Bell experiment would somehow prove non-locality and information FTL?

[JesseM]

But if the photons leave the box before Alice makes her choice of detector setting, how is that possible without the effects of Alice's choice traveling backwards in time?

Good point; I should add to the effect that: Alice's re-orientation time is short in relation to the detector dwell time. So the mismatch -- the number of ''prior-orientation'' photons in transit -- has little effect on the overall probability distribution.

The problem is that by making this assumption, you're sidestepping the whole reason that violations of Bell's inequalities rules out local realism! Obviously your setup wouldn't work at all if Alice was regularly switching her detector settings, and the time x in seconds between switches was smaller than the distance y in light-seconds from Alice to the source--in this case, under a local theory, your "yoking" scheme can't work because by the time the source learns of each new detector setting, Alice has already switched to a different (random) detector setting. Now, you'd have to ask someone more familiar with experimental tests of the Bell inequalities to learn if the condition above has in fact been met; but there's no denying that quantum theory still predicts the Bell inequalities would be violated in this situation, and it's precisely this prediction that poses the fundamental problem for anyone trying to come up with a local realistic theory to match QM's predictions.

Notice that when I was stating the assumptions behind Bell's theorem in post #133, I included the bolded part below:

do you agree or disagree that if we have two experimenters with a spacelike separation who have a choice of 3 possible measurements which we label A,B,C that can each return two possible answers which we label + and - (note that these could be properties of socks, downhill skiers, whatever you like), then if they always get opposite answers when they make the same measurement on any given trial, and we try to explain this in terms of some event in both their past light cone which predetermined the answer they'd get to each possible measurement with no violations of locality allowed (and also with the assumption that their choice of what to measure is independent of what the predetermined answers are on each trial, so their measurements are not having a backwards-in-time effect on the original predetermining event, as well as the assumption that the experimenters are not splitting into multiple copies as in the many-worlds interpretation), then the following inequalities must hold:

When I wrote this I was thinking of a well-known loophole in Bell's theorem, which I think would be explicitly ruled out with a statistical independence condition in any fully rigorous proof of the theorem. The loophole is that if the source is somehow able to "anticipate" the detector settings Alice and Bob choose ahead of time, then it can adjust the hidden variables based on this in such a way that Bell inequalities can be violated. This should be pretty obvious in the case where the source has foreknowledge of both Alice and Bob's detector settings--if they both choose the same detector, like B B, then the source just has to send out photons whose "hidden" states are identical for that setting, like {A+,B+,C-} and {A-,B+,C-}. On the other hand, if they choose different settings, like A C, the source can send out photons whose hidden states on those settings are different (like {A+, B-, C-} and {A+, B+, C-}) 3/4 of the time, and photons whose hidden states on those settings are identical (like {A-, B-, C+} and {A+, B-, C-}) 1/4 of the time, thus violating the Bell inequality which says that when Alice and Bob choose different detector settings, the probability they get the same answer must be greater than or equal to 1/3.

This idea has certainly been discussed before--for example, one of the main ideas of Huw Price's book https://www.amazon.com/dp/0195117980/?tag=pfamazon01-20 was that it might be possible to come up with a hidden-variables explanation for QM if we allow backwards causation, i.e. Alice and Bob's future choices having an effect on the source in the past. Of course, any theory allowing such backwards causation might not be deemed "local" even if one-way causes were restricted to stay within the cause's light cone, since an event A could have an effect on an event B in its past light cone, and B could have an effect on an event C in its future light cone, such that there was a spacelike separation between A and C. There's also a variation on this idea which I've seen discussed, which is that in a fully deterministic universe, Alice and Bob's choices would already be implicit in the state of the universe before or at the moment the source emits the photons, so that the source could have foreknowledge without technically violating locality. But since a wide variety of causes throughout Alice's past light cone may affect her decision even in a deterministic universe, it's hard to see how any reasonable theory would allow the source to "deduce" her future choice (especially since some of the events in Alice's past light cone may lie outside the source's past light cone), and this seems a bit like retrocausation by another name (in a deterministic universe it is also conceivable that the hidden variables of the particles emitted by the source on a given trial would somehow force Alice and Bob to make particular choices of settings, or that the initial conditions of the universe would be chosen in such a way as to insure this sort of correlation between the source and Alice and Bob's choice of detector settings on each trial, but this all seems to imply a weird cosmic conspiracy that wouldn't arise in a natural way from any simple fundamental physics equations).

Anyway, the point is that I have seen this idea--that there is a possible loophole in that the source might "know" in advance the detector settings and adjust its output accordingly--discussed in a number of places, so it seems to be well-understood that one of the key assumptions behind Bell's theorem must be the statistical independence of the source's output on a given trial and Alice and Bob's detector settings on the same trial. You haven't discovered anything fundamentally new with your example, and in any case, without some form of "retrocausation" the type of local hidden variables explanation in your example won't be able to cover all cases (again, it won't cover cases where Alice and Bob randomly switch detector settings at regular time-intervals, and the time x in seconds between switches is smaller than the distance y in light-seconds from them to the source).

 

[JesseM]

To add to my previous post, and to support my claim that a modern rigorous derivation of the Bell inequalities would include a condition about the source not "anticipating" the detector settings, check out this paper:

http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Aquant-ph%2F0312176

In particular, look at section D on p.6, where the "No conspiracy" assumption is discussed.

 

[wm]

In response to my:

Yes, that is correct. If the Alice-to-box link is broken then a DIFFERENT set of equations arises from Malus' Law. But (of course) they again reproduce exactly the results that would be found experimentally with the newly established system,

vanesch wrote:

You should show me how you derive your correlation cos^2(th_a - th_b). Because, as I said, this does NOT follow from a standard application of Malus' law at both sides. As Dr. Chinese pointed out, when you apply Malus' law on both sides, you find an "attenuated" form of correlation, which is compatible with the Bell inequalities, and NOT cos^2.

Dear vanesch; I would say that my original agreement (my paragraph at top) remains OK. So: Do we differ?

For I'm not clear on what you want me to show you; or, rather, I am not clear on the experimental setting that you require the correlation for?

Perhaps, with the deepest respect, you are confusing two very different experimental situations. (OR perhaps I implied somewhere that your correlation cos^2(th_a - th_b) applies to the DIFFERENT case?)

1. The correlation that you cite above IS derived from Malus' Law, AND is the correct result for the related experiment. (Let us identify that experiment -- which is the experiment described in post #166 https://www.physicsforums.com/showpost.php?p=1216247&postcount=166 -- as wmX1.) That is: That correlation -- cos^2(th_a - th_b) = cos^2 (a, b) -- would certainly be confirmed by experiment on a wmX1 setting.


2. In the second case, when you destroy or remove the mechanical Alice-to-box linkage, we have a very DIFFERENT experiment. Let us call it wmX2. BUT, again using Malus' Law on both sides, we can derive the correct (experimentally confirmed) correlation.

3. wmX2 certainly provides an attentuated correlation when compared to the correlation for wmX1; a correlation now consistent with a Bellian Inequality: For Alice is now on the same footing as Bob, her one-to-one correlation with the box (the source) gone; the overall correlation reduced (as you say).

4. To be clear: IF THE BOX REMAINS IN PLACE (as in wmX1 and wmX2), application of Malus' Law to both sides of the box will yield the correct (experimentally confirmed) correlation.

Do we differ?

Regards, wm

 

[JesseM]

Disagree with me...?

Well, the 2 issues are:

a) Are you performing a Bell-type test using entangled photons? If not, then I'm not interested anyway and there is no disagreement.

Well, what do you mean by "a Bell-type test"? He's suggesting an experiment similar to Bell's in that each experimenter can choose between three possible detector settings which will each give yes/no answers, and looking at the correlation depending on whether the experimenters use the same setting or different settings. But the "yoking" of the source to one experimenter's setting on each trial violates one of the basic assumptions that must be used when proving Bell's theorem rigorously (and as I mentioned in an earlier post to wm, this sort of yoking would be impossible under a local theory if the time between the experimenter switching detector settings was sufficiently small and the distance between the experimenter and the source was sufficiently large).

b) Assuming you are doing a Bell test: Are you looking to predict the outcome? If so, you will use the cos^2 function unless... you want to get the wrong answer. In which case again, I'm not interested anyway and there is no disagreement.

But the cos^2 rule would still work if you weren't talking about the probability of individual photons being detected, but instead talking about the reduction in intensity of classical EM waves of a single frequency as a polarized beam from the source passes through an experimenter's polarization filter, depending on the angle between their filter and the angle of the filter at the source (a setup like the one shown on http://scholar.hw.ac.uk/site/physics/topic6.asp?outline= ). And of course, a computer could use this ratio between (intensity of light getting through source's filter) and (intensity of light getting through experimenter's filter) as a probability to display a + on the experimenter's screen. The probabilities of getting a + vs. a - would be exactly the same, given the experiment wm described, as if + and - corresponded to individual entangled photons making it through/not making it through the experimenter's filter. So, the fact that he finds a violation of a Bell inequality does not really have anything to do with quantum physics, it's just a consequence of this "yoking".

 

[DrChinese]

4. To be clear: IF THE BOX REMAINS IN PLACE (as in wmX1 and wmX2), application of Malus' Law to both sides of the box will yield the correct (experimentally confirmed) correlation.

Do we differ?

I still do not understand the point of your twist. How does it change anything? Unless you can explain this point, I am about ready to drop out of the discussion. (Your argument so far amounts to a repeat of Bell's Theorem, which we were already happy with.)

And about the application of Malus' Law to both sides: keep in mind that Malus' Law can be applied in 2 completely different ways:

1. The way it is applied by QM: Assuming that the wave function for Alice & Bob's particles collapse on first observation of either, and we now know the polarization of the other; so we can predict the rate of correlation as cos^2(theta). This will agree with experiment.

2. The way a local realist would naturally want to apply it: entanglement is not real and there is a specific polarization for the 2 photons that is simply the same value; therefore you apply Malus on both sides (independently, then integrate) and get the .25+cos^2(theta)/2 formula. This formula deviates wildly from experimental results.

Once you follow these points - two very different ways of looking at cos^1 - we can drill into any questions about the specifics of these.

 

[DrChinese]

Well, what do you mean by "a Bell-type test"? He's suggesting an experiment similar to Bell's in that each experimenter can choose between three possible detector settings which will each give yes/no answers, and looking at the correlation depending on whether the experimenters use the same setting or different settings. But the "yoking" of the source to one experimenter's setting on each trial violates one of the basic assumptions that must be used when proving Bell's theorem rigorously (and as I mentioned in an earlier post to wm, this sort of yoking would be impossible under a local theory if the time between the experimenter switching detector settings was sufficiently small and the distance between the experimenter and the source was sufficiently large).

...So, the fact that he finds a violation of a Bell inequality does not really have anything to do with quantum physics, it's just a consequence of this "yoking".

I don't get the point of the "yoking". Assuming we are using entangled photons, you get a violation of the Bell Inequality. This is true whether or not we rigorously rule out locality violation. The only difference is that when the yoking is present, the results are not rigorous. That's a step backward, so that is why I don't understand the twist. What do we get for it?

