Can Quantum Mechanics Explain the Paradox in Modified EPR Experiments?

[zonde]

Lets look at two mind experiments.
Experiment 1.
We generate pair of entangle photons in opposite polarization states.
At Alice's wing we have polarizer with polarization axis oriented vertically and detector that registers "clicks".
At Bob's wing we have the same setup - polarizer with polarization axis oriented vertically and detector that registers "clicks".
And we have coincidence counter attached to Alice's and Bob's detectors.
As we register only photons with the same polarizations we should have perfect negative correlation e.g. no coincidences at all.

Experiment 2.
We take the same setup as in experiment 1. but slightly modify it.
We add two polarizers to Bob's wing after first polarizer - one rotated by 45° relative to first polarizer other rotated additional 45° relative to previous polarizer so that we have rotated polarization axis by 90° from that of first polarizer.
Now according to Malus law we have reduced intensity of light (count of photons) to 1/4 that of unmodified setup. But as we register only photons with opposite polarization states we should have perfect positive correlation e.g. maximum coincidences.

Are expected results correct from perspective of QM?

As I see we have exactly the same result if we replace all polarizers with polarization beam splitters and dump one unnecessary output.

Where I see paradox.
All photons that are registered in Bob's detector in second experiment should be absorbed by first polarizer (dumped in case of PBS) as demonstrated by first experiment.

If all above is correct then I think this clearly refutes fair sampling assumption in EPR experiments e.g. photons that are registered in Bob's detector in second experiment are undetected (and are "not entangled") in first experiment.

Does it seems correct?

 

[alexepascual]

Lets look at two mind experiments.
Where I see paradox.
All photons that are registered in Bob's detector in second experiment should be absorbed by first polarizer (dumped in case of PBS) as demonstrated by first experiment.
Does it seems correct?

I fail to see the paradox. The first polarizer the photons encoulter are always vertical (in both experiments). For photons that are vertically and horizontally polarized, no coincidences will be detected. This is regardless how you change the plane of polarization after the first polarizer. For photons polarized at a different angle, statistics should be the same in experiment 2 as in experiment 1.
I think the statistics will be determined by the first polarizer the photons encounter and not modified by any subsecuent polarizers.

 

[DrChinese]

Lets look at two mind experiments.
Experiment 1.
We generate pair of entangle photons in opposite polarization states.
At Alice's wing we have polarizer with polarization axis oriented vertically and detector that registers "clicks".
At Bob's wing we have the same setup - polarizer with polarization axis oriented vertically and detector that registers "clicks".
And we have coincidence counter attached to Alice's and Bob's detectors.
As we register only photons with the same polarizations we should have perfect negative correlation e.g. no coincidences at all.

Experiment 2.
We take the same setup as in experiment 1. but slightly modify it.
We add two polarizers to Bob's wing after first polarizer - one rotated by 45° relative to first polarizer other rotated additional 45° relative to previous polarizer so that we have rotated polarization axis by 90° from that of first polarizer.
Now according to Malus law we have reduced intensity of light (count of photons) to 1/4 that of unmodified setup. But as we register only photons with opposite polarization states we should have perfect positive correlation e.g. maximum coincidences.

Are expected results correct from perspective of QM?

As I see we have exactly the same result if we replace all polarizers with polarization beam splitters and dump one unnecessary output.

Where I see paradox.
All photons that are registered in Bob's detector in second experiment should be absorbed by first polarizer (dumped in case of PBS) as demonstrated by first experiment.

If all above is correct then I think this clearly refutes fair sampling assumption in EPR experiments e.g. photons that are registered in Bob's detector in second experiment are undetected (and are "not entangled") in first experiment.

Does it seems correct?

I don't follow your second example. Bob's intensity is reduced but that only means there will be a lot of situations in which there are no clicks on either side. What does that represent?

And I don't see any issue with the fair sampling assumption either. Most Bell tests are done with polarizing beam splitters so that a click occurs every time on both sides. That way it is clear that detection is unrelated to polarizer orientation.

 

[zonde]

I fail to see the paradox. The first polarizer the photons encoulter are always vertical (in both experiments). For photons that are vertically and horizontally polarized, no coincidences will be detected. This is regardless how you change the plane of polarization after the first polarizer. For photons polarized at a different angle, statistics should be the same in experiment 2 as in experiment 1.
I think the statistics will be determined by the first polarizer the photons encounter and not modified by any subsecuent polarizers.

So you propose different prediction about outcome of second experiment.
However you use classical hidden variable approach for that prediction (wave function collapse happens at the encounter of first polarizer) and this approach has proved to be poor guide in predicting outcomes of QM experiments.
Therefore I put emphasis on QM perspective. In QM wave function collapse happens when measurement is done and not sooner.
So can you work out outcome of second experiment in QM framework?

 

[zonde]

I don't follow your second example. Bob's intensity is reduced but that only means there will be a lot of situations in which there are no clicks on either side. What does that represent?

And I don't see any issue with the fair sampling assumption either. Most Bell tests are done with polarizing beam splitters so that a click occurs every time on both sides. That way it is clear that detection is unrelated to polarizer orientation.

My point is that not only Bob's intensity is reduced but polarization is different as well. If you assume that wave function collapse happens at the encounter of first polarizer then any polarizer after first should not change anything except intensity. But my point is that in QM perspective wave function collapse happens only when measurement is done so that polarization after last polarizer is significant.

Of course we can start talking about any fair sampling issues only if you will come to conclusion that prediction of second experiment is correct. There will be no point in discussing that if you think that prediction is wrong.

