What Is an Element of Reality?

[Cat]

EPR were exactly correct. They didn't prove that QM was incomplete, and they didn't prove that it violated locality; but they did prove it was *either* nonlocal or incomplete.

Agreed.

Re two dice (or, in my analogy, two spinning hexagons) being a reasonable analogy to illustrate entanglement, you say:

I don't think so. The results of two dice rolls will always be statistically independent unless there is some "mechanism" by which the result of one roll can affect the result of the other. Merely making one or the other "biased" in some way isn't at all the same as "linking" them. So, as long as they are independent, you will never find that the correlations violate a Bell inequality.

True, they will never violate a "genuine" Bell inequality, but I suspect that the fact that there are some "non-detections" means that they will violate the equivalent of the CHSH inequality, i.e. one in which the estimated test statistic is related to the detected pairs, not to the emitted ones.

When time, I'll work on this. Meantime I've having fun trying to produce a local realist model that will predict the outcome of one of the latest proposed "loophole-free" experiments -- that by Grangier's team, using PDC sources with "event-ready detectors" and balanced homodyne detection. Here, because, even without the event-ready detectors, we shall have (I think) some kind of record for every single emitted pair (i.e. no non-detections), I predict that the CHSH inequality will not be violated.

Cat

 

[vanesch]

Let us go for the strange world of Balls.

Imagine the following situation: in the world of Balls, we have a theory describing a curious experiment: a generator of pairs of blue balls sends one ball to a left observer, Alice, and another ball to the right observer, Bob.

It has been empirically verified that blue balls turn into red or black objects, piramids or cubes, smooth or hairy. However, it is only possible to observe one property: if you look at the color red or black, they become slimy balls ; if you look at the shape, they become blue, slimy shapes, and if you look at the surface quality, they become blue balls.
It has also been empirically verified that if we measure the same property of both balls coming out of the pair producer, they are always opposite.

For tens of years, people have tried to analyse these pairs of balls, but nothing seems to distinguish them until they change (about after half an hour or so) and we can do a measurement on them. So we've come to the conclusion that "pair of blue balls" completely describes the physical situation.
Even in a zargon-ray analysis, they give exactly the same diffraction patterns.

We have measured empirically since years the following probabilities for the pairs of blue balls measurements, and this has lead to the Stochastic Theory of Blue Ball Pairs (in Mathematica notation) which takes as fundamental postulate:

p[{hair, smooth}] = 1/2
p[{hair, hair}] = 0
p[{smooth, smooth}] = 0
p[{red, blue}] = 1/2
p[{red, red}] = 0
p[{blue, blue}] = 0
p[{piramid, cube}] = 1/2
p[{piramid, piramid}] = 0
p[{cube, cube}] = 0

p[{hair, blue}] = 1/2
p[{hair, red}] = 0
p[{smooth, blue}] = 0
p[{smooth, red}] = 1/2
p[{piramid, blue}] = 0
p[{piramid, red}] = 1/2
p[{cube, blue}] = 1/2
p[{cube, red}] = 0
p[{hair, cube}] = 1/2
p[{hair, piramid}] = 0
p[{smooth, cube}] = 0
p[{smooth, piramid}] = 1/2
p[{a_, b_}] := p[{b, a}]

the last equation indicating that the probabilities are symmetric.

It is interesting to note that from these 2-point correlations, we can deduce that the local probabilities of Alice, to find on a color measurement:
blue, has probability 1/2
red has probability 1/2

on a shape measurement:
cubes have probability 1/2
piramids have probability 1/2

on a surface aspect measurement:
hair has probability 1/2
smooth has probability 1/2

and this, independent on the choice of measurement Bob will make.

So Bob can not use its choice of measurement to send a message to Alice.

Is my stochastic theory local or not ?
Is in this theory P(B|A) equal to P(B)

Now compare it to the following theory, the theory of Blue Bells:

p[{hair, smooth}] = 1/2
p[{hair, hair}] = 0
p[{smooth, smooth}] = 0
p[{red, blue}] = 1/2
p[{red, red}] = 0
p[{blue, blue}] = 0
p[{piramid, cube}] = 1/2
p[{piramid, piramid}] = 0
p[{cube, cube}] = 0

p[{hair, blue}] = 0
p[{hair, red}] = 1/2
p[{smooth, blue}] = 1/2
p[{smooth, red}] = 0
p[{piramid, blue}] = 0
p[{piramid, red}] = 1/2
p[{cube, blue}] = 1/2
p[{cube, red}] = 0
p[{hair, cube}] = 1/2
p[{hair, piramid}] = 0
p[{smooth, cube}] = 0
p[{smooth, piramid}] = 1/2
p[{a_, b_}] := p[{b, a}]

Same questions...


cheers,
Patrick.

 

[Hans de Vries]

When time, I'll work on this. Meantime I've having fun trying to produce a local realist model that will predict the outcome of one of the latest proposed "loophole-free" experiments -- that by Grangier's team, using PDC sources with "event-ready detectors" and balanced homodyne detection. Here, because, even without the event-ready detectors, we shall have (I think) some kind of record for every single emitted pair (i.e. no non-detections), I predict that the CHSH inequality will not be violated.

I guess you are referring to this paper?
http://arxiv.org/abs/quant-ph/0403191

I also found a followup paper from a later data here:
http://arxiv.org/abs/quant-ph//0407181

The similar related papers from H. Nha and H.J. Carmichael:
http://arxiv.org/abs/quant-ph/0406101
http://arxiv.org/abs/quant-ph/0406102



If you are objecting to the Clauser, Horner, Shimony, Holt inequality
is it because the derrivation of the ≤ 2 assumes that the value E_b
is equal in both E_ab and E_a'b (see below) while in fact they are
generally selected subsets (~3%) after coincidence detection ?


|E_ab + E_a'b + E_ab' - E_a'b'| ≤ 2
≡
|(E_a + E_a')E_b + (E_a - E_a')E_b' | ≤ 2

(for individual measurements with outcome +1 or -1 either
(E_a+E_a')=0 or (E_a-E_a')=0 resulting in a maximum value of 2)


Regards, Hans

 

[ttn]

It is interesting to note that from these 2-point correlations, we can deduce that the local probabilities of Alice [...]
and this, independent on the choice of measurement Bob will make.

That's potentially misleading. The marginals (the probabilities for Alice gotten by summing
over the possible outcomes for Bob weighted by the appropriate probabilities) for alice to measure red/blue are indeed 50/50. But the conditional probability for Alice to measure red is *not* independent of the color of Bob's ball. ...e.g., the probability that Alice will find a blue ball when Bob's has already turned red, is 100%.

So, since you went out of your way to claim that there is no behind-the-scenes, local mechanism which can account for the correlations, i.e., that the description "two blue balls" is *complete*, there is a violation of Bell Locality here.

So Bob can not use its choice of measurement to send a message to Alice.

That's right. This example shows a violation of Bell Locality, but one that is washed out by randomness and so cannot be used to transmit information. Just like QM. Just like Bohm.

Is my stochastic theory local or not ?

Depends on what you mean. It's not Bell Local, but it is "information local".

Is in this theory P(B|A) equal to P(B)

No, definitely not. 100% =/= 50%.

 

[ttn]

Clearly "2 blue balls" is a complete description of the setup in that I cannot know more.

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description. Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing. The little switch in the door prevents me from knowing whether or not the light in the refrigerator really goes off or not when I shut the door -- but that doesn't mean I stop believing that, in fact, the light is either on or off. In that case, there are obviously more facts out there in the external world than I can know about directly, so my description "I think there's about a 99% chance that the light does go out when I shut the door" is an admittedly incomplete one.

In the QM case, we can't take anything for granted. It is by no means "obvious" there that there are further facts of reality beyond what is contained in or described by the wave function. But that is why EPR-like arguments are so clever. They allow you to say something, not about the completeness alone, but about the relationship between completeness and locality. EPR showed that, if you hold fast to the locality principle, there must exist "elements of reality" for more quantities than are consistent with the uncertainty principle; hence QM, if local, is incomplete. I think Einstein's argument is even better: he argues that (a) you must be willing to inject the wave function collapse rule into the dynamics in order to get the right correlations and so (b) there is *not* a one-to-one correspondence between physical states and theoretical descriptions since when you collapse the wf for a distant system by making a measurement "here", the wf for that distant system changes in a situation where (by locality) its physical state can not have changed. That ruins any claim of one-to-one correspondence. I also like the Bell-Locality-based argument for this same conclusion: if you assume that the wf alone does provide a complete description of the system described, it is trivial to note that Bell Locality is violated.

Anyway, my point is just to reject in the strongest possible terms the idea that what "completeness" means is somehow purely epistemological, e.g., that it means we've learned all we can or have said all we can say. Completeness involves a comparison between knowledge and the facts, not just a comparison of knowledge to itself.

