.
Bob uses the second polarised filter set at an angle beta and makes a measurement.
The intensity measured by Bob conforms to Malus's Law.

So the Malus experiment needs two polarising filters. One at the beginning and one at the end.
This is very similar to what is happening in my retro model for Bell.

Alice pre-polarises positrons.
Entanglement forces paired electrons to have the same polarisation as Alice's positrons.
Bob subsequently uses a polariser to measure these electrons.

And that is half of the Bell experiment which is equivalent to a single Malus experiment.

Interchange Alice and Bob and repeat to give the second Malus experiment.
Combine the two Malus experiments to give a whole Bell experiment.

[Gordon Watson]

Gordon Watson » Thu Nov 19, 2020 2:57 pm
...
4. As for the need for polarisation to get the Bell correlation: I trust you realise that the detectors are polariser-analyzers.

Thus the unpolarised particles are polarised via the polariser and detected by the analyser (which publishes the result ±1).
...

Not clear why you think I have it wrong.
Start with a Malus experiment using two polaroid sunglasses filters.
Let Alice have the first polarised filter.
She pre-polarises the beam along angle alpha and it travels on to Bob.
Bob uses the second polarised filter set at an angle beta and makes a measurement.
The intensity measured by Bob conforms to Malus's Law.

So the Malus experiment needs two polarising filters. One at the beginning and one at the end.
This is very similar to what is happening in my retro model for Bell.

Alice pre-polarises positrons.
Entanglement forces paired electrons to have the same polarisation as Alice's positrons.
Bob subsequently uses a polariser to measure these electrons.

And that is half of the Bell experiment which is equivalent to a single Malus experiment.

Interchange Alice and Bob and repeat to give the second Malus experiment.
Combine the two Malus experiments to give a whole Bell experiment.

You are describing two Malus' experiments that, together, do not represent Aspect's Bell-experiment.

In your first experiment, Alice's polarised particle somehow gets sent to Bob. In a Bell-test it instead goes to Alice's analyser AND Bob tests its pristine (thus unpolarised) twin that has been nowhere near Alice.

Vice-versa in the second experiment.

HTH, Gordon

[Austin Fearnley]

Gordon wrote
You are describing two Malus' experiments that, together, do not represent Aspect's Bell-experiment.

In your first experiment, Alice's polarised particle somehow gets sent to Bob. In a Bell-test it instead goes to Alice's analyser AND Bob tests its pristine (thus unpolarised) twin that has been nowhere near Alice.

Vice-versa in the second experiment.

Yes, it needs two retrocausal Malus experiments to make one retrocausal Bell experiment.

I will flesh out the retrocausal aspect.
Set the particle pathways inside a Feynman diagram.
The positrons travel backwards in time in the diagram (though this is generally considered to be a mathematical convenience).
So a Bell experiment, for a given particle pair, starts with the measurement of the positron and ends with the measurement
of the partner electron. Alice and Bob see this as instantaneous but the positron does a lot of travelling in between the two simultaneous measurements.
The positron has travelled from outside the experiment and is then measured by (say) Alice using an S-G detector.
The positron is polarised along spin direction + or - alpha when it leaves Alice and heads towards the (supposed) Source.
At the Source the positron passes its spin momentum to its partner electron.
So the electron travels forwards in time to Bob. This electron is polarised in the spin direction - or + alpha.
Bob then measures the electron with his S-G set at an angle beta.
So this corresponds to a communications loophole.

Gordon wrote
In your first experiment, Alice's polarised particle somehow gets sent to Bob. In a Bell-test it instead goes to Alice's analyser AND Bob tests its pristine (thus unpolarised) twin that has been nowhere near Alice.

OK, but you are describing the normal scenario which is not retrocausal. It does not happen in this way in my retrocausal interpretation.

[jreed]

OK, but you are describing the normal scenario which is not retrocausal. It does not happen in this way in my retrocausal interpretation.

