Why are Bell's inequalities violated?

[JK423]

Hello guys,

I am trying hard to understand the reason of the violation, and i hope you give me some help.

Here is my understanding so far:
Bell's inequalities are based on the measurement of non-commuting quantum observables, e.g. the measurement of the spin in x and z direction. This, to start with, raises red flags! That's because the proof of Bell's inequalities does not include a dependence on what observable we measure, instead it's assumed that both s_x and s_z have definite values and are not affected by the measurement.
But the experiments themselves, already tell us that this is not true! If you measure s_x then the value of s_z is altered! What this fact could mean is that the underlying "hidden variables" interact with the measuring device in an unknown physical way.
For example, throw an electron in a Stern-Gerlach aparratus (measuring s_z )and assume that this electron has well defined spins in all directions x,y,z before the interaction, described by an underlying local & realistic hidden variable theory. Ok, now the electron is seen to go upwards, i.e. it has s_z =+1. However, this interaction with the magnetic field may have altered s_x and s_y in an uncontrollable way! So, even if we had previously measured s_x, its new value after the measurement of s_z is different due to unknown underlying local, realistic physics!
That way, it seems quite obvious that Bell's inequality may be violated without assuming non-locality or absense of reality, since the derivation of Bell's inequality is based on the assumption that the measurement of s_z does not change the value of s_x.

What is your opinion on this? In the literature, has it been studied? Are there any physical arguments against it?

Thank you a lot!

Giannis

 

[DrChinese]

Here is my understanding so far:
Bell's inequalities are based on the measurement of non-commuting quantum observables, e.g. the measurement of the spin in x and z direction. This, to start with, raises red flags! That's because the proof of Bell's inequalities does not include a dependence on what observable we measure, instead it's assumed that both s_x and s_z have definite values and are not affected by the measurement.
But the experiments themselves, already tell us that this is not true! If you measure s_x then the value of s_z is altered! What this fact could mean is that the underlying "hidden variables" interact with the measuring device in an unknown physical way.

For example, throw an electron in a Stern-Gerlach aparratus (measuring s_z )and assume that this electron has well defined spins in all directions x,y,z before the interaction, described by an underlying local & realistic hidden variable theory. Ok, now the electron is seen to go upwards, i.e. it has s_z =+1. However, this interaction with the magnetic field may have altered s_x and s_y in an uncontrollable way! So, even if we had previously measured s_x, its new value after the measurement of s_z is different due to unknown underlying local, realistic physics!

That way, it seems quite obvious that Bell's inequality may be violated without assuming non-locality or absense of reality, since the derivation of Bell's inequality is based on the assumption that the measurement of s_z does not change the value of s_x.

This is the entire point of the Bell argument, and is well considered. Suppose what you say is correct. If so, then there are values for what the outcome would be IF you had measured at other angle settings. It turns out that you cannot come up with a set of those values in which the results here are independent of the setting there!

The easiest example to see this is with entangled photon pairs in which their polarization is always alike (ie from Type I down conversion crystals). Use the 3 angles 0, 120, 240 degrees. These are selected because the relative difference between any pair of these angle setting is either 0 degrees (same setting for Alice and Bob) or 120 degrees (any different setting for Alice and Bob). If you have a local realistic theory, the result for Bob cannot depend on the setting for distant Alice, right?

According to QM, the coincidence rate for Alice and Bob, when they compare their results, will be .25 (25%) which is cos^2(120 degrees). Of course this is when Alice and Bob independently choose different angle settings. When they happen to choose the same setting, they must ALWAYS get the same result.

Are you with me so far?

 

[JK423]

If so, then there are values for what the outcome would be IF you had measured at other angle settings. It turns out that you cannot come up with a set of those values in which the results here are independent of the setting there!

Correct.
A little while after my original post, i found a paper of A. Peres, "Unperformed experiments have no results" (Am. J. Phys. 46(7), July 1978), where he describes exactly this point.
So you are right, there are two kinds of results entering a Bell inequality: the actual results from experiments that were performed, and the hypothetical results coming from experiments that were never performed. And there is no possible way to fill the latter in order to account for the quantum mechanical predictions.

That's very nice :)

 

[DrChinese]

Correct.
A little while after my original post, i found a paper of A. Peres, "Unperformed experiments have no results" (Am. J. Phys. 46(7), July 1978), where he describes exactly this point.
So you are right, there are two kinds of results entering a Bell inequality: the actual results from experiments that were performed, and the hypothetical results coming from experiments that were never performed. And there is no possible way to fill the latter in order to account for the quantum mechanical predictions.