Of course, many people have tried to define completeness in a purely epistemological way, i.e., while dropping the assumption of realism. This (as with the attempt to define "locality" outside the context of realism) is literal nonsense. Tim Maudlin makes this point (about locality) very nicely in an article called "Space-time in the quantum world": "Physicists have been tremendously resistant to any claims of non-locality, mostly on the assumption (which is not a theorem) that non-locality is inconsistent with Relativity. The calculus seems to be that one ought to be willing to pay *any* price -- even the renunciation of pretensions to accurately describe the world -- to preserve the theory of Relativity. But the only possible view that would make sense of this obsessive attachment to Relativity is a thoroughly realistic one! These physicists seem to be so certain that Relativity is the last word in space-time structure that they are willing even to forego any coherent account of the entities that inhabit space-time." I believe parallel remarks apply as well to the concept of "completeness". Defenders of orthodox QM have been extremely resistant to any claims that QM might be incomplete... yet the only view that would make sense of this obsessive attachment to "completeness" is a thoroughly realistic one.

 

[vanesch]

...e.g., the probability that Alice will find a blue ball when Bob's has already turned red, is 100%.

So, since you went out of your way to claim that there is no behind-the-scenes, local mechanism which can account for the correlations, i.e., that the description "two blue balls" is *complete*, there is a violation of Bell Locality here.

And my second example ? The 2 Bells Theory ? Is it also violating Bell Locality ? The same example can be given about Alice's black ball and Bob's red ball...


cheers,
Patrick.

 

[ttn]

And my second example ? The 2 Bells Theory ? Is it also violating Bell Locality ? The same example can be given about Alice's black ball and Bob's red ball...

Maybe I'm just being dumb and/or not looking carefully enough, but I didn't see any difference between the two theories. Isn't the second just the same as the first with some of the (already
just meaningless, made-up) terms swapped around?

Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

I gather you are going to object to this, and say that my view is premised on a demand for explanation (which black box theories aren't intended to provide) or relies to heavily on realist commitments, or something to that effect. I guess I'm guilty as charged. By the way, you might enjoy the article "Do Correlations Need to be Explained" by Arthur Fine (in the Cushing/McMullin volume called "Philosophical Consequences of Quantum Theory"). He takes a position there that seems like the one you are evolving toward here -- namely, that if we are going to accept irreducible randomness at the individual-outcome-level, we should be equally willing to accept irreducible correlations between distant events. I don't agree with this position of course, but it's certainly out there.

Oh yeah, one other point I wanted to make that fits in nicely here. I was skimming through some of the other threads here, especially the ones on the "loopholes" in the Bell's Inequality experiments. Dr. Chinese made an excellent point there against the "local realism" people who refuse to admit that the experiments actually support the claim that Bell's Inequality is violated in nature. Paraphrasing, the point was: if you made these same sorts of objections on any other issue in science (e.g., claiming that different systematic errors in a bunch of different experiments all conspire magically to make those experiments give exactly the same results, claiming that the samples might be biased merely on the basis that the sample represents less than 100% of the population and without *any* statistical evidence to suggest a bias, etc.) you'd be branded a loony. Science would seriously grind to a complete and total halt if scientists were this willing, across the board, to consider conspiracy theories. It is relevant that the stakes are pretty high here -- one is talking about having to reject a premise (locality) that has been awfully important to physics for a long time. So there is *some* justification for a bit of extra skepticism, scrutiny, and thinking carefully about "loopholes", etc. But at some point you have to draw a line and say: enough. *All* of the evidence points to the QM predictions being correct, and *no* evidence suggests they are wrong. (And the lack of evidence against that proposition is not evidence for it!)

Anyway, I think similar comments apply to the question of whether we should try to explain correlations between distant events. The position of Arthur Fine in the article I mentioned (which I think Patrick would be symapthetic to?) amounts to shrugging and saying "well, some correlations can't be explained." But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

 

[vanesch]

My claim is that this "completeness" requirement means: there is an underlying deterministic theory that can generate the probabilities in a classical statistical mechanical way. You are fighting like a devil to show me that I do not need that word "deterministic" but I will try to show you that THAT is what you want, and as long as you don't have it, you call a theory "incomplete". This is not surprising, because it was indeed Einstein's programme. But, although you won't admit it, it comes down to regard any fundamentally statistical theory as "incomplete".

I hope you do not mean by "complete" the "ultimate theory describing the true nature of reality" because that theory will change every century or so, and we will never have a 'true description of reality'. Newtonian theory wasn't, Maxwell's theory wasn't, we now know that general relativity isn't, quantum field theory isn't so I think it is clear by now that nothing we will ever have to put our hands on will be "the true description of reality".
EVERY theory we will ever have is an approximate formalism and with a totally different paradigm than the previous one giving sufficiently accurate results when compared with the experimental results available by the technology of the moment.
Maybe some day we will have to stop, because it all fits logically together and we cannot perform technologically any experiment anymore that could possibly challenge the theory. But that doesn't mean we "arrived".
So it is very simple: if you mean that, by completeness, you can just as well stop and say that every theory is incomplete.

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

Ok, so "element of reality" must mean: determines precisely every outcome, potentially with certainty. I'll try to show you.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description.

No, once you have a determinisitic theory, you will be happy because there's nothing more to be added. What can be more "complete" than a deterministic theory which tells you individually, for each event, what will happen, with certainty ?

Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing. The little switch in the door prevents me from knowing whether or not the light in the refrigerator really goes off or not when I shut the door -- but that doesn't mean I stop believing that, in fact, the light is either on or off. In that case, there are obviously more facts out there in the external world than I can know about directly, so my description "I think there's about a 99% chance that the light does go out when I shut the door" is an admittedly incomplete one.

Indeed, you want to talk about the switch, and the fact that it determines with certainty that the light goes off.

In the QM case, we can't take anything for granted. It is by no means "obvious" there that there are further facts of reality beyond what is contained in or described by the wave function. But that is why EPR-like arguments are so clever. They allow you to say something, not about the completeness alone, but about the relationship between completeness and locality. EPR showed that, if you hold fast to the locality principle, there must exist "elements of reality" for more quantities than are consistent with the uncertainty principle; hence QM, if local, is incomplete.

Again, in a deterministic case, when it is "in principle" possible to determine with certainty each individual outcome.

I think Einstein's argument is even better: he argues that (a) you must be willing to inject the wave function collapse rule into the dynamics in order to get the right correlations and so (b) there is *not* a one-to-one correspondence between physical states and theoretical descriptions since when you collapse the wf for a distant system by making a measurement "here", the wf for that distant system changes in a situation where (by locality) its physical state can not have changed. That ruins any claim of one-to-one correspondence. I also like the Bell-Locality-based argument for this same conclusion: if you assume that the wf alone does provide a complete description of the system described, it is trivial to note that Bell Locality is violated.

Bell locality is violated for EVERY stochastic theory which gives you correlations and which does not include a deterministic model for each individual outcome in its "state description". See my Blue Balls and my Blue Bells examples. It is only when you give a potentially deterministic state description that you can avoid Bell locality to be violated and have correlations in certain cases.

Anyway, my point is just to reject in the strongest possible terms the idea that what "completeness" means is somehow purely epistemological, e.g., that it means we've learned all we can or have said all we can say. Completeness involves a comparison between knowledge and the facts, not just a comparison of knowledge to itself.

Yes, and the facts "determine" every individual outcome. Again, there is no room for a purely stochastic theory which *postulates* probabilities as fundamental concepts.

Of course, many people have tried to define completeness in a purely epistemological way, i.e., while dropping the assumption of realism. This (as with the attempt to define "locality" outside the context of realism) is literal nonsense. Tim Maudlin makes this point (about locality) very nicely in an article called "Space-time in the quantum world": "Physicists have been tremendously resistant to any claims of non-locality, mostly on the assumption (which is not a theorem) that non-locality is inconsistent with Relativity. The calculus seems to be that one ought to be willing to pay *any* price -- even the renunciation of pretensions to accurately describe the world -- to preserve the theory of Relativity. But the only possible view that would make sense of this obsessive attachment to Relativity is a thoroughly realistic one! These physicists seem to be so certain that Relativity is the last word in space-time structure that they are willing even to forego any coherent account of the entities that inhabit space-time." I believe parallel remarks apply as well to the concept of "completeness". Defenders of orthodox QM have been extremely resistant to any claims that QM might be incomplete... yet the only view that would make sense of this obsessive attachment to "completeness" is a thoroughly realistic one.

That's why I think that the only reasonable definition of locality is the one that avoids the paradox in relativity, which is that you receive your own information before sending it so that you can decide to send something else.
If *that* requirement is satisfied, the stochastic predictions of a theory are local.