You should read up on interpretations of quantum mechanics. What you are calling "your" interpretation is what is known as the Transactional Interpretation and has been around for some time.

[Austin Fearnley]

by jreed » Fri Nov 20, 2020 10:47 am

Austin Fearnley wrote:

OK, but you are describing the normal scenario which is not retrocausal. It does not happen in this way in my retrocausal interpretation.

You should read up on interpretations of quantum mechanics. What you are calling "your" interpretation is what is known as the Transactional Interpretation and has been around for some time.

Ok, but I did include the following two references in my paper.

7. Feynman’s Thesis. A New Approach to Quantum Theory. L. M. Brown (2005) World
Scientific
8. Wheeler–Feynman absorber theory.
https://en.wikipedia.org/wiki/Wheeler%E ... ber_theory

I agree with the approach of advanced and retarded waves. And the need of a particle to know where it is going before it is emitted (which I believe is part of superdeterminism). I have not found any clear setting out in practical terms of the solution that I have found. Please point out any similar method explained practically (I get downhearted reading purely philosophical expositions of retrocausality).

I have seen Feynman's Thesis and know that the advanced wave is to cater for an instantaneous kick of some kind at the moment of emission. And an advanced wave from the absorber can provide such an instantaneous kick. I am dubious about this explanation as IMO the emission of a photon from an electron is misunderstood. IMO a higgs particle/field (a hypothetical light higgs) is needed to initiate the emission. The weak isospin of the higgs is also needed to add or subtract the weak isospin which is not conserved in the SM interaction. I also do not like the idea of spontaneous emission. The higgs involvement can remove the spontaneity.

Nevertheless, my preon model does use advanced and retarded waves. It definitely uses preons and antipreons and that is one step from assuming antipreons travel backwards in time.
In my model, the universe has an arrow of time given by entropy. But the electrons and positrons are free to have their own arrows of time. So a positron can travel backwards in time literally in a Feynman diagram.
In a fractal sense, the electron has its own time arrow caused by entropy within the electron, but the electron also has forwards and backwards-in-time elements (preons) within it.
My preon model has the electron composed of three forwards-in-time preons and one backwards-in-time preon. And vice versa for the positron.
I use this structure to tell myself that although the electron travels forwards in time, it contains the forwards and backwards-in-time waves necessary for every particle to form a handshake in Feynman's thesis. But the electron's forwards-in-time entropy is of a different nature to the preon entropies within it.
So IMO the universe's arrow of time is independent of the positron's arrow of time. They are different things and the existence of the former should not debar the latter.

My paper also includes a computer program listing which can be used to generate Malus Law intensities, or S_G detector intensities, generated particle at a time using local hidden variables.

I am currently writing a further paper to bring more of this together, and I will be sure to mention the terms Transactional Interpretation.

[Gordon Watson]

Gordon wrote
In your first experiment, Alice's polarised particle somehow gets sent to Bob. In a Bell-test it instead goes to Alice's analyser AND Bob tests its pristine (thus unpolarised) twin that has been nowhere near Alice.

OK, but you are describing the normal scenario which is not retrocausal. It does not happen in this way in my retrocausal interpretation.

Austin, three short notes:

1. In Bell (1964), Bell relies on his inequality -- Bell 1964:(15) -- for proof of his theorem. As I show in my draft, Bell 1964:(15) is readily refuted by nothing more than high-school math.

2. jreed has given you a good pointer to a further theory similar to your own. Here's another:

http://prce.hu/w/preprints/QT7.pdf

Abstract. Bell’s theorem requires the assumption that hidden variables are independent of future measurement settings. This independence assumption rests on surprisingly shaky ground. In particular, it is puzzlingly time-asymmetric. The paper begins with a summary of the case for considering hidden variable models which, in abandoning this independence assumption, allow a degree of ‘back-ward causation’. The remainder of the paper clarifies the physical significance of such models, in relation to the issue as to whether quantum mechanics provides a complete description of physical reality.

