This may seem like an obscure technical point, but it helps explain differing views about Bell's Theorem:

Cornell solid-state physicist David Mermin has described the appraisals of the importance of Bell's theorem in the physics community as ranging from "indifference" to "wild extravagance".There has been a consensus since about 1930 that hidden variable theory is contrary to the core of quantum mechanics. So another experiment confirming Bell's Theorem is just another affirmation of the legitimacy of those Nobel prizes in 1932 and 1933.

That explains the indifference. So the Bell spooks need a better argument to justify their wild extravagance.

Here is one such attempt, from Wikipedia:

Whereas Bell's paper deals only with deterministic hidden variable theories, Bell's theorem was later generalized to stochastic theories[18] as well, and it was also realised[19] that the theorem is not so much about hidden variables, as about the outcomes of measurements that could have been taken instead of the one actually taken. Existence of these variables is called the assumption of realism, or the assumption of counterfactual definiteness.This is just a sneaky way of defining hidden variables. Quantum mechanics teaches that you cannot precisely measure position and momentum at the same time. If you assume that particles somehow have precise values for those in the absence of a measurement, then you are in the land of anti-QM hidden variables. If there were any merit to this, then much of XX century physics would be wrong.

John Bell himself later tried to fudge his theorem by pretending to be able to deduce hidden variables from other hypotheses:

Already at the time Bell wrote this, there was a tendency for critics to miss the crucial role of the EPR argument here. The conclusion is not just that some special class of local theories (namely, those which explain the measurement outcomes in terms of pre-existing values) are incompatible with the predictions of quantum theory (which is what follows from Bell's inequality theoremThe commentators are correct. The argument does begin with hidden variables.alone), but thatlocal theories as such(whether deterministic or not, whether positing hidden variables or not, etc.) are incompatible with the predictions of quantum theory. This confusion has persisted in more recent decades, so perhaps it is worth emphasizing the point by (again) quoting from Bell's pointed footnote from the same 1980 paper quoted just above: "My own first paper on this subject ... starts with a summary of the EPR argumentfrom locality todeterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables."

In my view, the core of the problem here that some physicists and philosophers refuse to buy into the positivist philosophy that comes with quantum mechanics. Quantum mechanics is all about making predictions for observables, but some people, from Einstein to today, insist on trying to give values for hypothetical things that can never be observed.

The comment asks:

Could you tell me what you mean by "deterministic and separable", and in particular could you tell me how your concept of "deterministic and separable" can account for the perfect anti-correlation without hidden variables?

By separable, I mean that if two objects are separated by a space-like 4-vector, then one can have no influence over the other. This is local causality, and says that physical causes act within light cones. It has been one of the main 3 or 4 principles of physics since about 1860. It is the core of relativity theory.

Determinism is a dubious concept. It has no scientific meaning, as there is no experiment to confirm or deny it. It has never been taught in textbooks, and few physicists have believed in it, with Einstein being a notable exception.

If determinism were true, then you could prepare two identical Potassium-40 atoms, wait about a billion years, and watch them both decay at the same time. But it is hopelessly impossible to prepare identical atoms, so this experiment cannot be done.

Some interpretations of quantum mechanics claim to be deterministic and some claim the opposite, and they all claim to be consistent with all the experiments. So this notion of determinism does not seem to tell us anything about quantum mechanics.

As I wrote last year:

If determinism means completely defined by observables or hidden variables obeying local differential equations, then quantum mechanics and chaos theory show it to be impossible.So I am not pushing determinism. It is an ill-defined and unscientific concept.

If some EPR-like process emits two equal and opposite electrons, then maybe those electrons are physically determined by the emission process. Or maybe they are intrinsically stochastic and have aspects that are not determined until a measurement. Or maybe it is all determined by events pre-dating the emission. I do not think that these distinctions make any mathematical or scientific sense. You can believe in any of these as you please, and positivists like myself will be indifferent.

When the experimenters get together later to compare their results, they make an astounding discovery: Every time the two experimenters happened to measure a pair of entangled electrons along the same direction, they ALWAYS got opposite results (one UP and one DOWN), and whenever they measured in different directions they got the same result (both UP or both DOWN) 3/4 of the time.What makes this astounding is if you try to model the electron spin by assuming that there is some underlying classical spin to explain all this. That means that there is always a quantitative value for that spin, or some related hidden variable, that defines the reality of the electron. Some people call this "realism", but it is more than that. It is identifying the electron with the outcomes of potential measurements that are never made.

Everything we know about electrons says that this is impossible. You can measure position, and mess up the momentum. You can measure the X-spin, and mess up the Y-spin. And we can only make these measurements by forcing the electron into special traps, thereby making obvious changes to the electron.

