No spooky action at a distance

[FrediFizzx]

Here is a spec for a program calculating conditional probabilities:

HV model for the singlet state

Code: Select all

Program for Spin1:
1.   Theory
•   Boundary conditions: photon pairs 0 ° / 90 ° and 90 ° / 0 ° in equal shares.
•   Photons A and B of a pair have the same property Lambda
•   Set polarizer PA to alpha and polarizer PB to beta
•   (alpha and beta between 0 and 180°)
•   Polarizer A selects A-photons with p-state alpha
•   This selection means a selection of the associated B-photons in p-state alpha+pi/2
•   Polarizer B selects B-photons with p-state and polarization beta.
2.   CountA := countB := 0
3.   n:=1000
4.   deltaA := beta – alpha -pi/2

photon pair 0°/90°
5.   deltaB := beta – pi/2
6.   For i= 0,n,1
7.   Lambda := i/n
8.   Call Hit(ResultB,deltaB,lambda,countB,1)
9.   If ResultB=1 then
10.   Call Hit(ResultA,deltaA,lambda,countA,1)
11.   End loop 6

photon pair 90°/0°
12.   deltaB := beta
13.   For i= 0,n,1
14.   Lambda := i/n
15.   Call Hit(ResultB,deltaB,lambda,countB,-1)
16.   If ResultB=1 then
17.   Call Hit(ResultA,deltaA,lambda,countA,-1)
18.   End Loop 13

19.   Conditional Probability P = CountA / CountB


Program for Spin1/2:
20.   Theory
•   Boundary conditions:
particle pairs with spin 0 ° / 180 ° and 180 ° / 0 ° in equal shares.
•   Particles A and B of a pair have the same property Lambda
•   Set SGA (Stern Gerlach A) to alpha and SGB to beta
•   (alpha and beta between 0 and 180°)
•   SGA selects A-particles with p-state alpha
•   This selection means a selection of the associated B-particles in p-state alpha+pi
•   SGB selects B-particles with p-state and spin beta.

21.   CountA := CountB := 0
22.   n:=1000
23.   deltaA := beta/2 – alpha/2 -pi/2

particle pair spin 0°/180°
24.   deltaB := beta/2 - pi/2
25.   For i= 0,n,1
26.   Lambda := i/n
27.   Call Hit(ResultB,deltaB,lambda,countB,1)
28.   If ResultB=1 then
29.   Call Hit(ResultA,deltaA,lambda,countA,1)
30.   End loop 25

particle pair spin 180°/0°
31.   deltaB := beta/2
32.   For i= 0,n,1
33.   Lambda := i/n
34.   Call Hit(ResultB,deltaB,lambda,countB,-1)
35.   If ResultB=1 then
36.   Call Hit(ResultA,deltaA,lambda,countA,-1)
37.   End Loop 32

38.   Conditional Probability P = CountA / CountB





a.   Subroutine: Hit(Result,delta,lambda,count,ind)
b.   Result=-1
c.   If delta <0 then delta = delta+pi
d.   If ind=1 then
e.   If 0<delta<pi/2 or pi<delta<3/2pi then
f.   If lambda <cos2 (delta) Then set Result := 1 and count := count + 1
g.   Exit
h.   Else
i.   If lambda >sin2 (delta) Then set Result := 1 and count := count + 1
j.   Exit

k.   If ind= -1 then
l.   If 0<delta<pi/2 or pi<delta<3/2pi then
m.   If lambda > cos2 (delta) Then set Result := 1 and count := count + 1
n.   Exit
o.   Else
p.   If lambda <sin2 (delta) Then set Result := 1 and count := count + 1
q.   Exit
r.   end

That doesn't look exactly like what you have in your paper. Lambda is not really random in the code above.
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[jreed]

That doesn't look exactly like what you have in your paper. Lambda is not really random in the code above.
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That's right Fred. I started to program it up, but it doesn't look like any simulation I've seen. No random variables.

[Esail]

There is a mathematical theorem informally stated by John Bell and since then expressed in formal mathematical terms by many scholars,

Bell has stated his theorem in his own words: “In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant.” In other words, Bell says, nature is not local as it cannot be described with local realistic models.

Bell's theorem is not a mathematical theorem but a statement about nature. The mathematics to derive the Bell inequality is not in question. Physically he only took into account noncontextual models. Insofar it is possible that a contextual model correctly predicts spin measurement results. Such a model has been presented.
By the way, analytic scientific models don't need to be proved by computer simulation. This is so since science exists. They can be assessed by analytical inspection and refuted by presenting counterexamples. Nonetheless, I have presented a computer program spec.