(It is almost like saying, Alice always selects A and Bob can select A, B or C. I think... )

 

[JesseM]

And about the application of Malus' Law to both sides: keep in mind that Malus' Law can be applied in 2 completely different ways:

1. The way it is applied by QM: Assuming that the wave function for Alice & Bob's particles collapse on first observation of either, and we now know the polarization of the other; so we can predict the rate of correlation as cos^2(theta). This will agree with experiment.

wm is not directly applying Malus' law to the correlation between Alice's result and Bob's result. wm's example just uses Malus' law to find the probability that each one individually sees a photon when they orient their polarizers at a certain angle, given that the angle of the polarizer at the source is "yoked" to Alice's polarizer (using ordinary classical signals, so there must be a built-in delay) in such a way that it has a 50% chance of being at the same angle and a 50% chance of being at a 90-degree angle relative to hers (the random element is included just to ensure that she sees a random mix of + and - results, rather than all +'s). In other words, the two angles being fed into the cos^2(angle_1 - angle_2) are not the angles of Alice and Bob's polarizers, they are the angles of Bob's polarizer and the source's polarizer. So any entanglement is irrelevant, if you were just using classical EM waves it would still be true that the light reaching Bob is reduced in intensity by a factor of cos^2(angle_1 - angle_2). And of course in QM, intensity is proportional to the number of photons making it through, or the probability an individual photon makes it through.

2. The way a local realist would naturally want to apply it: entanglement is not real and there is a specific polarization for the 2 photons that is simply the same value;

Yes, this is what is assumed in wm's example.

therefore you apply Malus on both sides (independently, then integrate) and get the .25+cos^2(theta)/2 formula.

That would be true if the source's polarization was statistically independent of Alice's choice of how to orient her polarizer, as would be assumed in a proof of Bell's theorem, but it's not true in wm's example because of the "yoking" he assumes. Of course if the yoking is done by classical means, there will be a delay which will cause wm's classical experiment to deviate somewhat from quantum predictions, and the classical setup will be wholly unable to replicate quantum predictions in the case where Alice is rapidly switching measurement angles in such a way that by the time a classical signal about each new angle has made it to the source, she has already switched to a different angle. In this case, all the Bell inequalities will be obeyed in wm's classical experiment, so this type of "yoking" will not allow a local hidden variables theory to replicate quantum predictions about entanglement in general.

 

[wm]

wm,

Vanesch is absolutely right, and I alluded to the same thing in an earlier post about the alternative formulae that some local realists put forth. Unfortunately, I am quite guilty of what Vanesch refers to because I reference Malus without supplying the entire story. Again, it comes back to the basics that I keep re-iterating.

1. IF you assume locality, realism (sometimes called hidden variables) and the QM formula (cos^2 theta) for predicting coincidences for entangled photon experiments, you end up with Bell's Inequality. You know this is correct, because you derived this relationship for yourself.

Doc: NOT quite TRUE; NOT quite CORRECT. The photons emerging from the box are dis-entangled. The calculations are clearly based on these NON-ENTANGLED photons; as I believe they must be if I want to give the CORRECT CLASSICAL derivation that I did give.

NOTE (and this may be the point of confusion here): I used an Aspect-style source of entangled photons, sandwiched between dichotomic linear polarisers, to create the NON-entangled photons that the calculations apply to. That's why I said earlier that Malus (1807) could have derived the result if he'd assumed the existence of such photon-pairs.

2. Tests of Bell's Inequality support the QM formula for predicting coincidences, within a very small margin of error. IF you accept these tests as valid, then you must reject either locality OR realism.

Interesting theory, Doc; IF .. THEN? (Might run better on the Pop-psychology Forum (perhaps)):

For here is the result of testing your theory:

1. I accept, without reservation, the validity of the results of Bell-Inequality-Tests (eg, Aspect's with photons).

2. I DO NOT reject locality or realism (properly defined)!

3. PS: Confident that Nature is local, I reject, without reservation, Bellian-realism.

3. It is perfectly acceptable to conclude, as you do, that realism should be rejected. One of the incentives for doing this is to keep relativity in a position as a fundamental law of nature.

Yes; and thank you. But PLEASE: With realism coming in so many flavours, there is no need to reject REALISM as such; only certain brands. Thus, having no taste for Bellian Realism, that's the flavour I reject.

PS: Per citation at foot, Bell had similar taste-buds: It seems John Bell had no taste at all (or a certain distaste) for his own cooking: ie, Bell's Theorem?

4. IF you create a classical test which respects both locality and realism, you cannot also have an algorithm that violates Bell's Inequality.

BUT I just did exactly that! What am I missing here, please?

Even if you could somehow do this, you still would not disprove Bell's Theorem, which states (in my words):

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

Well; I just did ''this'' (the classical experiment). As for disproving Bell's theorem, Doc: You know where my website is!

5. I think if we stick to the above issues, and ignore negative probabilities, "perverse" applications of Malus, etc., we can be more constructive and it will be a lot easier to see the true elements of the debate.
-DrC

I am happy to accept your position. As I see it, you move us to the central issue: No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

However, since that subject might be a hi-jacking of this thread, should you open a new one?

Pending that for now, let me say:

John Bell was not happy with this representation of his theorem (as I understand it).

Neither am I happy with his theorem! Convinced that Nature is local, I just go further and reject it.

To quote a leading authority in the field: ''To those for whom nonlocality is anathema, Bell's Theorem finally spells the death of the hidden variables program. But not for Bell. None of the no-hidden-variables theorems persuaded him that hidden variables were impossible.(Mermin, Rev. Mod. Phys. 65 page 814, 1993) [emphasis added].

Cheers, wm

 

[wm]

HEY JESSE, have you MISQUOTED wm. (Which certainly doesn't help his case at all.) Look at this:

Originally Posted by wm
2. The way a local realist would naturally want to apply it: entanglement is not real and there is a specific polarization for the 2 photons that is simply the same value;

That just doesn't look like anything that wm would say. Can you find the quote; or FIX IT please? Thanks.

 

[JesseM]

I don't get the point of the "yoking". Assuming we are using entangled photons, you get a violation of the Bell Inequality.

But with the yoking, you're making the entanglement irrelevant so it can be viewed as a classical problem, and of course wm is trying to show that violations of the Bell inequality can occur in classical situations. Think of it this way--the experiment would work exactly the same way if you took Alice out of the picture entirely and just used single photons, and you had the source itself randomly pick three angles A, B, and C, and then used some other event like an atomic decay to decide whether to have its polarizer be at the 0 degrees relative to the angle it had chosen or at 90 degrees relative to it. If you mark every trial where it picks 0 degrees as + and every trial where it picks 90 degrees as -, then the polarizer's recorded series of +'s and -'s are 100% guaranteed to be exactly the same as the series Alice would have recorded if you were using pairs of entangled photons and the source was yoked to Alice's choice of measurement angle (assuming you ignore the possibility of delays in the yoking which might allow occasional photons to be emitted between the time Alice changes her angle and the time the source updates its own angle in response). So the violation of Bell's inequality that wm derives would also occur if you were looking at correlations between the +'s and -'s recorded by the source (which were based on something like the decay of a radioactive atom which was not entangled with the photon emitted by the source) and the +'s and -'s recorded by Bob. Also, as noted above, you could get the exact same violation if you were assuming classical EM waves rather than photons, with Bob's computer choosing the probability to display a + on each trial based on the reduction in intensity of the light passing through his polarizing filter. But these are not genuine violations of Bell's theorem, because Bell's theorem only says the inequalities must be obeyed under certain conditions, and one of the conditions is the statistical independence of the properties of signals/particles emitted by the source and experimenters' choice of what to measure (not true in the case where the source is yoked to Alice's measurements via an ordinary classical signal), while another condition is that there be a spacelike separation between each pair of measurements (not true in the case of the radioactive decay and Bob's measurement, since the decay actually has a causal effect on Bob's measurement in terms of the source's polarizer angle depending on it).

 

[JesseM]

HEY JESSE, have you MISQUOTED wm. (Which certainly doesn't help his case at all.)

Yes, sorry, from the context I think it was pretty clear that I was quoting DrChinese and had just accidentally typed the wrong name. Fixed now.

 

[JesseM]

Even if you could somehow do this, you still would not disprove Bell's Theorem, which states (in my words):

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

Well; I just did ''this'' (the classical experiment).

As I pointed out earlier, your classical version will not work for arbitrary distances between Alice and the source and arbitrarily fast switching between measurement angles for Alice and Bob. In particular, if Alice and Bob randomly switch their measurement angles every x seconds, and their distance from the source is larger than x light-seconds (ensuring that by the time the source gets any signal about Alice's settings, she has already switched to a new random setting), then you won't be able to get any violation of the Bell inequality when you compare Alice and Bob's measurements at a given time, assuming you're doing a classical experiment involving non-entangled photons (or any classical object/signal, like classical EM waves or digital signals), and assuming there is a spacelike separation between each pair of measurements. Do you disagree?

 

[wm]

OK, just trying to make sure I understand the math here: Now, you said you were using the angles a = 0, b = 67.5, c = 45. So, calculating P(BC = S|bc), P(AC = D|ac) and P(AB = S|ab) explicitly, we have:

<CUT>

Now that I think I understand your proposal, I'll explain why it isn't a genuine violation of Bell's theorem in a followup post.

Jesse, I haven't checked all the details, but you seem to on the right path.

I just wanted to rush to you an issue that might be confusing much on this thread:

While I am confident that other work is a genuine violation of Bell's theorem, the proposal we are discussing is designed to violate Bell's theorem in the (limited) following way:

Peres, CHSH, etc give Bellian inequalities based on dichotomic + xor - outcomes. Such inequalities are often supported by ''simplistic'' classical examples (eg, down-hill skiers, dirty-socks). My proposal shows (I believe) that there are classical settings which breach their inequalities.

So Bell's Theorem is challenged to the extent that it leads to the common-garden Bellian-Inequalities.

There are multi-particle experimental results which call for more complex analysis. While I am happy to provide such, that was NOT the goal of the CLASSICAL experiment we are discussing. The one that you appear to be on top of.

Hope this clarifies somewhat, wm

 

[DrChinese]

But with the yoking, you're making the entanglement irrelevant so it can be viewed as a classical problem...

JesseM,

wm is saying there are no entangled photons. Ok, then there is nothing important to discuss, you end up coming back to a classical example with colored socks or similar. The issue is: QM, locality, realism and that is all anyone really cares about. I agree with your treatment of the issue but I do not see where any of it is going. Good luck helping wm.

wm,

Your understanding of the context and history of the Bell's Theorem is off, and you would be better served by additional research before you put forth your assertions. Bell's Theorem stands. Also, you seriously mischaracterize Bell's position. He was not sorry for creating his theorem, and as best I can tell evolved to believe in a non-local view of hidden variables.

I will continue to follow the thread, but will lay low for a while. I think wm's example has become so convoluted as to primarily touch on issues that are unproductive. I will chime again if I see something I might be able to add.

Cheers,

-DrC

 

[JesseM]

My proposal shows (I believe) that there are classical settings which breach their inequalities.