Thus, contrary to widespread beliefs, Bell's Theorem and its experimental tests say nothing about locality or determinism or randomness. They only rule out some hidden variable theories that everyone (but Einstein) thought were ruled out in 1930.

I am not saying anything radical or unusual here. This is just textbook quantum mechanics. Those textbooks do not say that Bell proves nonlocality or indeterminism. I don't think so, anyway. That is why so many physicists are indifferent to the subject, and no Nobel prize has been given for this work. It is just 1930s physics with some wrong philosophical conclusions.

Lubos Motl just posted a rant against a BBC documentary:

I have just watched the first of the two episodes of the 2014 BBC Four documentary The Secrets of Quantum Physics. ...I haven't watched it, but it sounds like a lot of other popular accounts of quantum mechanics. They get the early history pretty well, and then they tell how Einstein and Bell did not believe it, and tried to prove QM wrong. Then the experiments proved QM right and Einstein and Bell wrong. But then then end up with some crazy conclusions that do not make any sense.

Needless to say, after having said that Einstein's view has been conclusively disproven, Al-Khalili says that he believes in Einstein's view, anyway. Hilarious. Sorry, Mr Al-Khalili, but you just violate the basic rules of logic in the most obvious way. You should really reduce the consumption of drugs.

Before I watched the full episode, and even in 1/2 of it or so, I wanted to believe that it would be a documentary on quantum mechanics that avoids the complete idiocy and pseudoscience. Sadly, my optimism was misplaced. This is another excellent representative of the anti-quantum flapdoodle that is being spread by almost all conceivable outlets of the mass culture.

Update: There is some discussion in the comments below about whether Bell assumes hidden variables, and when he leaves Bohr's positivistic view of quantum mechanics as a possibility. You can see for yourself in Bell's 1981 socks paper, which is here, here, and here. He uses the letter lambda for the hidden variables.

Roger writes: "Then the experiments proved QM right and Einstein and Bell wrong"

ReplyDeleteThe word "proved" is predicated on a conviction that Bell's Theorem is an accurate model of physical space, which it isn't. It's a easy-to-prove mathematical model which is misapplied to real 3-space. Remember the map is not the territory.

Your response begins with quotes from Bell (and others) confirming exactly what I’ve been telling you, i.e., that the derivation of Bell’s theorem is not based on the assumption of hidden variables, it's based only on the assumption of locality (separability), and then proves that this is incompatible with quantum mechanics unless you posit what amounts to hidden variables, and it then goes on to prove that hidden variables are also incompatible with quantum mechanics, thereby completing the proof that separability (locality) is completely incompatible with quantum mechanics. This is exactly what I’ve been telling you.

ReplyDeleteTo get to the bottom of this, I asked you to explain “how your concept of deterministic and separable electrons can account for the perfect anti-correlation without hidden variables?” You now discard determinism (one of your two unshakable pillars!), and recite the standard definition of separability/locality. Then you offer three possible answers to the question:

1) First you say “Maybe those electrons are physically determined by the emission process.” Yes, that’s the “hidden variable” explanation, which can indeed account for the perfect anti-correlation at equal angles, but it is provably incompatible with the correlations at unequal angles, so it is ruled out.

2) Then you say “Maybe they are intrinsically stochastic and have aspects that are not determined until a measurement.” That hypothesis doesn’t yield perfect anti-correlation for the separate spin measurements at equal angles, assuming locality/separability. It’s fine to say the spin is “not determined until it is measured”, but it actually IS determined as soon as the OTHER electron’s spin in measured (at the same angle), and if we insist on separability/locality, that other measurement can’t cause this electron to suddenly have a determined spin, unless you go back to your first answer, i.e., the pair was pre-programmed to give opposite spins, so you’re back to hidden variables, which can’t account for the correlation at unequal angles.

3) Then you offer a third answer: “Maybe it is all determined by events pre-dating the emission.” Again, you are saying the electrons are “determined”, so you are back to hidden variables. Yes, this can account for the perfect anti-correlation at equal angles, but not for the correlations at unequal angles.

Finally you conclude: “I do not think that these distinctions make any mathematical or scientific sense. You can believe in any of these as you please, and positivists like myself will be indifferent.” No, you CAN’T believe in any of these as you please. They all fail to account for the facts. The only way you have offered to account for the perfect anti-correlation at equal angles is by the electrons being “physically determined”, either by the emission process or something pre-dating the emission. That is the hidden variable explanation, which is ruled out by the correlations at unequal angles. So, you have not provided any viable explanation for your claim that the electrons are deterministic and separable – or even just separable.

Seriously, I urge you to actually try to think of a way (observing strict locality as you’ve defined it) to account for both the perfect anti-correlation at equal angles AND the 3/4 correlations at unequal angles. Your comments give the very strong impression that you don’t yet understand the problem.

To be clear:

ReplyDeleteThe correlations are explained by quantum mechanics, not hidden variables.

