Proof of non-locality indep. of conservation law

[QMrocks]

EPR argument makes use of conservation of momentum between two outgoing particles. Einstein boxes argument makes use of conservation of particle numbers. Anybody can tell me an experiment which proves that QM is non-local without invoking conservation law?

 

[DrChinese]

Entanglement is due to a shared wave function between two or more particles. Conservation is involved because the input particles must have the same totals as the output particles (momentum, spin, etc.), and I cannot think of any EPR/Bell tests that don't make use of this fact.

As to whether QM is non-local, that is an entirely different subject and one that has recently generated a lot of discussion.

 

[Tez]

EPR argument makes use of conservation of momentum between two outgoing particles. Einstein boxes argument makes use of conservation of particle numbers. Anybody can tell me an experiment which proves that QM is non-local without invoking conservation law?

No conservation law is "invoked" in the EPR tests done with polarized photon pairs. In as much as the physical processes producing particles will obey conservation laws there will likely always be something conserved lurking around in the production process - but this doesn't necessarily have anything to do with the correlations, as is contained in the original EPR argumentation...

By using the tricks in:
http://xxx.lanl.gov/abs/quant-ph/0302111
one can go further and to Bell/GHZ tests with spin-1/2 particles where the local parties do not even need to agree on a rotational frame of reference, showing that conservation of angular momentum isn't important to the "nonlocal magic" as it were...

 

[QMrocks]

Entanglement is due to a shared wave function between two or more particles. Conservation is involved because the input particles must have the same totals as the output particles (momentum, spin, etc.), and I cannot think of any EPR/Bell tests that don't make use of this fact.

There lies my concern. If such entanglement results can be explained by the fact that conservation law has already imposed a constraint on the possible outcomes we can obtain, why are we still so mystified by such results?

Is the concept of non-locality invoked just to reinforce (or fill in the loop-holes?) the 'wavefunction is a physical reality' interpretation? In order words, if we dun invoke non-locality, we cannot have the quantum object as a wave interpretation.

 

[QMrocks]

No conservation law is "invoked" in the EPR tests done with polarized photon pairs.

will check this out. if you have a good reference for this, dun mind quote me.

 

[jtbell]

If such entanglement results can be explained by the fact that conservation law has already imposed a constraint on the possible outcomes we can obtain, why are we still so mystified by such results?

But the results of experiments such as Aspect et al. cannot be explained simply by the constraints imposed by conservation laws. It sounds like you're thinking e.g. of the two-particle experiments where the total angular momentum is zero and the two analyzers are aligned in the same direction so that one particle must register "spin up" and the other "spin down". The interesting results come from experiments where the two analyzers are not aligned in the same direction, so that there is some probability for both particles to register the same spin orientation along their respective (different) analyzer directions.

For a simple thought experiment that illustrates what the "problem" is, see

http://www.ncsu.edu/felder-public/kenny/papers/bell.html

You'll probably find it easiest to interpret his results if you assume that one of the analyzers in his setup is wired "backwards" so that both particles produce the same (not opposite) results when the analyzers are aligned in the same direction.

 

[QMrocks]

But the results of experiments such as Aspect et al. cannot be explained simply by the constraints imposed by conservation laws. It sounds like you're thinking e.g. of the two-particle experiments where the total angular momentum is zero and the two analyzers are aligned in the same direction so that one particle must register "spin up" and the other "spin down". The interesting results come from experiments where the two analyzers are not aligned in the same direction, so that there is some probability for both particles to register the same spin orientation along their respective (different) analyzer directions.

For a simple thought experiment that illustrates what the "problem" is, see

http://www.ncsu.edu/felder-public/kenny/papers/bell.html

You'll probably find it easiest to interpret his results if you assume that one of the analyzers in his setup is wired "backwards" so that both particles produce the same (not opposite) results when the analyzers are aligned in the same direction.

Thanks! Let me digest Aspect and Kenny first..

 

[jtbell]

For an example similar to Felder's (and which I think was the inspiration for Felder's version), see the following magazine article:

N. David Mermin, "Is the moon there when nobody looks? Reality and the quantum theory", Physics Today, April 1985, p. 38.

It's not freely available online, but if you have access to a university library, you might be able to find Physics Today there.