Sure, but Bell's theorem doesn't say the inequalities can never be violated in a classical universe, just there are certain specific conditions under which they won't be violated in a classical universe, such as the condition that there's a spacelike separation between the two measurements. If you look at an experiment which doesn't respect these conditions (as yours does not), violating the inequalities is quite trivial! For example, if Alice and Bob each ask me one of three yes-or-no questions every 10 minutes, and I only answer once I have heard both their questions, it'll be quite easy for me to make sure that I always give the same answer to both when they ask the same question, while giving different answers more than 1/3 of the time when they ask different questions. Your example doesn't challenge Bell's theorem any more than this one does.

 

[wm]

As I pointed out earlier, your classical version will not work for arbitrary distances between Alice and the source and arbitrarily fast switching between measurement angles for Alice and Bob. In particular, if Alice and Bob randomly switch their measurement angles every x seconds, and their distance from the source is larger than x light-seconds (ensuring that by the time the source gets any signal about Alice's settings, she has already switched to a new random setting), then you won't be able to get any violation of the Bell inequality when you compare Alice and Bob's measurements at a given time, assuming you're doing a classical experiment involving non-entangled photons (or any classical object/signal, like classical EM waves or digital signals), and assuming there is a spacelike separation between each pair of measurements. Do you disagree?

Given the above defined conditions, I fully agree.

BUT NOTE: You are adding conditions that were never intended to be addressed by the proposal. Please see a recent reply to vanesch: Alice sits beside her detector and the box, which are close-coupled (like much lab equipment), ON HER DESK. Bob is far away, etc.

This is another clarification which needs to be added to the proposal's specification to maintain its focus on a simple classical device.

Thanks, wm

 

[wm]

Sure, but Bell's theorem doesn't say the inequalities can never be violated in a classical universe, just there are certain specific conditions under which they won't be violated in a classical universe, such as the condition that there's a spacelike separation between the two measurements. If you look at an experiment which doesn't respect these conditions (as yours does not), violating the inequalities is quite trivial! For example, if Alice and Bob each ask me one of three yes-or-no questions every 10 minutes, and I only answer once I have heard both their questions, it'll be quite easy for me to make sure that I always give the same answer to both when they ask the same question, while giving different answers more than 1/3 of the time when they ask different questions. Your example doesn't challenge Bell's theorem any more than this one does.

I think that it does. Does your example breach the CHSH Inequality?

Please let me know, wm

 

[wm]

JesseM,

wm is saying there are no entangled photons.

Doc, enjoy your vacation; I hope you'll soon be back.

But for the record: I did not say so loosely ''there are no entangled photons''. From the very beginning I referred to Aspect's experiment (= entangled photons) ...

Ok, then there is nothing important to discuss, you end up coming back to a classical example with colored socks or similar. The issue is: QM, locality, realism and that is all anyone really cares about. I agree with your treatment of the issue but I do not see where any of it is going. Good luck helping wm.

I'm happy to acknowledge Jesse's help; help more than many (including Jesse) may appreciate.

wm,

Your understanding of the context and history of the Bell's Theorem is off, and you would be better served by additional research before you put forth your assertions. Bell's Theorem stands. Also, you seriously mischaracterize Bell's position. He was not sorry for creating his theorem, and as best I can tell evolved to believe in a non-local view of hidden variables.

I rely on the Mermin quote: ''To those for whom nonlocality is anathema, Bell's Theorem finally spells the death of the hidden variables program. But not for Bell. None of the no-hidden-variables theorems persuaded him that hidden variables were impossible.'' (Mermin, Rev. Mod. Phys. 65 page 814, 1993) [emphasis added].

NB: IT WAS WRITTEN AFTER BELL'S DEATH.

I'd (of course) welcome a citation from an equivalent authority giving a dissident view.

With best regards, wm

 

[JesseM]

I think that it does. Does your example breach the CHSH Inequality?

Please let me know, wm

In general, any inequality that's violated in QM should also be easy to violate in a classical question-and-answer game like the one I described, where I get to hear both questions before giving my answers--all I have to do is translate the questions into settings of some hypothetical inequality-violating quantum experiment, calculate in my head what the probability is that each experiment will get a + or - according to quantum mechanics, and then make my probabilities of answering "yes" or "no" proportional to these calculated probabilities! Obviously an ordinary classical computer can calculate the probabilities in any quantum experiment, so no actual quantum effects are needed here.

But I can try to come up with a simpler strategy to violate a given inequality in a question-and-answer game, if you like. I looked up the CHSH inequality and could only find it in the wikipedia article which stated it in terms of the expectation values, I'd like to restate it in terms of probabilities to make it easier to think up with an example. In terms of expectation values, if both Alice and Bob have two measurement settings A and B which can each yield two results + or -, assigned values +1 and -1, then the CHSH inequality says:

-2 <= X <= 2

('<=' stands for 'smaller than or equal to', when I typed the actual symbol the board's softward replaced it with a question mark)

where

X = E(Alice measures A, Bob measures A) - E(Alice measures A, Bob measures B) + E(Alice measures B, Bob measures A) + E(Alice measures B, Bob measures B)

Converting expectation values into probabilities should give:

1. E(Alice measures A, Bob measures A) = P(S|aa) - P(D|aa)
2. E(Alice measures A, Bob measures B) = P(S|ab) - P(D|ab)
3. E(Alice measures B, Bob measures A) = P(S|ba) - P(D|ba)
4. E(Alice measures B, Bob measures B) = P(S|bb) - P(D|bb)

Since P(D|aa) = 1 - P(S|aa) and so forth, this simplifies to:

1. E(Alice measures A, Bob measures A) = 2*P(S|aa) - 1
2. E(Alice measures A, Bob measures B) = 2*P(S|ab) - 1
3. E(Alice measures B, Bob measures A) = 2*P(S|ba) - 1
4. E(Alice measures B, Bob measures B) = 2*P(S|bb) - 1

So, that should give X = 2*[P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab)] - 3

which means -2 <= X <= 2 is equivalent to:

1/2 <= P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab) <= 5/2

Would this be a valid formulation of one case of the CHSH inequality? (the case when Alice and Bob both choose between the same two measurements A and B--from the way it was formulated on wikipedia it seems to be more general than that) Let me know if I made an error in math or understanding. Also, what is being assumed about the results when both choose the same detector settings? Are P(S|aa) and P(S|bb) equal to 1, or 0? Or can I just assume any probability between 0 and 1 for each of the four? Once I'm clear on the equation for the CHSH inequality in terms of probabilities, and on what assumptions are being made about identical settings, I should be able to come up with some simple strategy for answering the questions in a way that the inequality is violated.

 

[JesseM]

Also, you seriously mischaracterize Bell's position. He was not sorry for creating his theorem, and as best I can tell evolved to believe in a non-local view of hidden variables.

I rely on the Mermin quote: ''To those for whom nonlocality is anathema, Bell's Theorem finally spells the death of the hidden variables program. But not for Bell. None of the no-hidden-variables theorems persuaded him that hidden variables were impossible.'' (Mermin, Rev. Mod. Phys. 65 page 814, 1993) [emphasis added].

Isn't that exactly what DrChinese just said? (note the part I put in bold) Bell wasn't persuaded that hidden variables were impossible, so he looked for a non-local hidden variables theory (since he was not one 'for whom nonlocality is an anathema'), because Bell's theorem showed a local hidden variables theory wouldn't work.

 

[DrChinese]

I rely on the Mermin quote: ''To those for whom nonlocality is anathema, Bell's Theorem finally spells the death of the hidden variables program. But not for Bell. None of the no-hidden-variables theorems persuaded him that hidden variables were impossible.'' (Mermin, Rev. Mod. Phys. 65 page 814, 1993) [emphasis added].

You read this differently than I, I certainly have no argument with Mermin. Bell was a believer in non-local hidden variables at the end. There are other theorems which address the hidden variable issue other than Bell's Theorem, these usually address what is called non-contextual definiteness.

 

[MeJennifer]

... such as the condition that there's a spacelike separation between the two measurements.

But how can we exclude that there is no spacelike separation as you suggest?

For instance consider a quantum system with two photons each traveling in opposite direction with the speed of c. Now could we show they are causally disconnected? Both particles travel on a null path and hence are causally connected if we time reverse the path of each particle to the initial quantum state. Certainly photons do not violate time symmetry.

In this light think of Wheeler-Feynman like theories.

I am not claiming that that is actually the case, but can it be excluded?

 

[JesseM]

For instance consider a quantum system with two photons each traveling in opposite direction with the speed of c. Now could we show they are causally disconnected? Both particles travel on a null path and hence are causally connected if we time reverse the path of each particle to the initial quantum state. Certainly photons do not violate time symmetry.

That's not how spacelike vs. timelike separations work in relativity, it has nothing to do with "reversing paths", just on whether one event lies in the other's light cone, or whether (in an inertial coordinate system in flat spacetime) ds^2 = dx^2 + dy^2 + dz^2 - c^2*dt^2 is positive or negative. If two photons travel in opposite directions in flat spacetime, the two events of each photon being received by detectors will always have a spacelike separation. Two events with a spacelike separation that have a common cause are still "causally disconnected" in the sense that neither event can affect the other one, although they may both have been affected by some event which lies in both their past light cones, and they may both have an effect on some event which lies in both their future light cones.

 

[MeJennifer]

That's not how spacelike vs. timelike separations work in relativity, it has nothing to do with "reversing paths", just on whether one event lies in the other's light cone, or whether (in an inertial coordinate system in flat spacetime) ds^2 = dx^2 + dy^2 + dz^2 - c^2*dt^2 is positive or negative. If two photons travel in opposite directions in flat spacetime, the two events of each photon being received by detectors will always have a spacelike separation. Two events with a spacelike separation that have a common cause are still "causally disconnected" in the sense that neither event can effect the other one, although they may both have been affected by some event which lies in both their past light cones, and they may both have an effect on some event which lies in both their future light cones.

I am not talking about the detectors.
I am talking about the time-reversed null path of each photon towards the initial quantum state.

 

[JesseM]

I am not talking about the detectors.
I am talking about the time-reversed null path of each photon towards the initial quantum state.

OK, but you were quoting my statement "such as the condition that there's a spacelike separation between the two measurements", which referred to the detection-events. Certainly the two entangled photons have a common origin point in spacetime, but the proof of Bell's theorem doesn't forbid this. In fact, Bell's theorem is based on assuming that the reason entangled particles show perfect correlation when measured on the same axis is because they were generated from a common source in either identical or opposite states, and then showing that you can't explain the violation of Bell inequalities when different axes are measured without violating locality.

 

[Anonym]

Since the 1990s the experiments have been definitive; no physicist doubts the existence of nonlocality.

Under request, I will show you my documents.

The question wether - prior to observation - a particle is in a defined state, is something unknowable. Knowing the state of the particle requires an observation and this observation alters the state of the particle.

Dear Karl, you have no idea what you are talking about. Your followers would send you to Solovki for the presented level of knowledge of quantum physics. At least, ask your friend Friedrich what is his point of view.

I just read your discussions here as a matter of curiosity. I have two basic questions:

1. I lost track from “old” literature that said that the spin of free electron can’t be measured (N.Bohr, L.Rosenfeld, N.F.Mott, H.S.W. Massey). What is the current status?
2. What is the practical purpose of all that entanglement stuff? If Bob want to put Alice in his bed, why not to do that locally?