Bell and Einstein were trying to disprove quantum mechanics. They turned out to be wrong.

I looked again at Bell's 1980 paper. He includes a rant against the positivism of Bohr and others. He denies that his argument depends on determinism or hidden variables, but it plainly does. He defines "explicable" as being given by probabilities of hidden variables, and then his big conclusion is that the predictions of quantum mechanics are "locally inexplicable". That is, contrary to local hidden variable theory.

He concludes that there are 4 possibilities: (1) QM predictions are wrong, but he concedes that Aspect's experiment seem to show QM is right; (2) superdeterminism; (3) causal influences go faster than light; and (4) Bohr was right.

I say Bohr was right. Unperformed quantum experiments do not have numerical results.

You say “the correlations are explained by quantum mechanics”, but that doesn’t address the question, which is whether entangled electrons in quantum mechanics are separable. Bohr did not say that they are. According to Bohr, “The peculiar individuality of the quantum effects presents us, as regards the comprehension of well-defined evidence, with a novel situation unforeseen in classical physics and irreconcilable with conventional ideas...”, and he emphasized that in the application of the quantum mechanical formalism it is necessary to consider the WHOLE experimental arrangement, not just the separate parts. So an appeal to the authority of Bohr does not provide any support for the claim that entangled electrons are separable. Quite the contrary.

ReplyDeleteJust to reiterate, under the assumption of separability, you were unable to conceive of any way of explaining the perfect anti-correlation of spins at equal angles other than by hidden variables, which you agree is ruled out by the correlations at unequal angles. Thus, by your own reasoning, entangled electrons are not separable.

I was citing Bohr because Bell's 1980 paper cites him for alternative (4).

ReplyDeleteIf I wanted an authority on locality, I would cite Maxwell from about 1860. And the lack of any Nobel prizes going for a disproof of locality.

I think that the problem here is that you are not happy with arguments tied to observables. You are like someone who is unhappy with the special relativity twin paradox, and demands a more intuitive explanation in terms of a universal clock.

I am unable to conceive of a mathematical explanation for the electron, beyond what is in QM textbooks. I cannot do it with or without hidden variables. I do not know that it makes sense to ask for such an explanation, since it would probably involve untestable aspects. It appears to me that anything other than a hidden variable theory would be emotionally unsatisfying.

What is the point of the explanation you seek? Do you want to disprove QM? Do you think that it will be experimentally testable, in a way that QM is not? Will it enable faster-than-light communication, or quantum crypto, or quantum computers, or some other application? If not, what is the point?

The point is this: Your claim that "electrons are deterministic and separable" is inconsistent with quantum mechanics. Quantum mechanics, as you understand it (unknown to Maxwell, and for which multiple Nobel prizes were awarded, both for theory and for experiment), entails observable correlations between space-like separated events (including supposedly free choices of experimenters) that are inconsistent with any deterministic and separable account. You've effectively conceded this, first by explicitly disavowing any positivistic meaning to the concept of determinism, and then by effectively disavowing any positivistic meaning to the concept of separability in relation to the non-classical correlations. Thus, when pressed for a deterministic and separable account of the phenomena of quantum mechanics, you admit that no such account is possible (or at least that you are unable to conceive of any such account, and you will not dispute the proof that no such account is possible). In view of this, I say it is intellectually inconsistent for you to claim that electrons are deterministic and separable. You should say, instead, that the results of space-like separated measurements of entangled electrons exhibit correlations that defy any deterministic and separable account, but that these correlations do not imply that any information or energy propagates faster than light.

ReplyDeleteWhat I said was "The actual electrons may be deterministic and separable." I said "may" because there is no convincing proof that it is impossible. There is only a convincing proof if you add the hypothesis of local hidden variables, and I am convinced that those are impossible.

ReplyDeleteI disavow any positivistic meaning to the concept of determinism, but separability and locality are fine. They mean that causality is confined to the light cone.

I can't say for sure that the concept of determinism is useless. It might help to understand the perfect correlations of aligned spin measurements of EPR particles. But I do not accept that determinism is synonymous with hidden variables, and it is confusing to use the word that way.

Instead of what you say I should say, I would rather say: Based on everything we know from XX century physics, (1) causality is confined to the light cone and no information or energy propagates faster than light; and (2) the results of space-like separated measurements of entangled electrons exhibit correlations that defy any local hidden variable account. I do not see how any stronger statement can be made.

Here is the last paragraph in that 1980 Bell paper:

"Fourthly and finally, it may be that Bohr’s intuition was right — in that there is no reality below some ‘classical’ ‘macroscopic’ level. Then fundamental physical theory would remain fundamentally vague, until concepts like ‘macroscopic’ could be made sharper than they are today."

