Can grandpa understand the Bell's Theorem?

[DrChinese]

So, if the correlated photons are remained entangled after the wave plate and the outcome at point A restricts the outcomes at point B -- that means that both photons will exhibit the anntiparalel polarization. This means that QM and Bell’s paradigm should predict 100% correlation while EPR paradigm predicts 0% correlation.

And I keep telling you that entangled photons go through wave plates and rotate accordingly. If two were parallel to begin with and then one is rotated 90 degrees, they will be anti-parallel. This is in accordance with QM and, as far as I know, most realistic predictions as well.

You might want to learn the rules regarding manipulation of optics BEFORE making further assessments. If you would care to discuss your reasoning, I would be happy to point out where you are going wrong.

 

[miosim]

And I keep telling you that entangled photons go through wave plates and rotate accordingly. If two were parallel to begin with and then one is rotated 90 degrees, they will be anti-parallel. This is in accordance with QM and, as far as I know, most realistic predictions as well.

As I understand you contradict yourself. Just recently you told that photons could be either polarized or entangled, but not both:

"... If they are polarization entangled, then they are not polarized. They are in a superposition of polarization states. (By definition.) They will not be entangled as to polarization if you know their polarization. ..."

But regardless what you said, the QM paradigm is clear that you can’t change one entangled particle without affecting another. This is the main difference between QM and EPR that views correlated photons as fully independent after separation.

In my Gedanken Experiment the entangled photon are independent, based on the result you predicted, and therefore QM and Bell’s theories are in conflict with this prediction.

 

[DrChinese]

Just recently you told that photons could be either polarized or entangled, but not both:

"... If they are polarization entangled, then they are not polarized. They are in a superposition of polarization states. (By definition.) They will not be entangled as to polarization if you know their polarization. ..."

But regardless what you said, the QM paradigm is clear that you can’t change one entangled particle without affecting another. This is the main difference between QM and EPR that views correlated photons as fully independent after separation.

In my Gedanken Experiment the entangled photon are independent, based on the result you predicted, and therefore QM and Bell’s theories are in conflict with this prediction.

Polarization entangled photons do not have a definite polarization because they are in a superposition of polarization states. Nonetheless, a wave plate WILL rotate that superposition. This transformation is NOT communicated to its twin (because the wave state is still a superposition and will remain so until a measurement collapses them). That is traditional QM. EPR does NOT predict that a change to Alice will be communicated to Bob either.

I will remind you that most Bell tests involve a series of filters, wave plates, fiber, mirrors, etc. which have certain optical properties. These are respected by entangled photons as well as those in a pure state. For example, it is not unusual to send entangled photons through coiled fiber. Doesn't change anything.

So I will repeat: there is nothing about QM that leads to the prediction you are making. It would be pretty obvious since you could simply play with the wave plates to locate any unusual or unexpected effects. But there aren't any.

 

[DrChinese]

As I understand you contradict yourself.

I think you misunderstood my comment about entangled photons being parallel or anti-parallel (crossed, orthogonal, perpedicular). Perhaps the following recap will assist:

Type I PDC entangled photons are parallel (0 degrees of theta). They do NOT have a definite polarization because they are in a superposition of states. They yield perfect EPR correlations at identical angle settings. Without rotation, that will be 100% correlated.

Type II PDC entangled photons are crossed (90 degrees of theta). They do NOT have a definite polarization because they are in a superposition of states. They yield perfect EPR correlations at identical angle settings. Without rotation, that will be 0% correlated.

You can rotate either or both with wave plates, and adjust the theta stats accordingly. Use cos^2 rule as before.

 

[harrylin]

I think you misunderstood my comment about entangled photons being parallel or anti-parallel (crossed, orthogonal, perpedicular).

Probably so, as it also made me wonder. You wrote:

"And I keep telling you that entangled photons go through wave plates and rotate accordingly."

That sounded like a "realist" description. If a photon does not yet have a polarisation, what do you imagine to "rotate accordingly"?

You can rotate either or both with wave plates, and adjust the theta stats accordingly. Use cos^2 rule as before.

Assuming that you are right here, this rotation that changes the correlation is an interesting aspect that I had not thought of before. Doesn't that effectively kill the concept of magical action at a distance? For the measured photon should then instantly inform the entangled photon, not of its polarisation state, but of its history - and according to QM a photon does not have memory built in.

 

[DrChinese]

Probably so, as it also made me wonder. You wrote:

"And I keep telling you that entangled photons go through wave plates and rotate accordingly."