 

[DrChinese]

For an example similar to Felder's (and which I think was the inspiration for Felder's version), see the following magazine article:

N. David Mermin, "Is the moon there when nobody looks? Reality and the quantum theory", Physics Today, April 1985, p. 38.

It's not freely available online, but if you have access to a university library, you might be able to find Physics Today there.

Try this link:

http://xoomer.virgilio.it/baldazzi69/papers/mermin_moon.pdf

 

[DrChinese]

For a simple thought experiment that illustrates what the "problem" is, see

http://www.ncsu.edu/felder-public/kenny/papers/bell.html

I have a page that I humbly think expresses the ideas of the link you provided, but in a lot clearer (or at least shorter) fashion: Bell's Theorem with Easy Math

 

[Tez]

I have a page that I humbly think expresses the ideas of the link you provided, but in a lot clearer (or at least shorter) fashion: Bell's Theorem with Easy Math

Apart from the vague "neighboring measurement" comment in (b) on that page, I think its a bit unclear that you are talking about two separated photons! You may then also want to make it a bit clearer why the two photons have the same value of the hidden variable for the same setting (i.e. the [AA],[BB],[CC] cases). Also saying "at A" and "at B" makes them sound a bit like locations rather than settings (I realize that's pedantry - basically I'm just trying to see how you can ensure the maximum number of people "get it" as it were..)

 

[QMrocks]

I have a page that I humbly think expresses the ideas of the link you provided, but in a lot clearer (or at least shorter) fashion: Bell's Theorem with Easy Math

Thanks for both the links. Your write-up looks cool, will take a look later. But i had already read Mermin paper. It a pretty easy read. i think i finally have an appreciation of the problem..

 

[DrChinese]

Apart from the vague "neighboring measurement" comment in (b) on that page, I think its a bit unclear that you are talking about two separated photons! You may then also want to make it a bit clearer why the two photons have the same value of the hidden variable for the same setting (i.e. the [AA],[BB],[CC] cases). Also saying "at A" and "at B" makes them sound a bit like locations rather than settings (I realize that's pedantry - basically I'm just trying to see how you can ensure the maximum number of people "get it" as it were..)

Thanks, Tez, I will make these adjustments. Let me know if you have more suggestions... I am trying to create a page that is very easy for someone new to the subject to follow the logic with the fewest possible steps - and the least complicated math too!

 

[QMrocks]

OK, let me summarize my thoughts here...

1) i previously tried to understand the QM problem from the EPR and Einstein box arguments. The papers i read overstressed the correlation feature which i feel may undermine the true essence of the problem. As Born's explanation to Einstein said: "objects far apart in space which have a common origin need not be independent. i believe this concept cannot be denied and simply has to be accepted. Dirac has based his whole book on this." (is he referring to Dirac's formulation of this two correlated particle problem with the tensor product of two Hilbert space?) In order words, conservation laws has already placed a contraint on the possibles particle states; the correlated result is hence solely derived from this. Nothing else. So what's the big deal? The big deal lies in the reasoning that to obtain such correlated result in experiment, the two particles must in the first place have an instruction set (or reality as coined Einstein) before measurement. Else it will require non local effects to communicate the measurement result of the first particle to the second particle state. Now, before knowing Bell's result and Aspect experiment, i can stick to the conviction that the particles must themselves have an instruction sets. Of course, by holding on to this conviction, i have wrestle with the dilemma as to whether i should regard the probability wave as a state of reality or that it is just a statistical description of the possible result which has already been predetermined before measuremnt. But since i am reluctant to embrace non-locality, i have to go with the latter view.

2) OK, then here comes the crunch. Bell derived the inequality that must be satisfied for measurements of particles each with an instruction set. And the experiment was conducted by Aspect and has been shown that Bell inequality was not obeyed. Now, i have not really go through the details of Aspect experiment. But even without Aspect experiment, i knew that Bell inequality will not be obeyed. The reason being that Bells derivation of the inequality is based on the context that the instruction set is a one-to-one mapping with the measurement outcomes. Whereas in the experiment using polarization of light, the polarization of the photon and the measurement outcomes is a one-to-many mapping. This is due to the fact that a photon of a given polarization can be projected to more than one possible outcomes (depending on the number on polarization measuremnet axes). Therefore Bell inequality was naturally not obeyed. So now i think i need to understand the physical mechanisms of how a polarization can be projected onto another polarization axis. One should not argue this result independent of the physical mechanism of polarization measurement.