Crosson version is only slightly more complicated:” Here is a description of EPR:Imagine that there is a pair of (literally) identical twin brothers who are interested in dating a pair of identical twin sisters. The brothers live together, but their dates live separate lives on opposite sides of town.” Again,why not to do that locally?

In separate Fock spaces.

 

[heusdens]

Under request, I will show you my documents.
Dear Karl, you have no idea what you are talking about. Your followers would send you to Solovki for the presented level of knowledge of quantum physics. At least, ask your friend Fridrich what is his point of view.

I just read your discussions here as a matter of curiosity. I have two basic questions:

1. I lost track from “old” literature that said that the spin of free electron can’t be measured (N.Bohr, L.Rosenfeld, N.F.Mott, H.S.W. Massey). What is the current status?
2. What is the practical purpose of all that entanglement stuff? If Bob want to put Alice in his bed, why not to do that locally?

Crosson version is only slightly more complicated:” Here is a description of EPR:Imagine that there is a pair of (literally) identical twin brothers who are interested in dating a pair of identical twin sisters. The brothers live together, but their dates live separate lives on opposite sides of town.” Again,why not to do that locally?

In separate Fock spaces.

Greetings to you.

The discoveries of the material sciences had lead to progress in the human understanding of the world and in technology, but the working class is hardly any better of.

Although I and Friedrich are very unfamiliar with this field of knowledge since we studied it, we can not escape from telling that these new discoveries do not conlict with dialectical materialism. Science has found what we already expected to find, that the material world is unlimitedless.

Althoug we must say, some interpretations of the quantum mechanics, which have made statements that seem to reject materialism. This interpretation however can however not be made, since the senseous experiment of the material world are so to say "acts of the flesh" and not "acts of the mind".

"Motion is the mode of existence of matter. Never anywhere has there been matter without motion, or motion without matter, nor can there be."

"Change of form of motion is always a process that takes place between at least two bodies, of which one loses a definite quantity of motion of one quality (e.g. heat), while the other gains a corresponding quantity of motion of another quality (mechanical motion, electricity, chemical decomposition).

"Dialectics, so-called objective dialectics, prevails throughout nature, and so-called subjective dialectics (dialectical thought), is only the reflection of the motion through opposites which asserts itself everywhere in nature, and which by the continual conflict of the opposites and their final passage into one another, or into higher forms, determines the life of nature."

Fredrick Engels
Dialectics of Nature

But dialectical materialism insists on the approximate relative character of every scientific theory of the structure of matter and its properties; it insists on the absence of absolute boundaries in nature, on the transformation of moving matter from one state into another, that from our point of view [may be] apparently irreconcilable with it, and so forth.

Vladimir Lenin
Materialism and Empirio-criticism Karl.

 

[heusdens]

Here's another example of brilliant dialectical thougt, which predicts that the attraction of gravity is only one-sided approach, and that even gravity must have both sides (attraction and repulsion). This kind of gravity repulsive force is conceived of in current cosmological models in the form of cosmological inflation.

Gravity as the most general determination of materiality is commonly accepted. That is to say, attraction is a necessary property of matter, but not repulsion. But attraction and repulsion are as inseparable as positive and negative, and hence from dialectics itself it can already be predicted that the true theory of matter must assign as important a place to repulsion as to attraction, and that a theory of matter based on mere attraction is false, inadequate, and one-sided. In fact sufficient phenomena occur that demonstrate this in advance. If only on account of light, the ether is not to be dispensed with. Is the ether of material nature? If it exists at all, it must be of material nature, it must come under the concept of matter. But it is not affected by gravity. The tail of a comet is granted to be of material nature. It shows a powerful repulsion. Heat in a gas produces repulsion, etc.

* * *​

Attraction and gravitation. The whole theory of gravitation rests on saying that attraction is the essence of matter. This is necessarily false. Where there is attraction, it must be complemented by repulsion. Hence already Hegel was quite right in saying that the essence of matter is attraction and repulsion.[194] And in fact we are more and more becoming forced to recognise that the dissipation of matter has a. limit where attraction is transformed into repulsion,. and conversely the condensation of the repelled matter has a limit where it becomes attraction.

* * *​

The transformation of attraction into repulsion and vice versa is mystical in Hegel, but in substance he anticipated by it the scientific discovery that came later. Even in a gas there is repulsion of the molecules, still more so in more finely-divided matter, for instance in the tail of a comet, where it even operates with enormous force. Hegel shows his genius even in the fact that he derives attraction as something secondary from repulsion as something preceding it: a solar system is only formed by the gradual preponderance of attraction over the originally prevailing repulsion. – Expansion by heat=repulsion. The kinetic theory of gases.

(from Dialectics of Nature)

 

[Anonym]

Dear Karl,

One very famous physicist (level compatible with A. Einstein) wrote:” We are facing here the perennial question whether we physicists do not go beyond our competence when searching for philosophical truth.”

The philosophy is far beyond my competence. I can’t argue against you. I may only ask you a question that was interested me during all my life: Roots of the dialectical materialism lies in the ancient Indian philosophy (niaa and vaisheishika, sorry if I write not correctly). How the closely related to them dialectical materialism was translated to deterministic applications of Solovki,Gulag and similarly in other countries?

Personally, I hate the dialectical materialism. I was supposed to spend several years in jail only for absence of knowledge of the dialectical materialism. Unbelievable courage of idealistic philosophy professor which did not know me at all saved me.

From Dialectics of Nature:

“Gravity as the most general determination of materiality is commonly accepted. That is to say, attraction is a necessary property of matter, but not repulsion. But attraction and repulsion are as inseparable as positive and negative, and hence from dialectics itself it can already be predicted that the true theory of matter must assign as important a place to repulsion as to attraction, and that a theory of matter based on mere attraction is false, inadequate, and one-sided. In fact sufficient phenomena occur that demonstrate this in advance. If only on account of light, the ether is not to be dispensed with. Is the ether of material nature? If it exists at all, it must be of material nature, it must come under the concept of matter. But it is not affected by gravity. The tail of a comet is granted to be of material nature. It shows a powerful repulsion. Heat in a gas produces repulsion, etc.
* * *

Attraction and gravitation. The whole theory of gravitation rests on saying that attraction is the essence of matter. This is necessarily false. Where there is attraction, it must be complemented by repulsion. Hence already Hegel was quite right in saying that the essence of matter is attraction and repulsion.[194] And in fact we are more and more becoming forced to recognise that the dissipation of matter has a. limit where attraction is transformed into repulsion,. and conversely the condensation of the repelled matter has a limit where it becomes attraction.
* * *

The transformation of attraction into repulsion and vice versa is mystical in Hegel, but in substance he anticipated by it the scientific discovery that came later. Even in a gas there is repulsion of the molecules, still more so in more finely-divided matter, for instance in the tail of a comet, where it even operates with enormous force. Hegel shows his genius even in the fact that he derives attraction as something secondary from repulsion as something preceding it: a solar system is only formed by the gradual preponderance of attraction over the originally prevailing repulsion. – Expansion by heat=repulsion. The kinetic theory of gases.”

I do not see any difference compare with writings of Northerdamus. However, “The whole theory of gravitation rests on saying that attraction is the essence of matter” is completely wrong statement. The whole theory of gravitation rests on the universally valid experimental result that the inertial mass is identical to the gravitation mass.
By the way, my physical intuition says to me that the gravitation is only attractive similarly to the strong interaction.

Dany.

P.S. It is written in your reference: Frederick Engels (1873-1886).
Does it mean that FE lived only 13 years?

 

[DrChinese]

Dear Karl,

One very famous physicist (level compatible with A. Einstein) wrote:” We are facing here the perennial question whether we physicists do not go beyond our competence when searching for philosophical truth.”

The philosophy is far beyond my competence...

Dear Anonym,

This material is far off thread and belongs elsewhere, perhaps in the philosophy section. You should probably review the forum posting guidelines.

Regards,

-DrC

 

[wm]

Dear Karl,

<SNIP>

The transformation of attraction into repulsion and vice versa is mystical in Hegel, but in substance he anticipated by it the scientific discovery that came later. Even in a gas there is repulsion of the molecules, still more so in more finely-divided matter, for instance in the tail of a comet, where it even operates with enormous force. Hegel shows his genius even in the fact that he derives attraction as something secondary from repulsion as something preceding it: a solar system is only formed by the gradual preponderance of attraction over the originally prevailing repulsion. – Expansion by heat=repulsion. The kinetic theory of gases.”

<SNIP>

[Emphasis added above] Some light relief; of more than passing interest; in partial explanation of a current pre-occupation; welcome to Comet McNaught:

http://news.nationalgeographic.com/news/2007/01/070118-comet.html

 

[mgelfan]

... Two events with a spacelike separation that have a common cause are still "causally disconnected" in the sense that neither event can affect the other one ...

The statistics accumulated via spacelike separated events in EPR-Bell experiments are not independent of each other. An initial detection at either A or B affects the sample space of the other. That is, a detection at one end causes the sample space at the other end to be modified from a random to a non-random sampling (of the incident optical disturbances) for that pairing.

This (dependence of A upon B, and/or vice versa) is why the mathematical formulation chosen to represent locality (ie., factorability) does not represent locality -- at least regarding the way in which EPR-Bell tests are usually prepared.

Quantum theory assumes that the analyzers/filters at A and B have, in effect, analyzed/filtered the same incident optical disturbance for paired detection attributes.

Once this assumption is made, and preparations are made to insure that disturbances emitted in opposite directions during the same transition/emission interval are being paired via coincidence circuitry, then the quantum mechanical predictions just follow from elementary classical optics, more or less.

No spooky action at a distance. No nonlocality.

 

[wm]

I think that it does. Does your example breach the CHSH Inequality?

Please let me know, wm

In general, any inequality that's violated in QM should also be easy to violate in a classical question-and-answer game like the one I described, where I get to hear both questions before giving my answers--all I have to do is translate the questions into settings of some hypothetical inequality-violating quantum experiment, calculate in my head what the probability is that each experiment will get a + or - according to quantum mechanics, and then make my probabilities of answering "yes" or "no" proportional to these calculated probabilities! Obviously an ordinary classical computer can calculate the probabilities in any quantum experiment, so no actual quantum effects are needed here.

Jesse, I'm happy for you to explore any realistic option that you can think of. I want to encourage you to do so.

For it seems to me that Bell's theorem [as reflected in the vast literature on Bellian inequalities (BI)] is, in general, FALSE. And it seems to me that this falsity derives from the associated REALISM.

That is, to be clearer: Models satisfying a Bellian inequality will be NOT be satisfactory as a general representation of realism. For they will be based on the subset thereof -- known as Bell realism (or naive realism; or strong realism ... ).

But I can try to come up with a simpler strategy to violate a given inequality in a question-and-answer game, if you like.

Well I think that this approach would be closer to the spirit of the BI literature and my question re CHSH. (Otherwise, you may as well stand beside the experiment and call the results; or feed the results directly to the computer; as I read the above?)