That's very nice :)

Yes, and keep in mind that Quantum Mechanics does NOT make the statement that the hypothetical unobserved (counterfactual) experiments have results. This is exclusively in the realm of the local realistic theory. Really, a Bell test is simply confirmation of the cos^2(theta) prediction of QM and nothing more. The Bell Inequality is simply a mechanism for showing that there exist situations in which a local realistic theory would make nonsensical predictions if QM IS correct.

 

[JK423]

What do you mean "if QM IS correct"?
The experiments violate the local realistic predictions irrespectively of QM's validity, right?

 

[DrChinese]

What do you mean "if QM IS correct"?
The experiments violate the local realistic predictions irrespectively of QM's validity, right?

Yes, true. The inequalities are usually oriented (and experiments designed) so that local realistic (LR) theories are on one side and QM on the other. But that is not an absolute requirement. Technically, both LR and QM could be wrong.

 

[nanosiborg]

Hello guys,

I am trying hard to understand the reason of the violation, and i hope you give me some help.

Here is my understanding so far:
Bell's inequalities are based on the measurement of non-commuting quantum observables, e.g. the measurement of the spin in x and z direction. This, to start with, raises red flags! That's because the proof of Bell's inequalities does not include a dependence on what observable we measure, instead it's assumed that both s_x and s_z have definite values and are not affected by the measurement.
But the experiments themselves, already tell us that this is not true! If you measure s_x then the value of s_z is altered! What this fact could mean is that the underlying "hidden variables" interact with the measuring device in an unknown physical way.
For example, throw an electron in a Stern-Gerlach aparratus (measuring s_z )and assume that this electron has well defined spins in all directions x,y,z before the interaction, described by an underlying local & realistic hidden variable theory. Ok, now the electron is seen to go upwards, i.e. it has s_z =+1. However, this interaction with the magnetic field may have altered s_x and s_y in an uncontrollable way! So, even if we had previously measured s_x, its new value after the measurement of s_z is different due to unknown underlying local, realistic physics!
That way, it seems quite obvious that Bell's inequality may be violated without assuming non-locality or absense of reality, since the derivation of Bell's inequality is based on the assumption that the measurement of s_z does not change the value of s_x.

What is your opinion on this? In the literature, has it been studied? Are there any physical arguments against it?

Thank you a lot!

Giannis

You're on the wrong track. As far as I'm aware your approach has been explored and doesn't lead to understanding what it is that makes Bell's formulation incompatible with qm and experiment.
There's no argument that some property (or properties) of the incident disturbances in relation to analyzer orientation determines individual detection, or that this property exists before, and is changed by, interaction with the analyzers.

Bell's theorem has to do with how an lhv model of quantum entanglement might be written.
There's still no universally accepted answer as to why it can't take the form that Bell proposed, or why Bell inequalities are violated.

Maybe it's that nature really is nonlocal and this nonlocality is manifested uniquely in Bell tests. This seems unlikely and a bit too convenient for some.
Maybe it has to do with the way the functions for individual detection are combined.
Maybe Bell's locality condition encodes a restriction that has nothing to do with locality.

These approaches, and more, are being explored. No definitive answer yet. Your thread question is an open question in physics.

 

[StevieTNZ]

We don't know if Bell's inequality is going to be violated in a loophole free test.

Taking the conclusion from one experiment that closes x loophole, and coupling that with the conclusion from another experiment that closes y loophole doesn't mean it is going to hold if one experiment closes x and y loopholes.

Though it seems unlikely, the physics community seems to be jumping up and down over non-locality being real when no such test confirms it.

 

[DrChinese]

We don't know if Bell's inequality is going to be violated in a loophole free test.

Taking the conclusion from one experiment that closes x loophole, and coupling that with the conclusion from another experiment that closes y loophole doesn't mean it is going to hold if one experiment closes x and y loopholes.

Though it seems unlikely, the physics community seems to be jumping up and down over non-locality being real when no such test confirms it.

You don't require the same level of loophole-free scientific proof for anything else, why for Bell? (That's a rhetorical question. )

I would certainly be interested in hearing about a local realistic theory that fails when locality is maintained, AND fails when the full universe is tested, but succeeds when both locality is maintained AND the full universe is tested at the same time. Exactly how do you think that would work?

Oh, and how is it that QM is so wrong for every type of entanglement ever tested so far? That is, considering there is no such thing as entanglement in a local realistic world?

 

[Nugatory]

We don't know if Bell's inequality is going to be violated in a loophole free test.

We don't, but that's true of every experimental test of every proposition.

At this point, the odds of finding a loophole (in Bell's argument and the experiments that support the violation of the equality) that would allow us to bring back a local realistic theory of the sort that EPR hoped for are pretty slim.

 

[bohm2]

Maybe it's that nature really is nonlocal and this nonlocality is manifested uniquely in Bell tests. This seems unlikely and a bit too convenient for some.