3. I suspect your theorising is heading toward the "backward causation" family of theories: which may have begun with the late Olivier Costa de Beauregard (said to be Louis de Broglie's star pupil)?

HTH, but suggesting that you first get past my elementary refutation of Bell 1964:(15);

Gordon

[Austin Fearnley]

Thanks Gordon. I will follow up your references on retrocauality and similarly for those of jreed. I do not like what I have read on retrocausality so far, except in a very general way, but the path I have taken seems to be the same way.

Now for Bell's Theorem which you say I should start with. Local's computer print out is a perfect place to start. It shows that for a=0 and b= approx 45 degrees then Bell correl = approx 0.5. If you have better functions for A and B then try them out to try to achieve correl= - 0.707.

Not using computers is a handicap in this. My own favourite subject was pure maths. But then I took on statistics. And subsequently computing. I learned statistics in the late 60s before computers were generally available. But we managed using paper and pen. And log tables, though engineers preferred slide rules. And the Brunsviga mechanical calculators where to divide you had to whirl (for each and every decimal place calculation) the rotor arm until a bell rang. Then you had to reverse the rotor arm twirl direction a few times. And to perform a square root on the Brunsviga was even more exotic. As a student, to understand that SQRT method better I learned how to calculate square roots and then cube roots by hand.
Using a Brunsviga then makes me appreciate now the convenience and computing power of desktop PCs. From the early 70s, I had access to a mainframe computer using Fortran.

But you could just take a=0, b=45 and p=30 (p for particles) and work out by hand the numerical value of your A and B functions for that one pair of particles.

By Bell's Theorem in normal 3D space using local hidden variables and no loopholes, you will not find functions to give correl = 0.707. Well, I have never managed it and I tried quite a few times using the speed and convenience of modern computers.

A second place to look is the quantum Randi challenge. That shows you that formulae for A and B cannot be deterministic. That is, for a=0 and b=45 degrees the formula for say A must have a random element such that the outcome is sometimes +1 but, on other occasions, the same formula [for the same inputs of a, b and p] yields the outcome -1. So counterfactual determinism does not hold.

So my own retrocausal method does use a random element in the A and B functions. I think of that as the particle always having a (polarisation or gyroscopic) average direction to point at but the direction can [somehow ...] vary systematically, such as by precession, within that overall average direction. I worked out the formula for that statistical envelope of directions by reverse engineering from Malus's Law. So I am using a classical solution.

I do not really have any interest in finding for myself a theoretical proof or disproof of Bell's Theorem since I accept computationally that correl -> 0.5 and not 0.707 when using counterfactual determinism and deterministic formulae for A and B.

[local]

But you could just take a=0, b=45 and p=30 (p for particles) and work out by hand the numerical value of your A and B functions for that one pair of particles.

GW doesn't have any functions so he can't do that. Earlier, he did present some but they turned out to be Bell's functions that do not integrate to -a.b. Then he pretended not to have suggested them and subsequently called them "Bell's failed functions". All we have now from him is some 'functions' presented in unintellible notation that only he claims to understand and seemingly requiring us to integrate statements of equivalence relations, which is totally nonsensical, among other incoherencies. Don't hold your breath waiting for actual functions that can be used to generate real outcomes.

And don't forget that he earlier claimed that his proof obtains -a.b independent of the outcome functions. Now he equivocates about that and won't give a direct answer about it.

I've concluded that he is a troll. A more charitable interpretation is that he made a sign error in his first proofs and is now unable to complete the proofs with that corrected, and he's too embarrassed to confess. Either way, I suggest you don't waste any more time with him, Austin.

[Gordon Watson]

Thanks Gordon. I will follow up your references on retrocauality and similarly for those of jreed. I do not like what I have read on retrocausality so far, except in a very general way, but the path I have taken seems to be the same way.

Now for Bell's Theorem which you say I should start with. Local's computer print out is a perfect place to start. It shows that for a=0 and b= approx 45 degrees then Bell correl = approx 0.5. If you have better functions for A and B then try them out to try to achieve correl= - 0.707.