I take "no reality" and "fundamentally vague" to mean that we do not have a successful quantitative theory of non-observables at the atomic level. Just quantum mechanics of observables.

Taking your paragraphs one at a time:

ReplyDelete1) Again, hidden variables is not an assumption in the derivation of Bell’s inequality, it appears in that derivation as a consequence of the assumption of separability, combined with the perfect anti-correlation of the separate spins when measured at equal angles. When you disputed this (oddly, by quoting authorities who agreed with me, and then asserting that you think they are wrong too), I asked you to explain how you could account for the perfect anti-correlation while respecting separability, without invoking hidden variables. You gave three possibilities, all of which entailed hidden variables! When I pointed this out, you conceded that, in fact, you cannot think of any viable argument against the reasoning in Bell’s derivation. Now you’ve apparently purged all of this from your memory, and returned to square one.

2) Okay, you’re dispensing with determinism (let’s hope this sticks), so we’re down to just talking about separability. You say separability means “causality is confined to the light cone”, but surely the concept of “causality” has no more positivistic meaning than the concept of “determinism”. In fact, causality has always been the poster child for concepts that have no positivistic content. A more meaningful concept is the proposition that no energy or information propagates faster than light. Everyone agrees with this, although not everyone agrees that this captures the entire content of what should be called “locality”. The word “non-separable” is often taken to encompass things like the non-classical correlations implicit in quantum mechanics (for which the joint probabilities do not factor into separate probabilities). With these definitions we would say the electrons are local but not separable.

3) The argument is not whether determinism is synonymous with hidden variables. The point of the derivation is that separability combined with the perfect anti-correlation of spins implies hidden variables.

4) For your first item, you should omit the claim about causality, since (as discussed above) that has no positivistic meaning, and the claim about energy and information is the entire positivistic content. For your second statement, see 1) above. The first half of the derivation of Bell’s theorem proves that the assumption of separability is incompatible with the perfect anti-correlation at equal angles, UNLESS we posit hidden variables, and then the second part of the derivation shows that hidden variables can’t account for the correlations at UNequal angles. Hence separability is incompatible with quantum mechanics.

5) You take “no reality” to mean we don’t have a quantitative theory of non-observables at the atomic level. That’s not right, because the non-classical correlations implicit in quantum mechanics are quite observable (and are not just at the atomic level). Your position rests on the denial of these observable facts. In contrast, Bohr (who, you claim, had a correct understanding) did not deny these facts, nor did he deny that they require a thorough revision of the classical concept of causality. He wrote in response to the EPR paper “The apparent contradiction [described by EPR] in fact discloses only an essential inadequacy of the customary viewpoint of natural philosophy for a rational account of physical phenomena... Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails the necessity of the final renunciation of the classical ideal of causality and a radical revision of our attitude towards the problem of physical reality.” Thus Bohr finds it necessary to renounce the classical ideal of causality in order to account for the phenomena of quantum mechanics, in particular, the non-classical correlations for spacelike-separated measurements. The specific aspect of the classical ideal of causality that he sacrifices is separability.

I say that local hidden variables are necessary to the derivation of Bell's inequality. Every source I have includes this assumption. Yes, Bell denies it, but I looked at his paper, and he plainly makes the assumption.

ReplyDeleteI am certainly not dispensing with causality. Causality is fundamental and essential to quantum field theory, relativity, electromagnetism, and everything else. Bohr only renounces the "classical ideal of causality", whatever that means. Maybe it means local hidden variables or some other classical explanation by deterministic differential equations.

Bohr had a positivist philosophy that said that it does not make much scientific sense to talk about what we cannot measure. All of these Bell paradoxes are rooted in making some assumption about measurements not made. Drop that, and nothing is so mysterious.

We just cannot give a complete mathematical description of the spin of an electron. We can force it into a Stern-Gerlach apparatus, and measure UP or DOWN. But that also changes the electron. It allows giving probabilities on subsequent spin measurements, but again, that is not necessarily the full story.

Seeking the full story seems to be a classical prejudice. Physics is about observables. If you are predicting outcomes, then maybe that is all science can do.

1) You yourself have admited you can’t see any flaw in Bell’s deduction of hidden variables from the assumption of separability and the perfect anti-correlation at equal angles, so it’s hard to see why you continue to claim that his deduction is flawed. Regarding the “socks” paper (which is just one of many that Bell wrote on the subject), it says very clearly: “Let us summarize 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 coinflict with those of quantum mechanics.” This is exactly what I’ve been telling you (note that “hidden variables” is not assumed, it is an intermediate deduction), and you yourself admitted you could see no alternative to this reasoning.

ReplyDelete2) The correlations between entangled particles in quantum mechanics violate causality in the sense that distant correlations arise with no local cause, i.e., no common cause (hidden variables) and no transfer of energy or information between the separate events.