Why do you think it's unlikely and too convenient?

 

[StevieTNZ]

Oh, and how is it that QM is so wrong for every type of entanglement ever tested so far? That is, considering there is no such thing as entanglement in a local realistic world?

We don't know if QM is correct, if the loopholes are all closed in one experiment. We only know QM is correct is we allow certain loopholes.

 

[StevieTNZ]

You don't require the same level of loophole-free scientific proof for anything else, why for Bell? (That's a rhetorical question. )

How do you know I don't?

 

[DrChinese]

We don't know if QM is correct, if the loopholes are all closed in one experiment. We only know QM is correct is we allow certain loopholes.

We DO know for ALL tests performed to date. Same as for general relativity, our theories of galaxy formation and astrophysics in general, chemistry, atomic structure, evolution, standard model, etc etc etc.

As I said, there is no scientific reason to mention that loophole-free tests of ALL theories have never been performed. No one is claiming we know everything. All we are claiming is that if QM is correct, there are no local hidden variable theories. And every test supports QM, which is all you can say for any theory.

In normal everyday speak: a theory with sound experimental support is called "CORRECT".

 

[DrChinese]

At this point, the odds of finding a loophole (in Bell's argument and the experiments that support the violation of the equality) that would allow us to bring back a local realistic theory of the sort that EPR hoped for are pretty slim.

True. About as likely as discovering that relativity doesn't exist. Then we would wake up in a Newtonian local realistic universe*.

*I am guessing one that is also about 4000 years old.

 

[nanosiborg]

Why do you think it's unlikely and too convenient?

Unlikely because it's an assumption without evidence. Convenient because, using Bell's formulation, assuming nonlocality allows that the results at one end depend on the analyzer settings at the other end. Too convenient for my taste. Maybe not yours and others. But at this point it is just a matter of taste.

I think that something other than nonlocality will eventually answer the thread question.

 

[Nugatory]

How do you know I don't?

Because we don't see you over in the relativity forum worrying about loopholes in the M-M experiments?

 

[harrylin]

You don't require the same level of [..] scientific proof for anything else, why for Bell? (That's a rhetorical question. ) [..]

Some rhetorical questions deserve an answer. Extreme claims require extreme evidence. Thus I require the same level of scientific proof as for perpetuum mobilae.

 

[bohm2]

I think that something other than nonlocality will eventually answer the thread question.

There seems to be only 3 options based on assumptions made by Bell:

1. Non-locality
2. Anti-realism
3. Superdeterminism (no freedom of choice)

 

[DrChinese]

Some rhetorical questions deserve an answer. Extreme claims require extreme evidence. Thus I require the same level of scientific proof as for perpetuum mobilae.

Well, first of all, the observed results match theory. That isn't true of perpetual motion machines.

Second, I guess you answered the question about why you don't demand the same proof for relativity. The answer is that what is "extreme" is subjective (to you). You consider relativity "reasonable" in light of experimental proof but falsification of local realism "unreasonable" in light of experimental proof. Ergo you essentially conclude that which you sought to prove.

The reason I called it a rhetorical question is because of this point. If you are a local realist in 2013, you aren't going to let evidence affect your viewpoint. So no point in trying to answer the question.

 

[harrylin]

Well, first of all, the observed results match theory. That isn't true of perpetual motion machines.

Second, I guess you answered the question about why you don't demand the same proof for relativity. The answer is that what is "extreme" is subjective (to you). You consider relativity "reasonable" in light of experimental proof but falsification of local realism "unreasonable" in light of experimental proof. Ergo you essentially conclude that which you sought to prove.

The reason I called it a rhetorical question is because of this point. If you are a local realist in 2013, you aren't going to let evidence affect your viewpoint. So no point in trying to answer the question.

For sure perpetual motion machines match the theory of such experimenters, or so they claim (I did look into a few of them, so I know what I'm talking about). And not surprisingly, those experimenters reply in quite the same manner, claiming that no evidence is ever good enough for the scientific community - however, that's not true; only the requirements are extremely strict. But thanks for clarifying why your question was rhetorical.

 

[DrChinese]

For sure perpetual motion machines match the theory of such experimenters, or so they claim (I did look into a few of them, so I know what I'm talking about).

Ah, that is still not the same at all. Bell involves no modification to preexisting, accepted theory that forms our common ground. (I assume you don't disagree with QM pre-Bell.) So you can't really object that it hypothesizes new effects. There aren't any. The only new thing is realizing that QM did predict entanglement, and thus you can have a field day with experiments in that vein that are derived from orthodox QM. Of course, orthodox QM itself is falsifiable on a variety of fronts.