That sounded like a "realist" description. If a photon does not yet have a polarisation, what do you imagine to "rotate accordingly"?
Assuming that you are right here, this rotation that changes the correlation is an interesting aspect that I had not thought of before. Doesn't that effectively kill the concept of magical action at a distance? For the measured photon should then instantly inform the entangled photon, not of its polarisation state, but of its history - and according to QM a photon does not have memory built in.

And I keep repeating what QM says and what actually happens: the entangled photon can be bounced off mirrors, go through color filters, be rotated through wave plates, follow optical fiber - all without losing its polarization entanglement and without any way altering its polarization twin.

If the media affects the polarization by rotating it or otherwise altering it, you would need to consider that when predicting the results of correlation measurements. In other words: I can rotate the superposition of H> + V> by 90 degrees and it becomes V> + H>. And I can do that without causing collapse.

I think you and grandpa have a confused idea of what entangled particles do. A general change to one does NOT affect the other by action at a distance (as far as I know anyway). No one here has implied that. A measurement outcome causing wave function collapse on one will cause a suitable wave function collapse on the remainder of the entangled system regardless of spacetime distance. That is as far as it goes. If the outcomes are not restricted as a result of a measurement, there is no collapse. The rule is that you cannot use entangled particles to gain more information about one than the Heisenberg Uncertainty Principle allows. I hope this clarifies things.

 

[miosim]

I think you and grandpa have a confused idea of what entangled particles do. A general change to one does NOT affect the other by action at a distance (as far as I know anyway). No one here has implied that. A measurement outcome causing wave function collapse on one will cause a suitable wave function collapse on the remainder of the entangled system regardless of spacetime distance. That is as far as it goes. If the outcomes are not restricted as a result of a measurement, there is no collapse. The rule is that you cannot use entangled particles to gain more information about one than the Heisenberg Uncertainty Principle allows. I hope this clarifies things.

Actually I get more confused. First, I have no idea what “A general change … ” is, because I am talking about very specific change in one of polarization entangled photons that must affect (according to QM) both photons; otherwise these photons will loose their entanglement.

By saying that "A general change to one does NOT affect the other ..." you seem to contrdict yourself, as folows:

... the entangled photon can be bounced off mirrors, go through color filters, be rotated through wave plates, follow optical fiber - all without losing its polarization entanglement and without any way altering its polarization twin…

…that in reference to my Gedanken Experiment means that correlation in the Aspect experiment shouldn’t change (remains 100%) after introduction of the wave plate while the EPR interpretatation expects that this correlation will drop to 0%.

 

[DrChinese]

Actually I get more confused. First, I have no idea what “A general change … ” is, because I am talking about very specific change in one of polarization entangled photons that must affect (according to QM) both photons; otherwise these photons will loose their entanglement.

By saying that "A general change to one does NOT affect the other ..." you seem to contrdict yourself, as folows:

…that in reference to my Gedanken Experiment means that correlation in the Aspect experiment shouldn’t change (remains 100%) after introduction of the wave plate while the EPR interpretatation expects that this correlation will drop to 0%.

If it makes it more clear, just take out the word "general". You keep saying that QM predicts X when it actually predicts Y.

I have told you that a wave plate rotates the polarization state of any photon, entangled or not. It does not cause collapse of the wave function for entangled photons. It does not change the polarization in any way for other photons. Is there any element of that which is not specific or clear? This is the same predicted result for both QM and classical setups.

 

[DrChinese]

And a note for miosim: an EPR state is one in which the polarization of Alice can be predicted with certainty by reference to Bob. This is the starting point of Aspect style experiments. It is not assumed, it is demonstrated so that things begin where EPR left off - there are elements of reality present.

That in and of itself rules out an entire class of local realistic theories. I.e. those which assume you could only obtain a Product state correlations from a seemingly random distribution of outcomes. In other words, if any of the randomness is introduced at the time of observation, you would have Product State statistics and the EPR state would NOT be achieved.

 

[harrylin]

And I keep repeating what QM says and what actually happens: the entangled photon can be bounced off mirrors, go through color filters, be rotated through wave plates, follow optical fiber - all without losing its polarization entanglement and without any way altering its polarization twin.

If the media affects the polarization by rotating it or otherwise altering it, you would need to consider that when predicting the results of correlation measurements. In other words: I can rotate the superposition of H> + V> by 90 degrees and it becomes V> + H>. And I can do that without causing collapse.