3) You have a very inaccurate understanding of Bohr’s philosophy of complimentarity. I suspect you would find his views repugnant if you really knew what they were. Ironically, you often talk as if you are channeling Einstein in his defense of locality and causality against Bohr’s ill-defined and somewhat mystical notions of complimentarity. Also, your belief that a positivistic approach to science somehow makes entangled electrons separable, when in fact the observed correlations prove that they are not separable, is very misguided. It was recognized long ago that positivism is nothing but half-baked solipsism, which enables those who espouse it to believe whatever they like. As Bell said, “Solipsism cannot be refuted. But if such a theory were taken seriously, it would hardly be possible to take anything else seriously."

4) and 5) In general, you seem to think the non-classical correlations between entangled particles have no significance for the notion of separability, if we simply accept the fact that non-commuting variables don’t commute, or that physical theory should only concern observables. Vague allusions such as that don’t really constitute rational arguments, and they really don't have any bearing on the causal separability of spacelike-separated entangled electrons.

1) You yourself have admited you can’t see any flaw in Bell’s deduction of hidden variables from the assumption of separability and the perfect anti-correlation at equal angles, so it’s hard to see why you continue to claim that his deduction is flawed. Regarding the “socks” paper (which is just one of many that Bell wrote on the subject), it says very clearly: “Let us summarize 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 coinflict with those of quantum mechanics.” This is exactly what I’ve been telling you (note that “hidden variables” is not assumed, it is an intermediate deduction), and you yourself admitted you could see no alternative to this reasoning.

ReplyDelete2) The correlations between entangled particles in quantum mechanics violate causality in the sense that distant correlations arise with no local cause, i.e., no common cause (hidden variables) and no transfer of energy or information between the separate events.

3) You have a very inaccurate understanding of Bohr’s philosophy of complimentarity. I suspect you would find his views repugnant if you really knew what they were. Ironically, you often talk as if you are channeling Einstein in his defense of locality and causality against Bohr’s ill-defined and somewhat mystical notions of complimentarity. Also, your belief that a positivistic approach to science somehow makes entangled electrons separable, when in fact the observed correlations prove that they are not separable, is very misguided. It was recognized long ago that positivism is nothing but half-baked solipsism, which enables those who espouse it to believe whatever they like. As Bell said, “Solipsism cannot be refuted. But if such a theory were taken seriously, it would hardly be possible to take anything else seriously."

4) and 5) In general, you seem to think the non-classical correlations between entangled particles have no significance for the notion of separability, if we simply accept the fact that non-commuting variables don’t commute, and that physical theory should only be concerned with observables. Vague methodological allusions such as that don’t really constitute rational arguments with any bearing on the issues of causal separability for entangled electrons.

You keep misstating what I wrote. All the proofs of Bell's inequality assume hidden variables.

ReplyDeleteYou reveal the core of your prejudices when you say it was "recognized long ago that positivism is nothing but half-baked solipsism". This is nonsense. Positivism is crucial to XX century physics, and I defend it here. To say that positivism is solipsism is to reject much of modern science.

I haven't mis-stated what you wrote. The proofs of Bell's inequality do NOT assume hidden variables, as has been explained in detail. The fact that some authors prefer to split off the first part of Bell's derivation separately, and refer only to the second part as "Bell's theorem" is purely a matter of convention. The point is that Bell's inequalities follow from the assumptions of separability, determinism, and quantum mechanics (and in fact the more sophisticated versions dispense with determinism and apply to stochastic models as well).

ReplyDeletePositivism can be useful by prompting us to give operational meanings to our terms, and to carefully examine the epistemological foundations of our concepts. However, carried to its logical conclusion, positivism becomes solipsism, so a physicist needs to wield positivism with tact if he is to avoid degenerating into irrelevancy.

Most of the physical concepts (space, time, causation, etc.) that you fully accept without question actually have no positivistic justification, since the only evidence you ever have is your own raw sense impressions, which do not give unambiguous warrant to any of those high-level concepts. In fact, one of the forefathers of logical positivism, David Hume, famously took "causation" as a prime example of a concept with no positivistic meaning or justification.

If you were willing to dispense with such high-level concepts as space, time, multiplicity, otherness, separability, and causation, then you could legitimately dismiss claims that quantum mechanics implies non-separability of entangled particles, by simply denying that the concept of separability has any positivistic meaning. But if you wish to retain those high-level concepts (as you do), then positivism does not justify ignoring the observable but apparently acausal joint correlations of measurements of entangled particles.

Barring solipsistic arguments, the non-classical correlations in quantum mechanics are observable facts for free measurements of spacelike-separated entangled particles, and the joint probabilities do not factor into separate individual probabilities, and there is no common cause or causal communication to account for those correlations. This is what people mean when they say that quantum mechanics does not obey separability, even though no energy or information propagates faster then light.