Am i making any sense here?

 

[DrChinese]

OK, let me summarize my thoughts here...
1) i previously tried to understand the QM problem from the EPR and Einstein box arguments. The papers i read overstressed the correlation feature which i feel may undermine the true essence of the problem. As Born's explanation to Einstein said: "objects far apart in space which have a common origin need not be independent. i believe this concept cannot be denied and simply has to be accepted. Dirac has based his whole book on this." (is he referring to Dirac's formulation of this two correlated particle problem with the tensor product of two Hilbert space?) In order words, conservation laws has already placed a contraint on the possibles particle states; the correlated result is hence solely derived from this. Nothing else. So what's the big deal? The big deal lies in the reasoning that to obtain such correlated result in experiment, the two particles must in the first place have an instruction set (or reality as coined Einstein) before measurement. Else it will require non local effects to communicate the measurement result of the first particle to the second particle state. Now, before knowing Bell's result and Aspect experiment, i can stick to the conviction that the particles must themselves have an instruction sets. Of course, by holding on to this conviction, i have wrestle with the dilemma as to whether i should regard the probability wave as a state of reality or that it is just a statistical description of the possible result which has already been predetermined before measuremnt. But since i am reluctant to embrace non-locality, i have to go with the latter view.

2) OK, then here comes the crunch. Bell derived the inequality that must be satisfied for measurements of particles each with an instruction set. And the experiment was conducted by Aspect and has been shown that Bell inequality was not obeyed. Now, i have not really go through the details of Aspect experiment. But even without Aspect experiment, i knew that Bell inequality will not be obeyed. The reason being that Bells derivation of the inequality is based on the context that the instruction set is a one-to-one mapping with the measurement outcomes. Whereas in the experiment using polarization of light, the polarization of the photon and the measurement outcomes is a one-to-many mapping. This is due to the fact that a photon of a given polarization can be projected to more than one possible outcomes (depending on the number on polarization measuremnet axes). Therefore Bell inequality was naturally not obeyed. So now i think i need to understand the physical mechanisms of how a polarization can be projected onto another polarization axis. One should not argue this result independent of the physical mechanism of polarization measurement.
Am i making any sense here?

Keep in mind that there is no (local) "instruction set" since Bell's Inequality is violated. Also, there is nothing different about photons than other particles. Any non-commuting observables for any particles - position and momentum for example (i.e. where PQ is not equal to QP) - will also lack an "instruction set". The spin characteristics (for photons or electrons) are most easily adapted for creation of a Bell Inequality. However, other similar relations can be seen with other observables.

 

[Sherlock]

If such entanglement results can be explained by the fact that conservation law has already imposed a constraint on the possible outcomes we can obtain, why are we still so mystified by such results?

Entanglement results can't be explained by conservation laws. (Afaik, there is no 'explanation' for entanglement results.) In the EPR scenario, where the detectors are aligned, then the correlated results would be explained by classical mechanics using the conservation law. But quantum theory treats the situation differently. The combined angular momentum is an interference property of the combined wave functions. (Quantum theory does incorporate the classical conservation laws, but they're not used to calculate the results of correlation experiments ... at least afaik.)

Is the concept of non-locality invoked just to reinforce (or fill in the loop-holes?) the 'wavefunction is a physical reality' interpretation? In order words, if we dun invoke non-locality, we cannot have the quantum object as a wave interpretation.

The 'quantum object' can be interpreted as a wave as long as definite phase relations between different parts of the wave function exist. These exist, and interference is possible, as long as no measurement takes place.

What happens on detection at A or B is that the system changes from having a definite combined angular momentum and an indefinite value of the spin component for each particle to having a definite value of the spin component for each particle and an indefinite combined angular momentum.

In qm the combined wave functions interact (via the principle of linear superposition), but once a particle is produced via measurement then definite phase relations are destroyed and no such interaction is possible. The 'collapse' of the wave function following a measurement leaves open, for some, the possibility of non-local 'communication' between A and B.
But, the correlations don't imply that either A or B is affected by the other on measurement. If you evaluate the mean value of any function of the spin variables of, say, particle B, with the wave function before a measurement, then it's the same as what you'll get after a measurement is recorded at A.

So now i think i need to understand the physical mechanisms of how a polarization can be projected onto another polarization axis.

