Quantum Realism and Bell Locality

[G Delta]

TL;DR Summary

A question about reality

I would like to pose a question (previously posed to DrChinese in a personal message) regarding Bell Locality.

From PeterDonis in another thread:

"Locality" means that the joint probability function for the two measurements factorizes, i.e., schematically, P(A,B|a,b,λ)=P(A|a,λ)P(B|b,λ), where A,B are the measurement results, a,b are the measurement settings, and λ are the hidden variables.

Bell assumes that local realism requires the factorizability of the joint probability function. Most of the efforts to justify this assumption have been directed toward the condition of locality but my question is about realism.

Quantum theory holds and empirical evidence confirms that the correlation between successive photon polarization measurement outcomes is predicted by P = cos(θ)² where θ is the angle between polarizer settings. This equation takes a two dimensional (circular) relationship between measurement settings and projects it onto a single dimension defined by the settings themselves. The probability of correlation between measurements is directly related to the relative distance between their settings on a strait line rather than on a curved arc as a classical observer would expect. All measurement outcomes are therefore dependent on a one dimensional rather than two dimensional relationship between the settings, and the joint probability of correlation between outcomes cannot be factorized. Quantum reality doesn’t allow Bell to factorize the joint probability function and therefore the inequalities derived with that assumption don’t apply to photons.

With regard to experimental tests of Bell’s theorem—if we look at the probability of correlation with a hypothetical third measurement we clearly see that the probability depends directly on which of the other two settings we choose to correlate with. There is no need for any of the outcomes to be affected by a distant measurement setting and locality or the lack thereof has nothing to do with the outcomes.

So my question is this: is it possible that Bell locality does not accurately reflect reality? Is it possible that the photon’s polarity exists outside of three dimensional space in an additional, otherwise imperceptible dimension?

 

[PeterDonis]

Bell assumes that local realism requires the factorizability of the joint probability function.

No, Bell just defines "locality" for his purposes as meaning the factorizability of the joint probability function. (Note that Bell does not define "realism" to mean this.)

With regard to experimental tests of Bell’s theorem—if we look at the probability of correlation with a hypothetical third measurement we clearly see that the probability depends directly on which of the other two settings we choose to correlate with. There is no need for any of the outcomes to be affected by a distant measurement setting and locality or the lack thereof has nothing to do with the outcomes.

I'm not sure what you mean here. Experimentally the Bell inequalities are violated, which means that no model that has the factorizability property can account for the experimental results. So clearly that form of "locality" has been disproven.

Is it possible that the photon’s polarity exists outside of three dimensional space in an additional, otherwise imperceptible dimension?

This question is not well-defined as it stands. If it's just your personal speculation, please review the PF rules on that. If you are trying to describe some actual physical model you've read about somewhere, please give a reference.

 

[A. Neumaier]

is it possible that Bell locality does not accurately reflect reality?

It is not ony possible but it is a fact. There are many experiments that show that the consequences of Bell locality (in the sense you use the term) are violated.

 

[G Delta]

No, Bell just defines "locality" for his purposes as meaning the factorizability of the joint probability function. (Note that Bell does not define "realism" to mean this.)

I’m not sure how you separate realism from locality. Without realism, locality is meaningless. Since Bell was specifically addressing EPR and their “elements of reality”, it doesn’t make much sense to exclude realism from his definition of locality—at least not to me.

I'm not sure what you mean here. Experimentally the Bell inequalities are violated, which means that no model that has the factorizability property can account for the experimental results. So clearly that form of "locality" has been disproven.

Without a doubt.

What I’m trying to get at is the physical meaning of the term cos²(θ). It literally gives us a proportional, one-dimensional distance between a set of two-dimensional measurement settings. It’s almost as if we’re taking measurements of a one-dimensional property from a higher, two-dimensional perspective. Quantum reality—as far as photon polarization measurements go—seems to be one-dimensional while our classical expectations are two-dimensional.

My point in the passage you quoted was that this fact would explain why the joint probability function is not factorizable without invoking non locality.

This question is not well-defined as it stands. If it's just your personal speculation, please review the PF rules on that. If you are trying to describe some actual physical model you've read about somewhere, please give a reference.

It certainly is not well defined—I’m struggling with it. It is definitely speculation and since that violates the forum rules I understand if you decide to delete my post. Nevertheless, I feel that it’s a valid line of inquiry. I had posted it to another member of the forum in a personal message. He told me that he preferred to address my question in public on the forum so I posted it here. Mea culpa.

 

[PeterDonis]

I’m not sure how you separate realism from locality.

Then read Bell's paper and see how he does it.

Without realism, locality is meaningless.

Without specific definitions of "realism" and "locality", statements like this are meaningless.

What I’m trying to get at is the physical meaning of the term cos²(θ).

Um, the square of the cosine of the angle between the two measurement directions?

It literally gives us a proportional, one-dimensional distance between a set of two-dimensional measurement settings.

No, it gives us an angle between two vectors. Any two vectors will always lie in some plane and will have some well-defined angle between them. That's all there is to it.

It’s almost as if we’re taking measurements of a one-dimensional property from a higher, two-dimensional perspective. Quantum reality—as far as photon polarization measurements go—seems to be one-dimensional while our classical expectations are two-dimensional.

I have no idea what any of this means.

I had posted it to another member of the forum in a personal message. He told me that he preferred to address my question in public on the forum so I posted it here.

Was it another moderator? If so, who?

 

[G Delta]

Without specific definitions of "realism" and "locality", statements like this are meaningless.

In the paragraph you quoted from I brought up both Bell locality and EPR’s “elements of reality”, both of which are fairly well defined. Do you need a better definition?

No, it gives us an angle between two vectors.

cos²(θ) doesn’t give us an angle. You’re not even trying to understand anything I’ve written, you’re just sniping.

Was it another moderator? If so, who?

I already gave you that information.

 

[PeterDonis]

In the paragraph you quoted from I brought up both Bell locality and EPR’s “elements of reality”, both of which are fairly well defined. Do you need a better definition?

I don't, but apparently you do, since you don't appear to grasp the fact that Bell locality and EPR "elements of reality" are entirely separate concepts, and a statement like "without realism, locality is meaningless" makes no sense with those definitions. So I assumed you must be using different definitions, but I didn't know what they were.

cos²(θ) doesn’t give us an angle. You’re not even trying to understand anything I’ve written, you’re just sniping.

You're correct that I don't understand what you meant by several things you said, and I said so. But instead of clarifying what you meant or addressing the substantive points I've made, you're just complaining. So this discussion is going nowhere, and this thread is therefore closed.