[Esail]

That doesn't look exactly like what you have in your paper. Lambda is not really random in the code above.
.

Lambda covers the range 0<lambda<1. It is quite a random variable. The order of the calculation does not matter.

[Joy Christian]

Bell's theorem is not a mathematical theorem but a statement about nature.

That is not correct. The claim of Bell and his followers is not directly a claim about Nature but about what kind of theory can describe Nature. The precise claim of Bell's theorem is that no local and realistic theory of the kind espoused by Einstein can reproduce all of the statistical predictions of quantum theory. Note carefully that this claim says nothing about Nature itself.

The mathematics to derive the Bell inequality is not in question.

The mathematics to derive the Bell inequality may not be in question but Bell's theorem is still not a valid "theorem." It is, in fact, an invalid "theorem": https://arxiv.org/abs/1704.02876.

Physically [Bell] only took into account noncontextual models.

This statement is quite wrong. It ignores the history of how Bell arrived at his theorem. In his 1966 paper, which was written before his famous 1964 paper, Bell points out the mistake von Neumann had made regarding the possibility of general non-contextual hidden variable theories. Having done so, Bell then provides a correct theorem that rules out the possibility of any noncontextual theory that can reproduce the predictions of quantum theory. The latter theorem is also independently proved by Kochen & Specker. It is now known as Bell-Kochen-Specker theorem. Thus by the time Bell wrote his famous 1964 paper he was more than aware of the fact that noncontextual models have been ruled out, quite generally, because he was one of the people who had decisively ruled them out! Therefore his famous theorem of 1964 explicitly considers contextual hidden variable models and claims that, while contextual models are still possible [albite Bell does not use this language because Shimony had not yet introduced the word "contextual" in the literature on Bell's theorem], any such realistic model must be nonlocal (or remotely contextual). Thus it is quite wrong to claim that "physically [Bell] only took into account noncontextual models." On the contrary, Bell explicitly considered contextual models.

Insofar it is possible that a contextual model correctly predicts spin measurement results. Such a model has been presented.

It remains to be seen whether your model is indeed local and realistic. As Gill has noted, countlessly many have tried and failed.

By the way, analytic scientific models don't need to be proved by computer simulation.

I agree with this. But computer simulations do help in bringing out the flaws in a claimed local-realistic model of the singlet correlation. It remains to be seen whether your model passes the tests of locality. I must admit, however, that I have not looked at the details of your model. I trust that others in this forum will bring out the nonlocality of your model sooner or later.

***

[gill1109]

Again, you are simply mixing up Bell's so called "theorem" with Gill's "theorem". Please provide an online reference other than your own that describes Bell's "theorem" like you mention above. The experiments merely confirm the mathematical predictions of quantum mechanics. They have nothing to do with deciding about locality, freedom and no conspiracy.
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Dear Fred, I’m happy to oblige. You don’t need to look at my work. I suggest you take a look at the writings of Boris Tsirelson, for instance his tutorial on quantum entanglement and Bell’s theorem, http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Entanglement_(physics).html. If you like heavy duty formal maths, see the mathematical theorems of Cator and Landsman, https://arxiv.org/abs/1402.1972.

Yes, the experiments confirm the predictions of quantum mechanics. Bell’s theorem says that certain of those predictions cannot be reproduced by a local hidden variables theory ... unless you cheat. It’s obvious that we need the ban on cheating. I could time and time again create two settings and two outcomes, in a completely local way, and later throw away some proportion of the resulting four-tuples in such a way that what’s left perfectly mimicks some QM predictions for a particular state and particular measurements. The post-sekection can be done in a completely local way. People showed how this could be done using the detection loophole long, long, ago. Hence everyone knew that Aspect’s experiment had not settled the matter. Hence the physicists worked really hard in order to do experiments whose results could not be so simply explained away. They finally succeeded in 2015.

People came up with local realistic computer simulations which reproduced Aspect’s results, long, long ago. Nobody has done the same yet for the 2015 Delft, Munich, Vienna, and NIST experiments. I believe it can’t be done. The experimenters believe it can’t be done. That belief was the raison d’etre of those experiments.

Obviously, you don’t have to believe me. Go ahead, show the whole world that I’m wrong. It will rock the entire physics establishment to its foundations when you succeed. Thanks to internet nobody will be able to suppress your findings. You write some computer programs which deliver the goods. Nobody needs to check your code: it is easy to check whether you are cheating or not, by running a suite of tests, simply running the program many times, checking that Bob’s outcome does not use Alice’s setting.