Bell-locality is a requirement that doesn't only depend upon the stochastic predictions a theory makes, but also upon what is considered as a state description, and can only avoid calling any correlation as non-local if that state description is potentially deterministic. But it will call ANY stochastic description 'non-local'. Bell locality has no meaning for theories which are inherently stochastic, meaning: out of which come simply rules to calculate probabilities.

There is more room for such stochastic theories than for deterministic theories with local mechanisms to make up probabilities which do not violate "information transfer" locality, and QM happens to hit in that extra room.

So you can redefine qualifiers such as "complete" or "realist" or whatever, what you really mean is "deterministic", or "potentially deterministic".

By "potentially deterministic" I mean partly deterministic and partly stochastic theories, of which the stochastic parts can trivially be converted in deterministic ones by adding (hidden) variables.

cheers,
Patrick.

 

[vanesch]

Maybe I'm just being dumb and/or not looking carefully enough, but I didn't see any difference between the two theories. Isn't the second just the same as the first with some of the (already
just meaningless, made-up) terms swapped around?

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

cheers,
Patrick.

 

[vanesch]

Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

And if the correlations are only born when the two events are already in the past, like in an MWI approach ? When the "remote measurement" didn't take place *until you got news of it because it is YOU who determined the outcome* ?

I gather you are going to object to this, and say that my view is premised on a demand for explanation (which black box theories aren't intended to provide) or relies to heavily on realist commitments, or something to that effect.

I go even further: what you call "realist" means deterministic, even if you don't want to admit it. But I'll find a way to make you talk

Dr. Chinese made an excellent point there against the "local realism" people who refuse to admit that the experiments actually support the claim that Bell's Inequality is violated in nature. Paraphrasing, the point was: if you made these same sorts of objections on any other issue in science (e.g., claiming that different systematic errors in a bunch of different experiments all conspire magically to make those experiments give exactly the same results, claiming that the samples might be biased merely on the basis that the sample represents less than 100% of the population and without *any* statistical evidence to suggest a bias, etc.) you'd be branded a loony. Science would seriously grind to a complete and total halt if scientists were this willing, across the board, to consider conspiracy theories. It is relevant that the stakes are pretty high here -- one is talking about having to reject a premise (locality) that has been awfully important to physics for a long time. So there is *some* justification for a bit of extra skepticism, scrutiny, and thinking carefully about "loopholes", etc. But at some point you have to draw a line and say: enough. *All* of the evidence points to the QM predictions being correct, and *no* evidence suggests they are wrong. (And the lack of evidence against that proposition is not evidence for it!)

I don't think locality (in the relativity sense) is the issue, I think it is a certain form of realism (which you call somehow complete, and which I'm sure means "determinisitic"). I think that at the moment, we cannot give up on the first (and happily QM DOESN'T violate locality in the relativity sense in generating an information paradox). But I easily give up on the second condition.

Anyway, I think similar comments apply to the question of whether we should try to explain correlations between distant events. The position of Arthur Fine in the article I mentioned (which I think Patrick would be symapthetic to?) amounts to shrugging and saying "well, some correlations can't be explained." But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

If I were the judge, I'd try to send information through the patients, by given certain days the drug to the people, and certain days not. The receiver which would be the grand jury, and should then try to decode my message by looking at how people die. My message would be: "Cut this guy his head off - stop - repeat - cut this guy his head off" coded in ASCII 7 bit. Bit one: I give them the drug, and they die. Bit 0, they get a placebo and they live.
Hmm, if my phrase contains 80 characters, that means 560 bits to send, with at least 10 people per bit ; ok but half of them will have bit 0 and live, so I'll need to kill 2800 people for this message to be sent...
If they can read my message, I'd say that there is a causal link

cheers,
Patrick.

 

[DrChinese]

That is not clear at all. "Completeness" is not a statement merely about what can be known. Completeness is a shorthand for something like "complete description of reality." Einstein talked about it as requiring a one-to-one correspondence between physical states and state-descriptions in some theory. EPR of course urged that every "element of reality" must have a counterpart in the theoretical description. etc.

It is admittedly difficult if not impossible to know whether a given state description represents a complete description. Personally I think Bohr was off his rocker for making this kind of claim in the first place -- what in the world could have counted as evidence for it? The mere fact that the Heisenberg principle seems to prevent us from obtaining *knowledge* of certain things? That of course proves nothing.

Probably you are right that Bohr should not have asserted QM was complete. I think that statement carries too much baggage with it.

EPR thought they had a pretty clever argument by throwing the singlet state into the equation along with the HUP. They argued that at least a "more complete" specification of the system was possible, even if you accepted QM's predictions. They tried, in other words, to use the logic of the HUP against the idea that QM was complete.

Bell said that EPR's argument - which also tried to define what an element of reality was - did not actually work as they had pictured it. The problem being that their assumption - elements of reality exist independent of the measurement - was flawed. As we now know, Bell's Inequality shows that these elements of reality cannot have predetermined values and still yield experimental results consistent with QM. This is true - in my opinion - whether the theory is local or non-local: unmeasured quantum properties do not correspond to elements of reality. This conclusion is diametrically opposed to the closing words of EPR. However, I do not think this is semantically equivalent to the statement that QM is complete.

 

[DrChinese]

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

cheers,
Patrick.

You have a lot of balls (sorry couldn't resist).

The only detail I would comment on is this: you can construct a local hidden variable theory as you have above which appears to provide certain correspondence to the Bell model, but that correspondence is superficial. You can't do it AND give the same predictions as QM. That is the essence of Bell! There is no $$\theta$$ in your formula. Functions exist which respect the Bell Inequality as $$\theta$$ varies; but they will not match the $$cos^2\theta$$ predictions of QM.

 

[DrChinese]

1. Any time you tell me there are persistent, law-like correlations between separated events and that there is *nothing* in the shared past of those events which made them be so correlated, I am going to say this violates Bell Locality. That kind of "magical" correlation between separated events is precisely what Bell Locality forbids.

...

2. But imagine that view being taken seriously by, say, the drug industry or biologists or chemists or anybody else in science. "Hmmm, people who live in these two widely separated towns all simultaneously came down with a rare disease that hasn't been observed anywhere else on Earth for 100 years... <shrug> oh well, coincidences happen all the time. When's lunch?" Or: "Well yes, your honor, there is a strong correlation between patients having undergone Medical Procedure X and, ahem, dying the next day -- but some correlations are just inexplicable." etc... you get the point.

1. I guess you could use this as an operating definition of Bell Locality. But there is yet one more item to consider: who is saying that there is no connection between these events? I say there is a connection between the events. But I deny that there are more "elements of reality" than actually measured.

2. Good point. Would you bet your life that there is no causality to the correlation? If you wouldn't - as a strategy - then you believe the correlation is not spurious.

I don't believe the connection between the correlations is spurious, but I don't know what is the cause and what is the effect. Presumably, causes must precede effects but maybe that does not apply. If you see time as symmetric then maybe causes only precede effects in some frames.

 

[Cat]

My claim is that this "completeness" requirement means: there is an underlying deterministic theory that can generate the probabilities in a classical statistical mechanical way.

Yes, in any case this is what I would mean, but this does not lead necessarily to the requirement that every "elements of reality" has to determine outcomes in a Bell test completely. Any given element of reality may need (as explained by Bell and by Clauser and Horne) the company of other elements of reality, mostly local to the detectors, before it yields a definite outcome. Without this extra input, our element of reality set at the source may determine only the probability of each possible outcome.

Ok, so "element of reality" must mean: determines precisely every outcome, potentially with certainty. I'll try to show you.

This is the actual statement that I'm challenging. It is probably not essential to your point but it's as well to be clear what is meant.

Yes, and the facts "determine" every individual outcome. Again, there is no room for a purely stochastic theory which *postulates* probabilities as fundamental concepts.

Ah yes, that's a more correct way of saying it. The "facts" can include more than one element of reality.

Bell locality has no meaning for theories which are inherently stochastic, meaning: out of which come simply rules to calculate probabilities.

There is more room for such stochastic theories than for deterministic theories with local mechanisms to make up probabilities which do not violate "information transfer" locality, and QM happens to hit in that extra room.

But doesn't that imply that QM operates by magic?

By "potentially deterministic" I mean partly deterministic and partly stochastic theories, of which the stochastic parts can trivially be converted in deterministic ones by adding (hidden) variables.

This sounds reasonable.

The interesting question now is whether or not experiments have in fact ruled out such "potentially deterministic" theories. Isn't the fact that they [e.g. Grangier's team, and Nha and Carmichael -- see Hans de Vries post earlier] are still looking for "loophole-free" tests an indication that the evidence against such theories is, to date, not conclusive? Of course, by Bell's theorem, if this kind of theory really does underly everything it means that QM is not quite correct, but it's probably nearly correct, or perhaps sufficiently near to correctness that the various applications of entanglement are effectively valid.