Not using computers is a handicap in this. My own favourite subject was pure maths. But then I took on statistics. And subsequently computing. I learned statistics in the late 60s before computers were generally available. But we managed using paper and pen. And log tables, though engineers preferred slide rules. And the Brunsviga mechanical calculators where to divide you had to whirl (for each and every decimal place calculation) the rotor arm until a bell rang. Then you had to reverse the rotor arm twirl direction a few times. And to perform a square root on the Brunsviga was even more exotic. As a student, to understand that SQRT method better I learned how to calculate square roots and then cube roots by hand.
Using a Brunsviga then makes me appreciate now the convenience and computing power of desktop PCs. From the early 70s, I had access to a mainframe computer using Fortran.

But you could just take a=0, b=45 and p=30 (p for particles) and work out by hand the numerical value of your A and B functions for that one pair of particles.

By Bell's Theorem in normal 3D space using local hidden variables and no loopholes, you will not find functions to give correl = 0.707. Well, I have never managed it and I tried quite a few times using the speed and convenience of modern computers.

A second place to look is the quantum Randi challenge. That shows you that formulae for A and B cannot be deterministic. That is, for a=0 and b=45 degrees the formula for say A must have a random element such that the outcome is sometimes +1 but, on other occasions, the same formula [for the same inputs of a, b and p] yields the outcome -1. So counterfactual determinism does not hold.

So my own retrocausal method does use a random element in the A and B functions. I think of that as the particle always having a (polarisation or gyroscopic) average direction to point at but the direction can [somehow ...] vary systematically, such as by precession, within that overall average direction. I worked out the formula for that statistical envelope of directions by reverse engineering from Malus's Law. So I am using a classical solution.

I do not really have any interest in finding for myself a theoretical proof or disproof of Bell's Theorem since I accept computationally that correl -> 0.5 and not 0.707 when using counterfactual determinism and deterministic formulae for A and B.

Austin, you raise several interesting matters.

1. To be clearer re this: "Now for Bell's Theorem which you say I should start with."

My suggestion was to start with my refutation of Bell's proof. That is, Bell (1964) relies on his famous inequality Eqn (15).

Via high-school math, I show that his inequality, Eqn (15, is false. [Which does not prove his theorem false, but is a good pointer the the fact that it may be. So I go on to show that it is!]

2. As I understand it, the Quantum Randi challenge prevents/forbids me from using an element of physical reality that I take to be at the heart of the matter.

3. #2 is on the back burner for now.

4. Note that you in someways seem close to the "true realism" component of my core principle of true local realism (TLR). TLR is the union of true locality (or relativistic causality: no influence propagates superluminally, after Einstein) and true realism (or non-naive realism: some existents change interactively, after Bohr).

5. I see no reason to abandon TLR

6. NB: I accept all the results of quantum theory. Where you do not accept such: there we differ.

Cheers; Gordon

[Austin Fearnley]

Gordon

It has been pointed out to me privately that, not for the first time, I have referred to counterfactual determinism when the proper term is counterfactual definiteness. My apologies.

I dislike the terms local and realism. My own image of my model has it as being both local and real as long as I view the universe as the block universe. So I can wander anywhere (in my imagination) in the block universe, set within a Feynman diagram, travelling forwards in time along particle paths and backwards in time along antiparticle paths. Every particle path is accessible in an analytical manner.

I am reasonably happy with QM but there are a few places where I see it as wrong. In particular I see the emission of a photon differently to that in the Standard Model. I have my doubts about QFT wrt locality. How do annihilation and creation operators sit wrt locality. A magician puts a frog into his hat (annihilates it) and then magically pulls out a rabbit (creates it). Locality? On the other hand I do like the QFT maths (as performed/explained by Susskind) of these operators.

I have no more advice to give, and I have no wish to read formal proofs or disproofs of Bell's Theorem as I have already moved on to find where the loophole lies.

Best wishes.