As I said, the serious researchers today who do believe in local realism either embrace non-locality or adopt “conspiracy”. And I’m not talking about some fringe amateurs. I’m talking about famous and influential people like Sabine Hossenfelder and Gerard ‘t Hooft. They wouldn’t be working on those radical new approaches if they thought there was a chance you’re right. I believe that Bell’s theorem is the underlying reason no-one has yet unified quantum and relativity theory.

[Joy Christian]

Dear Fred, I’m happy to oblige. You don’t need to look at my work. I suggest you take a look at the writings of Boris Tsirelson, for instance his tutorial on quantum entanglement and Bell’s theorem, http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Entanglement_(physics).html. If you like heavy duty formal maths, see the mathematical theorems of Cator and Landsman, https://arxiv.org/abs/1402.1972.

There is nothing to see here. Both Tsirelson's tutorial and theorems of Cator and Landsman use the same trick that Bell's original theorem used. They do so to obfuscate the flaw in all Bell-type theorems. Moreover, all experiments "violate" Bell-type inequalities by using the same old magician's trick of bait-and-switch. As I said, there is nothing to see in what Gill has linked.

Gill, you need to wake up from your dogma and smell the coffee. What you are preaching is yesterday's dogma. It has long been overcome: http://einstein-physics.org/about-the-centre/

***

[Esail]

The claim of Bell and his followers is not directly a claim about Nature but about what kind of theory can describe Nature.


***

correct, any theorem can only predict how we regard nature

Therefore his famous theorem of 1964 explicitly considers contextual hidden variable models
***

Can you, please, show where Bell in his 1964 paper uses any contextual approach that is to say that a physical property depends on the setting of an instrument?



***[/quote]

[Joy Christian]

Therefore his famous theorem of 1964 explicitly considers contextual hidden variable models.

Can you, please, show where Bell in his 1964 paper uses any contextual approach that is to say that a physical property depends on the setting of an instrument?

Contextuality is explicit in the very first equation of Bell's 1964 paper. The equation reads:



Here the vectors and represent experimental contexts (or settings) freely chosen by Alice and Bob, respectively. In his theorem, Bell then explicitly uses his Eq. (1).

You can read more about contextuality in Bell's theorem in the following paper by Shimony: https://arxiv.org/abs/physics/0105046. See the first paragraph on page 11.

***

[FrediFizzx]

Dear Fred, I’m happy to oblige. You don’t need to look at my work. I suggest you take a look at the writings of Boris Tsirelson, for instance his tutorial on quantum entanglement and Bell’s theorem, http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Entanglement_(physics).html. If you like heavy duty formal maths, see the mathematical theorems of Cator and Landsman, https://arxiv.org/abs/1402.1972.

There is nothing to see here. Both Tsirelson's tutorial and theorems of Cator and Landsman use the same trick that Bell's original theorem used. They do so to obfuscate the flaw in all Bell-type theorems. Moreover, all experiments "violate" Bell-type inequalities by using the same old magician's trick of bait-and-switch. As I said, there is nothing to see in what Gill has linked.
...
***

Right; nothing to see about Gill's "theorem" in those references. So..., I'm still waiting to see any other reference about Gill's "theorem". I've looked around and couldn't find anything that says that Bell's so-called "theorem" is about producing the negative cosine curve from the A and B +/-1 outcomes only. That is about modelling Nature and the experiments. Not necessary to compare a local model with the predictions of quantum mechanics which is what Bell's so-called "theorem" is about. I've got a new GAViewer simulation that I will be posting soon about this.
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[Esail]

Contextuality is explicit in the very first equation of Bell's 1964 paper. The equation reads:



Here the vectors and represent experimental contexts (or settings) freely chosen by Alice and Bob, respectively. In his theorem, Bell then explicitly uses his Eq. (1).

***

It is no surprise that the measured value depends on the position of the instrument in projective measurements. For example, the yield of a solar collector depends on the angle to the sun.

But contextuality is something completely different. The point here is that the instrument position creates a selection and thus a context that influences the measurement result.
In equation (15) of his 1964 paper, Bell has replaced the product
1: A (a, lambda) A (c, lambda) by
2: A (b, lambda) A (c, lambda) * A (a, lambda) A (b, lambda) assuming that A (c, lambda) is the same in both cases, i.e. context-independent.

B (c, lambda) = - A (c, lambda), however, depends on the context that is set by A (a, lambda) in 1: or A (b, lambda) in 2.

Bell's derivation is therefore not contextual and therefore cannot reproduce the predictions of QM.
In my model, the polarization is context dependent. Therefore my model correctly reproduces the predictions of the QM.

[Joy Christian]

In my model, the polarization is context dependent. Therefore my model correctly reproduces the predictions of the QM.