On the other hand, PMM advocates ARE proposing modifications to pre-existing, accepted theory (so there is not common ground). Those should be falsifiable if they are to be useful (otherwise they would be "ad hoc").

In my book, you pick and choose what evidence you accept, in order to be consistent with your pre-ordained conclusion.

 

[JK423]

Another question came up..
The CHSH quantity,
S_j = A_j\left( {{a_1}} \right)B_j\left( {{b_1}} \right) + A_j\left( {{a_1}} \right)B_j\left( {{b_2}} \right) + A_j\left( {{a_2}} \right)B_j\left( {{b_1}} \right) - A_j\left( {{a_2}} \right)B_j\left( {{b_2}} \right),
where A_j\left( {{a_i}} \right) = \pm 1 and B_j\left( {{b_i}} \right) = \pm 1, and j denoting a particular photon pair,
is always {S_j} = \pm 2, for any measurement result A and B.
When we take the mean value over all photon pairs, \,\left\langle S \right\rangle = \frac{1}{N}\sum\limits_{i = 1}^N {{S_j}} we find it to be bounded, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2.
This quantity is bounded whatever the values of A and B for the photon pairs.

Say that the choice of the angles a_i,b_i is not random but they are correlated to each other. I don't see how this inequality could be violated by a local and realistic model.. Can you help? I am trying to understand how this *loophole* works..

 

[DrChinese]

Another question came up..
The CHSH quantity,
S_j = A_j\left( {{a_1}} \right)B_j\left( {{b_1}} \right) + A_j\left( {{a_1}} \right)B_j\left( {{b_2}} \right) + A_j\left( {{a_2}} \right)B_j\left( {{b_1}} \right) - A_j\left( {{a_2}} \right)B_j\left( {{b_2}} \right),
where A_j\left( {{a_i}} \right) = \pm 1 and B_j\left( {{b_i}} \right) = \pm 1, and j denoting a particular photon pair,
is always {S_j} = \pm 2, for any measurement result A and B.
When we take the mean value over all photon pairs, \,\left\langle S \right\rangle = \frac{1}{N}\sum\limits_{i = 1}^N {{S_j}} we find it to be bounded, i.e.
- 2 \le \,\left\langle S \right\rangle \le 2.
This quantity is bounded whatever the values of A and B for the photon pairs.

Say that the choice of the angles a_i,b_i is not random but they are correlated to each other. I don't see how this inequality could be violated by a local and realistic model.. Can you help? I am trying to understand how this *loophole* works..

The word "loophole" is not usually used in this context, as it has a rather different meaning altogether.

A local realistic model will always have S<=2, do you see that? (Since S is between -2 and +2.)

However, experiments typically give a value of S>2, often in the 2.2 to 2.4 range depending on the particulars of the setup and efficiency. The usual value given for the QM predicted theoretical value is about 2.7 (again this varies somewhat depending on assumptions). So quantum theory and experiment are in reasonable agreement, but are at odds with predictions based on local realistic assumptions.

Does that address your question?

 

[JK423]

Thank you for your answer, although i don't think i understood your point.

You are saying that a local realistic model will always give |S|<=2.
So does this hold for any choice of the angles?
There is no demand for random non-correlated choice of angles?
Then what is all the fuss about free will of the observers etc and superdeterminism?

I thought that by using correlations between the choice of the angles, you could make a local realistic model violate the inequality.
Am i wrong?

 

[nanosiborg]

There seems to be only 3 options based on assumptions made by Bell:

1. Non-locality
2. Anti-realism
3. Superdeterminism (no freedom of choice)

Assuming either superdeterminism or nonlocality is not informative.

The answer is in the realm of anti-realism, which has to do with modeling restrictions.

 

[Nugatory]

You are saying that a local realistic model will always give |S|<=2.
So does this hold for any choice of the angles?
There is no demand for random non-correlated choice of angles?
Then what is all the fuss about free will of the observers etc and superdeterminism?

I thought that by using correlations between the choice of the angles, you could make a local realistic model violate the inequality.
Am i wrong?

At the risk of putting words in DrChinese's mouth (but if I get it wrong we'll find out), I expect that he meant "non-conspiratorial local realistic model". If the choice of angles is deterministic and the source knows what the determining rule is, or if the source is allowed to influence the choice of direction, then the source can produce pairs tailored to produce any results it pleases.

We tend to leave out the qualifier because the conspiratorial models are either uninteresting or reduce to some form of superdeterminism, or both.

 

[DrChinese]

Thank you for your answer, although i don't think i understood your point.

a) You are saying that a local realistic model will always give |S|<=2.
So does this hold for any choice of the angles?
There is no demand for random non-correlated choice of angles?

b) Then what is all the fuss about free will of the observers etc and superdeterminism?

c) I thought that by using correlations between the choice of the angles, you could make a local realistic model violate the inequality.
Am i wrong?