You want to "understand the physical mechanisms of how a polarization can be projected onto another polarization axis." Well, so would everybody else it seems. :-) Unfortunately, quantum *mechanics* isn't a very mechanical description of nature. (Some have suggested that perhaps it should be called "quantum nonmechanics".) There *is* a justification of sorts for the 'projection' postulate -- but, I'm not sure I understand it well enough to discuss it. Maybe some of the mentors/advisors can give us their versions of the reasons for it.

I think that the correlations in, say, experiments involving polarizers, have more to do with the phases and amplitudes of paired, incident disturbances than with their polarization, per se. Anyway, I'm just a beginner. I hope you don't mind me offering my two cents worth wrt your questions. I like to jump into these threads with my sketchy knowledge because it makes me think and read a bit more than I probably otherwise would. The questions you're asking indicate that you're ready to get into a quantum theory textbook if you haven't done so already. (Then, in probably a relatively short time, you can join with others in explaining this stuff to me.)

 

[Sherlock]

By using the tricks in:
http://xxx.lanl.gov/abs/quant-ph/0302111
one can go further and to Bell/GHZ tests with spin-1/2 particles where the local parties do not even need to agree on a rotational frame of reference, showing that conservation of angular momentum isn't important to the "nonlocal magic" as it were...

From the article you referenced:
Our communication scenario consists of two parties that have access to a quantum channel but do not possesses a SRF. For simplicity, we consider a noiseless channel that transmits qubits (our results can be extended to noisy channels or higher-dimensional systems). Such a channel defines an isomorphism between Alice’s and Bob’s local experimental operations. ... We define the lack of a SRF as a lack of any knowledge of this isomorphism.
Is the 'trick' that they actually share a rotational reference frame, but are unaware of it? If so, then does this mean that there actually is a definite combined angular momentum, so that measurements by Alice and Bob are correlated in such a way that the sum of any pair is 0?

 

[QMrocks]

Entanglement results can't be explained by conservation laws. (Afaik, there is no 'explanation' for entanglement results.) In the EPR scenario, where the detectors are aligned, then the correlated results would be explained by classical mechanics using the conservation law. But quantum theory treats the situation differently. The combined angular momentum is an interference property of the combined wave functions. (Quantum theory does incorporate the classical conservation laws, but they're not used to calculate the results of correlation experiments ... at least afaik.)

Lets put it this way, if we use the Einstein box argument, then the conservation of particle number can be used to predict the explain accurately i.e. if the particle is in box A, then there must be no particle in box B etc. The quantum weirdness comes in when we set up measurement apparatus that allows a state to project itself into more than a unique outcome. For e.g. the polarization can be projected onto two orthogonally aligned polarizer. So that's why i said that how a polarization can be projected into two orthogonally aligned polarizer is the reason why Bell inequality was not obeyed.

You want to "understand the physical mechanisms of how a polarization can be projected onto another polarization axis." Well, so would everybody else it seems. :-) Unfortunately, quantum *mechanics* isn't a very mechanical description of nature. (Some have suggested that perhaps it should be called "quantum nonmechanics".) There *is* a justification of sorts for the 'projection' postulate -- but, I'm not sure I understand it well enough to discuss it. Maybe some of the mentors/advisors can give us their versions of the reasons for it.
I think that the correlations in, say, experiments involving polarizers, have more to do with the phases and amplitudes of paired, incident disturbances than with their polarization, per se. Anyway, I'm just a beginner. I hope you don't mind me offering my two cents worth wrt your questions. I like to jump into these threads with my sketchy knowledge because it makes me think and read a bit more than I probably otherwise would. The questions you're asking indicate that you're ready to get into a quantum theory textbook if you haven't done so already. (Then, in probably a relatively short time, you can join with others in explaining this stuff to me.)

Yes! What exactly is the whole physical mechanisms for a polarization to be projected onto another polarization. There got to be a rigorous explanation from atomic/molecular theory right? Oh, i already completed my fundamental QM courses and now taking a field theory course. But it seems that what we learn is mostly the technical aspect and not the philosophical. So i hope to make up for these deficiency from a forum discussion.

 

[QMrocks]

Keep in mind that there is no (local) "instruction set" since Bell's Inequality is violated. Also, there is nothing different about photons than other particles. Any non-commuting observables for any particles - position and momentum for example (i.e. where PQ is not equal to QP) - will also lack an "instruction set". The spin characteristics (for photons or electrons) are most easily adapted for creation of a Bell Inequality. However, other similar relations can be seen with other observables.