I looked up the CHSH inequality and could only find it in the wikipedia article which stated it in terms of the expectation values, I'd like to restate it in terms of probabilities to make it easier to think up with an example. In terms of expectation values, if both Alice and Bob have two measurement settings A and B which can each yield two results + or -, assigned values +1 and -1, then the CHSH inequality says:

-2 <= X <= 2

('<=' stands for 'smaller than or equal to', when I typed the actual symbol the board's softward replaced it with a question mark)

where

X = E(Alice measures A, Bob measures A) - E(Alice measures A, Bob measures B) + E(Alice measures B, Bob measures A) + E(Alice measures B, Bob measures B)

I think CHSH is more general than that. More like:

(CHSHI) |<AB>+<BC>+<CD> - <DA>| </= 2

Converting expectation values into probabilities should give:

1. E(Alice measures A, Bob measures A) = P(S|aa) - P(D|aa)
2. E(Alice measures A, Bob measures B) = P(S|ab) - P(D|ab)
3. E(Alice measures B, Bob measures A) = P(S|ba) - P(D|ba)
4. E(Alice measures B, Bob measures B) = P(S|bb) - P(D|bb)

Since P(D|aa) = 1 - P(S|aa) and so forth, this simplifies to:

1. E(Alice measures A, Bob measures A) = 2*P(S|aa) - 1
2. E(Alice measures A, Bob measures B) = 2*P(S|ab) - 1
3. E(Alice measures B, Bob measures A) = 2*P(S|ba) - 1
4. E(Alice measures B, Bob measures B) = 2*P(S|bb) - 1

So, that should give X = 2*[P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab)] - 3

which means -2 <= X <= 2 is equivalent to:

1/2 <= P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab) <= 5/2

Would this be a valid formulation of one case of the CHSH inequality?

In that the central expression can equal 2, then you've confirmed CHSH.

(the case when Alice and Bob both choose between the same two measurements A and B--from the way it was formulated on wikipedia it seems to be more general than that)

Yes; the relation you need to target is:

(CHSHI) |<AB>+<BC>+<CD> - <DA>| </= 2.

Let me know if I made an error in math or understanding. Also, what is being assumed about the results when both choose the same detector settings? Are P(S|aa) and P(S|bb) equal to 1, or 0? Or can I just assume any probability between 0 and 1 for each of the four?

Your task (as I see it) is to define an experiment in your own terms; then rebut CHSH. Alternatively or in parallel: Use my experiment to rebut CHSH and see if that helps in you building your own model.

Once I'm clear on the equation for the CHSH inequality in terms of probabilities, and on what assumptions are being made about identical settings, I should be able to come up with some simple strategy for answering the questions in a way that the inequality is violated.

I would say rather: The specific experiment provides the Probability for identical settings; no further assumptions needed, as I see it.

Hope this helps, wm

 

[JesseM]

Jesse, I'm happy for you to explore any realistic option that you can think of. I want to encourage you to do so.

For I claim that Bell's theorem [as reflected in the vast literature on Bellian inequalities(BI)] is, in general, FALSE. AND (according to me): This falsity derives from the associated REALISM.

You misunderstand me, I'm not "exploring realistic options" for QM, I'm just pointing out that it's a quite trivial observation that you can violate the Bell inequalities classically when you violate some of the conditions on the experiment stipulated by Bell theorem, but that this is of course not a violation of Bell's theorem. Bell's theorem says, in effect, "under conditions X,Y,Z it is impossible for a local realist theory to reproduce the Bell inequalities". All you have shown is a statement to the effect of "if I am allowed to set up an experiment which does not respect condition Y, then I can violate the Bell inequalities with a local realist theory." But this is completely obvious--it's the whole reason they bothered to stipulate those conditions!

All I am pointing out with my examples is how trivial it is that you can violate the Bell inequalities classically if you (the 'source') are aware of what questions you'll be asked ('measurements') before you have to give answers (the 'results' of each measurement). But suppose me and a friend have to travel at close to the speed of light in opposite directions, and then the events of our each being asked a question have a spacelike separation, with the two experimenters picking their questions at random at that moment. In this case, there is no prearranged strategy me and the friend can use to come up with answers that are always the same (or opposite) when asked the same question, but which violate the Bell inequalities when asked different questions, unless we have some kind of faster-than-light psychic connection, or have precognitive abilities that allow us to know what the experimenters will ask in advance, or are able to split ourselves and the experimenters into multiple copies and decide which copies of experimenter 1 are matched with which copies of experimeter 2 later. That's what Bell's theorem is telling you, it doesn't say a thing about there being a problem with violating the Bell inequalities in circumstances where the source can be informed in advance what one or both of the measurements will be.

Well I think that this approach would be closer to the spirit of the BI literature and my question re CHSH. (Otherwise, you may as well stand beside the experiment and call the results; or feed the results directly to the computer; as I read the above?)

No, the strategy of just calculating what quantum mechanics would predict for the probabilities, and basing your answers on these probabilities, can only work if you know what both of the measurements are before making your calculation. Therefore, as I said above, it won't work if you and a friend must travel apart to both experimenters, and the events of being asked the two questions have a spacelike separation, and you each have to answer before there's been time for a signal to pass from one to the other informing each what question the other was asked.

I think CHSH is more general than that. More like:

(CHSHI) |<AB>+<BC>+<CD> - <DA>| </= 2

I realize that, but that's why I said at the end of my last post I was just trying to come up with a specific case: "Would this be a valid formulation of one case of the CHSH inequality? (the case when Alice and Bob both choose between the same two measurements A and B--from the way it was formulated on wikipedia it seems to be more general than that)"

1/2 <= P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab) <= 5/2

Would this be a valid formulation of one case of the CHSH inequality?

In that the central expression can equal 2, then you've confirmed CHSH.

Actually, now that I think about it I think there must be an error either in my understanding or the way it's stated on wikipedia. Even if I respect all the conditions of Bell's theorem, it seems like it wouldn't be too hard to violate this inequality--all I have to do is send one object/signal in state {A = +1, B = +1} to Alice and another in state {A = -1, B = -1} to Bob, and then it's guaranteed that the probability of them getting the same result is 0, no matter what they measure; thus the sum of all those P(S|xx)'s is 0, which is smaller than 1/2. And in terms of expectation values, the product of Alice and Bob's answer is guaranteed to be -1, and the sum (-1) - (-1) + (-1) + (-1) is -3, which of course is smaller than -2. edit: D'oh! Curse you, simple arithmetic! See post #240 below.

I looked on arxiv.org for stuff on the CHSH inequality and I found this paper which I think gives the answer to the problem. Instead of the way it's written on wikipedia, in eq. 24 it states the CHSH inequality as:

|E(a,b) - E(a,b')| + |E(a',b') + E(a',b)| <= 2

where a and a' are Alice's two choices of experimental settings, and b and b' are Bob's. You can see that when stated this way, if the expectation value is -1 in each case, then it becomes |0| + |-2| <= 2, which works.

Anyway, it's still not hard to violate this inequality in a question-and-answer game where I know both questions before I have to give an answer. All I have to do is make sure to always give the same answer in cases (a,b), (a',b'), and (a',b), so the expectation value for these is 1, and always give different answers in case (a,b'), so the expectation value for this case is -1. Again, this just shows that it's extremely trivial to violate various Bell inequalities classically when you don't respect the conditions of Bell's theorem, but as I said, this is clearly not a disproof of Bell's theorem, since the theorem is only about the impossibility of violating the inequalities classically when all the conditions are respected.

 

[wm]

Jesse; sorry; I was in middle of editing that post when you replied; essentially no change to technical content though. So:

You misunderstand me, I'm not "exploring realistic options" for QM, I'm just pointing out that it's a quite trivial observation that you can violate the Bell inequalities classically when you violate some of the conditions on the experiment stipulated by Bell theorem, but that this is of course not a violation of Bell's theorem. Bell's theorem says, in effect, "under conditions X,Y,Z it is impossible for a local realist theory to reproduce the Bell inequalities". All you have shown is a statement to the effect of "if I am allowed to set up an experiment which does not respect condition Y, then I can violate the Bell inequalities with a local realist theory." But this is completely obvious--it's the whole reason they bothered to stipulate those conditions!

OK. So while you're working to classically rebut CHSH or a similar Bellian Inequality, it would be good to get those X, Y, and Z clearly expressed in your terms. That will certainly help us to understand which of them are breached.

All I am pointing out with my examples is how trivial it is that you can violate the Bell inequalities classically if you (the 'source') are aware of what questions you'll be asked ('measurements') before you have to give answers (the 'results' of each measurement). But suppose me and a friend have to travel at close to the speed of light in opposite directions, and then the events of our each being asked a question have a spacelike separation, with the two experimenters picking their questions at random at that moment. In this case, there is no prearranged strategy me and the friend can use to come up with answers that are always the same (or opposite) when asked the same question, but which violate the Bell inequalities when asked different questions, unless we have some kind of faster-than-light psychic connection, or have precognitive abilities that allow us to know what the experimenters will ask in advance, or are able to split ourselves and the experimenters into multiple copies and decide which copies of experimenter 1 are matched with which copies of experimeter 2 later. That's what Bell's theorem is telling you, it doesn't say a thing about there being a problem with violating the Bell inequalities in circumstances where the source can be informed in advance what one or both of the measurements will be. No, the strategy of just calculating what quantum mechanics would predict for the probabilities, and basing your answers on these probabilities, can only work if you know what both of the measurements are before making your calculation.

Is this correct??

Because my simple example appears to BEAT this both requirement. The source in my example has no knowledge of (nor access to) Bob's setting at any stage.

Therefore, as I said above, it won't work if you and a friend must travel apart to both experimenters, and the events of being asked the two questions have a spacelike separation, and you each have to answer before there's been time for a signal to pass from one to the other informing each what question the other was asked. I realize that, but that's why I said at the end of my last post I was just trying to come up with a specific case: "Would this be a valid formulation of one case of the CHSH inequality? (the case when Alice and Bob both choose between the same two measurements A and B--from the way it was formulated on wikipedia it seems to be more general than that)" Actually, now that I think about it I think there must be an error either in my understanding or the way it's stated on wikipedia. Even if I respect all the conditions of Bell's theorem, it seems like it wouldn't be too hard to violate this inequality--all I have to do is send one object/signal in state {A = +1, B = +1} to Alice and another in state {A = -1, B = -1}, and then it's guaranteed that the probability of them getting the same result is 0, no matter what they measure; thus the sum of all those P(S|xx)'s is 0, which is smaller than 1/2. And in terms of expectation values, the product of Alice and Bob's answer is guaranteed to be -1, and the sum (-1) - (-1) + (-1) + (-1) is -3, which of course is smaller than -2.

I looked on arxiv.org for stuff on the CHSH inequality and I found this paper which I think gives the answer to the problem. Instead of the way it's written on wikipedia, in eq. 24 it states the CHSH inequality as:

|E(a,b) - E(a,b')| + |E(a',b') + E(a',b)| <= 2

where a and a' are Alice's two choices of experimental settings, and b and b' are Bob's. You can see that when stated this way, if the expectation value is -1 in each case, then it becomes |0| + |-2| <= 2, which works.

Anyway, it's still not hard to violate this inequality in a question-and-answer game where I know both questions before I have to give an answer. All I have to do is make sure to always give the same answer in cases (a,b), (a',b'), and (a',b), so the expectation value for these is 1, and always give different answers in case (a,b'), so the expectation value for this case is -1.