Cat

 

[DrChinese]

Isn't the fact that they [e.g. Grangier's team, and Nha and Carmichael -- see Hans de Vries post earlier] are still looking for "loophole-free" tests an indication that the evidence against such theories is, to date, not conclusive?

That is a logical flaw. You want it both ways. You refuse to accept it as conclusive evidence when folks stop looking; and you see it as supporting your position when they are looking! From your logic, it makes no sense to repeat an experiment, either! (Presumably that would mean that the experimented does not accept the initial results.) There are a lot of reasons to do experiments, even ones in which the essential results are not in question.

 

[ttn]

I hope you do not mean by "complete" the "ultimate theory describing the true nature of reality" because that theory will change every century or so, and we will never have a 'true description of reality'. Newtonian theory wasn't, Maxwell's theory wasn't, we now know that general relativity isn't, quantum field theory isn't so I think it is clear by now that nothing we will ever have to put our hands on will be "the true description of reality".
EVERY theory we will ever have is an approximate formalism and with a totally different paradigm than the previous one giving sufficiently accurate results when compared with the experimental results available by the technology of the moment.
Maybe some day we will have to stop, because it all fits logically together and we cannot perform technologically any experiment anymore that could possibly challenge the theory. But that doesn't mean we "arrived".
So it is very simple: if you mean that, by completeness, you can just as well stop and say that every theory is incomplete.

Good point, I totally agree. This is exactly why I think Bohr should never have been taken seriously when he claimed QM was complete.

Perhaps, then, what really makes you uncomfortable with all of this is not that the EPR-type argument against Bohr's claim is unsound, but that it is totally unnecessary. Why work so hard to refute something that is preposterous on its face? There is no grounds whatsoever for thinking QM is complete, so just forget about the whole issue and get on with life. Einstein et al were *obviously* right to reject the completeness doctrine, and they shouldn't have opened unnecessary cans of worms arguing against it. Is this more or less what you think?

No, once you have a determinisitic theory, you will be happy because there's nothing more to be added. What can be more "complete" than a deterministic theory which tells you individually, for each event, what will happen, with certainty ?

It's true; if you have a deterministic theory that explains everything, you'd at least have some evidence that maybe the theory is complete. On the other hand, any time you have a stochastic theory, it's always possible to wonder if the randomness is merely due to incomplete information, i.e., if an underlying deterministic theory could give rise to the stochastic theory already in hand.

But that doesn't mean I simply equate "complete" with "deterministic". Perhaps nature really is not deterministic. Who knows. (Actually, as someone who believes in free will, I'm really pretty open to this possibility.) My only point is: if you have a stochastic theory that predicts correlations which cannot be locally explained (with the usual stochastic sense of "explained"), you should admit that your stochastic theory is nonlocal. And, say, if it is possible to remove that nonlocality (i.e., construct a local theory that makes the same predictions) by filling in the description a bit (maybe leaving you with a deterministic underlying theory, or maybe a still-stochastic but more detailed underlying theory) you should be open to that possibility.

Indeed, you want to talk about the switch, and the fact that it determines with certainty that the light goes off.

It's not so much that I *want* to talk about this stuff. But if talking about this stuff allows me to get around a shocking and troublesome problem (which would be that thinking my stochastic statement about the fridge light was a complete description, led to my fridge theory being nonlocal -- which makes no sense in this example, but oh well) then I should be open to the possibility.

That's my only point. It's totally simple. People who claim QM is complete should admit that their theory is nonlocal. (...and they should therefore quit dismissing, out of hand, theories like Bohm's because of their nonlocality.)

Bell locality is violated for EVERY stochastic theory which gives you correlations and which does not include a deterministic model for each individual outcome in its "state description". See my Blue Balls and my Blue Bells examples.

That's not true. You yourself revealed that there exists a local, stochastic theory that can explain all the observational results you catalogued for the Blue Bells example. (It's stochastic because it's random which of the two goobers goes which way -- and for all I know, maybe it's *really*, irreducibly random.)

That's why I think that the only reasonable definition of locality is the one that avoids the paradox in relativity, which is that you receive your own information before sending it so that you can decide to send something else.
If *that* requirement is satisfied, the stochastic predictions of a theory are local.

We've been here before. I agree this is an important and interesting definition of locality, definitely worth considering. The problem is that "information" is a very high level idea, and it's possible for theories to be local in this "no info transfer" sense while being fundamentally, in their guts, quite blatantly nonlocal. Bohm's theory is the obvious non-controversial example. Orthodox QM is another obvious example that is, for reasons I frankly don't understand, controversial. (I guess, the reason it's controversial is that people are happy to emblazon Bohm's theory with the scarlet letter "NL" based on its violating Bell Locality, then they like to switch to the "no info transfer" definition so that QM gets the label "Local". But as I've said several times, that's just stupid naked inconsistency and shouldn't be tolerated by serious thinkers.)

 

[vanesch]

You have a lot of balls (sorry couldn't resist).

I hope you realize that the names have been carefully choosen
The Blue Balls theory is very preposterous, and violates Bell's inequalities much more than QM (hence Balls ) - at least if I didn't make an error.

The Bells theory is compatible with a local hidden variable model and hence will satisfy Bell's inequalities.

I took on purpose NOT a cover-up of a prediction of QM because that would be seen as too cheap. In fact, I tried to make the two correlation functions as much alike as I could, with similar values of correlations, but in different cases.

Note that what ttn defined as Bell Locality is not the Bell's inequalities (but they can be derived from it). He defines Bell Locality as the fact that if you take into account a "complete state description", then the correlation P(A,B) factorizes in P(A) x P(B).

I wanted to show how inevident it is to apply this to a stochastical theory, by showing two very similar stochastical theories.

The only detail I would comment on is this: you can construct a local hidden variable theory as you have above which appears to provide certain correspondence to the Bell model, but that correspondence is superficial. You can't do it AND give the same predictions as QM. That is the essence of Bell! There is no $$\theta$$ in your formula. Functions exist which respect the Bell Inequality as $$\theta$$ varies; but they will not match the $$cos^2\theta$$ predictions of QM.

The only "theta" I have is discrete: colors, shapes and surface type. 3 values is sufficient.

cheers,
Patrick.

 

[ttn]

Hehe

The second theory (Blue Bells) HAS a hidden variable explanation:

you have a hairy, red cube going one side and a smooth blue piramid going the other way. So ADDING this deterministic hidden variable model will turn my Bell-locality violating theory into a Bell-respecting theory.

The first theory (Blue balls) hasn't such a potentially underlying model.

Please admire it for at least 3 seconds, it took me some puzzling to find it .

It's a nice example, no doubt. But I still think you are missing my point. In fact, your example helps me make my point even stronger, so thank you.

My claim was that the Blue Bells theory violated Bell Locality -- ***if*** you asserted that the theory is complete. It's just like EPR: the conclusion is not a blanket claim for in-completeness or non-locality, but a dilemma: if you want to believe the theory is complete, you must admit that it violates locality. Or: if you insist on avoiding nonlocality, you must admit that the theory is incomplete.

So your example is helpful in that it illustrates this dilemma very clearly. Regarded as a complete specification of the system, the Blue Bells model is nonlocal. The probabilities violate Bell Locality. Of course, you can get around this conclusion easily, by admitting that maybe, after all, the theory was not complete, and considering the very local-hv account you provided.

Really, this is exactly like the coin-in-two-hands or Einstein's Boxes example I mentioned a while back. Put a particle in a box, split the box in two so half the wf goes each way, separate the halves, and then look in one to see if the particle is there. If you *insist* on regarding the wf as a complete description of the state of the particle prior to looking in the boxes, you can then identify the wf with Bell's "L" and infer that Bell Locality is violated. QM, if complete, is nonlocal. But in this example there is, just like in yours, a rather obvious local way to understand the probabilities involved (specifically, that the joint probability for finding the particle in *both* boxes is not simply the product of the individual probabilities for the two boxes = 50% * 50% = 25%) as arising from a deeper level of description -- namely, one in which the particle just is in one of the two boxes the whole time, prior to measurement. Then opening the boxes merely reveals the pre-existing location of the particle. *Obviously* local. But -- and this is the whole point -- the price of *doing* this is regarding the original wf-only description as *incomplete*. QM, if local, must be incomplete. Or equivalently: QM, if complete, is nonlocal. All of that follows from this trivial example.

Of course, less trivial examples (involving spin correlations along several distinct axes, or the equivalent of the case of the Blue Balls -- which, by the way, is not a sherlock holmes story I'd particularly like to read) yield different results. Sometimes it is *not* possible to elude the apparent nonlocality of the quantum predictions merely by giving up the idea that the wf provides a complete description. That is Bell's theorem. But that doesn't undo what we already showed with the simpler example, namely, that QM, if complete, is nonlocal.

