What is the explanation for the 25% probability in Bell's Gedanken Experiment?

[rlduncan]

I find A. Aspect's experiment to be very interesting and even profound. D. Mermin's article: Is the moon there when nobody looks? Reality and the quantum theory was well written. I have organized the data of this experiment in chart form and I believe your viewers would be interested in seeing this chart so I posted it at the following website http://www.svcc.edu/~duncanb/Bell.html" . I also suggest a possible explanation for this observation.

[Edit: I have reinstated the link - Doc Al]​

 

[Doc Al]

I have reinstated the link to rlduncan's site. Have at it!

 

[Doc Al]

I also suggest a possible explanation for this observation.

Unfortunately, your proposed explanation violates Mermin's stipulation that there is no communication between detector settings and source.

From your proposal:

"The photon pairs are complementary and when the polarizer angles are set the same the detectors receive this undisturbed complementary or entangled information. However, when the switches are different then the complementary information is disturbed and no longer synchronized and the photons oscillate independent of each other."​

This implies that somehow the source must know the settings of the detectors ahead of time. Mermin was well aware that if communication is allowed between detectors and source it is trivial to explain the correlations. In his article "Spooky Actions at a Distance", he describes how to eliminate that "loophole":

But the detectors are not connected to the source. Indeed, the concern that the device might exploit such hidden connections can be simply disposed of by arranging for the switches not to be set until after the particles have left the source, but before they have arrived at the detectors. If the experiment is thus refined, the character of the data does not change at all.

 

[ueit]

This implies that somehow the source must know the settings of the detectors ahead of time. Mermin was well aware that if communication is allowed between detectors and source it is trivial to explain the correlations. In his article "Spooky Actions at a Distance", he describes how to eliminate that "loophole":

But the detectors are not connected to the source. Indeed, the concern that the device might exploit such hidden connections can be simply disposed of by arranging for the switches not to be set until after the particles have left the source, but before they have arrived at the detectors. If the experiment is thus refined, the character of the data does not change at all.

The "refinement" proposed by Mermin is useless.

Let's say that a LHV theory proposes that the particles (let's say an electron-positron pair) are produced with spins determined by the EM fields generated by the detectors (Stern - Gerlach). So, only if the two detectors are set on the same axis the particles are generated with opposite spins, otherwise they will have their spins in accordance with QM's prediction.

Mermin relies on a hidden assumption, that a "static" detector generates the same field like one which changes its orientation. This is unacceptable from the point of view of a deterministic theory where it is not possible for two identical detectors to evolve differently in the future.

To be more clear, to change a detector orientation you have to use an engine of some sort. This engine generates a field itself and the influence of this field has to be taken into account.

 

[rlduncan]

Unfortunately, your proposed explanation violates Mermin's stipulation that there is no communication between detector settings and source.

Please expand on this statement. I am fullly aware that the switch settings are totally random (obvious from the 1/3 probability shown in Table 2) and that there is no communication between the detector settings and the source.

From your proposal:

"The photon pairs are complementary and when the polarizer angles are set the same the detectors receive this undisturbed complementary or entangled information. However, when the switches are different then the complementary information is disturbed and no longer synchronized and the photons oscillate independent of each other."​

This implies that somehow the source must know the settings of the detectors ahead of time. Mermin was well aware that if communication is allowed between detectors and source it is trivial to explain the correlations. In his article "Spooky Actions at a Distance", he describes how to eliminate that "loophole":

If the switch settings are selected randomly (and they are) the source cannot know the settings of the switches. The communication is in the photon pairs. Again this is obvious from the data, for how would you explain the fact that when the switches are randomly set to the same setting the lights always flash different colors. It is the properties of the photon that needs explaining and a hint of these properties is in contained in the probabilities.

 

[DrChinese]

...Mermin was well aware that if communication is allowed between detectors and source it is trivial to explain the correlations.

Just a small quibble, Doc. I would not call it trivial to explain how the detectors communicate in a way as to cause the results to match the predictions of QM. New forces must be postulated, since existing mechanisms do not support this. Such a new force - or a significant modification to existing theory - must only appear in Bell tests since it is otherwise not apparent.

But I understand the concept... it would be possible, in principle.

 

[Doc Al]

Please expand on this statement. I am fullly aware that the switch settings are totally random (obvious from the 1/3 probability shown in Table 2) and that there is no communication between the detector settings and the source.

Unless I misunderstood your proposal, it depends on the photon pairs being matched (complementary) when the random switch settings are the same, but unmatched when the switch settings are different. How does the source know what photon pairs to emit unless the detectors communicate with the source?

If the switch settings are selected randomly (and they are) the source cannot know the settings of the switches. The communication is in the photon pairs. Again this is obvious from the data, for how would you explain the fact that when the switches are randomly set to the same setting the lights always flash different colors. It is the properties of the photon that needs explaining and a hint of these properties is in contained in the probabilities.

So, are you saying that the nature of the right photon somehow depends on the random detector setting experienced by the left photon? Sounds like nonlocal signaling to me! Mermin's challenge was to explain the observed correlations without positing some nonlocal influence passing between the two photons--to explain things in a purely local manner with "instruction sets" carried by the photons.

Perhaps you can restate your proposal.

 

[Doc Al]

Just a small quibble, Doc. I would not call it trivial to explain how the detectors communicate in a way as to cause the results to match the predictions of QM. New forces must be postulated, since existing mechanisms do not support this. Such a new force - or a significant modification to existing theory - must only appear in Bell tests since it is otherwise not apparent.