This not quite clear to me: You say it's quite easy to breach CHSH in ...

Have you yet done that?

Again, this just shows that it's extremely trivial to violate various Bell inequalities classically when you don't respect the conditions of Bell's theorem, but as I said, this is clearly not a disproof of Bell's theorem, since the theorem is only about the impossibility of violating the inequalities classically when all the conditions are respected.

The XYZ elements that you mention will help us here. Especially if they are in your own words. And I don't mean that extremes like FTL, psychic, magic etc have to be included in such a specification. Just common-sense boundary conditions.

PS: It is still not clear to me that the paper you cited helps on this. ''The events of type C+-/ii are not supposed to be influenced by the measuring operations Li and Rj. ...''.

In my model C+- is not so influenced, is it? The +- there being random and beyond the control of Alice and Bob?

wm

 

[JesseM]

Bell's theorem says, in effect, "under conditions X,Y,Z it is impossible for a local realist theory to reproduce the Bell inequalities". All you have shown is a statement to the effect of "if I am allowed to set up an experiment which does not respect condition Y, then I can violate the Bell inequalities with a local realist theory." But this is completely obvious--it's the whole reason they bothered to stipulate those conditions!

OK. So while you're working to classically rebut CHSH or a similar Bellian Inequality, it would be good to get those X, Y, and Z clearly expressed in your terms. That will certainly help us to understand which of them are breached.

Sure. I'm not a great expert on all the technical details of Bell's theorem, but these are the conditions I'm aware of, with #2 being the one violated in your example:

1. spacelike separation between the two measurement-events

2. source has no foreknowledge of either of the measurement choices on each trial; state of signals/objects sent out by source is statistically independent of measurement settings. In a universe obeying local realism, this condition can be guaranteed by setting things up so that the time between randomly choosing a measurement setting for a given trial and finishing the measurement period for that trial is smaller than the time it would take for a signal moving at the speed of light to travel from the measurement apparatus to the source and back.

3. only a single definite outcome to each measurement--this rules out "many-worlds" type solutions

There may also be additional conditions for specific inequalities derived for specific types of experiments--for example, some inequalities depend on the assumption that Alice and Bob are both choosing between an identical set of binary measurements, and that whenever they choose the same measurement, they always get identical (or opposite, depending on the experiment) results. The CHSH inequality is the most generally-applicable one I've seen, since it doesn't depend on this sort of assumption.

All I am pointing out with my examples is how trivial it is that you can violate the Bell inequalities classically if you (the 'source') are aware of what questions you'll be asked ('measurements') before you have to give answers (the 'results' of each measurement). But suppose me and a friend have to travel at close to the speed of light in opposite directions, and then the events of our each being asked a question have a spacelike separation, with the two experimenters picking their questions at random at that moment. In this case, there is no prearranged strategy me and the friend can use to come up with answers that are always the same (or opposite) when asked the same question, but which violate the Bell inequalities when asked different questions, unless we have some kind of faster-than-light psychic connection, or have precognitive abilities that allow us to know what the experimenters will ask in advance, or are able to split ourselves and the experimenters into multiple copies and decide which copies of experimenter 1 are matched with which copies of experimeter 2 later. That's what Bell's theorem is telling you, it doesn't say a thing about there being a problem with violating the Bell inequalities in circumstances where the source can be informed in advance what one or both of the measurements will be. No, the strategy of just calculating what quantum mechanics would predict for the probabilities, and basing your answers on these probabilities, can only work if you know what both of the measurements are before making your calculation.

Is this correct??

What specifically are you asking about?

Because my simple example appears to BEAT this both requirement. The source in my example has no knowledge of (nor access to) Bob's setting at any stage.

But what I said was "it doesn't say a thing about there being a problem with violating the Bell inequalities in circumstances where the source can be informed in advance what one or both of the measurements will be." It's true that in your experiment the source does not have foreknowledge of both measurements, but foreknowledge of "one or both" of the measurements is violating a condition of Bell's theorem.

Anyway, it's still not hard to violate this inequality in a question-and-answer game where I know both questions before I have to give an answer. All I have to do is make sure to always give the same answer in cases (a,b), (a',b'), and (a',b), so the expectation value for these is 1, and always give different answers in case (a,b'), so the expectation value for this case is -1.

This not quite clear to me: You say it's quite easy to breach CHSH in ...

Have you yet done that?

Yes, that's what I just did in the quoted paragraph. Alice can ask me question a or a', Bob can ask me b or b'; so my strategy is that if the questions they ask are (a,b) or (a',b') or (a',b), then I give the same answer to both questions ('yes, yes' or 'no, no'), but if they ask me the questions (a,b') then I give different answers to both questions ('yes, no' or 'no, yes'). With "yes" assigned value +1 and "no" assigned value -1, and the result of each trial being the product of the two answers, this means E(a,b) = 1, E(a',b') = 1, E(a',b) = 1, and E(a,b') = -1. So, |E(a,b) - E(a,b')| + |E(a',b') + E(a', b)| = |1 - (-1)| + |1 + 1| = |2| + |2| = 4, violating the CHSH inequality which says that |E(a,b) - E(a,b')| + |E(a',b') + E(a', b)| <= 2.

The XYZ elements that you mention will help us here. Especially if they are in your own words. And I don't mean that extremes like FTL, psychic, magic etc have to be included in such a specification. Just common-sense boundary conditions.

Well, see above. Also, it's not actually necessary for me to have no-FTL as one of the "X,Y,Z conditions" since I summarized Bell's theorem as "under conditions X,Y,Z it is impossible for a local realist theory to reproduce the Bell inequalities", and "impossible for a local realist theory" already presupposes we are talking only about theories that say FTL is impossible.

PS: It is still not clear to me that the paper you cited helps on this. ''The events of type C+-/ii are not supposed to be influenced by the measuring operations Li and Rj. ...''.

In my model C+- is not so influenced, is it? The +- there being random and beyond the control of Alice and Bob?

wm

In http://www.citebase.org/fulltext?format=application%2Fpdf&identifier=oai%3AarXiv.org%3Aquant-ph%2F0312176 , the i's are variables whose value can be anyone of the three orientation settings, which are labeled 1,2,3. As mentioned on p.4, C is a "common cause" which is put forth to explain the correlations you see when Bob and Alice both pick the same orientation setting. And as they say, "in the case of a perfect correlation no generality is achieved by allowing for a more than two-valued common cause variable"--for example, if Bob and Alice always get opposite results when they both choose axis 2, then the signals/objects emitted by the source must either be of type C+-/22 (meaning the properties of the object/signal are such that it is predetermined that if Bob and Alice both choose setting 2, Alice gets a + and Bob gets a -) or of type ~C+-/22 (the properties of the object/signal are such that it is predetermined that if Bob and Alice both choose setting 2, Alice gets a - and Bob gets a +) on the subset of trials where they both pick setting 2. Likewise, every pair of objects/signals emitted by the source must either be of type C+-/11 or ~C+-/11 (predetermined to get either Alice +/Bob - or Alice -/Bob + if they both choose setting 1) on the subset of trials where they both pick setting 1, and every pair must either be of type C+-/33 or ~C+-/33 (predetermined to get either Alice +/Bob - or Alice -/Bob + if they both choose setting 3) on the subset of trials where they both pick setting 3.

If the source has no prior knowledge of either one's settings before it emits the signals/objects, then if every pair of signals/objects is of type C+-/22 or ~C+-/22 on the subset of trials where they both pick 2, then it must also be true that every pair is of one type or the other on all trials. Your example is more complicated, because the source has foreknowledge of Alice's setting; if she picks 2, then the polarized light emitted by the source is at one of two possible angles such that if they are both on setting 2, then they're guaranteed to get either +- or -+ (I realize that in your example, they were originally guaranteed to get either ++ or -- on the same setting, but I hope you don't that I'm modifying your example to match the convention of the paper, which could be done practically by having the polarizer on the end of the source pointing at Bob always be at a 90 degree angle from the one on the end of the source pointing at Alice). However, if polarized light at either one of these same two angles were measured when they were both on setting 1 or 3, there would be some nonzero probability of getting all four results +-, -+, ++ and --, so in the case where Alice picks 2 we can't say the signal must either be of type C+-/11 or ~C+-/11, and likewise we can't say the signal must either be of type C+-/33 or ~C+-/33.

So I guess you're right that it's not exactly the no-conspiracy condition you're violating, since they state the no-conspiracy condition in a way that assumes some prior conditions which you've already violated. In particular, you're violating the condition that the "common cause variable" that they introduce on p. 2, whose value represents all the properties of the signal/object emitted by the source that are relevant to the probabilities of different outcomes (in your case, the common cause is the polarized light emitted at Alice and Bob by the source, and the possible values of q for the common cause variable V_q would just be the possible polarization angles of the light emitted by the source), "should not be correlated with the measurement choices" as they say in the second paragraph on p. 3. If this condition is respected, then if it's true that the common cause variable is always of type C+-/22 or ~C+-/22 on trials where they both choose setting 2, then it must be of one of these two types on all trials; but if you violate this condition then it won't necessarily work that way any more, as your example shows.

This paragraph also has a reference to this paper on common causes as an explanation for EPR-type results, and note that it includes the same sort of condition on p. 5:

6) Also, because the choices of the measurements are free in the sense that there is no mysterious conspiracy between the things that determine the choices of the measurements and those that determine the outcomes, one can assume that the measurement choices are independent of the common cause. ... These findings are partly read off from the empirical data (6) or they are straightforward consequences of the prohibition of superluminal causation.

And again, one consequence of the "prohibition of superluminal causation" is that if the time between randomly choosing a measurement setting and completing the measurement with that setting is smaller than the time it would take a light signal to travel from the measurement apparatus to the source and back, then the choice of setting on a given trial must (assuming a local classical theory) be statistically independent of the properties of whatever signals/objects the measurement apparatus is receiving from the source for the duration of that trial.

 

[vanesch]

See above, I think it works if you just assume that the probability Bob sees a photon get through is equal to cos^2(angle of source polarization - angle of Bob's polaroid), and likewise that the probability Alice sees a photon get through is equal to cos^2(angle of source polarization - angle of Alice's polaroid), with the condition that the source is "yoked" to Alice's polaroid so there's a 50% chance it's parallel to hers and a 50% chance it's at 90 degrees relative to hers. Of course, the problem is that this yoked condition actually violates one of the basic assumptions behind Bell's theorem, namely that any properties of what it emits, "hidden" or otherwise, should be statistically independent of Alice and Bob's choice of detector settings on each trial.

Uh, you mean:

Alice sets her polarizer to an absolute angle (say, with the sight line to Sirius) th_Alice, and then the SOURCE is rotated (with the box) such that the source only sends out light pulses OR perfectly PARALLEL to th_Alice, or PERFECTLY perpendicular to Alice, but nothing in between (in other words, this is not an isotropic source) ?

And this is supposed to prove that Bell's theorem is erroneous ?

That's not very LOCAL as a setup !

 

[vanesch]

Notice that when I was stating the assumptions behind Bell's theorem in post #133, I included the bolded part below: When I wrote this I was thinking of a well-known loophole in Bell's theorem, which I think would be explicitly ruled out with a statistical independence condition in any fully rigorous proof of the theorem. The loophole is that if the source is somehow able to "anticipate" the detector settings Alice and Bob choose ahead of time, then it can adjust the hidden variables based on this in such a way that Bell inequalities can be violated.