Ok, so when you wrote that "entangled photons go through wave plates and rotate accordingly", you imagine a superposition of H and V as something "real", relative to which a photon (or its future polarisation?) can rotate - thanks for the clarification.

I think you and grandpa have a confused idea of what entangled particles do. A general change to one does NOT affect the other by action at a distance (as far as I know anyway). No one here has implied that.

I told you that I assume that you are right about this. And that we agree on this doesn't mean that we are confused!

A measurement outcome causing wave function collapse on one will cause a suitable wave function collapse on the remainder of the entangled system regardless of spacetime distance. That is as far as it goes. If the outcomes are not restricted as a result of a measurement, there is no collapse. The rule is that you cannot use entangled particles to gain more information about one than the Heisenberg Uncertainty Principle allows. I hope this clarifies things.

A "suitable" wave function collapse implies that the two photons have polarisations that may be not anti-parallel. I'm afraid that you still do not realize the consequence for information... If you believe in action at a distance from the one photon to the other, where do you propose that the information about the correct ("suitable") phase difference exists? Where is the superposition stored?

 

[miosim]

… I have told you that a wave plate rotates the polarization state of any photon, entangled or not. ... Is there any element of that which is not specific or clear?

It is very confusing that a wave plate can rotate a polarization that doesn’t exist! As you stated before for photons …

If they are polarization entangled, then they are not polarized.

 

[DrChinese]

It is very confusing that a wave plate can rotate a polarization that doesn’t exist! As you stated before for photons …

The polarization is a superposition of states. As to the phrase "doesn't exist", this is purely semantics and is not fully representative. All I can really say is that is not in a "definite" polarization in the context of QM. A wave plate will rotate the superposition state, and that is a simple observational fact. The EPR state survives.

 

[miosim]

... A wave plate will rotate the superposition state, and that is a simple observational fact. ...

How in your opinion a rotation of the "…superposition state…" affects observable mutual polarization of the photon’s pair?
I give you a hint: without this “rotation” the photon’s pair would exhibit observable antiparallel polarization.

 

[SpectraCat]

How in your opinion a rotation of the "…superposition state…" affects observable mutual polarization of the photon’s pair?
I give you a hint: without this “rotation” the photon’s pair would exhibit observable antiparallel polarization.

I think part of the problem is that the states under discussion are not really the Bell states, at least not as I understand them. The Bell states are defined as superpositions in the PRODUCT space of the two possible outcomes at detectors A & B:

\Psi=(|H_A>\otimes|V_B> + |V_A>\otimes|H_B>)

So, if you rotation the polarization of the, say, the A beam by some arbitrary angle, you change the detection basis at detector A to |H'> and |V'>. That means now you are in the superposition:


\Psi=(|H'_A>\otimes|V_B> + |V'_A>\otimes|H_B>)

So what? You could have started out in that basis if you wanted to ... the vector spaces representing the polarizations of the two photons are independent. In my understanding, this is why non-destructive manipulations of the two different beams going to A and B can be made without destroying the entanglement.

 

[miosim]

... the vector spaces representing the polarizations of the two photons are independent. In my understanding, this is why non-destructive manipulations of the two different beams going to A and B can be made without destroying the entanglement.

So what is the observable mutual polarization of the photon’s pair you expect after one of them passed 90 deg wave plate?

 

[SpectraCat]

So what is the observable mutual polarization of the photon’s pair you expect after one of them passed 90 deg wave plate?

Please define mutual polarization ... I don't know what you mean.

 

[miosim]

Please define mutual polarization ... I don't know what you mean.

I mean the angle between observable photons’ polarization (parallel, antiparallel or anything in between).

I just realized that I made a mistake that causes a major confusion.
While asking about observable polarization of the photon’s pair after one of them passed 90 deg wave plate I thought that antiparallel polarization means 180 degree, while 90 degree represents the middle point between parallel and antiparallel polarization. But I was wrong because 90 degree is difference between parallel and untiparalell polarization so 45 degree is a middle point.

I am sorry for this confusion.

Let me correct my previous question. What happens if one of the entangled photons passed 45 deg wave plate? Would the observable polarization of this photon's pair remain antiparallel or will be shifted by 45 degree?

 

[harrylin]

I [..] You could have started out in that basis if you wanted to ... the vector spaces representing the polarizations of the two photons are independent. In my understanding, this is why non-destructive manipulations of the two different beams going to A and B can be made without destroying the entanglement.