And that's really all I'm interested in claiming. The nonlocality that is *apparent* in the QM predictions is actually *real* -- it cannot be escaped by dropping the completeness assumption or anything else. Nature is nonlocal (in the Bell sense, though, yes, possibly local in some other senses). You're going to be stuck with a Bell-Nonlocal theory whether you regard QM as complete or not. This is not a proof that QM *isn't* complete. Duh. But it is a proof that the people who dismiss theories like Bohmian mechanics out of hand (on the grounds of their violating Bell Locality) should shut up.

 

[vanesch]

That's not true. You yourself revealed that there exists a local, stochastic theory that can explain all the observational results you catalogued for the Blue Bells example. (It's stochastic because it's random which of the two goobers goes which way -- and for all I know, maybe it's *really*, irreducibly random.)

That's where we differ.
IF you consider this theory as "Bell Local" it is obviously deterministic, in that for each pair of bells emitted, you are in case A (cube left, piramid right) or you are in case B (cube right, piramid left). If you are in case A, all the probabilities are 1 or 0, and if you are in case B, idem. So if the case is determined, everything is deterministic. Now, if you think you have the right to put the "case" into the "complete description of nature" then I have also the right to say that this complete description of nature determines all outcomes with certainty, and that's what I call a deterministic theory.
Whether this CASE information is accessible in principle to us, observers, or not (in which case it is a "hidden variable") doesn't change anything: if you consider it part of a complete description, it "is there".
It is our lack of information about the CASE variable, so that we have to consider an ensemble of these variables, that gives us the ONLY randomness in the outcomes. Now, or (as in the case of statistical mechanics) this is just a problem in practice, or somehow it is "fundamentally hidden", so whatever we do, we'll never find out. In that last case you could maybe try to claim that your theory is fundamentally stochastic, but then I can claim that your variable is so well hidden that it shouldn't be part of a state description in the first place ! But if you do that, your Bell locality condition falls on its face again...
As I said elsewhere, you could pro forma introduce some finite probabilities in such hidden variable theories to make em look like a stochastic theory, but by adding a few more variables, you easily turn them in fully deterministic theories out of which (when including them in the "complete state description") come only 1 and 0 as probabilities.

cheers,
Patrick.

 

[vanesch]

And that's really all I'm interested in claiming. The nonlocality that is *apparent* in the QM predictions is actually *real* -- it cannot be escaped by dropping the completeness assumption or anything else. Nature is nonlocal (in the Bell sense, though, yes, possibly local in some other senses). You're going to be stuck with a Bell-Nonlocal theory whether you regard QM as complete or not. This is not a proof that QM *isn't* complete. Duh. But it is a proof that the people who dismiss theories like Bohmian mechanics out of hand (on the grounds of their violating Bell Locality) should shut up.

I had the impression (but I can be wrong) that if you take the hidden variables in Bohm for real (and you have to, if you consider them part of the reality description), that LOCAL probability distributions of these hidden variables can have expectation values which change according to what happens elsewhere, so that these probability distributions of these hidden variables are not local in the sense of relativity (in that we can send information that way, if only we had local access to these hidden variables).
It is in *that* sense that I thought that Bohm was non-local.

I honestly don't care about Bell locality itself which is, in my opinion, just a statement about probabilities generated by deterministic, local theories. So I agree with you that I wouldn't mind Bohm only to violate Bell Locality. The same rules have to count for everybody.

cheers,
Patrick.

 

[ttn]

I had the impression (but I can be wrong) that if you take the hidden variables in Bohm for real (and you have to, if you consider them part of the reality description), that LOCAL probability distributions of these hidden variables can have expectation values which change according to what happens elsewhere, so that these probability distributions of these hidden variables are not local in the sense of relativity (in that we can send information that way, if only we had local access to these hidden variables).
It is in *that* sense that I thought that Bohm was non-local.

Yes, that's exactly right. But (and this is becoming something of an anthem on my part..) it's just the same for QM. If you could actually discover somehow what the wave function for some entity next to you was, you would be able to use this information to send messages. Send your friend one of the boxes with "half a particle" in it. The value of the wf over by your friend is 1/sqrt(2). [or something like that... technically I'm talking about the mod of the wf integrated over the volume of the box, but who cares about that detail.] But as soon as you open your box and either find or don't find the particle there, the value of the wf over by your friend will immediately change to either zero or one (respectively). And if he had access to that change -- if he knew that the value of the wf in his box had suddenly jumped, he'd know that you had just opened your box. Hence, information transfer.

Of course, everybody knows that you can't just "learn the value of the wf at some point". So you can't actually use this underlying non-locality in orthodox QM to transmit information. But if this kind of argument gets QM off the hook, it ought to get bohmian mechanics off the hook too. They're really equivalent -- both are theories about some quantity/quantities (wave functions only for QM, wf's plus particle positions for Bohm) which are affected nonlocally by various fiddling that can be done at distant locations. And if only you had access to the exact local state (as indicated by the local values for the quantities your theory is *about*) you could use this nonlocality to transmit information and thus get into all sorts of hot water with relativity. But, in both theories, you *don't* have access to the exact local state, so you are *prevented* from using the nonlocality to transmit information, and hence (by the "info" type definition of locality) both theories turn out to be *local*. But this has a very uncomfortable, conspiratorial feel to it, which people have no trouble expressing when it comes to Bohm. They all say more or less what you said above: "come on, the underlying *physics* in Bohm's theory is blatantly nonlocal -- so the fact that this nonlocality is washed out and can't be put to use is irrelevant." For some reason people aren't as willing to say what is, I think, obviously and equally true of QM: "the underlying *physics* of QM is blatantly nonlocal [specifically, the collapse postulate] -- the fact that this is washed out and can't be put to use is irrelevant."

By the way, the kind of statements you are making here about Bohm's theory -- that it is obviously nonlocal if you take it seriously -- is exactly what bothered Bell about Bohm's theory at first. It is, I suspect, part of why he was motivated to come up with clean mathematical condition by which one could judge deep/fundamental locality [or what he called "local causality"]. Remember, Bohm's theory is *local* by the standard of info transfer, so *some* clean way of expressing its "obvious" nonlocality is needed. What he came up with -- "Bell Locality" -- does the job beautifully. It's because Bohmian mechanics violates this condition that we all feel good about saying: "ahh, OK, so despite the fact that you can't send messages FTL in Bohm's theory, it really is nonlocal behind the scenes." But then you notice that orthodox QM violates this same condition -- something which people remain far less comfortable about, but which is painfully obvious nevertheless.

 

[ttn]

That's where we differ.
IF you consider this theory as "Bell Local" it is obviously deterministic, in that for each pair of bells emitted, you are in case A (cube left, piramid right) or you are in case B (cube right, piramid left). If you are in case A, all the probabilities are 1 or 0, and if you are in case B, idem. So if the case is determined, everything is deterministic. Now, if you think you have the right to put the "case" into the "complete description of nature" then I have also the right to say that this complete description of nature determines all outcomes with certainty, and that's what I call a deterministic theory.
Whether this CASE information is accessible in principle to us, observers, or not (in which case it is a "hidden variable") doesn't change anything: if you consider it part of a complete description, it "is there".

Yes, you're entirely right about this. My mistake. I shouldn't have said that picking between cases A and B in some "irreducibly stochastic" way made the theory genuinely stochastic. It doesn't, for just the reasons you give.

I don't think this changes anything significant, though. I still maintain that it's possible to have a genuinely stochastic theory that either does or does not satisfy Bell Locality -- i.e., the Bell Locality condition makes perfect sense applied to genuinely stochastic theories -- i.e., that condition isn't somehow uniquely applicable to deterministic theories.

We already have on the table an example of a genuinely stochastic theory that, I think, we've agreed violates Bell Locality. (namely, QM) So maybe it would help to make up an example of a genuinely stochastic theory that is Bell Local. Would that help?? I'm actually a bit confused now about what you're even claiming, so maybe this won't help at all. In fact, I'm pretty sure it won't since it's so damn trivial. But, for what it's worth, here's an example of a genuinely stochastic theory that is consistent with Bell Locality:

Alice and Bob shake hands, walk to opposite sides of the room, and then each flips a fair coin (or some other event we're willing to pretend is irreducibly random). The joint probability for Alice and Bob both getting heads factors: 50% for Bob times 50% for Alice = 25% for two heads. Bell Locality is respected.

Stupid, huh? Admittedly so, but it's an example of applying Bell Locality to a stochastic situation. Maybe you'll think what's special about this example is that there are actually no correlations at all between the two sides. If so, modify the scenario in another admittedly stupid way: say Alice and Bob each have two coins in their pockets, a two-headed coin and a regular heads/tails coin. After separating, Alice and Bob each independently decide, with irreducibly random probability, whether to flip their H/H coin or their H/T coin. Say there is a 99% chance each time that they'll choose the H/H coin, and only a 1% chance that they'll decide to flip the regular H/T coin. So... a large fraction of the time, Alice and Bob both end up with a "heads" outcome.