Yes, that's so-called "superdeterminism". The idea is that whatever physics is going to determine the settings of the polarizers (say, the state of your brain when you decide to turn the polarizers etc...), in a deterministic universe, this is entirely determined on a sufficiently remote spacelike surface in the past, which can also influence the source. Of course any explicit mechanism by which there is a common origin to the polarization of the light pulses from the source and your brain deciding which polarizing angle to choose, is rather unknown.

The problem with this view is that if you stick to it, there is no way to test any law of nature, because every correlation observed in nature can be simply due to a "common cause in the past". Consider a pharmaceutical company testing a new drug: it is not because it has been administered "blindly" to 10000 patients which all got cured, and a placebo was administered to 10000 patients, of which 95% died, that one can conclude that the drug is effective: a common cause in the past could be such that the process which made the "random blind choice" of the first 10000 patients was 100% correlated with a specific condition of their illness which made them get better.

 

[JesseM]

Uh, you mean:

Alice sets her polarizer to an absolute angle (say, with the sight line to Sirius) th_Alice, and then the SOURCE is rotated (with the box) such that the source only sends out light pulses OR perfectly PARALLEL to th_Alice, or PERFECTLY perpendicular to Alice, but nothing in between (in other words, this is not an isotropic source) ?

Right, that is wm's proposed setup.

And this is supposed to prove that Bell's theorem is erroneous ?

That's not very LOCAL as a setup !

Yeah, I'm trying to convince wm that this is obviously not a valid disproof of Bell's theorem for that reason.

 

[JesseM]

Actually, now that I think about it I think there must be an error either in my understanding or the way it's stated on wikipedia. Even if I respect all the conditions of Bell's theorem, it seems like it wouldn't be too hard to violate this inequality--all I have to do is send one object/signal in state {A = +1, B = +1} to Alice and another in state {A = -1, B = -1} to Bob, and then it's guaranteed that the probability of them getting the same result is 0, no matter what they measure; thus the sum of all those P(S|xx)'s is 0, which is smaller than 1/2. And in terms of expectation values, the product of Alice and Bob's answer is guaranteed to be -1, and the sum (-1) - (-1) + (-1) + (-1) is -3, which of course is smaller than -2.

Uhhh, me are stupid, I just realized that (-1) - (-1) + (-1) + (-1) is -2, not -3. This also means that my equation 1/2 <= P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab) <= 5/2 should actually be 0 <= P(S|aa) + P(S|ba) + P(S|bb) - P(S|ab) <= 2. But it doesn't affect my argument about the CHSH inequality being easy to violate when you are allowed to violate the condition that the source has no foreknowledge of what measurements will be made, though, since both the form of the CHSH inequality in the wikipedia article and the form I was using in my argument (namely |E(a,b) - E(a,b')| + |E(a',b') + E(a',b)| <= 2) are presumably correct.

 

[heusdens]

Continuation of my attempts to come up with a "classical" (non-quantum) example of an "exeperiment" that beats the Bell Inequality"

{in fact the 'experiment' is neither classical nor quantum, it is a pure abstract experiment}

Design of a new experiment. (thought experiment)

Some definitions:streams:
x, y, z,...

We don't know what they contain...just that they contain some element, which is input for a detector outcome for each side.
We design the experiment so that each stream element has an order (like saying that they are numbered) and for the correlation it is assumed then that we use the outcomes of detectors with stream elements of the same number (order).
Basically that is all we say about the streams. Note that we do not say that each element is split into two separate elements!
Further, we do not even know if there are more as one stream, or how many.
So, wherever you see x,y,z notice that it can mean one stream or many (sub)streams.

Detectors:
A(1), A(2), A(3) -- at the side of Alice
B(1), B(2), B(3) -- at the side of Bob

Results:

Outcome(detector, stream) is of form + or -

Constraint:

Outcome(detector, stream) [for detector is A(n), B(n), C(n) for n=1,2,3 and stream is x,y,z] is random (+ and - each likely)

{each outcome for any individual detector is random, i.e. + and - as likely}

Correlations:

Correlation(outcome-alice, outcome-bob)

note that it is symmetrical, so Correlation(outcome-alice, outcome-bob) is equal to Correlation(outcome-bob, outcome-alice)

can be either:

random/uncorrelated

all possible values emerge equally (that is, ++,+-,-+,-- have each equal likelihood)

Same outcomes 100%

any values ++ and -- occur (with equal likelihood)

Same outcomes 25%

values of ++ and -- occur only with probability 0.25 (++ as likely as --)
values of +- and -+ occur with probability 1-0.25=0.75 (+- as likely as -+)

Now here is what the correlations are:

Correlation(Outcome(A(n), s), Outcome(B(m), s)) is "Same 100%" for s = x,y,z and n=1,2,3 and m=n [detector settings the same for Alice and Bob]

Correlation(Outcome(A(n), s), Outcome(B(m), s)) is "Same 25%" for s=x,y,z and n=1,2,3 and m!=n [detector settings different for Alice and Bob]{NB. Notice that this "experiment" - although expressed differently - is functionally the same as the experiments worked our earlier, and are analogous to certain quantum experiments}

=====================================

Now the question is this:

Can we give the stream and dector outcomes some mathematical properties in such a way that this results in the correlations we measure?

This is to say, design some mathematical designations (like numbers, matrices, operators, functions, etc) to the element of each stream and for detector outcomes and correlations between detector outcomes.

{This needs to be elaborated of course... I merely speculate it can be done.}What we (intentionally) didn't infer was that we know anything about the stream(s). The only thing we state is that stream contains elements which occur in an order, which is to say that we can state that a detector outcome on one side coincided with a detector outcome on the other side, and that this coincidence is based on the same element of the stream.

What we can not tell is wether there is only one or more streams and what each element contains, nor can we make any assumptions about wether detector settings can have influence on the selected stream(s).
So it might be that some detector setting combination might filter out some streams (which is the same as to say that it selects some (sub)streams).

For one detector only, however, we know that whatever this detecor setting infers for the stream(s) selected, we get random outcomes.
For combination of detector selections, we know about the correlations as mentioned above.

The logical conclusion is that each (pair) of detector settings selects a (sub)stream which shows the correlation. The (sub)stream selection can be triggerd by either or both detector settings. In this point of view, it is not necessary to talk about actions at a distance any more.

The selection of the stream occurs instantaniously. However, the setting on detector, determine what streams can be selected on the other detector.
Same detector settings have outcomes always positive correlated (either ++ or --) which means that the (sub)streams selected operate in a way that only those outcomes are possible. It does not infer that detector settings which are equal (of which 3 distinct pairs exista) are necessarily selecting the same stream, the only thing we can observe is that the stream selected results in the same detector outcome correlations.
For the other combination (unequal detector settings) a same kind of reasoning, but with a different correlation, can be applied.

My point is that, in the mathematical sense, we can in theory make a mathematical description of this system that explains all the results.
However, if we were to infer that is a stream of elements which is determined on forehand (contains elements with fixed properties), independent of detector settings (which is to say, that in all cases we have always the same stream), it is not possible to explain the results.

We know from one detector setting only, that the detector outcomes give random results.
This is valid for every detector. As we mentioned, it can be the case each detector setting invokes a selection of one or more streams.
For two detector settings the same applies. The selection of streams is then dependent on both detector settings.
This is the same as to saying that there is only one stream, but that specific elements of that stream are filtered out dependent on detector settings.
This is equal to saying that by selecting different detector settings and combinations of detector settings, we are creating substreams, which behave different then other substreams.

 

[mgelfan]

The idea of locality is that these [events at A and B] ARE indeed independent physical happenings ...

The events at A and B can be (causally) independent of each other, while the statistics (paired detection attributes) accumulated at A and B aren't independent of each other.

The problem of constructing a general lhv model which has a viable locality condition still hasn't been solved.

Bell's locality condition isn't actually a locality condition. The assumption that (regarding paired results) A and B had filtered/analyzed the same thing is sufficient to account for the cos^2 theta angular dependence of the results.

So, unless someone comes up with a tighter way to represent the locality condition, Bell inequalities don't reveal anything about nonlocality in nature. Nevertheless, the experiments themselves and subsequent processing of inequalities and data are useful for several other important reasons (for example, associated experimental design innovations and various improvements in instrumentation and detection devices as well as being used to produce and determine the presence of entanglement).

 

[JesseM]

Now here is what the correlations are:

Correlation(Outcome(A(n), s), Outcome(B(m), s)) is "Same 100%" for s = x,y,z and n=1,2,3 and m=n [detector settings the same for Alice and Bob]

Correlation(Outcome(A(n), s), Outcome(B(m), s)) is "Same 25%" for s=x,y,z and n=1,2,3 and m!=n [detector settings different for Alice and Bob]{NB. Notice that this "experiment" - although expressed differently - is functionally the same as the experiments worked our earlier, and are analogous to certain quantum experiments}

=====================================

Now the question is this:

Can we give the stream and dector outcomes some mathematical properties in such a way that this results in the correlations we measure?

This is to say, design some mathematical designations (like numbers, matrices, operators, functions, etc) to the element of each stream and for detector outcomes and correlations between detector outcomes.

{This needs to be elaborated of course... I merely speculate it can be done.}

No, it can't be done, not if the source emitting the streams has no foreknowledge of Alice and Bob's detector settings, and their measurements are made at a spacelike separation. Bell's theorem proves that.

Would you agree that under these conditions, if we find that Alice and Bob always get the same answers when they pick setting 2, that must be because the properties x,y,z of the streams were set by the source in such a way that it was predetermined that Alice and Bob would get a certain answer if they measured that stream using setting 2? There can't be any random element when they each measure their signal, or else there would be some probability of getting different answers...if Alice gets a string with properties x', y', z' and Bob gets a string with properties x'', y'', z'', and they both choose setting 2 and get the answer +, it must be true that (string with properties x', y', z' AND measurement on setting 2 -> 100% chance of getting +) and (string with properties x'', y'', z'' AND measurement on setting 2 -> 100% chance of getting +).

What's more, the source doesn't know in advance on which trials they'll both choose setting 2. So if it's true on trials where they both choose setting 2 that the source always sends out signals with properties that make it 100% certain they'll both get a +, or signals with properties that make it 100% certain they'll both get a -, then this must be true on all trials, even the ones where they don't in fact choose to measure using setting 2. So we can say that every signal sent out by the source must either be of "type 2+" (meaning that its properties are such that if the detector is set to 2, the result is guaranteed to be +) or of "type 2-" (meaning on setting 2 you're guaranteed to get -). The source always sends both a signal of type 2+, or it sends them both a signal of type 2-; this is the only way to explain how they always get the same answer when they both choose setting 2, without violating local realism.

And the same reasoning shows that each signal must have a predetermined answer for whether it would give a + or - on setting 1, or setting 3; every signal must either be of type 1+ or type 1-, and likewise every signal must be either of type 3+ or type 3- (obviously the different-number types aren't mutually exclusive--if a signal is of type 2+ and 3-, that just means the signal has properties that make it guaranteed that if you measure using setting 2 you'll get +, and if you measure using setting 3 you'll get -).