Yes, DrChinese also clarified that. And this raised a question, as we now established that the detected polarization of the entangled photon is irrelevant for the polarization of its twin. Perhaps you can answer it? if one believes that "collapse of the wave function" corresponds to an instantaneous physical signal to the other photon, then where is the relevant information of the wave function stored?

Thanks,
Harald

 

[DrChinese]

I mean the angle between observable photons’ polarization (parallel, antiparallel or anything in between).

I just realized that I made a mistake that causes a major confusion.
While asking about observable polarization of the photon’s pair after one of them passed 90 deg wave plate I thought that antiparallel polarization means 180 degree, while 90 degree represents the middle point between parallel and antiparallel polarization. But I was wrong because 90 degree is difference between parallel and untiparalell polarization so 45 degree is a middle point.

I am sorry for this confusion.

Let me correct my previous question. What happens if one of the entangled photons passed 45 deg wave plate? Would the observable polarization of this photon's pair remain antiparallel or will be shifted by 45 degree?

It will shift it by 45 degrees, corresponding to the wave plate.

 

[DrChinese]

Yes, DrChinese also clarified that. And this raised a question, as we now established that the detected polarization of the entangled photon is irrelevant for the polarization of its twin. Perhaps you can answer it? if one believes that "collapse of the wave function" corresponds to an instantaneous physical signal to the other photon, then where is the relevant information of the wave function stored?

Please, I beg you to be careful with the words you use. They can often get in the way, and we end up "debating" items which are not physics so much as semantics. There IS a correlation between entangled Alice and Bob as to their polarization state, as I have mentioned.

Where is the information stored? It "could" be with the particle. I don't think a firm (meaningful) answer to this question is possible.

 

[miosim]

It will shift it by 45 degrees, corresponding to the wave plate.

It means that the entangled photons may exhibit independence of their entangled characteristic. It is well within EPR paradigm but I thought that this is prohibited within QM and Bell’s paradigm; otherwise it would open the huge jar of worm-like questions.
Just couple of them are:
1. How you define entangled property (other than in the EPR terms) if they can be changed independently for each particle.
2. Does the change at one entangled photon is reflected in the wave function? If not, is QM wave function is complete description of events?

And of cause this should undermine the initial conditions of Bell’s theorem and interpretation of Aspect’s experiment that are based on the notion that “… correlations predicted by QM depends only on the orientations of polarizers …” (Bell’s Theorem : The Naive View Of an Experimentalist (page 14).

 

[DrChinese]

It means that the entangled photons may exhibit independence of their entangled characteristic. It is well within EPR paradigm but I thought that this is prohibited within QM and Bell’s paradigm; otherwise it would open the huge jar of worm-like questions.
Just couple of them are:
1. How you define entangled property (other than in the EPR terms) if they can be changed independently for each particle.
2. Does the change at one entangled photon is reflected in the wave function? If not, is QM wave function is complete description of events?

And of cause this should undermine the initial conditions of Bell’s theorem and interpretation of Aspect’s experiment that are based on the notion that “… correlations predicted by QM depends only on the orientations of polarizers …” (Bell’s Theorem : The Naive View Of an Experimentalist (page 14).

1. I have defined this any number of times: they are in a superposition of states. You can change the velocity (direction) of one without changing the velocity of the other as well. How is that any different?

2. The QM description is an complete as it gets. Otherwise, you would exceed the limits of the HUP. Which is what Bell tests demonstrate.

The correlations depend solely on the relative orientations of the polarizers (theta). What about this is hard to follow? Are you trying to say that the presence of a wave plate changes this statement somehow? You may as well say that whether or not my hand is blocking the detector on one side is a factor too. It would be helpful if you would use more common scientific terminology rather than trying to stretch the ordinary meaning of jargon. In controlled experiments, no other underlying physical variables have ever been detected other than theta. The QM correlation prediction depends on the wave state being produced, which of course changes when a wave plate is present. Or when my hand is present to disrupt things.

 

[miosim]

I have defined this any number of times: they are in a superposition of states. You can change the velocity (direction) of one without changing the velocity of the other as well. How is that any different?

If you do this for the velocity-entangled particles, do they LOSE their ENTANGLEMENT?

The QM description is an complete as it gets. Otherwise, you would exceed the limits of the HUP. Which is what Bell tests demonstrate.

In my opinion, the result of Gedanken Experiment you predicted severely damage the initial conditions of Bell’s theorem and the interpretation of Aspect’s experiment.