There are a batch of different issues in your comments. I will do my best to address.

a) Yes, LR models always yield |S|<=2 and that is for any choice of angles.

c) The LR model predicts results that are consistent with the inequality. However, those results do not happen in experimental situations. So the real world violates the inequality, not the LR model.

b) OK, the idea of superdeterminism is something I routinely criticize as non-scientific. But some folks I respect think it is worth mentioning, so I will attempt to describe the argument in as objective terms as able. I am answering this after c) so you can read c) again as needed.

The idea is that the angle settings that we think we are freely selecting correspond to ones in which the inequality will be violated, but that we are actually choosing ones in which this result was predetermined to violate the inequality even though the inequality is NOT really violated. So the results are predetermined, and further the results were predetermined in such a way to be misleading.

Imagine we are playing 3 card monte with queen and 2 jacks. You are trying to pick the queen each hand. I bend the queen card (but not the other 2) and shuffle them around. You pick the bent card and I turn it over to reveal a jack. You thought you freely chose the card but I fooled you ('cause I am sneaky). Every time we do it, you pick a jack. Eventually you conclude there is no queen. But actually there was one, you just didn't pick it.

Do you see that in this case, if there is something influencing you that you are not aware of, you might come to a false conclusion? This is the *analogy* to the superdeterminism argument. So all you have to do is acknowledge that IF your choice was somehow influenced with bias and you were not aware of it, THEN you could come to the wrong conclusion. This is superdeterminism.

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

Keep in mind that I vehemently deny that random angle choices has anything to do with a Bell test OTHER THAN to enforce strict Einsteinian separability. That was demonstrated in 1998 by Weihs et al. In a normal Bell test, you do not need to do ANYTHING other than show that the cos^2(theta) relationship predicted by QM is consistent with your results. The multiple angles thing is not needed at all and tends to confuse everyone. The reason is that Bell demonstrated that LR theories will not be able to yield datasets consistent with QM's cos^2(theta). So if QM is right (confirmed experimentally) then LR cannot be.

You don't need to know anything about Bell's proof or inequality if you simply try to construct a local realistic dataset of your own (I supplied some example angles at the beginning of this thread). Just try to create a dataset and you will see it cannot ever match the cos^2(theta) at those angles. If QM is experimentally right about the cos^2 relationship, then LR is logically excluded.

 

[DrChinese]

At the risk of putting words in DrChinese's mouth (but if I get it wrong we'll find out), I expect that he meant "non-conspiratorial local realistic model". If the choice of angles is deterministic and the source knows what the determining rule is, or if the source is allowed to influence the choice of direction, then the source can produce pairs tailored to produce any results it pleases.

We tend to leave out the qualifier because the conspiratorial models are either uninteresting or reduce to some form of superdeterminism, or both.

That's true, but I equate:

Conspiracy <=> Superdeterminism <=> Hand of god

in the sense that all of these are "outs". Of course these apply equally for all theories: evolution, cosmology, relativity, etc. I have no idea why any of these should be included as an qualification for a scientific discussion. You don't say "the universe is 13.7 billion years old UNLESS it is really 4000 years old and there is superdeterminism at work." I think everyone understands that if we are ALL being hoodwinked, then all bets are off on anything we might think we know.

 

[JK423]

At the risk of putting words in DrChinese's mouth (but if I get it wrong we'll find out), I expect that he meant "non-conspiratorial local realistic model". If the choice of angles is deterministic and the source knows what the determining rule is, or if the source is allowed to influence the choice of direction, then the source can produce pairs tailored to produce any results it pleases.

We tend to leave out the qualifier because the conspiratorial models are either uninteresting or reduce to some form of superdeterminism, or both.

Hmm i think that this helped! Thank you.
So, if i understand correctly:

The reason why a local realistic (non-conspirational) model will always satisfy Bell's inequality is due to the factorization of S_j (second line):
\begin{array}{l}<br /> {S_j} = {A_j}\left( {{a_1}} \right){B_j}\left( {{b_1}} \right) + {A_j}\left( {{a_1}} \right){B_j}\left( {{b_2}} \right) + {A_j}\left( {{a_2}} \right){B_j}\left( {{b_1}} \right) - {A_j}\left( {{a_2}} \right){B_j}\left( {{b_2}} \right) \\ <br /> = {A_j}\left( {{a_1}} \right)\left( {{B_j}\left( {{b_1}} \right) + {B_j}\left( {{b_2}} \right)} \right) + {A_j}\left( {{a_2}} \right)\left( {{B_j}\left( {{b_1}} \right) - {B_j}\left( {{b_2}} \right)} \right) \\ <br /> = \pm 2 \\ <br /> \end{array}. (1)
In order to violate Bell's inequality, this factorization should not be possible.
For example, non-locality would force the following change:
{A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _1}} \right) \to A_j\left( {{a_1},{\beta _1}} \right) \cdot {B_j}\left( {{a_1},{\beta _1}} \right),
{A_j}\left( {{a_1}} \right) \cdot {B_j}\left( {{\beta _2}} \right) \to A_j\left( {{a_1},{\beta _2}} \right) \cdot {B_j}\left( {{a_1},{\beta _2}} \right), (2)
etc.
This change allows the violation of the inequality because in general it's
A_j\left( {{a_1},{\beta _1}} \right) \ne A_j\left( {{a_1},{\beta _2}} \right), (3)
preventing the factorization as in (1), so S_j=±2 won't be always true and a violation of Bell's inequality is possible.

