Preserving local realism in the EPR experiment

[akvadrako]

If your algorithm for determining the result of A's measurement requires knowledge of B's setting, or if you need to know A's setting to determine B's results: then you are not using a separable algorithm. Thus the "cheat" and it is not simulating local realism. If you allow the "cheat", you CAN simulate QM/entanglement. But that is the only way.

Another cheat is to allow post-selection or flexible coincidence matching, like in https://arxiv.org/abs/0712.3693

 

[Mentz114]

I don't know exactly what it is that you are describing here. This is the answer to what question?

This statement

But in a Monte Carlo simulation, the inputs are generated, as well as the outputs, which means that the inputs (the detector settings, in this case) are known in advance.

I take to be an objection of some kind. But it does not make sense in the context of a MC simulation. I respectfully suggest that you try to understand how the MC works.

To simulate a coin toss we can draw a random number in the range [0,1]. If we simulated a lot of coin tosses the results would be indistinguishable from a real experiment providing we have quality RNs. If we have have a process where a later event depends on the value of a random variate then the joint distribution of the first and second variates can be generated in this way.

(I'm trying to do it analytically but it's very hard)

I understand the impossibility of doing a space-time/dynamic simulation of the experiment. We only have probabilities so this would be a non-starter anyway.

 

[stevendaryl]

I take to be an objection of some kind. But it does not make sense in the context of a MC simulation.

I guess I don't understand why Monte Carlo simulations are relevant [edit: to this thread]. Of course, we can simulate the probabilistic predictions of quantum mechanics. What we can't do, as implied by Bell's inequality, is simulate it in a way that respects the causal relationships between the parts, namely,

• there are no signals propagating between the two detectors
• there are no signals propagating back from the detectors to the source
• the detector settings are unpredictable

 

[Mentz114]

I guess I don't understand why Monte Carlo simulations are relevant. Of course, we can simulate the probabilistic predictions of quantum mechanics. What we can't do, as implied by Bell's inequality, is simulate it in a way that respects the causal relationships between the parts, namely,

• there are no signals propagating between the two detectors
• there are no signals propagating back from the detectors to the source
• the detector settings are unpredictable

The first two things you've listed belong in space-time and dynamic simulations. The third is a about probability and is respected in the simulation.

The probabilites used are these [ which I think are correct, but I could be wrong]

$P_{11} = {\cos\left(( \theta_A-\theta_0\right)/2) }^{2}\,{\cos\left(( \theta_A-\theta_B\right)/2) }^{2}$
$P_{10} = {\cos\left( (\theta_A-\theta_0)/2\right) }^{2}\,{\sin\left( (\theta_A-\theta_B)/2\right) }^{2}$
$P_{01} = {\sin\left(( \theta_A-\theta_0)/2\right) }^{2}\,{\cos\left( (\theta_0-\theta_B)/2\right) }^{2}$
$P_{00} = {\sin\left( (\theta_A-\theta_0)/2\right) }^{2}\,{\sin\left(( \theta_0-\theta_B)/2\right) }^{2}$

which sum to 1. $\theta_0$ is a random variable uniform in the range $[0,2\pi)$, $\theta_A$ and $\theta_B$ are random variates with two equal probability values.

The presence of $\theta_A$ in the second terms of the first two probabilities reflects the fact that the entangled pair always have the same polarization angle. So if A has projected their photon, B's photon must have the same value.

 

[vanhees71]

I don't really know what you (@vanhees71) mean by a "Monte Carlo" simulation for this experiment, but the only way you can reproduce the predictions of quantum mechanics for this case is if the settings for the detectors are known by the simulation code. In other words, by cheating (according to the rules laid out).

Of course, the settings of the detectors have to be known by the simulation code and also in the real experiment to be able to analyze it. That's in the very foundations of QT, and that's at the heart of all these interpretation issues: You need to know both the prepared quantum state and the setup of the experiment (i.e., knowledge about what's measured) to get the probabilities according to Born's rule, no matter when you choose the setup of the measurement devices (often also using a random choice in post-selection mode, but of course, to test QT you need to know which choice has been made in the coincidence measurements to be able to analyze the experiment in comparison to QT, i.e., the measurement protocol must contain for each event the randomly chosen orientation of the polarizers and the like).

 

[stevendaryl]

Of course, the settings of the detectors have to be known by the simulation code and also in the real experiment to be able to analyze it. That's in the very foundations of QT, and that's at the heart of all these interpretation issues: You need to know both the prepared quantum state and the setup of the experiment (i.e., knowledge about what's measured) to get the probabilities according to Born's rule, no matter when you choose the setup of the measurement devices (often also using a random choice in post-selection mode, but of course, to test QT you need to know which choice has been made in the coincidence measurements to be able to analyze the experiment in comparison to QT, i.e., the measurement protocol must contain for each event the randomly chosen orientation of the polarizers and the like).

I really don't understand the point that is being made. In an actual EPR experiment, it is not necessary to know the two settings of the detectors ahead of time. The setting choices can be made at the last moment, using independent means. For comparison with QM, it's only necessary to record the settings afterward.