The correlations depend solely on the relative orientations of the polarizers (theta). What about this is hard to follow?

This “flies in the face” of the result of Gedanken Experiment you predicted, because a wave plate (and who knows what else) also affects the correlation

 

[DrChinese]

1. If you do this for the velocity-entangled particles, do they LOSE their ENTANGLEMENT?

2. In my opinion, the result of Gedanken Experiment you predicted severely damage the initial conditions of Bell’s theorem and the interpretation of Aspect’s experiment. This “flies in the face” of the result of Gedanken Experiment you predicted, because a wave plate (and who knows what else) also affects the correlation

1. Depends on whether you learn sufficient information about that velocity (momentum is the observable). HUP rules, that is as simple as I can say it. That is why entangled particles exhibit non-LR characteristics.

2. As to your opinion: it is clearly not based on the relevant science, as that has already been expressed to you many times in this thread. It makes me laugh to imagine you telling this to Bell, Aspect, or any other scientist (as if you discovered an important new fact that they failed to consider in their haste). But hey, otherwise good luck with that.

 

[Jonathan Scott]

There's a pair of photons which are in a combined unknown state, as a pair.

If you do anything to either one of them which does not involve resolving the state into a pure state, such as rotating it, reflecting it or whatever, then that operation acts on that half of the pair but does not affect the other one and doesn't tell you anything about the state. If however you do anything which definitely does resolve the state, such as putting it through a polarizing filter or a beam splitting device then observing it with a photo-detection device, then that also means that the state at the other end is now also known.

Obviously if you rotate or reflect a photon before observing it, then when you've resolved its state you have to backtrack through those operations to deduce the original state and hence the state of the other photon.

 

[SpectraCat]

I mean the angle between observable photons’ polarization (parallel, antiparallel or anything in between).

I just realized that I made a mistake that causes a major confusion.
While asking about observable polarization of the photon’s pair after one of them passed 90 deg wave plate I thought that antiparallel polarization means 180 degree, while 90 degree represents the middle point between parallel and antiparallel polarization. But I was wrong because 90 degree is difference between parallel and untiparalell polarization so 45 degree is a middle point.

I am sorry for this confusion.

Let me correct my previous question. What happens if one of the entangled photons passed 45 deg wave plate? Would the observable polarization of this photon's pair remain antiparallel or will be shifted by 45 degree?

This question is ill-defined. All that you can talk about are the following experimental parameters:

1) The settings of the detectors at A & B (i.e. the angle at which you set your polarizer).

2) Manipulations of the beams going to A and/or B (i.e. optical elements, including those that may rotate the polarization)

3) Statistics of detection events, either detector-local (i.e. only considering the detection statistics at A or B individually) or coincident (i.e. considering the correlations between time-coincident detections at both detectors).

The language that you use suggests that you think it makes sense to talk about "the polarization of an entangled photon" in between the point where it was generated, and the point where it was detected. In my opinion, such statements have no scientific basis.

So, let's modify your gedanken experiment. Let's talk about a setup where the "detectors" at A & B are actually polarizing beam splitters, each with two detectors that detect the polarization states |H> and |V>. Let us further assume that these are 100% efficient, so that each of the photons coming through is guaranteed to be detected at one of the detectors. Our entangled pairs are being generated by type II parametric down conversion, so that the polarizations of the two photons are anti-correlated in the |H> and |V> basis, corresponding to the entangled wavefunction:

\Psi=(|H_A>\otimes|V_B> + |V_A>\otimes|H_B>)

We start our experiment with both the A & B detectors aligned to detect in the same basis (i.e. |H>=|H_A>=|H_B>, etc.). In this configuration, we will find that each individual detector sees a 50-50 split between |H> and |V> detection events, and there is perfect anti-correlation between the coincidence measurements ... that is, if for a particular entangled pair the |H_A> detector clicks, then the |V_B> detector will also click, and vice-versa.

Now say that we put a 45 degree rotation on the polarization of the A beam. The statistics of the individual detections will not change .. i.e. each detector will still see a 50-50 split between |H> and |V>. However the coincident statistics for pairwise detection will be drastically different. In fact, you will find NO correlation for coincident detections. In other words, when |H_A> is detected, you will have an equal chance of observing |H_B> or |V_B> for that pair. This is in agreement with the predictions of Q.M., and with Malus' Law.