Now in the case of superdeterminism and conspirational models (but still local and realistic), Eq. (3) seems to hold as well. If the source knows beforehand what is to be measured, it can prepare the photon A in such a way so that e.g.
A_j\left( {{a_1},{\beta _1}} \right) = + 1 and
A_j\left( {{a_1},{\beta _2}} \right) = - 1,
being different like in (3), having the potential to lead to a violation of Bell's inequality.

Hope that i got this right!Update: DrChinese i just saw your new post, thank you a lot for your detailed description, it clarifies lots of misconceptions that i had.

 

[kith]

That's true, but I equate:

Conspiracy <=> Superdeterminism <=> Hand of god

in the sense that all of these are "outs". Of course these apply equally for all theories: evolution, cosmology, relativity, etc.

I'm not sure if this is really the case. In classical theories, the state of a system remains unchange by measurements, because the interaction of the observer with the system can be made arbitrarily small. So the measurement outcome doesn't depend on the past of the observer because it doesn't depend on the observer at all. In QM, the interaction between the observer leads to a physical change of the state of the system. So at least the assumption that the measurement outcome doesn't depend on the past of the observer is not as easily justifiable as in a classical theory.

 

[Nugatory]

So at least the assumption that the measurement outcome doesn't depend on the past of the observer is not as easily justifiable as in a classical theory.

That argument strikes me as a bit of a red herring. Yes, a superdeterministic quantum theory must include the observer whereas a deterministic theory (whether classical or merely EPR-friendly) need not. But that doesn't make superdeterminism any more palatable¹; and experiment has already rejected the deterministic observer-independent theories.

1: De [strike]gustibus[/strike] interpretationes non disputandum est.

 

[kith]

That argument strikes me as a bit of a red herring. Yes, a superdeterministic quantum theory must include the observer whereas a deterministic theory (whether classical or merely EPR-friendly) need not.

We know as a fact that measurements on a quantum mechanical system may change the state of this system, so every fundamental theory needs to include the observer somehow. This is a key difference between classical theories and QM. It isn't an argument for superdeterminism by itself. It simply shows that the question of superdeterminism has different implications in QM than in classical theories. In classical mechanics, the physics of the system is independent of the question wether the observer is free to chose what observables he wants to measure. In QM it's not.

I am not an advocate of superdeterminism. I just replied to a statement by DrChinese with which I don't agree.

 

[DrChinese]

I'm not sure if this is really the case. In classical theories, the state of a system remains unchange by measurements, because the interaction of the observer with the system can be made arbitrarily small. So the measurement outcome doesn't depend on the past of the observer because it doesn't depend on the observer at all. In QM, the interaction between the observer leads to a physical change of the state of the system. So at least the assumption that the measurement outcome doesn't depend on the past of the observer is not as easily justifiable as in a classical theory.

That does not make sense, kith. It doesn't matter whether a theory is classical or not! That is a completely arbitrary designation.

The fact is, there is no theory - now or ever - which explains how the observer's past has anything whatsoever to do with ANY experiment. That includes QM. It is just a blind ad hoc hypothesis thrown out by a few people. So you cannot explain WHY it should apply to entanglement more (or less) than the age of the universe or measurements of c or anything else.

 

[kith]

The fact is, there is no theory - now or ever - which explains how the observer's past has anything whatsoever to do with ANY experiment.

Usually, we have a system S and an observer O measuring some observable of the system. As soon as we consider the combined system S+O as a physical system (which may be observed by another observer O'), we acknowledge that the current state of S and O influences the evolution of the combined system. This evolution may of course include interactions between S and O. What's wrong with this kind of thinking?

 

[nanosiborg]

That does not make sense, kith. It doesn't matter whether a theory is classical or not! That is a completely arbitrary designation.