Any disagreement with any of this so far? If so please explain which point you think is wrong, and if not I'll move on to showing how this guarantees the truth of Bell's theorem.

 

[JesseM]

... Two events with a spacelike separation that have a common cause are still "causally disconnected" in the sense that neither event can affect the other one ...

The statistics accumulated via spacelike separated events in EPR-Bell experiments are not independent of each other. An initial detection at either A or B affects the sample space of the other. That is, a detection at one end causes the sample space at the other end to be modified from a random to a non-random sampling (of the incident optical disturbances) for that pairing.

But changing the sample space is not the type of causation I'm talking about. Suppose someone puts a piece of red paper in one envelope and a piece of blue paper in another, and randomly sends one to me and one to you. If I open up my envelope and find the red paper, it increases my estimate of the probability that you will find the blue paper in your envelope from 0.5 to 1, but my finding the red paper didn't cause you to have the blue paper in a physical sense, both events had a common cause in the other guy sending the red paper to me and the blue paper to you.

Once this assumption is made, and preparations are made to insure that disturbances emitted in opposite directions during the same transition/emission interval are being paired via coincidence circuitry, then the quantum mechanical predictions just follow from elementary classical optics, more or less.

What do you mean by that? If you perform a classical optical experiment which respects the conditions of Bell's theorem such as a spacelike separation between measurements and the source having no foreknowledge of what measurements will be made, then you will find no violation of any Bell inequality in the results. wm's example worked according to classical optical laws, but it only violated an inequality because it violated the condition on the source not having foreknowledge of Alice's detector setting.

Do you think it's possible to come up with an experiment which uses only classical optics, which respects the conditions of Bell's theorem, and which shows a violation of some Bell inequality? If so, can you provide it?

 

[calamero]

Im sorry lads if i my contribution is nonseicle rubbish as I am not an expery on qm or anything really but i have been reading bout physics for a while now and i have noticed something wrong with the way qm theory works...might be rubbish th

I ve noticed that in qm measurements they always start from scratch for each expiriment / measurement which i think is silly becuase its ignoringthe facts what the expirementer has previoudly learned about the system under study..

Einstein beleived that everything in nature has a set value ..even if he didnt know the value of something at the time the thing has a value and that value never changes..

Looking at the 1st post i think what the guy is saying is if bob measures the angle of spin at a and mary when measuring the spin at b finds out there the same result then after getting results over time that always gives corelation at an observed angle then mary is no longer needed becuse if bobs measured angle at a is same as it was the last 100 timres he did it with mary then he pretty damn sure he knows what the outcome will be at point b without having mary there to tell him the result as he already knew by seeing what the reultat a was...bells theorem says that in order to have realism or an epr outcome them there must be hidden variables WHY?..Surely when the particle pair leave the source on there way to points a and b at the time of leaving they have a definite spin ,angle or whatever and although we don't knowthere state at that time we know if we measure there state at one of the 2 popints then we willknow both states..the result at a doesn't change the result at b or vice versa it just is that's thee way it played out ..no hidden varialbes or instruction sets that's nature...as i say qm's problem is it doesn't "learn" from past events it just throws everything learned away and starts from scraych again..nature reality isn't like that imo...reason i got into physics was to try and understand electrons and the slit expirament and i began to thinkthat elecrons or anything at the quantum level had a "history"..now I am thinking maybe he problem is not nature itself keeping a record but the way qm looks at it ...?

my 2 cents...sorry i won't jump into posts again till i understand things a bit better but that how i feel and not dumb..history has a part to play here wether qm needs to incoperate somehow or nature itself carries some about with it :)

 

[DrChinese]

Looking at the 1st post i think what the guy is saying is if bob measures the angle of spin at a and mary when measuring the spin at b finds out there the same result then after getting results over time that always gives corelation at an observed angle then mary is no longer needed becuse if bobs measured angle at a is same as it was the last 100 timres he did it with mary then he pretty damn sure he knows what the outcome will be at point b without having mary there to tell him the result as he already knew by seeing what the reultat a was...bells theorem says that in order to have realism or an epr outcome them there must be hidden variables WHY?..Surely when the particle pair leave the source on there way to points a and b at the time of leaving they have a definite spin ,angle or whatever and although we don't knowthere state at that time we know if we measure there state at one of the 2 popints then we willknow both states..the result at a doesn't change the result at b or vice versa it just is that's thee way it played out ..no hidden varialbes or instruction sets that's nature...as i say qm's problem is it doesn't "learn" from past events it just throws everything learned away and starts from scraych again..nature reality isn't like that imo...reason i got into physics was to try and understand electrons and the slit expirament and i began to thinkthat elecrons or anything at the quantum level had a "history"..now I am thinking maybe he problem is not nature itself keeping a record but the way qm looks at it ...?

Hi Calamero, and welcome to PhysicsForums.

QM does not "ignore" the history. There simply isn't any. Each and every observation puts a particle into a new eigenstate. Once that happens, the particle has no "memory" of earlier states. I know that does not sound reasonable. Neither is it "reasonable" that a pair of entangled particles do NOT have definite spin at the time they are created.

That is why Bell's Theorem is so important. I will repeat the generally accepted conclusion of Bell:

No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics.

Keep in mind that experiments support the predictions of Quantum Mechanics and do NOT support the predictions of local Hidden Variables. You must abandon your assumptions about either locality (speed of light is an upper limit) or realism (particles have definite attributes at all times).

I hope this helps.

 

[wm]

Jesse, I appreciate your effort here, and am not neglecting earlier matters; BUT

wm's example worked according to classical optical laws, but it only violated an inequality because it violated the condition on the source not having foreknowledge of Alice's detector setting.

wm response: The core boundary condition on the CHSH Inequality (it is an IDENTITY) is that the outputs in each wing be: PLUS ONE XOR MINUS ONE.

My classical model meets this core condition. As far as I know: The condition that you invoke is nowhere mentioned in relation to the CHSH Inequality.

That's what makes the model so interesting; it, along with QM, evidently breaches an IDENTITY that is closely identified with Bell's theorem. (The CHSH Inequality was developed in relation to that theorem).

(More on this another time, if needed.)

I'm tied up now, but hope it helps, wm

 

[wm]

<SNIP>You must abandon your assumptions about either locality (speed of light is an upper limit) or realism (particles have definite attributes at all times). Emphasis added.

Doc, a quick question re realism: I understand that some stellar sources produce ''unpolarised light'' -- which (of course) can become readily polarised.

Is this a classical example of ''particles NOT having definite attributes at all times''?

Thanks, wm

 

[JesseM]

wm response: The core boundary condition on the CHSH Inequality (it is an IDENTITY) is that the outputs in each wing be: PLUS ONE XOR MINUS ONE.

That's one of the conditions, but it's certainly not the only one. And as a side note, I think they should just be called "conditions", not "boundary conditions"--in physics boundary conditions usually refer to conditions on the boundaries of the region of space and time you're analyzing which have to be put in by hand before calculating the behavior of the system within that region, like a set of initial conditions for a system which you use as a starting point to calculate its future behavior, or the fact that one end of a heated rod is being kept at a fixed temperature.

My classical model meets this core condition. As far as I know: The condition that you invoke is nowhere mentioned in relation to the CHSH Inequality.

As far as you know maybe, but that isn't worth much unless you have actually studied some rigorous derivations of the CHSH inequality, which explicitly stated all the conditions necessary to guarantee it will be satisfied in a classical situation, and made certain that they don't contain the sort of condition I invoke. I doubt you have done this; if you have, you probably weren't reading carefully enough. I was able to come up with a very simple way of violating the CHSH inequality classically in a situation where I am asked two questions and I get to hear both before giving a +1 or -1 response to each one--I think it took me less than a minute to think this up once I understood what the CHSH inequality was saying, do you really think this is the sort of thing that would come as a shock to physicists? In general, if you find a really simple argument that seems to suggest the entire physics community is wrong about something, as a default it is best to assume that something in your understanding of the issue is incorrect, and to try to figure out where your error lies, rather than assuming from the start that all those physicists are actually that clueless and rushing off to tout your important discovery.

Anyway, just doing a quick search of arxiv.org using keywords "CHSH inequality source settings" I found the paper quant-ph/0304115 which says, on the first page:

Most derivations of the Bell/CHSH inequalities[2–4], in making the assumption of locality, assume that the hidden variable (\lambda) is not an explicit function of the detector settings (at the time of detection).

 

[heusdens]

No, it can't be done, not if the source emitting the streams has no foreknowledge of Alice and Bob's detector settings, and their measurements are made at a spacelike separation. Bell's theorem proves that.

In this abstract form, there is no spacelike separation any more.
The stream doesn't have foreknowledge of detector settings, rather the other way, the detector combination selects a (sub)stream.

Would you agree that under these conditions, if we find that Alice and Bob always get the same answers when they pick setting 2, that must be because the properties x,y,z of the streams were set by the source in such a way that it was predetermined that Alice and Bob would get a certain answer if they measured that stream using setting 2? There can't be any random element when they each measure their signal, or else there would be some probability of getting different answers...if Alice gets a string with properties x', y', z' and Bob gets a string with properties x'', y'', z'', and they both choose setting 2 and get the answer +, it must be true that (string with properties x', y', z' AND measurement on setting 2 -> 100% chance of getting +) and (string with properties x'', y'', z'' AND measurement on setting 2 -> 100% chance of getting +).

The element of the stream (not string) that reaches the detectors of Alice and Bob is the same.

What's more, the source doesn't know in advance on which trials they'll both choose setting 2. So if it's true on trials where they both choose setting 2 that the source always sends out signals with properties that make it 100% certain they'll both get a +, or signals with properties that make it 100% certain they'll both get a -, then this must be true on all trials, even the ones where they don't in fact choose to measure using setting 2. So we can say that every signal sent out by the source must either be of "type 2+" (meaning that its properties are such that if the detector is set to 2, the result is guaranteed to be +) or of "type 2-" (meaning on setting 2 you're guaranteed to get -). The source always sends both a signal of type 2+, or it sends them both a signal of type 2-; this is the only way to explain how they always get the same answer when they both choose setting 2, without violating local realism.

The source does not know the settings, but it is rather the effect of choosing detector combinations that filters the stream in such a way that detector outcomes show non-random behaviour.
So your assumption is not justified.

And the same reasoning shows that each signal must have a predetermined answer for whether it would give a + or - on setting 1, or setting 3; every signal must either be of type 1+ or type 1-, and likewise every signal must be either of type 3+ or type 3- (obviously the different-number types aren't mutually exclusive--if a signal is of type 2+ and 3-, that just means the signal has properties that make it guaranteed that if you measure using setting 2 you'll get +, and if you measure using setting 3 you'll get -).

What signal?
A stream consists of elements, and an element and detector setting gives an outcome/result. We do not assume we have any further knowledge about elements. Just that the stream characteristics when different combinations of detector settings are used, lead to different results and correlations.
The stream may consist of substreams, but whatever substream is selected when just one detector result is monitored, the outcome is random.

[btw. Signal is inappropriate. ]

Any disagreement with any of this so far? If so please explain which point you think is wrong, and if not I'll move on to showing how this guarantees the truth of Bell's theorem.

See my notes.