I think it is obvious that Bell Locality is still 100% respected. Yet the correlation coefficient

P(H,H) + P(T,T) - P(H,T) - P(T,H)

is not zero.

So it isn't merely the lack of correlations between separated events that permits one to apply Bell Locality to stochastic situations.

I dunno, somehow I doubt any of this will help move the conversation forward. Maybe you could remind me/us what exactly you object to in applying Bell Locality to stochastic theories (in particular, what precisely you object to in my claim that QM, so long as you believe that the wf is a complete description of the system, violates Bell Locality)...

 

[ttn]

Bell said that EPR's argument - which also tried to define what an element of reality was - did not actually work as they had pictured it.

That is *definitely* not true! Bell was emphatic that the EPR argument *had indeed* established that, if complete, QM itself was nonlocal. This was the first part of his two-part argument that nature violates Bell-Locality. (The second part is, of course Bell's Theorem: you can't get rid of the apparent nonlocality of QM by rejecting the completeness doctrine, i.e., by building a hidden variable theory.)

Perhaps you are confusing the proposition that EPR actually argued for (QM is either incomplete or nonlocal) with the conclusion they (naturally, at the time) drew from this: since locality is true, QM must be incomplete. That is, EPR showed that, for QM, locality --> incompleteness. Then as a separate premise, they postulated: locality. Combining these obviously gives the conclusion: incompleteness.

Bell's later work undermines the "separate premise: locality" but in no way undermines the important dilemma that EPR argued for, namely, "locality --> incompleteness." Indeed, as I said, Bell continued to cite EPR as having provided the first half of the argument which proves that locality fails, period (whether or not one subscribes to completeness).

The problem being that their assumption - elements of reality exist independent of the measurement - was flawed.

This was hardly an *assumption* of EPR! They proved (under the assumption of locality) that these pre-measurement elements of reality must exist.

 

[DrChinese]

That is *definitely* not true! Bell was emphatic that the EPR argument *had indeed* established that, if complete, QM itself was nonlocal. This was the first part of his two-part argument that nature violates Bell-Locality. (The second part is, of course Bell's Theorem: you can't get rid of the apparent nonlocality of QM by rejecting the completeness doctrine, i.e., by building a hidden variable theory.)

Perhaps you are confusing the proposition that EPR actually argued for (QM is either incomplete or nonlocal) with the conclusion they (naturally, at the time) drew from this: since locality is true, QM must be incomplete. That is, EPR showed that, for QM, locality --> incompleteness. Then as a separate premise, they postulated: locality. Combining these obviously gives the conclusion: incompleteness.

...

This was hardly an *assumption* of EPR! They proved (under the assumption of locality) that these pre-measurement elements of reality must exist.

No, not so! Bell may have said various things, same Einstein, but their work speaks for itself. Bell's Theorem does not rest upon locality, and neither does EPR, and in both of these papers locality is barely mentioned. Replace the word "locality" with "causality" (which is I think is close to your Bell locality) and we are in the same ballpark.

EPR claimed that if the result of a measurement could be predicted in advance, then the observable must correspond to an element of reality and that that observable was in fact predetermined. Bell explored this idea too.

While you are talking about the locality of the observable, I am talking about the reality of the observable. EPR said: "Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted."

Bell showed that we should insist on the more restrictive definition of reality; i.e. that quantum attributes are not objectively real if we can't measure or predict them. Bell represented the reality condition within his theorem explicitly - see his (2) with $$\lambda$$. Under this criteria, then, EPR does not prove that QM is incomplete by admission of EPR because they assumed that these elements of reality existed.

EPR never claimed that they proved that QM was non-local if complete, although I can see why that would be a logical deduction IF you didn't know about Bell. After all, they considered predetermined "elements of reality" to be a given. Now that we know this is questionable, evertyhing looks different.

 

[ttn]

No, not so! Bell may have said various things, same Einstein, but their work speaks for itself. Bell's Theorem does not rest upon locality, and neither does EPR, and in both of these papers locality is barely mentioned.

Bell's Theorem does not rest upon locality? Are you kidding? Read any of Bell's papers -- I think you'll find (a) that the theorem assumes that the theories the theorem is about satisfy the Bell Locality condition and (b) Bell spends a lot of time and energy arguing for this condition. See especially the article "La Nouvelle Cuisine", re-printed as the final chapter in the new 2nd edition of Speakable and Unspeakable.

Re: Einstein, you are right in one sense: the actual EPR paper barely mentions the locality issue. But Podolsky wrote that paper, and Einstein wrote in a letter (later in '35) to Schroedinger that he thought the point he considered crucial (namely, the completeness-locality dilemma) had been "smothered by the formalism" in Podolsky's paper!

Here are Einstein's words from the "Reply to Criticisms" essay in the Schilpp volume:

"By this way of looking at the matter it becomes evident that the paradox [EPR] forces us to relinquish one of the following two assertions:
1. the description by means of the \psi-function is complete.
2. the real states of spatially separated objects are independent of each other."

For more detail on this point, see the first few chapter of Arthur Fine's wonderful book, "The Shaky Game." One notable line: "It is important to notice that the conclusion Einstein draws from EPR is not a categorical claim for the incompleteness of quantum theory. It is rather that the theory poses a dilemma between completeness and separation; both cannot be true." The paper "Einstein's Boxes" in the Feb. '05 American Journal of Physics also discusses this issue in some detail.

Bell showed that we should insist on the more restrictive definition of reality; i.e. that quantum attributes are not objectively real if we can't measure or predict them.

This sounds nothing like the Bell I know and love.

Under this criteria, then, EPR does not prove that QM is incomplete by admission of EPR because they assumed that these elements of reality existed.

EPR proved that QM, if complete, is nonlocal.
Bell proved that if QM is *not* complete, the resulting hidden variable theory has to be nonlocal.
Combined, these two arguments prove that nature is nonlocal. *That* is what Bell proved -- at least, it is what I think he proved... which wouldn't count for much except that this matches what Bell himself thought he proved.

EPR never claimed that they proved that QM was non-local if complete, although I can see why that would be a logical deduction IF you didn't know about Bell. After all, they considered predetermined "elements of reality" to be a given. Now that we know this is questionable, evertyhing looks different.

Yes, the actual EPR paper obscured the importance of the locality issue, and generally failed to make clear what Einstein (later) did -- that the real point of EPR was (supposed to be!) that there is a dilemma, for QM, between completeness and locality. You seem to think EPR just *assumed* the existence of the elements of reality they needed to show that QM was incomplete. Wouldn't that make their argument trivially circular/empty? I don't think it was empty at all. They didn't just assume the desired conclusion; they showed that it followed from the locality assumption -- an assumption which was indeed, as you say, a logical one until/unless one knows about Bell. After Bell, you realize that you're stuck with a nonlocal theory regardless of your position re: completeness. See quant-ph/0408105 for further details on this.

 

[DrChinese]

Bell's Theorem does not rest upon locality? Are you kidding? Read any of Bell's papers -- I think you'll find (a) that the theorem assumes that the theories the theorem is about satisfy the Bell Locality condition and (b) Bell spends a lot of time and energy arguing for this condition. See especially the article "La Nouvelle Cuisine", re-printed as the final chapter in the new 2nd edition of Speakable and Unspeakable.

Re: Einstein, you are right in one sense: the actual EPR paper barely mentions the locality issue. But Podolsky wrote that paper, and Einstein wrote in a letter (later in '35) to Schroedinger that he thought the point he considered crucial (namely, the completeness-locality dilemma) had been "smothered by the formalism" in Podolsky's paper!

Here are Einstein's words from the "Reply to Criticisms" essay in the Schilpp volume:

"By this way of looking at the matter it becomes evident that the paradox [EPR] forces us to relinquish one of the following two assertions:
1. the description by means of the \psi-function is complete.
2. the real states of spatially separated objects are independent of each other."

The EPR paper and Bell's 1964 follow up say it all:

I. EPR proves: "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operaters corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

II. Bell proves both cannot be true: (1) QM is incomplete (as represented by the $$\lambda$$ in his formulas; and (2) the predictions of QM are correct. To quote: "The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics was not complete but should be supplemented by additional parameters... In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics."

III. Accepting both EPR and Bell as correct (as I do), as well as Aspect, you must conclude that:

a) Aspect et al proves that the predictions of QM are correct (please Cat stay out of this discussion as we are not interested in debating this).
b) If QM is correct, then Bell (2) is true; therefore Bell (1) is false.
c) If Bell (1) is false, then EPR (1) is also false as they are equivalent by design.
d) If EPR (1) is false, then EPR (2) is true.