There is plenty of positivistic support for concepts like space and time. In fact the positivist definitions are the best ones we have.

ReplyDeleteI looked again at the Bell 1980 socks paper, and he very explicitly assumes a hidden variable that he calls lambda. Every other derivation also assumes a hidden variable. If you want to cite a paper that does not require an assumption of hidden variables, go ahead and post it.

One paper that doesn't require the assumption of hidden variables is the very paper you are reading. I already pointed quoted for you the passage that explains: "Let us summarize the logic that leads to the impasse [i.e., the logic of Bell's theorem]. 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 quantum mechanics.” Here he is explaining why, if we rule out communication, the perfect anti-correlation at equal angles obliges us to admit that the results are determined in advance, by common cause, i.e., by extra variables. You see, this is not an assumption, it is the only remaining causal option, deduced from the assumption of separability combined with the perfect anti-correlation at equal angles. And you cannot in good conscience disagree with this, because when you yourself were challenged to explain the perfect anti-correlation at equal angles (under the assumption of separability), the only answer you could imagine was hidden variables. As you know, this wasn't an assumption on your part, it was the result of you doing your best to conceive of how the perfect anti-correlation at equal angles could exist without communication and assuming separability. So you yourself are in agreement with Bell, you just don't realize it.

ReplyDeleteOn the next few pages (following the above overview of the argument), Bell describes the details in a general way, and introduces the extra variables (lambda) by noting that, although the joint probability doesn't factor, there is one remaining possibility, namely, we can hope that it might be made factorable (without communication) by introducing sufficiently many causal factors such that the residual fluctuations will be independent (factorable). This is not introduced as an assumption, it is introduced as the only conceivable way that we can render the joint probability factorable. You confirmed this yourself! Of course, it turns out that even if we do this, we arrive at a contradiction (the correlations at unequal angles), so even this last desperate escape route is blocked. Thus the entangled particles are not separable.

You yourself have claimed to espouse Bohr's Copenhagen interpretation, which says (according to your preferred source, Wikipedia):

"Non-separability of the wave function

The domain of the wave function is configuration space, an abstract object quite different from ordinary physical space–time. At a single "point" of configuration space, the wave function collects probabilistic information about several distinct particles, that respectively have physically space-like separation. So the wave function is said to supply a non-separable representation."

Can I assume you realize that Bohr said quantum mechanics is fundamentally irreconcilable with any causal account in the context of space and time?

Speaking of which, there is no positivistic support for concepts like the imagined spatio-temporal structure of the objective world. In fact, there is no positivistic support for the objective world. Positivism is ultimately self-defeating. Every adolescent passes through a phase of enthusiasm for positivism, as it begins by unfolding some surprising insights, but before long a person realizes that, if carried to its logical conclusion, it degenerates into solipsism. Only those who can't see it through to its conclusion can remain deceived by it for long.

Your flaw is in where you say: "by extra variables ... this is not an assumption, it is the only remaining causal option, deduced from the assumption ..."

ReplyDeleteNo, it is not deduced at all. It is assumed to be the only remaining causal option. Maybe it follows if you assume some model of classical mechanics, but then you are just showing that the quantum is not classical.

Bell's argument just states that if there is a common cause, then it must be hidden variables. But maybe there is a physical quantum common cause, and a quantum is not representable by hidden variables.

Again, all you can get out of this argument is that hidden variables do not work.

Saying that positivism is ultimately self-defeating is like saying that science is self-defeating, or democracy is self-defeating, or philosophy is self-defeating. You are just trying to turn it into a straw man.

I have read the philosophers who reject positivism. They are wrong, for reasons that I have explained on this blog. Rejecting positivism means rejecting much of what has made science successful.

Yes, the wave function is a non-separable representation.

Bohr probably said that quantum mechanics is fundamentally irreconcilable with any causal classical account. If so, he was correct. I am not sure that he got everything right. Some philosophers deny that Bohr was a positivist. He seems positivist to me. At any rate, the textbook accounts of QM were heavily influenced by Bohr and by positivism, and not by Einstein-Bohm-Bell. Modern books have refined Bohr's ideas somewhat with decoherence and other concepts, but the essence is what Bohr defended in the 1930s.

The derivation of Bell's inequality doesn't depend on whether the putative common cause is classical or quantum. It works for any common cause that accounts for the perfect anti-correlation at equal angles. The cause need not be deterministic (provided it gives the perfect anti-correlation), and you are free to stipulate that it satisfies Heisenberg's uncertainty principle, etc. The only requirement is that it yields the observed perfect anti-correlation at equal angles, and it enables us to factor the joint probability into two separate probabilities. If it doesn't, the electrons are not separable. If it does, then Bell's inequality follows, and then we can show that this is violated by the correlations at unequal angles.