It is important to note that the loss of correlation in the coincidence statistics in the above example is due to the specific choice of 45 degrees as the rotation angle. If you choose a different rotation angle, you will measure coincidence statistics that are somewhere between perfectly anti-correlated and uncorrelated (i.e. random), with the precise coincidence rate given by Malus' law, with theta as the difference between the rotation angle, and the angle of the polarizing beam-splitter.

I suspect that most of this has already been laid out in this thread, but perhaps not in this form, and at the very least not for several pages . Hopefully this will help clear up some of the confusion.

 

[DrChinese]

Thanks SpectraCat & Jonathan! Your comments add a lot.

 

[miosim]

”… The language that you use suggests that you think it makes sense to talk about "the polarization of an entangled photon" in between the point where it was generated, and the point where it was detected. … In my opinion, such statements have no scientific basis….

I understand that within QM the polarization of entangled photons doesn’t make sense.
I also understand and agree with your description of your gedanken experiment (that I think isn’t differ from mine in the post #326). I also I agree with your prediction of the result of this experiment that matches with the prediction of DrChinese in post #327 (that time he ignored mistake with 90 degree (instead of 45 deg), but he understood what I ment).

Looks like we are on the same page and ready to move forward.

The reason I proposed this gedanken experiment is because I tried to falsify Bell’s and QM paradigms that, as I thought, would prohibit any changes of one of entangled particle without affecting another. Actually, as you pointed correctly, even asking the question what happens with photon that passes the wave plate prior to a wave function collapse would be an ill-defined question within the scope of the empirical QM theory that have nothing to offer about what happens with photon prior to a measurement.

So my question is how we can assume that a wave plate can rotate the polarization of an entangled photon if this is an ill-defined process within the scope of the QM? Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

 

[SpectraCat]

I understand that within QM the polarization of entangled photons doesn’t make sense.
I also understand and agree with your description of your gedanken experiment (that I think isn’t differ from mine in the post #326). I also I agree with your prediction of the result of this experiment that matches with the prediction of DrChinese in post #327 (that time he ignored mistake with 90 degree (instead of 45 deg), but he understood what I ment).

Looks like we are on the same page and ready to move forward.

The reason I proposed this gedanken experiment is because I tried to falsify Bell’s and QM paradigms that, as I thought, would prohibit any changes of one of entangled particle without affecting another. Actually, as you pointed correctly, even asking the question what happens with photon that passes the wave plate prior to a wave function collapse would be an ill-defined question within the scope of the empirical QM theory that have nothing to offer about what happens with photon prior to a measurement.

So my question is how we can assume that a wave plate can rotate the polarization of an entangled photon if this is an ill-defined process within the scope of the QM? Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

We say that the polarization is rotated because that is what is observed for non-entangled photons with well-defined polarizations. However, that is not supposed to imply that we somehow know what is going on with the entangled pairs. Rather, what we are saying is that, we know that if detect before the waveplate, we detect either |H> of |V>, AND we know that the waveplate rotates photons with well-defined polarization |H> to have well-defined polarization |H'> (and |V> to |V'>). It is thus more accurate to say that we are rotating the detection basis for the measurement, which is how I have tried to reflect things in my past few posts, although the idiomatic language implying that there is rotation of the polarization of the photon itself can be hard to avoid.

Basically you are worrying about the internal aspects of a process for which QM and experiment can only provide *definitive* answers about inputs and outputs. I know that it is unsatisfying to treat the rest of the process as a black-box, but the sad truth is that there are several interpretations of QM which propose models for "what actually happens" to the system internally, but so far there are no experimental tests that can tell us which of these interpretations is correct, and NONE of them can give us the complete story yet (at least not as far as I know).

That is why Mermin quipped, "Shut up and calculate!" ... I don't quite agree with that, because I still find it useful to ponder some of the interesting paradoxes that arise when aspects of interpretations are discussed, but I don't fool myself into think any of those interpretations provide anything approaching a complete description of reality.

 

[DrChinese]

...Explanation in terms of rotation of the superposition of H> + V> state isn’t sufficient because, as I understand, this mathematical tools is intended for calculation, but not for explanation.

The mathematical formalism IS the explanation. Same is true for relativity. We, as humans, want something that is not going to be supplied. So that is why interpretations were invented. Which is partially why they are all somewhat unsatisfying. They don't REALLY explain anything at all.

There is nothing really difficult about the idea that a superposition can be rotated. Each component of the superposition H + V is transformed: to H' + V'. And in fact, you can even separate those components and do different things to each. With suitable precision (this is extremely difficult in practice), you could later recombine them after having them go different paths.