 

[stevendaryl]

Do you have locality then?

You mean in an actual QM EPR experiment? I don't know. There is certainly no possibility of FTL communication, so by that definition, it's local.

 

[entropy1]

You mean in an actual QM EPR experiment? I don't know. There is certainly no possibility of FTL communication, so by that definition, it's local.

Sorry, I mixed your name up with Mentz's.

 

[Mentz114]

I really don't understand the point that is being made. In an actual EPR experiment, it is not necessary to know the two settings of the detectors ahead of time. The setting choices can be made at the last moment, using independent means. For comparison with QM, it's only necessary to record the settings afterward.

This business of the settings being 'known' or not is irrelevant. When a photon interacts with a polarizer the only things that matter are the 1) photons polarization and 2) the polarizer angle at that time. To do the simulation only those quantities can and must be used. In a real experiment it is the same. The photon knows nothing, we know nothing but those things have a value.

 

[stevendaryl]

This business of the settings being 'known' or not is irrelevant. When a photon interacts with a polarizer the only things that matter are the 1) photons polarization and 2) the polarizer angle at that time. To do the simulation only those quantities can and must be used. In a real experiment it is the same. The photon knows nothing, we know nothing but those things have a value.

But you don't need to know the photon's polarization in an actual EPR experiment. That's a hidden variable, which Bell's theorem rules out.

If you want to assume a "collapse" interpretation, then I guess you could reason that the photons are unpolarized (or have a random polarization) before being measured, but after one photon is measured, the other photon changes state to be polarized the same as the first. But that's a nonlocal interpretation. The topic is "Preserving local realism".

 

[Mentz114]

Another cheat is to allow post-selection or flexible coincidence matching, like in https://arxiv.org/abs/0712.3693

Yes, if you want to break the CHSH limit of 2, cheating is required. But there is no cheating in the MC simulation and I suspect it can never violate that bound.

However it reproduces closely some experimental results. For example in this is paper
arXiv:1508.05949v1 [quant-ph] 24 Aug 2015
The distribution of coincidences and and anti-coincidences in fig 4c look very like runs of the simulation. The effect of the entanglement is to greatly increase coincidences ( for the symmetric case) and the reverse for the anti-symmetric case.

 

[Mentz114]

But you don't need to know the photon's polarization in an actual EPR experiment. That's a hidden variable, which Bell's theorem rules out.

If you want to assume a "collapse" interpretation, then I guess you could reason that the photons are unpolarized (or have a random polarization) before being measured, but after one photon is measured, the other photon changes state to be polarized the same as the first. But that's a nonlocal interpretation. The topic is "Preserving local realism".

Of course I assume

that the photons are ... have a random polarization ... before being measured, but after one photon is measured, the other photon changes state to be polarized the same as the first.

otherwise the simulation would be impossible.
The MC simulation agrees well enough with real experiments so no interpretation is needed.

 

[stevendaryl]

Of course I assume

otherwise the simulation would be impossible.
The MC simulation agrees well enough with real experiments so no interpretation is needed.

Collapse is explicitly a nonlocal effect, so I don't see the relevance to this thread.

 

[Mentz114]

Collapse is explicitly a nonlocal effect, so I don't see the relevance to this thread.

OK, I'll go. Under protest. Please don't associate any 'interpretation' with me. They are all rubbish.

 

[kurt101]

Zonde, thanks for the link to informal proof of bell inequality. This is a very helpful proof, but I think it suffers from the same problem as the hypothetical 3 polarizer experiment. It relies on the same counterfactual definiteness, what would have happened logic, which I think only works if the two entangled photons are exactly the same or exactly opposite. Can someone confirm or deny that the entangled photons have to be the same or opposite for CFD to work for this proof? What about for Bell's theorem?

Is it possible for two entangled photons be different, other than the exact opposite state?

 

[zonde]

It relies on the same counterfactual definiteness, what would have happened logic, which I think only works if the two entangled photons are exactly the same or exactly opposite.

You can replace "what would have happened" reasoning with "what will happen" reasoning. And "what will happen" reasoning is done by any model that can make predictions i.e. any scientific model.
I don't understand why you think that "exactly the same or exactly opposite" matters for this proof.

There is another short proof, but unfortunately it is behind paywall https://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.R747
It assumes very little but it's locality definition is somewhat specific.

 

[vanhees71]

I really don't understand the point that is being made. In an actual EPR experiment, it is not necessary to know the two settings of the detectors ahead of time. The setting choices can be made at the last moment, using independent means. For comparison with QM, it's only necessary to record the settings afterward.

Of course, to calculate the probabilities (or expectation values) in the Bohm version of the EPR experiment (I assume we discuss about this most simple version which has been verified in various real-world experiment with and without delayed-choice setups and verified the correlations described by entanglement and the corresponding violation of Bell's inequality) you have to know the relative orientations of the polarization filters. You can make the setting randomly and in the delayed-choice way, but to be able to analyze the outcome of the experiment you have to put the information which actual setting in each event was randomly chosen.