OK, now let's say my photon polarization are either horizontal or vertical. And my detection apparatus at the two ends are polarizer to detect either horizontal or vertical ONLY. Now, will Bell inequality still be obeyed?

 

[Sherlock]

Lets put it this way, if we use the Einstein box argument, then the conservation of particle number can be used to predict the explain accurately i.e. if the particle is in box A, then there must be no particle in box B etc. The quantum weirdness comes in when we set up measurement apparatus that allows a state to project itself into more than a unique outcome. For e.g. the polarization can be projected onto two orthogonally aligned polarizer. So that's why i said that how a polarization can be projected into two orthogonally aligned polarizer is the reason why Bell inequality was not obeyed.

Ok.

What exactly is the whole physical mechanisms for a polarization to be projected onto another polarization. There got to be a rigorous explanation from atomic/molecular theory right? Oh, i already completed my fundamental QM courses and now taking a field theory course. But it seems that what we learn is mostly the technical aspect and not the philosophical. So i hope to make up for these deficiency from a forum discussion.

It would be nice to get an explanation of this from a forum discussion. Especially if it were in a simple enough form that *even I* could understand it *right now*. Unfortunately, that doesn't seem likely to happen.
As Heisenberg says in, The Physical Principles of the Quantum Theory, This assumption is one of the formal postulates of quantum theory and cannot be derived from any other considerations.
As far as I've been able to find out, there isn't any *physical mechanism* for, as you put it, "a polarization to be projected onto another polarization".
One approach is to go back to the beginning and try to follow the line(s) of reasoning of the original developers of the theory in deviating from a course that would have allowed a geometrically visualizable formulation.
I got a book, Classics of Science, Volume Five -- Sources of Quantum Mechanics , published by Dover (it's relatively cheap) that has 17 of the seminal papers (translated into English where necessary) in the development qm published between 1916 and 1926. The answer to your question, or rather, the reason why your specific question (about what is exactly the whole physical mechanism involved) *can't* be answered, might be in some of those papers (especially in the papers by Heisenberg, Born and Jordan).

 

[QMrocks]

Ok.
It would be nice to get an explanation of this from a forum discussion. Especially if it were in a simple enough form that *even I* could understand it *right now*. Unfortunately, that doesn't seem likely to happen.
As Heisenberg says in, The Physical Principles of the Quantum Theory, This assumption is one of the formal postulates of quantum theory and cannot be derived from any other considerations.
As far as I've been able to find out, there isn't any *physical mechanism* for, as you put it, "a polarization to be projected onto another polarization".
One approach is to go back to the beginning and try to follow the line(s) of reasoning of the original developers of the theory in deviating from a course that would have allowed a geometrically visualizable formulation.
I got a book, Classics of Science, Volume Five -- Sources of Quantum Mechanics , published by Dover (it's relatively cheap) that has 17 of the seminal papers (translated into English where necessary) in the development qm published between 1916 and 1926. The answer to your question, or rather, the reason why your specific question (about what is exactly the whole physical mechanism involved) *can't* be answered, might be in some of those papers (especially in the papers by Heisenberg, Born and Jordan).

OK. Thanks for the tips. BTW, i love Dover books. That definitely looks like one i should have in my collection too.

 

[DrChinese]

OK, now let's say my photon polarization are either horizontal or vertical. And my detection apparatus at the two ends are polarizer to detect either horizontal or vertical ONLY. Now, will Bell inequality still be obeyed?

You won't see any "strange" behavior at that point because there is a "naive" explanation that works pretty well: if you measure the exact same attribute on entangled particles, then naturally you will get the same result. Of course, this explanation falls apart pretty fast when you examine it more closely.

To get a Bell Inequality, you normally look at specific angle setting combinations. Many angle settings, such as the ones you specified, do not lead to a difference between QM and Local Reality.

 

[QMrocks]

You won't see any "strange" behavior at that point because there is a "naive" explanation that works pretty well: if you measure the exact same attribute on entangled particles, then naturally you will get the same result. Of course, this explanation falls apart pretty fast when you examine it more closely.
To get a Bell Inequality, you normally look at specific angle setting combinations. Many angle settings, such as the ones you specified, do not lead to a difference between QM and Local Reality.