That sounds like explicit nonlocality.

Can you write down here the functions and that are used in your model to produce the singlet correlation? Thanks.

If you cannot write down such functions explicitly, then your model has nothing to do with refuting Bell's argument or with local realism.

***

[Esail]

You can find these functions explicitly in the paper. See paragraphs 2.3 and 3.3 for photons (eqs. 5-8 ) and spin 1/2 particles respectively (eqs. 5a-8a)

[Joy Christian]

You can find these functions explicitly in the paper. See paragraphs 2.3 and 3.3 for photons (eqs. 5-8 ) and spin 1/2 particles respectively (eqs. 5a-8a)

As I suspected, these functions are manifestly nonlocal. Both A and B depend on the same "delta" in addition to the shared randomness lambda. That makes the model manifestly nonlocal.

According to the functions written down in your paper, Alice can influence Bob's result by changing the value of delta, and Bob can influence Alice's result by changing the value of delta.

To put it differently, delta in A and B is not freely chosen by Alice and Bob. That is pretty seriously nonlocal. It would violate even special-relativistic causality (or parameter independence).

***

[Esail]

As I suspected, these functions are manifestly nonlocal. Both A and B depend on the same "delta" in addition to the shared randomness lambda. That makes the model manifestly nonlocal.
***

The model is local. delta can be set freely on both sides. Only with the same delta, we have perpendicular polarizer setting and 100% coincidence.
Function values for arbitrary a and b (alpha/beta) can be obtained from the program spec provided in a post above.

[Joy Christian]

As I suspected, these functions are manifestly nonlocal. Both A and B depend on the same "delta" in addition to the shared randomness lambda. That makes the model manifestly nonlocal.

The model is local. delta can be set freely on both sides. Only with the same delta, we have perpendicular polarizer setting and 100% coincidence.
Function values for arbitrary a and b (alpha/beta) can be obtained from the program spec provided in a post above.

Sorry. Your model is manifestly nonlocal. You have the same delta-dependence in both A and B. Which means Alice must know what delta Bob has chosen and vice versa. That is nonlocal.

Perhaps you will convince others in the forum of locality, but not me. Good luck with your efforts.

***

[FrediFizzx]

As I suspected, these functions are manifestly nonlocal. Both A and B depend on the same "delta" in addition to the shared randomness lambda. That makes the model manifestly nonlocal.
***

The model is local. delta can be set freely on both sides. Only with the same delta, we have perpendicular polarizer setting and 100% coincidence.
Function values for arbitrary a and b (alpha/beta) can be obtained from the program spec provided in a post above.

Sorry, Joy is right your model is non-local. You would have to at least have delta_a and delta_b for A and B with no dependency between them.
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[Esail]

You have the same delta-dependence in both A and B.
***

The reason for the same delta-dependence is that the same rules apply locally on both sides. There is nothing obscure with that.

[Joy Christian]

You have the same delta-dependence in both A and B.

The reason for the same delta-dependence is that the same rules apply locally on both sides. There is nothing obscure with that.

But that makes you model manifestly nonlocal. As Fred says in his post, for the model to be local, delta for A and delta for B must be completely independent of each other.

***

[Esail]

I want you and all the other readers to understand how the model works.

The system consists of photon pairs A-B. Half of these have polarization A: 0 ° and B: 90 ° and the other half have polarization A: 90 ° and B: 0 °. The photons of a pair each have the same value of the parameter lambda.
We now consider photon pairs A-B with polarization 0 ° of photon A and 90 ° of photon B.
We set the polarizer PA to the angle alpha. The difference angle between polarizer PA and the polarization of photon A is delta = alpha-0 ° = alpha.
All photons A with lambda <cos2 (delta) will take the exit of the polarizer alpha. That's what the model says. The others take the exit alpha + 90 °. So it is
A (delta, lambda) = 1 for delta = alpha and lambda <cos2 (delta). The polarizer thus selects the photons with lambda <cos2 (delta).

For the B photons as partners of a selected A photon, it applies that they have the same value of lambda. We now set the polarizer PB offset by 90 ° to PA on alpha + 90 °. The photon B has a polarization of 90 °. Then delta = alpha + 90 ° -90 ° = alpha. We see in this chosen case delta = alpha is the same on both sides. The photons PB, for which lambda <cos2 (delta) applies, thus go into the polarizer output alpha + 90 °. But these are exactly the photons B that have a partner photon A, namely a value lambda <cos2 (delta). So for all partner photons B (delta, lambda) = 1 for delta = alpha and lambda <cos2 (delta). This is also what the model says, because the rules for A and B are the same.