For me, but here we again enter the realm of interpretation, the success of QT in the delayed-choice setting, is the strongest argument against naive collapse interpretations ever! What we observe concerning entanglement is precisely what QT in the minimal interpretation says: it's describing correlations due to state preparation before any measurement and/or (delayed) choice has been made; the correlations are not due to measurements/manipulations of the individual parts of the system measured.

 

[zonde]

Of course, to calculate the probabilities (or expectation values) in the Bohm version of the EPR experiment (I assume we discuss about this most simple version which has been verified in various real-world experiment with and without delayed-choice setups and verified the correlations described by entanglement and the corresponding violation of Bell's inequality) you have to know the relative orientations of the polarization filters. You can make the setting randomly and in the delayed-choice way, but to be able to analyze the outcome of the experiment you have to put the information which actual setting in each event was randomly chosen.

You can look at experiment as consisting of two sides. One side is all the things done by experimentalist. The other side is done by theoretician who calculates prediction. Then the experimentalist meets the theoretician and after they confirm that they are talking about equivalent situations they compare two numbers - their results (experimentalist has some error margins for his number). If the two numbers are the same (within error margins) theory is confirmed.
Now if we look at entanglement experiment that way we could see that experimentalist does not need the measurement angles to calculate his number (to count the coincidences) but he needs measurement angle when he compares his result with theoretical prediction so that he knows that the prediction is the right one for his particular setup.

For me, but here we again enter the realm of interpretation, the success of QT in the delayed-choice setting, is the strongest argument against naive collapse interpretations ever! What we observe concerning entanglement is precisely what QT in the minimal interpretation says: it's describing correlations due to state preparation before any measurement and/or (delayed) choice has been made; the correlations are not due to measurements/manipulations of the individual parts of the system measured.

But you should compare apples with apples. Collapse interpretations are trying to say something about individual events while minimal interpretation speaks only about ensembles.
And it seems you could make your reasoning clearer by splitting calculation of prediction and experiment (with some theory independent data processing) into two separate parts. You have mixed together prediction with experimental result and speak about it as a single thing.

 

[jerromyjon]

Is it possible for two entangled photons be different, other than the exact opposite state?

In the maximum entangled case two anti-correlated photons will always have the opposite state at the same detector angle. This equates to both polarizers Horizontal or both polarizers Vertical, you will always get hits on both detectors. (in the ideal sense) With the detectors 90 degrees offset (one H and one V) you will always get a hit on one detector and never on the other. (again, in the ideal sense, as if it were a perfect experiment with perfect components) If you give your photons an exact polarization angle (which equates to a hidden variable, and I don't think is realistic as far as experimental preparation is concerned) you could feed them through 45 degree offset filters and you would only get classical probability of hits on the detectors. QT predicts more hits of correlation and you would not be able to reproduce the result no matter how many extra variables you try to pin on the photons.

 

[jerromyjon]

a N degree rotation of a polarizer or any object for that manner, does not actually rotate the internals of the object in a naive linear fashion, but with some sort of relativistic time dilation effect

The actual physics is that a force is transmitted though the solid mass at most at the speed of sound in that mass. Nothing "relativistic" is occurring!

 

[kurt101]

I don't understand why you think that "exactly the same or exactly opposite" matters for this proof

If polarizer A is 0° and polarizer B is 30° you get results for each side that come out to a difference of 25%. If you would have switched polarizer A with an orientation of -30° the results for side B would be the same and side A would have to come out to a result that was unknown, but different than B by 75%. If you would have switched polarizer B with a 0° polarizer and compared it to the result of what would have happened if you switched A with a -30°, you don't know what the result of A or B would have been, but you do know the difference would have been 25%. Can you see what I am getting at? The only way you can infer what the results would have been in the last case is if you knew the the input was the same for both sides A and B, and then you could have said the result for B at 0° would have been the same result for A at 0°; and from that information you could have concluded there is a conflict between the actual result and the what would have been result that leads to the spooky action at a distance conclusion.

 

[kurt101]

If polarizer A is 0° and polarizer B is 30° you get results for each side that come out to a difference of 25%. If you would have switched polarizer A with an orientation of -30° the results for side B would be the same and side A would have to come out to a result that was unknown, but different than B by 75%. If you would have switched polarizer B with a 0° polarizer and compared it to the result of what would have happened if you switched A with a -30°, you don't know what the result of A or B would have been, but you do know the difference would have been 25%. Can you see what I am getting at? The only way you can infer what the results would have been in the last case is if you knew the the input was the same for both sides A and B, and then you could have said the result for B at 0° would have been the same result for A at 0°; and from that information you could have concluded there is a conflict between the actual result and the what would have been result that leads to the spooky action at a distance conclusion.

It just hit me that the results for two polarizers at the same angle are always going to be the same result. So in the last case, I can infer what the results are for both A and B, and can reach the conclusion that communication between the polarizers is necessary for the results to be the way they are.

Thanks for the help! I won't say how many simulations I tried before reaching this conclusion, but as you can see from code snippet, it was more than 32.