Yes. To defy the Bell inquality, we must require the measurement setup to allow the state to project itself into more than one outcome. What i call a one-to-many mapping situation of the local variables. So if we understand the physical mechanism for this process of a state projecting into another state, then the mystery is solve.

 

[sameandnot]

i wish someone would please pay attention to david bohm. the quantum potential and the implicate order not only connect relativity and quantum mechanics, but explains, in perfect clarity, the occurrence of action at a distance... non-locality. please, please refer to "science, order and creativity" as well as specific searches into the "quantum potential", via the 2-slit experiment, and the "implicate and explicate orders". i promise that this will make great sense. Einstein met with Bohm for 6 months discussing quantum mechanics, as Bohms explanation was the finest Einstein had ever read, or heard. f. david peat helped write the book mentioned earlier, but i promise every single person in the scientific fields, especially physics... quantum, reltivistic, classical or theoretical, will be endowed with unforseeable insight, if their minds are ripe. i am promising you all. i know that you cannot make a person read a book, or open their minds for that matter, so if you are genuinely concerned i am sure that you will check it out... if you are not genuinely concerned, i guess that your opinion and perspective aren't worth socks any way. peas.

 

[Tez]

OK, now let's say my photon polarization are either horizontal or vertical. And my detection apparatus at the two ends are polarizer to detect either horizontal or vertical ONLY. Now, will Bell inequality still be obeyed?

yes.

you cannot violate a Bell inequality without having the persons doing the measurements randomly switching between at least two different (incompatible) measurements. A projection onto horizontal/vertical is ONE measurement (with 2 outcomes)...

 

[DrChinese]

you cannot violate a Bell inequality without having the persons doing the measurements randomly switching between at least two different (incompatible) measurements. ...

The "randomly" requirement is ONLY necessary if you are also testing to determine if Alice's measurement apparatus is somehow influencing Bob's outcome (or vice versa) using a mechanism which is operating at light speed or below. There is no such known mechanism and no one (including Santos) has postulated any *specific* mechanism that I am aware of.

This has been conclusively* ruled out in experiments by Aspect et al (1981) and again by Weihs et al (1998). Random switching while the photons are mid-flight do not affect the outcome whatsoever.

-----------

*Although the results are conclusive to me, there are some local realists who postulate that there might exist new mechanisms which serve to affect the experimental outcomes in Bell tests. These mechanisms have the following attributes, according to this hypothesis:

a) The first mechanism appears only when detection efficiency is low and random switching prevents signals between measuring devices. The sample is biased, and this "explains" the null result obtained in the Weihs experiment mentioned above.
b) The second mechanism appears only when detection efficiency is high but there is a chance that there is signalling between measuring devices. The measurement devices reach some kind of equilibrium. This only shows up in tests in which there can be no sample bias as all results are used, such as http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v409/n6822/abs/409791a0_fs.html. This also explains the null results in this experiment.
c) These mechanisms only appear in Bell tests, and are not noticable at any other time by any other experiment. That is why they have never been noticed before.
d) They switch in and out in just such a way that the net result is EXACTLY what it takes to agree with QM - no more, no less. This serves to make us think that QM is correct when it really isn't, according to the hypothsis.
e) There is also a tooth fairy involved. OK, I made this last one up, but I really think it is as reasonable as a)-d).

 

[Tez]

The "randomly" requirement is ONLY necessary if you are also testing to determine if Alice's measurement apparatus is somehow influencing Bob's outcome (or vice versa) using a mechanism which is operating at light speed or below. There is no such known mechanism and no one (including Santos) has postulated any *specific* mechanism that I am aware of.
This has been conclusively* ruled out in experiments by Aspect et al (1981) and again by Weihs et al (1998). Random switching while the photons are mid-flight do not affect the outcome whatsoever.
-----------

I presume we agree that a Bell inequality is simly a mathematical expression, which to violate you need expectation values of at least two non-commuting observables on each side. How would I obtain the appropriate expectation values if I wasn't using random switching? The only way I see would be to use a large number of runs with fixed settings A1,B1 and then one of them change to a new setting and so on. The problem with this (other than it allowing an LHV explanation) is that we imagine (and quantum mechanics certainly says so) that the correlation functions apply to each and every instance of the experiment and not to a large ensemble. (Much like the density matrix applies to a single system). So I think what you're advocating (if I've understood it) will lead up the path of confusion if nothing else...