ReplyDeleteNone of the other things you mentioned (science, democracy, philosophy) is inherently solipsistic, but positivism is inherently solipsistic. So the self-defeating aspect of positivism due to its reduction to solipsism doesn't apply to any of those other things.

I'm glad you agree that the quantum wave function for space-like separated entangled electrons is non-separable. For most people that would be the end of the discussion. As you know, Bohr and Heisenberg insisted that there is nothing other than the wave function (no hidden variables!), and since the wave-function for two space-like separated entangled electrons is non-separable, the electrons are non-separable. Anyone telling Bohr that the electrons were separable would have been in for a long stern lecture.

It's interesting that you agree with many things when stated one way, but when the same thing is stated in another completely equivalent way, you disagree with it vehemently. For example, you say you agree with Bohr, but you disagree with practically everything he actually said. You guess that Bohr was ruling out only classical causal accounts, rather than space-time causal accounts, but you are apparently unaware that, for Bohr and Heisenberg, classical accounts and space-time accounts are the same thing.

You are mistaken in what you think Bohr "probably said". (Why not read up on what he said. You will be appalled.) He and Heisenberg labored for a long time to craft the verbiage of the Copenhagen interpretation. As they summarized it, phenomena can be described in terms of space and time, but then we have non-causal features. On the other hand, we can give causal account of phenomena, but only in terms of the non-separable wave function in configuration space, and "causal descriptions of phenomena in the context of space and time is impossible".

It's well known that Bohr's interpretation and philosophy was (and continues to be) almost completely omitted from quantum mechanics textbooks. At most, a few texts include a few a few perfunctory mentions of complementarity, but without explanation, because no one (including Bohr) has ever known what it means.

I don't know why you keep bad-mouthing Bohr. Many textbooks do teach the Copenhagen interpretation, and many physicists subscribe to it. Maybe even most of them. His defense of QM and refutation of Einstein was excellent.

ReplyDeleteGo ahead and post a link to a Bell inequality paper that does not assume hidden variables, if you can find one. There is no such correct argument.

I think that your problem is your rejection of positivism. Positivists believe in finding evidence and proofs for their beliefs. Anti-positivists do not, and accept conclusions in other ways. So if hidden variables or non-locality seem reasonable to you, then you can believe in them. Positivists have higher standards.

The reason I suggested that you read what Bohr actually wrote is that you seem to think he espoused your views, whereas I think you would find his ideas anathema to your beliefs.

ReplyDeleteIronically, the champion of the beliefs that you have voiced here was actually Einstein, who argued for strict locality, separability, and even causality for the descriptions of events in space and time (although he recognized that causality may be ultimately undecidable). Einstein was against spookiness, whereas Bohr embraced the spookiness.

The EPR argument essentially showed that we can't have both separability and completeness. Since EPR insisted on separability, they concluded that quantum mechanics must be incomplete. Bohr said no, quantum mechanics is complete but not separable. He argued that we must simply accept the spooky quantum correlations with no causal account possible in ordinary space and time. Bohr may well have been correct about this, but I don't think YOU think Bohr was correct about this. You claim that entangled electrons may be deterministic and separable, just as Einstein tried to argue, but Bohr strongly rejected your claim.

The weirdness of this discussion is mainly due to the fact that you believe a set of things, but at the same time you vehemently claim to reject those things. Most notably, your beliefs about how quantum correlations between entangled particles are causally enforced by common cause is tantamount to hidden variables, and yet you claim to reject hidden variables.

I've already pointed out a paper that explains the logic of Bell's theorem, the first part of which is the inference of either common cause or non-local communication to account for the perfect anti-correlation at equal angles. If we reject non-locality, the only remaining option (as you yourself admitted) is common cause, from which the rest of the derivation follows.

Einstein refused to accept quantum mechanics. I fully accept it. Einstein was a believer in determinism. I am not. Einstein argued that QM was incomplete, and that seemed to be largely his belief in hidden variables, or something similar. I reject hidden variables. I am not sure if Einstein believed in causality, as he rarely talked about it.

ReplyDeleteYou seem to think that common cause is the same as hidden variables. It is not.

I am not the only one to side with Bohr over Einstein. Almost the entire physics community did, and the great majority of physicists and textbooks are still of that opinion.

Some corrections and clarifications: Prior to 1927 Einstein tried to find ways to falsify quantum mechanics, but after that date he accepted the correctness of it. He simply maintained that it was incomplete, because on principle he didn't think we should relinquish causal and separable relations in space and time. Einstein did not demand that a theory be deterministic, and many times he explicitly stated this (and discounted the one off-hand and droll remark about dice). You, on the other hand, claimed that electrons may be deterministic and separable.