The fact is, there is no theory - now or ever - which explains how the observer's past has anything whatsoever to do with ANY experiment. That includes QM. It is just a blind ad hoc hypothesis thrown out by a few people. So you cannot explain WHY it should apply to entanglement more (or less) than the age of the universe or measurements of c or anything else.

I agree with this. The assumption of superdeterminism is useless for understanding why Bell's lhv formulation is inappropriate (ie., why it produces incorrect predictions) for modeling Bell tests.

 

[harrylin]

[..]
In my book, you pick and choose what evidence you accept, in order to be consistent with your pre-ordained conclusion.

Why would you do that? Or was it meant as a personal attack?

 

[kith]

I agree with this. The assumption of superdeterminism is useless for understanding why Bell's lhv formulation is inappropriate (ie., why it produces incorrect predictions) for modeling Bell tests.

Do you think the observer obeys the laws of nature, i.e. can be considered as a physical system?

 

[nanosiborg]

Do you think the observer obeys the laws of nature, i.e. can be considered as a physical system?

Sure. But the OP is concerned with why Bell's inequalities are violated. How will an ad hoc metaphysical assumption, such as superdeterminism, inform regarding that?

 

[kith]

Sure.

Do you agree that in a deterministic theory, the behaviour of a physical system is determined by its past or current state? Do you agree that in such a theory, the behaviour of the observer is determined by its past or current state if we treat him as a physical system?

But the OP is concerned with why Bell's inequalities are violated. How will an ad hoc metaphysical assumption, such as superdeterminism, inform regarding that?

Bell's theorem makes the assumption that the probability distributions for Alice and Bob are independent. If you don't make this assumption, you can't derive the inequality in the first place. So discussing this assumption seems relevant to me. Personally, I haven't completely wrapped my mind around superdeterminism and want to understand the arguments more deeply.

 

[bohm2]

Assuming either superdeterminism or nonlocality is not informative.The answer is in the realm of anti-realism, which has to do with modeling restrictions.

Just to be clear, when you are using the term "anti-realism", do you mean: no pre-existing properties (non-counterfactuals). I'm asking because this stuff is a bit confusing as there are problems even with what is meant by "realism" also. For instance Wood and Spekkens write:

It has always been rather unclear what precisely is meant by "realism". Norsen has considered various philosophical notions of realism and concluded that none seem to have the feature that one could hope to save locality by abandoning them. For instance, if realism is taken to be a commitment to the existence of an external world, then the notion of locality-that every causal influence between physical systeems propagates subluminally already presupposes realism.

The lesson of causal discovery algorithms for quantum correlations: Causal explanations of Bell-inequality violations require fine-tuning
http://arxiv.org/pdf/1208.4119v1.pdf

Perhaps, Maccone's definition of "realism" seems as one of the more clearer ones:

Let us define “counterfactual” a theory whose experiments uncover properties that are pre-existing. In other words, in a counterfactual theory it is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out. Sometime this counterfactual definiteness property is also called “realism”, but it is best to avoid such philosophically laden term to avoid misconceptions. Bell’s theorem can be phrased as “quantum mechanics cannot be both local and counterfactual”. A logically equivalent way of stating it is “quantum mechanics is either non-local or non-counterfactual”.

Simplest proof of Bell’s inequality
http://arxiv.org/pdf/1212.5214v1.pdf

But I always have trouble understanding this. If something is not pre-existing, would not the Wood and Spekkens argument above hold?

 

[DrChinese]

Usually, we have a system S and an observer O measuring some observable of the system. As soon as we consider the combined system S+O as a physical system (which may be observed by another observer O'), we acknowledge that the current state of S and O influences the evolution of the combined system. This evolution may of course include interactions between S and O. What's wrong with this kind of thinking?

It can apply to any theory equally! It certainly applies to special relativity, that is it's very reason to exist is to account for observer reference frames. There is absolutely no reason to suspect that there is anything special in that regards about QM. And not the slightest evidence to suspect that the observer's PAST influences the outcome (only the observer's choice of measurement setting).

 

[DrChinese]

Why would you do that? Or was it meant as a personal attack?

I don't attack people, sorry if anything I said implied otherwise.

However, I think it is clear that you value a specific view that is usually excluded by Bell+experiment. You are certainly not the only one. However, it is very difficult to discuss the subject meaningfully when you assume that which you seek to prove.

Of course, for all I know you might say the same thing about my viewpoint.

 

[Dan Fitzgibbon]

Unlikely because it's an assumption without evidence. Convenient because, using Bell's formulation, assuming nonlocality allows that the results at one end depend on the analyzer settings at the other end. Too convenient for my taste. Maybe not yours and others. But at this point it is just a matter of taste.

I think that something other than nonlocality will eventually answer the thread question.