IV. Ergo: Aspect + Bell + EPR -> Reality fails ("when the operates corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality"). This is the logical result of the chain, and you can clearly see that locality is not a factor by examining the formalisms.

A close look at the arguments of EPR (as you have seen) and Bell, you will see that whether QM is local or non-local is not a factor in any way. The only requirement Bell mentions is that "the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past." However, this requirement is not actually represented in any way in Bell's formalism (that I can see - perhaps you can find a *formula* which embodies this). The only assumption Bell actually makes is that there is an A, B and C when we can measure only 2 at a time. In other words, his conclusion is correct and his derivation is correct; but his description strays a bit in ways that do not affect his work in any way.

Put another way in my own words: so what if there are hidden variables across the universe when t=0? There still cannot be an A, B and C which are simultaneously real at t=0. Therefore, it is the measurement at t=T which creates the reality. The location of the hidden variables is not a factor, there is no A, B and C regardless.

 

[ttn]

A close look at the arguments of EPR (as you have seen) and Bell, you will see that whether QM is local or non-local is not a factor in any way. The only requirement Bell mentions is that "the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past." However, this requirement is not actually represented in any way in Bell's formalism (that I can see - perhaps you can find a *formula* which embodies this).

Are you kidding?? How about the requirement that the joint probabilities factor, as expressed, e.g., in Bell's equation (14) [of "On the E-P-R paradox"]. The discussion in his later papers is much clearer: check out, e.g., section 4 of "Bertlmann's socks...", or the very extensive and detailed discusison in "La Nouvelle Cuisine."

Here is a nice statement (from "Bertlmann's socks...", one of his later papers, after he had had lots of time to get his thinking straight on exactly what he had proved):

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of QM. So we *cannot* dismiss intervention on one side as a causal influence on the other." (pg 149-50 of Speakable...)

I don't see any possible way of interpreting this, other than the one I have been advocating here. Bell is saying: under the assumption of locality ("if we do not accept the intervention on one side as a causal influence on the other") we are led to conclude that there exist local hidden variables determining the outcomes. [that is the EPR argument!] But as he goes on to point out, this assumption (that there exist local hv's) leads to a contradiction with the experimentally observed results. [that is Bell's theorem.]

In other words, the only way of trying to interpret QM as a local theory (namely, by dropping the completeness assumption and trying for a local hidden variable theory) does not work. You cannot get rid of the nonlocality.


I'd like to keep this as positive as possible, but your anti-realist comments are really inexcusable. There is just no reasonable way of believing that somehow the upshot of EPR/Bell is that it's impossible to believe in realism or elements of reality or whatever. Bohmian mechanics exists. It is an unambiguous counterexample to any such claims.

 

[DrChinese]

I don't see any possible way of interpreting this, other than the one I have been advocating here. Bell is saying: under the assumption of locality ("if we do not accept the intervention on one side as a causal influence on the other") we are led to conclude that there exist local hidden variables determining the outcomes. [that is the EPR argument!] [1]But as he goes on to point out, this assumption (that there exist local hv's) leads to a contradiction with the experimentally observed results. [that is Bell's theorem.]

In other words, the only way of trying to interpret QM as a local theory (namely, by dropping the completeness assumption and trying for a local hidden variable theory) does not work. You cannot get rid of the nonlocality.

I'd like to keep this as positive as possible, but your anti-realist comments are really inexcusable. There is just no reasonable way of believing that somehow the upshot of EPR/Bell is that it's impossible to believe in realism or elements of reality or whatever. Bohmian mechanics exists. It is an unambiguous counterexample to any such claims.

Anti-realist comments are "inexcusable"? Say that to Einstein and Bell, not me. I am quoting him (EPR): "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality". That is what the paper is all about, and Einstein clearly took it - as obviously you do - that (2) is false. (That, by the way, is not the same as your EPR argument above.) I realize your opinion is different than mine, but these are the actual relevant words from the actual paper, and not an out of context comment made later. The fact is, Einstein didn't miss a trick as his actual words allowed for him to be wrong about (1) and right about (2) and therefore right - again - in the end when it mattered. He publicly supported the (1) position and yet - here is it again - (2) is the anti-realist position you disdain.

Bell (14): $$P(a,b)=-\int d\lambda p(\lambda) A(a,\lambda) A(b,\lambda)$$

Perhaps you can explain how this has anything to do with the location of the hidden variables. On the other hand, Bell's realist assumption follows on the very next line... "It follows that c is another unit vector" and thereafter there is a, b and c. This is the explicit labeling of attributes that do not commute; and that we now know does not have simultaneous reality. In his paper, Bell states: "the quantum mechanical expectation value cannot be represented, either accurately or arbitrarily closely, in the form (2)" which is

$$P(a,b)=\int d\lambda p(\lambda) A(a,\lambda) B(b,\lambda)$$

That means to me that there are NO hidden variables ANYWHERE. So how could *you* argue otherwise? I am sure that in most ways our position is more alike than different.

I agree with your deduction [reference 1 above] that an observation on one side is causally connected to the results on the other. And the reason I believe that has nothing to do with whether QM is local or non-local! I believe that because I believe in the QM formalism and that is what it says is the most complete specification of the system possible. Therefore, I agree with the conclusion (2) of EPR, and I specifically deny (1). That conclusion is 100% in keeping with EPR, Bell and Aspect and I would challenge you to deny that is a logical deduction from the facts (see again III my preceding post for a recap).

So if you want to say that "proves" QM is non-local, then I say fine. If someone else says that conclusion is not part of the formalism of QM, then I say fine to that too. But if you try to tell me that there is simultaneous reality to non-commuting quantum attributes, I say... prove it by experiment. (You can't.)

 

[vanesch]

Yes, that's exactly right. But (and this is becoming something of an anthem on my part..) it's just the same for QM. If you could actually discover somehow what the wave function for some entity next to you was, you would be able to use this information to send messages. Send your friend one of the boxes with "half a particle" in it. The value of the wf over by your friend is 1/sqrt(2). [or something like that... technically I'm talking about the mod of the wf integrated over the volume of the box, but who cares about that detail.] But as soon as you open your box and either find or don't find the particle there, the value of the wf over by your friend will immediately change to either zero or one (respectively).

Ah we're home
You think of "collapse of the wavefunction". Well, let me tell you something: EVERYBODY AGREES that collapse of the wavefunction in this way would be bluntly non-local. So I fully agree with you that such a thing is just as ugly non-local as Bohm ! And it is one of the reasons many people don't like it. ( (There is also another reason that I find even more severe: that is that we don't know what physical process could ever lead to such a collapse)
But in an MWI-like view of QM THERE IS NO SUCH COLLAPSE AT A DISTANCE.
So if Bob "could locally look at your part of the wavefunction" nothing special would happen when Alice "looks at her part of the wavefunction"
And if they see the wavefunction, they wouldn't see any result of a measurement. It is only because of a property of observers that apparently they have to choose a result that they 1) obtain a result and 2) experience some randomness in that result. But the wavefunction itself nicely continues to evolve in all its splendor, whether you have looked or not (well, except for your OWN part of the wavefunction, which gets smoothly entangled, locally, with what you are measuring and of which you have to pick one branch).

That's what I've been trying to tell you.
In the "internal information sense":

Bohm is non-local
Copenhagen QM is non-local
MWI QM is local

In the "external information sense"
Bohm is local
Copenhagen and MWI QM are local

In the "Bell local sense"
Bohm is nonlocal
Copenhagen and MWI QM are non local

cheers,
Patrick.

 

[vanesch]

I dunno, somehow I doubt any of this will help move the conversation forward. Maybe you could remind me/us what exactly you object to in applying Bell Locality to stochastic theories

I do not object to applying Bell locality to stochastic theories, I tell you that it is a criterium *designed* on the basis of deterministic theories, and that stochastic theories that by coincidence obey it, can (that's exactly the MEANING of Bell Locality) simply be turned into deterministic local hidden variable theories, so that ALL the randomness comes about from the lack of knowledge of local variables, which, if we would know them, determine all outcomes with certainty.

Bell Locality is a criterion that says: from *this* theory, it is possible to make a local, deterministic hidden variable theory.

That's why I consider it as a too severe criterion to judge locality on.


cheers,
Patrick.

 

[DrChinese]

Ah we're home
You think of "collapse of the wavefunction". Well, let me tell you something: EVERYBODY AGREES that collapse of the wavefunction in this way would be bluntly non-local. So I fully agree with you that such a thing is just as ugly non-local as Bohm !

cheers,
Patrick.

Well said! (And the same "non-local" collapse happens in single particle experiments too, not just in EPR setups. In EPR setups, we see it more clearly.)