 

[DrChinese]

The only way I see would be to use a large number of runs with fixed settings A1,B1 and then one of them change to a new setting and so on. The problem with this (other than it allowing an LHV explanation) is that we imagine (and quantum mechanics certainly says so) that the correlation functions apply to each and every instance of the experiment and not to a large ensemble.

Sure, leave the settings fixed for a long enough period to collect a sufficient sample size. There is absolutely NO reason to switch them randomly - since this makes the experiment a lot more difficult - UNLESS you are trying to rule out local influences related to the measurement devices themselves. If you accept QM, this is not an issue. This is why almost all tests of Bell Inequalities DO NOT perform random switching. The violation of a Bell Inequality is often used these days for demonstrating that you have entanglement - not for demonstrating that LR is ruled out. Examples are the multi-photon entanglement setups (N>2). Although a lot of experiments also show violation of a Bell Inequality for the purpose of showing that every entanglement scenario imaginable can be used as a vehicle for supporting the predictions of QM. Examples of this are GHZ tests, tests of observables other than spin, etc.

On the other hand, if you are an advocate of LHV theories, you already know this has been ruled out as a factor in the Aspect and Weihs experiments - although there are some that are not satisfied with these experiments.

----------------

(Not to be obnoxious, but: normally in science, once it is demonstrated that a particular variable makes no difference to experimental outcomes, that variable is not required to be tested in every subsequent experiment. For example, does QM operate differently on Saturdays in the southern hemisphere versus Mondays in the Canadian winter? Or more practically: does using a 405 nm laser to create entangled photons tend to support QM, while using a 780 nm laser wouldn't? You wouldn't expect EVERY experiment to be performed with every possible variation considered just to be considered as a useful experiment with useful results. On the other hand, if someone comes up with an experiment that shows that some particular *combination* of variables makes a difference to the outcome of a Bell test - when those same variables make no difference individually - then I would be very interested to see that.)

 

[Tez]

From the article you referenced:
Our communication scenario consists of two parties that have access to a quantum channel but do not possesses a SRF. For simplicity, we consider a noiseless channel that transmits qubits (our results can be extended to noisy channels or higher-dimensional systems). Such a channel defines an isomorphism between Alice’s and Bob’s local experimental operations. ... We define the lack of a SRF as a lack of any knowledge of this isomorphism.
Is the 'trick' that they actually share a rotational reference frame, but are unaware of it? If so, then does this mean that there actually is a definite combined angular momentum, so that measurements by Alice and Bob are correlated in such a way that the sum of any pair is 0?

Yep - the two observers are presumed to not be rotating with respect to each other.

 

[Tez]

Sure, leave the settings fixed for a long enough period to collect a sufficient sample size. There is absolutely NO reason to switch them randomly - since this makes the experiment a lot more difficult - UNLESS you are trying to rule out local influences related to the measurement devices themselves. If you accept QM, this is not an issue. This is why almost all tests of Bell Inequalities DO NOT perform random switching.

Well its not a "test" of a Bell Inequality in such a scenario. Actually what happens in practise (except in the cases that violation of local realism IS being tested) is that state tomography is done in a manner such as you described - multiple runs with one pair of settings, multiple ones at another and so on. The reconstructed density matrix is subjected to certain maximum-likelihood estimation to produce a "physical" density matrix (i.e. one with positive eigenvalues, which is not what the tomography always gives!), and then sometimes from this reconstructed density matrix a value that would have occurred were one to try and violate the inequality is computed. This latter part is simply a way of demonstrating "how entangled" one's state was with a single parameter, but of course has nothing to do with "testing" Bell's theorem...

Sometimes I get papers to referee that are basically people trying to come up with loopholes in the various tests that have been performed. My inclination is to reject them (and often theyre not novel anyway). However, in all fairness there is still a large experimental effort to do the first "loophole free" (actually closing only detector/fair sampling loopholes) test of Bells theorem. So sometimes I accept them if they point out a subtlety those guys may have to think about. This is more likely with the current experiments which are going to use "photon subtracted" squeezed states and homodyne detection (followed by a complicated binning procedure). Still, I sure as heck ain't going to spend my time working on such things...