Suppose there are two sorts of time, one in which the entangled particles in Aspect's experiment both change state at the same time and one (the usual one) in which their change of state should be separated by the amount of time it takes for the effect to travel between the two events at the speed of light, but is not observed to do so, hence our problem. Would that help?

 

[nanosiborg]

Do you agree that in a deterministic theory, the behaviour of a physical system is determined by its past or current state? Do you agree that in such a theory, the behaviour of the observer is determined by its past or current state if we treat him as a physical system?

I agree with what DrChinese said. It's irrelevant.

Bell's theorem makes the assumption that the probability distributions for Alice and Bob are independent. If you don't make this assumption, you can't derive the inequality in the first place. So discussing this assumption seems relevant to me. Personally, I haven't completely wrapped my mind around superdeterminism and want to understand the arguments more deeply.

I believe that superdeterminism is clutching at straws, and that it will not help us to understand the incompatibility between the lhv formalism and experiment. On the other hand, Bell's formulation of the independence assumption (his locality condition) is relevant, and some people (eg., Jarrett) think that a component of it (which, re Jarrett's analysis, doesn't necessarily inform regarding locality/nonocality in nature) might be the effective cause of BI violation.

Here's another way to approach the OP question. What is it about a basic Bell lhv model that produces a linear correlation (which is incompatible with the nonlinear one produced by qm and experiment) between θ and rate of coincidental detection?

Just to be clear, when you are using the term "anti-realism", do you mean: no pre-existing properties (non-counterfactuals). I'm asking because this stuff is a bit confusing as there are problems even with what is meant by "realism" also.

I should have said that I think the answer has to do with some aspect of the realism of Bell's formulation, which includes the separable functions A and B (which describe individual detection) expressed in terms of λ, and the expression of the independence (locality) assumption in terms of the functions A and B -- with the result of the Bell lhv program being against realism or "anti-realism" in that only nonrealistic models of quantum entanglement, such as in standard qm or MWI, are allowed (unless you assume ftl or instantaneous action at a distance, such as in dBB).

But I always have trouble understanding this. If something is not pre-existing, would not the Wood and Spekkens argument above hold?

I don't know. I don't understand the Wood and Spekkens article. Maybe you can explain it?

Suppose there are two sorts of time, one in which the entangled particles in Aspect's experiment both change state at the same time and one (the usual one) in which their change of state should be separated by the amount of time it takes for the effect to travel between the two events at the speed of light, but is not observed to do so, hence our problem. Would that help?

I don't see how it would. There's no particularly compelling reason to posit effects traveling between the two events. Paired detection events aren't correlated with each other except when the analyzer settings are aligned, in which case a local common cause explanation suffices.

 

[bohm2]

...only nonrealistic models of quantum entanglement, such as in standard qm or MWI, are allowed.

MWI is a "realistic" interpretation.

 

[nanosiborg]

MWI is a "realistic" interpretation.

Ok, then change ...
"with the result of the Bell lhv program being against realism or 'anti-realism' in that only nonrealistic models of quantum entanglement, such as in standard qm or MWI, are allowed (unless you assume ftl or instantaneous action at a distance, such as in dBB)"
... to ...
"with the result of the Bell lhv program being against realism or 'anti-realism' in that only models of quantum entanglement which don't employ hidden variables, such as in standard qm or MWI, are allowed (unless you assume ftl or instantaneous action at a distance, such as in dBB)".

So my answer to your question ...
"Just to be clear, when you are using the term "anti-realism", do you mean: no pre-existing properties ... ?"
... would be that when I'm using the term "anti-realism", I mean no hidden variables.

 

[harrylin]

[..]
Simplest proof of Bell’s inequality
http://arxiv.org/pdf/1212.5214v1.pdf

But I always have trouble understanding this. If something is not pre-existing, would not the Wood and Spekkens argument above hold?

Thanks for that link - regretfully they handle the assumption that it "is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out." However I see no reason to believe that this must always be applicable, and I thought that also Bell did not impose such a requirement to "realism" (or did I overlook it somewhere?).

 

[DrChinese]

I thought that also Bell did not impose such a requirement to "realism" (or did I overlook it somewhere?).

Yes, sadly Bell does not highlight this point. I guess he thought it was obvious. It is the spot after his (14) where he says, "It follows that c is another unit vector". The idea is that a, b and c are simultaneously real (i.e. elements of reality). So this is the spot where that assumption takes place, and without it he would not be able to continue to derive his conclusion.

 

[harrylin]

Yes, sadly Bell does not highlight this point. I guess he thought it was obvious. It is the spot after his (14) where he says, "It follows that c is another unit vector". The idea is that a, b and c are simultaneously real (i.e. elements of reality). So this is the spot where that assumption takes place, and without it he would not be able to continue to derive his conclusion.

I never realized that, and will have to check it out - thanks!