You caught me, DrC! What Mermin actually said was more along the lines of "to avoid the possibility of the detectors somehow communicating with the source..." Certainly an explanation of just how such communication could take place would be far from trivial! (And Mermin certainly never said any such thing.)

 

[rlduncan]

Unless I misunderstood your proposal, it depends on the photon pairs being matched (complementary) when the random switch settings are the same, but unmatched when the switch settings are different. How does the source know what photon pairs to emit unless the detectors communicate with the source?

From the data, when the switch settings are different they are unmatched 1/4 of the time. This is an experimental fact. The source randomly emits a photon pair (which carries information) but the detector does not communicate with the source. Contained in this information are the instructions for the detectors when the polarizer angles are the same and when they are different.

So, are you saying that the nature of the right photon somehow depends on the random detector setting experienced by the left photon? Sounds like nonlocal signaling to me! Mermin's challenge was to explain the observed correlations without positing some nonlocal influence passing between the two photons--to explain things in a purely local manner with "instruction sets" carried by the photons.

Perhaps you can restate your proposal.

The experimental data cleary indicates that the photon pairs are complementary 100% of the time when the polarizer angles are set the same and 25% of the time when they have different settings. The "instruction sets" carried by the photons must reflect these probabilities. I attempted to give a simple set of instructions carried by the photons to account for the experimental data.

 

[Doc Al]

From the data, when the switch settings are different they are unmatched 1/4 of the time. This is an experimental fact.

The data is not in question.

The source randomly emits a photon pair (which carries information) but the detector does not communicate with the source. Contained in this information are the instructions for the detectors when the polarizer angles are the same and when they are different.

I assume you mean that each photon carries the information it needs to decide how to respond to any detector setting it may encounter? But you also seem to be saying that what happens to the left going photon depends on the detector setting encountered by the right going photon. How do the photons communicate?

The experimental data cleary indicates that the photon pairs are complementary 100% of the time when the polarizer angles are set the same and 25% of the time when they have different settings.

Again, no quarrel with the data, only with your proposed "instruction sets".

The "instruction sets" carried by the photons must reflect these probabilities. I attempted to give a simple set of instructions carried by the photons to account for the experimental data.

Your "instruction sets" require non-local signalling between the two photons! Mermin's challenge was for the reader to devise instruction sets carried with each photon that are fully self-contained and that do not depend on what the other photon is doing or how the other detector is set. Your proposal fails to do that.

 

[DrChinese]

From the data, when the switch settings are different they are unmatched 1/4 of the time. This is an experimental fact. The source randomly emits a photon pair (which carries information) but the detector does not communicate with the source. Contained in this information are the instructions for the detectors when the polarizer angles are the same and when they are different.

The data you are referring to - 25% - is the actual value when the polarizer settings are set at a *specific* angle relative to each other. In the Mermin example, it is 120 degrees apart, and the value is arrived at as follows:

cos^2(120 degrees) = .25

It is important to realize that you don't get those same results at all angle settings for Mermin's example. However, the issue is that you shouldn't be able to get that value for ANY angle setting if the local realism assumptions are correct.

The concept that the photon has an embedded instruction set is what Mermin is explicitly rejecting. So I don't follow what you are trying to say.

 

[NateTG]

Just a small quibble, Doc. I would not call it trivial to explain how the detectors communicate in a way as to cause the results to match the predictions of QM. New forces must be postulated, since existing mechanisms do not support this. Such a new force - or a significant modification to existing theory - must only appear in Bell tests since it is otherwise not apparent.

Bohmian Mechanics admits determinism but is considered non-local because of the quantum potential. However, if we also postulate a big bang, then we have a singular origin were everything is co-local, a deterministic model for moving forward, and a deterministic predictive model for the quantum potential can be inferred from the predictive model for particles. (Although it's quite probably computationally intractable for anything big.)

Notably, because the the state is truly 'hidden' this interpretation does not provide any additional, or different predictions from another.

Moreover, it's worth pointing out that this sort of interpertation is agnostic with respect to realism, since 'unmeasured hidden properties' are in fact meaningless in this interpretation.

This interpretation -- Bohmian Mechanics plus Big Bang -- does not introduce any new forces, is known to be prediction equivalent to orthodox QM, readily admits realism, and is strongly deterministic, and hence local.

 

[rlduncan]

The data you are referring to - 25% - is the actual value when the polarizer settings are set at a *specific* angle relative to each other. In the Mermin example, it is 120 degrees apart, and the value is arrived at as follows:

cos^2(120 degrees) = .25

It is important to realize that you don't get those same results at all angle settings for Mermin's example. However, the issue is that you shouldn't be able to get that value for ANY angle setting if the local realism assumptions are correct.

Yes, the 25% is when the polarizer angle is 120 degrees relative to each other. My point is that there can be "instruction sets" for this setting to explain the 25% probability. In a future post I will try to give more detail and be more compelling. I believe Mermin challenged his reader to explain this observation with embedded instruction sets.

 

[DrChinese]

My point is that there can be "instruction sets" for this setting to explain the 25% probability. In a future post I will try to give more detail and be more compelling. I believe Mermin challenged his reader to explain this observation with embedded instruction sets.

Sure there can, if there is communication between the 2 sides! Not otherwise, which was Mermin's point.