 

[Istvan Mezo]

If we have an electron source and a screen, we see that the electron hits the screen. This means that the wave function of the electron will be a Dirac-delta at a specified spacetime point. But before the detection, the probability density is nowhere zero.

It seems that the reduction of the wave function happens instantaneously. Do I understand well?

 

[zonde]

It seems that the reduction of the wave function happens instantaneously. Do I understand well?

I am probably not the right person to provide answer about standard interpretation of QM but as far as I know it is something like that.
I assume that you don't ask for some nonstandard interpretation.

 

[DrChinese]

My point is that not only Bob's intensity is reduced but polarization is different as well. If you assume that wave function collapse happens at the encounter of first polarizer then any polarizer after first should not change anything except intensity. But my point is that in QM perspective wave function collapse happens only when measurement is done so that polarization after last polarizer is significant.

Of course we can start talking about any fair sampling issues only if you will come to conclusion that prediction of second experiment is correct. There will be no point in discussing that if you think that prediction is wrong.

There is a reduction in intensity because the 2 extra polarizers filter out some of the photons. There is nothing unusual about the change in polarization that results, that would be expected under ANY scenario (semi-classical or quantum). The detection itself is not significant; as that is not the point at which the collapse occurs, it occurs when the first polarizer is encountered.

(Now strictly speaking, there is not a universally accepted time point at which the wave function collapses, especially with entangled particles. There are experiments which play tricks with this, such as quantum erasers, but the results are always in keeping with the predictions of QM.)

 

[DrChinese]

If we have an electron source and a screen, we see that the electron hits the screen. This means that the wave function of the electron will be a Dirac-delta at a specified spacetime point. But before the detection, the probability density is nowhere zero.

It seems that the reduction of the wave function happens instantaneously. Do I understand well?

Yes, that is correct, it is considered to be instantaneous. That leads to strange conclusions if the collapse is considered to be a physical process. But otherwise works fine.

 

[JK423]

In the case of two entangled photons going to opposite directions, if one of them is absorbed by an atom (aka disappeared) what would happen to it`s entangled partner??
(sry if I am a little offtopic)

 

[DrChinese]

In the case of two entangled photons going to opposite directions, if one of them is absorbed by an atom (aka disappeared) what would happen to it`s entangled partner??
(sry if I am a little offtopic)

That absorption does not change the other one directly. However, any information you gain from that process would be HUP-consistent with any information you gained from an examination of the other.

 

[zonde]

The detection itself is not significant; as that is not the point at which the collapse occurs, it occurs when the first polarizer is encountered.

I found long thread that you started - "When does entanglement end?" https://www.physicsforums.com/showthread.php?t=250187"
At the start it seems that you had quite different viewpoint. But maybe in this thread there are post that illustrate the viewpoint you are expressing now?

 

[DrChinese]

I found long thread that you started - "When does entanglement end?" https://www.physicsforums.com/showthread.php?t=250187"
At the start it seems that you had quite different viewpoint. But maybe in this thread there are post that illustrate the viewpoint you are expressing now?

I still agree with the viewpoint from earlier. That is why I added this caveat:

"(Now strictly speaking, there is not a universally accepted time point at which the wave function collapses, especially with entangled particles. There are experiments which play tricks with this, such as quantum erasers, but the results are always in keeping with the predictions of QM.)"

The experiment I mentioned is one of those tricks. You can recombine probability streams to re-create entanglement. This is some of what quantum erasers do. If you can recreate a state in which it is not possible, in principle, to know the outcome (which path) of an earlier observation (of some superposition), then the system can be returned to that earlier state. Or something close to it anyway.

 

[alexepascual]

So you propose different prediction about outcome of second experiment.
However you use classical hidden variable approach for that prediction (wave function collapse happens at the encounter of first polarizer) and this approach has proved to be poor guide in predicting outcomes of QM experiments.?

Every time the photon goes through a polarizer, there is a sort of wave function collapse. If you made both perpendicular orientations of polarization to take different paths and then recombine them you would be preventing collapse. But in this case, one of the perpendicular orientations is filtered out by the polarizer. This is collapse.
With respect to collapse being instantaneous, that's what was assumed in the original formulation of QM. Today the process is better explained by decoherence which shows collapse to be a process that usually happens in a very short time but not instantaneously.
Now, you say that assuming collapse at the first polarizer has proved to be a poor guide in predicting outcomes of QM experiments. But you are not saying which experiments prove this.

Therefore I put emphasis on QM perspective. In QM wave function collapse happens when measurement is done and not sooner.
So can you work out outcome of second experiment in QM framework?

You are right that wave function collapse happens when measurement is done and not sooner. In the Copenhagen Interpretation of quantum mechanics, collapse happens when a quantum system interacts with a macroscopic apparatus in an irreversible manner. But even systems that are very small can act effectively as a measurement device (even if you don't take a reading of the result). In this case, the polarizer is a macroscopic system and the type of interaction is irreversible. So the polarizer represents measurement. Of course you can't know the result of the measurement without putting a detector right bahind the polarizer, but that would destroy the photon and in your example you wnat to make ot go through another polarizer. So, the first polarizer makes a measurement, the second polarizer makes another measurement, and the detector a final measurement. This is the way your example is alnalyzed form the perspective of QM.

 

[zonde]

Thank you for your answers, DrChinese and alexepascual.
I still do not agree with you that entanglement ends completely after first polarizer and only way to restore entanlement is by joining two paths back together.
As I understand your view is not entirely classical QM and still needs to be proven as useful.
And after all there is possibility that someone curious enough with access to required equipment will conduct some experiment that will resolve this question.
I will make a new post in separate thread that I hope will illustrate better why exactly I do not agree with you both. I hope to see your comments about my next post.
Cheers!