 

[vanesch]

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of QM. So we *cannot* dismiss intervention on one side as a causal influence on the other." (pg 149-50 of Speakable...)

Well, again, we've switched vocabulary, but Bell is wrong on this issue. "causal influence" in my book, corresponds to information transfer. It is because he cannot get rid of the old paradigm of deterministic theories in which of course ALL correlations between A and B are related to 1) direct causal influence or 2) indirect "common cause" causal influence.

The reason for this, in a deterministic paradigm, is that we only know of one mechanism to have randomness, namely the lack of information we have of internal degrees of freedom. And then it is clear that upon the observation of correlations between the observed randomness of A and B, you have somehow to "transport these internal degrees of freedom", or, directly from A to B (1), or you had to transport them from a common origin C to A and to B (2). And Bell cannot get out of that view. (1) is non-local, and (2) is Bell Locality. He cannot conceive the possibility that these correlations "just are", and are not related to a lack of knowledge. After all, it has been the paradigm that has been with us for all of classical physics. Einstein was apparently a bit smarter: he believed in this paradigm too, but understood that it could be different (but he didn't want to accept it "God doesn't play dice").

But if you now switch to another paradigm, which is the one of fundamentally stochastic theories, "god does play dice" and the fundamental quantity this time is the probability distribution (the n-point correlation function ; usually in our examples 2-point correlations are sufficient) then you do not need to assume that all randomness is related to lack of knowledge of internal degrees of freedom. And thus you do not need anymore to conclude that correlations can only come about through 1) or through 2). It is by forcing such a fundamentally stochastic theory in the deterministic paradigm that you end up drawing conclusions about locality or about the age of your mother in law.

The deterministic paradigm (randomness only comes about by incomplete knowledge of internal degrees of freedom) comes under many terms:
"complete state" (the internal degrees of freedom), "realism", Bell Locality, ...

cheers,
Patrick.

 

[Cat]

That is a logical flaw. You want it both ways. You refuse to accept it as conclusive evidence when folks stop looking; and you see it as supporting your position when they are looking!

Of course it's not "conclusive evidence" if they stop looking! It just means that they've given up the search for common-sensical explanations for the time being.

From your logic, it makes no sense to repeat an experiment, either! (Presumably that would mean that the experimented does not accept the initial results.) There are a lot of reasons to do experiments, even ones in which the essential results are not in question.

You're right in a way, in that I'm so convinced the world is both real and local that I'll eat my hat if Grangier's team's experiment manages to infringe the CHSH test!

The proposal in question is:

R. García-Patrón Sánchez, J. Fiurácek , N. J. Cerf , J. Wenger , R. Tualle-Brouri , and Ph. Grangier, “Proposal for a Loophole-Free Bell Test Using Homodyne Detection”, Phys. Rev. Lett. 93, 130409 (2004)
http://arxiv.org/abs/quant-ph/0403191

Though the result as it stands is a forgone conclusion, the experiment could, I think, be modified so as to settle the matter of how the detection loophole works once and for all. As it stands, they propose to treat as the + results all voltage differences greater than zero, and - all negative ones. Since there will always (except on a set of measure zero) be some voltage difference they will have no non-detections. [Even if I've misinterpreted their intentions slightly here, they've got the "event-ready" detectors to ensure that they define their sample before analysing the results, so it will be, by definition, "fair".]

But they could instead look at the raw voltages and digitise these, using (as in Aspect's experiments) some minimum threshold voltage to decide what to count. They could then explore what happens as the threshold is altered. When it is zero, we have effectively "perfect" detectors; when very high we have very low efficiency ones and lots of non-detections. What then happens to the CHSH test statistic? Under local realism, this is predicted to increase and eventually infringe the inequality, as per Pearle's 1970 argument.

Cat

 

[ttn]

I am quoting him (EPR): "...[...]"

As I noted here earlier, Einstein did not write the EPR paper. Podolsky did. And Einstein was rather disappointed with how the paper turned out. This is a well-documented historical fact. So you can't quote the EPR paper and assert that this is revealing the views of Einstein. I quoted a passage that was actually written by Einstein in which he states with complete clarity that he thought the point of EPR -- the point that was unfortunately "smothered" in Podolsky's text -- is that there is a *dilemma* between locality and completeness. Both cannot be true for QM. This is hardly an "out of context comment made later." This was rather Einstein's attempt to set the historical record straight given that the author had, in Einstein's own written opinion, flubbed the argument in the EPR paper.

Re: Bell, I suppose we will have to agree to disagree. I simply don't understand how you can claim that what he proved has nothing to do with (i.e., is not openly premised on) locality. The whole point of the theorem is that a theory in which the outcomes of measurements are pre-determined by some kind of "instruction set" in the particles -- AND THAT RESPECTS THE BELL LOCALITY CONDITION -- cannot agree with experiment. i.e., local hidden variable theories are ruled out.

BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

That means to me that there are NO hidden variables ANYWHERE.

Bell was for about 20 years pretty much the only living human being who actively pursued, lectured on, wrote about, and studied Bohmian mechanics. To claim that he believed he had proved that hidden variables theories as such are impossible, is thus rather odd.

I agree with your deduction [reference 1 above] that an observation on one side is causally connected to the results on the other. And the reason I believe that has nothing to do with whether QM is local or non-local!

Then you must be confused about what Bell proved. Bell's theorem shows that, if you try to "complete" QM by adding local hidden variables, the theory you get cannot both respect the Bell Locality condition and agree with experiment. So, as lots of people say, if you want a local theory, you'd better stick with QM and its completeness doctrine, and not go down the hidden variables road. But that strategy obviously presupposes that QM itself is local -- otherwise, saying "you should stick with QM and not pursue hidden variable theories, on pain of nonlocality" just makes no sense.

And the final piece: Bell states openly that, he thinks, nonlocality is a fact, period -- that it's *not* something which merely afflicts hv theories. As he says, you *cannot* dismiss the operations on one side as causal influences on the other. How can he believe this? What else would he need to have to believe to make this claim given the above paragraph? Obviously he would have to think that orthodox QM was *also* nonlocal. IF it wasn't, there'd be no grounds for claiming that all possible alternatives -- i.e., nature -- were nonlocal.

I believe that because I believe in the QM formalism and that is what it says is the most complete specification of the system possible.

Perhaps you could explain why you believe the completeness doctrine. Bell's theorem is no argument in its favor, since QM itself is just as nonlocal as the hidden variable theories you'd want to dismiss on Bellian grounds. And if anything has come out very clearly in this thread, it's that Bohmian mechanics (a real honest to god hidden variable theory that reproduces all the predictions of QM) and regular QM are exactly parallel when it comes to their various senses of locality and nonlocality. So how could there possibly be a conclusive argument in favor of the completeness doctrine? I have never heard one, but I would certainly like to if it exists.

 

[vanesch]

BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

It is indeed trivial to associate to every stochastic theory a deterministic nonlocal hidden variable theory, which gives you exactly the same outcome.
A stochastic theory is fully determined when the n-point correlation functions are given as a function of all the parameters of free choice that are given to the user(s), such as the choice of the polarizer, activating or not a laser etc...
It is of course possible to set up a hidden variable theory with as random variable an n-tuple of numbers which has the same n-point correlation function as a function of the parameters, call these random variables "hidden variables" which determine the outcomes in a strict 1-1 way and I'm done.

So there's no point in saying that such a theory is possible. It is always possible.

What is more interesting is to do what Bell did: to prove that a certain stochastic theory (in casu QM) predicts probabilities that cannot be generated by deterministic local hidden variable theories, where local means local in the internal information sense, which, together with the deterministic part, leads to the Bell locality condition ; which leads to the Bell inequalities.

So the choice is between respect of the internal information locality or determinism.

Given the fact that a theory like QM is on the outside information-local, I prefer to sacrifice determinism, because I would consider sacrificing internal information-locality as a kind of conspiracy (why does the internal machinery not respect it, but does the outside user not notice it ?).

cheers,
Patrick.

EDIT: just to repeat: what I mean by "information-local" is that the probability distribution of all quantities pertaining to something local at A cannot depend on all FREE CHOICE parameters which are fixed elsewhere at B. If it were, I have an information channel that allows me, by doing experiments at A, to know what was the message, sent by B (by making use of his free choice of parameters).
What I mean by "external information-local" is what I said above, with real, executable measurements. What I mean by "internal information-local" applies moreover to a super-creature that has access to all local hidden variables at A even if some strange principle forbids me to turn them into real experiments.
But the free choice of settings at B remains fundamental.

I repeat again that it is *this* locality which is required by relativity in order to avoid the paradox of receiving as a message, what will be my free choice later (so that I can make another choice and lead to a paradox). This is the reason why I stick to it. If it weren't for this property, I wouldn't give a damn about locality.