# Why are Bell's inequalities violated?

1. Jan 15, 2013

### 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 sx and sz 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 sx then the value of sz 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 sz )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 sz =+1. However, this interaction with the magnetic field may have altered sx and sy in an uncontrollable way! So, even if we had previously measured sx, its new value after the measurement of sz 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 sz does not change the value of sx.

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

Last edited: Jan 15, 2013
2. Jan 15, 2013

### DrChinese

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?

3. Jan 15, 2013

### JK423

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 :)

4. Jan 15, 2013

### DrChinese

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.

5. Jan 15, 2013

### JK423

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

Last edited: Jan 15, 2013
6. Jan 15, 2013

### DrChinese

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.

7. Jan 15, 2013

### nanosiborg

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.

8. Jan 15, 2013

### 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.

9. Jan 15, 2013

### DrChinese

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?

10. Jan 15, 2013

### Staff: Mentor

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.

11. Jan 15, 2013

### bohm2

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

12. Jan 15, 2013

### StevieTNZ

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.

13. Jan 15, 2013

### StevieTNZ

How do you know I don't?

14. Jan 15, 2013

### DrChinese

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".

15. Jan 15, 2013

### DrChinese

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.

16. Jan 15, 2013

### nanosiborg

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.

17. Jan 15, 2013

### Staff: Mentor

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

18. Jan 16, 2013

### harrylin

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

19. Jan 16, 2013

### bohm2

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)

Last edited: Jan 16, 2013
20. Jan 16, 2013

### DrChinese

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.

21. Jan 16, 2013

### harrylin

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.

22. Jan 16, 2013

### DrChinese

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.

23. Jan 16, 2013

### 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..

24. Jan 16, 2013

### DrChinese

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.

25. Jan 16, 2013