Is Bells theorem correct?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Is Bells theorem correct?

Postby Esail » Fri Feb 02, 2018 2:43 am

Heinera wrote:
The best way for you to prove just one example of rotational invariance of your model is to show that



give the same values as





A(alpha, lambda) and B(beta, lambda) are not unambiguous functions of alpha or beta respectively.
The function B(beta, lambda) is defined as Beta(delta,lambda) where delta= beta-polarization angle of incoming photon 2. Thus B(beta, lambda) depends on the setting alpha of P1. delta(beta) = beta-alpha-pi/2.
The rotational invariance comes from the fact that the polarization of photon 2 is perpendicular to the setting of the polarizer P1 for any setting of P1.

Esail wrote:If everything were rotated polarizer P1 were at angle 0° and Photon 1 had the polarization - alpha and photon 2 had the polarization - alpha + pi/2. This would not reproduce the probability sin**(beta-alpha).


This is an error. Please drop this sentence.
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Re: Is Bells theorem correct?

Postby minkwe » Sat Feb 03, 2018 5:34 pm

Heinera wrote:The best way for you to prove just one example of rotational invariance of your model is to show that



give the same values as




This cannot be right because it implies that

and, the angle is irrelevant, and same for B. But the lambda's are defined according to a given basis, which means changing the basis changes the definition of the lambdas. Rotational invariance means: "rotating the basis does not change the outcome", it does NOT mean "rotating the setting, within the same basis, does not change the outcome". Perhaps you mean



give the same values as


Where are defined according to a new basis rotated by -10 degrees.
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Re: Is Bells theorem correct?

Postby Heinera » Sun Feb 04, 2018 5:08 am

I mean he must show that



gives the same correlation value as



since he simply evaluates all correlations with the first polarizer stuck at .
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Re: Is Bells theorem correct?

Postby minkwe » Sun Feb 04, 2018 2:57 pm

Heinera wrote:I mean he must show that



gives the same correlation value as



since he simply evaluates all correlations with the first polarizer stuck at .

I'm saying that does not make sense to expect that. What's the point of the functions A, B if the angle setting is irrelevant?
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Re: Is Bells theorem correct?

Postby Heinera » Mon Feb 05, 2018 3:18 am

minkwe wrote:
Heinera wrote:I mean he must show that



gives the same correlation value as



since he simply evaluates all correlations with the first polarizer stuck at .

I'm saying that does not make sense to expect that. What's the point of the functions A, B if the angle setting is irrelevant?

Well, it is possible for some local models to have

and

but still have



If it wasn't possible, we could dismiss LHV models right there, and would have no need for Bell's theorem.

But Esail hasn't shown that his model has this property.
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Re: Is Bells theorem correct?

Postby Esail » Mon Feb 05, 2018 4:48 am

Heinera wrote:
but still have



If it wasn't possible, we could dismiss LHV models right there, and would have no need for Bell's theorem.

But Esail hasn't shown that his model has this property.


With P1 setting =0° and delta(alpha=0°) =0 and P2 setting = 45° delta(beta=45°) = 45°-0°-90°=-45° ,see my manuscript after equation 16, we get cos(2delta)= 0.
Then we get A(0,lambda) = 1 and B(-45°,lambda)= -1 for -1<lambda<=0 and B(-45°,lambda)= +1 for 0<lambda <1.
With P1 setting =10° and delta(alpha=10°) =0 and P2 setting = 55° delta(beta=55°) = 55°-10°-90°=-45° ,see my manuscript after equation 16, we get cos(2delta)= 0.
Then we get A(0,lambda) = 1 and B(-45°,lambda)= -1 for -1<lambda<=0 and B(-45°,lambda)= +1 for 0<lambda <1.


As the values for A and are identical in both cases so are the correlations.
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