ReplyDeleteEinstein sought a causal foundation for physics, although he acknowledged that ultimately it will never be possible to decide with certainty whether the world is causal or not (because he understood the limitations of epistemology). You claim to reject hidden variables, but you actually believe quantum correlations are due to a common cause, which is indeed the same as hidden variables (barring super-determinism, etc). You say you are not the only one to side with Bohr over Einstein, but in fact you side with Einstein over Bohr. The problem is, the principles that you attribute to Bohr were actually Einstein's, and the principles you attribute to Einstein were actually Bohr's. And the terms that you say you disagree with ("hidden variables, determinism) are actually the things you believe, whereas the things you claim to believe (causation, separability) are actually inconsistent with your beliefs.

Since you seem most comfortable discussing what authorities say, rather than rationally engaging with the ideas, you might want to take a look at the article on Bell’s Theorem at Scholarpedia, written by four respected scholars in the field. You can find it at

http://www.scholarpedia.org/article/Bell's_theorem

They give a nice account of the actual two-part structure of Bell’s Theorem, and the reason for the confusion: “Because of the editorial accident mentioned above, Bell had answered his own question before the paper in which it appeared was even published. The answer is contained in what we will here call "Bell's inequality theorem", which states precisely that "any hidden variable account of quantum mechanics must have this extraordinary character", i.e., must violate a locality constraint that is motivated by relativity. But the more general result we here call "Bell's theorem" is much more than this: combined with the Einstein–Podolsky–Rosen (EPR) argument "from locality to deterministic hidden variables", the inequality theorem establishes a contradiction between locality as such (and not merely some special class of local theories) and the (now experimentally confirmed) predictions of quantum theory.”

You see, they’re saying exactly what I’ve been telling you (except for using the word locality for what I’m calling separability). This is the same as what your other sources (including Bell himself) told you, and what Bohr never denied. Remember, Bohr did not dispute the fact that quantum mechanics must either be incomplete (hidden variables) or violate separability. The only disagreement was that Bohr said QM is complete (no hidden variables) and accepted that it is not separable (in space and time), whereas EPR said it must be separable (in space and time) so it must be incomplete (hidden variables). If we accept non-separability, we’re done (Bohr’s position). If we insist on separability (as you and Einstein do), then you are forced to hidden variables, in which case the second part of Bell’s Theorem (which these authors call “Bell’s inequality theorem” to distinguish it from the full theorem) leads to Bell’s inequality, which contradicts quantum mechanics.

My post above quotes that Scholarpedia article. I had looked for something taking your side of this issue. It appears to be a minority view. Wikipedia says that Einstein was a strict determinist.

ReplyDeleteIt often seems necessary to cite your own references to you. For example, you now report that a Wikipedia article (written at the grade school level of historical sophistication) assures us that Einstein was a strict determinist, and yet Bell's socks paper, which you have cited here, presents Einstein's actual views, as reported by Pauli: Einstein does not consider the concept of determinism to be as fundamental as it is frequently held to be (as he told me emphatically many times)... he disputes that he uses as a criterion for the admissibility of a theory the question: 'Is it rigorously deterministic?'" How do you reconcile this with your claim that Einstein was a "strict determinist"? And how do you meta-reconcile your apparent rejection of determinism now with your original statement that electrons may be deterministic and separable? And how do you reconcile your rejection of determinism with your embrace of causality in space and time, which is incompatible with quantum mechanics (as taught by Bohr and Heisenberg, with whom you claim to agree)? And why do you dismiss Einstein's championing of locality and causality, if you actually agree with him?

ReplyDeleteYou say the article by Goldstein, Norsen, Tausk, and Zanghi, four noted scholars in the field, "appears to be a minority view". Similarly, in reference to Bell's own account of his theorem (which miraculously agrees exactly with this "minority" article), you dismissed it by saying "John Bell himself later tried to fudge his theorem by pretending to be able to deduce hidden variables from other hypotheses". But this is a completely spurious charge, as you surely know, since the very quote that you referenced points to Bell's earliest paper (1964) in which he did indeed note how we can "deduce hidden variables" from the hypothesis of separability and the perfect anti-correlation at equal angles. I'm not aware of any references that dispute any of this, but I'm also not particularly interested in tabulating the numbers of published accounts of Bell's theorem that emphasize this point, versus those that don't. I'm much more interested in understanding (myself) whether the point is valid.

You seem to scrupulously avoid any cognitive engagement with the actual subject. Your interest seems to be focused entirely on appeals to (or, more often, unsupported dismissals of) authority, rather than actually engaging in a discussion of the subject itself. For example, only once was I able to tempt you into defending your actual views of the subject, when I asked how YOU would account for the perfect anti-correlation at equal angles under the assumption of separability and without hidden variables. The only three possible answers you could think of were all forms of hidden variables. This was good, because it exposed the real source of the mis-understanding. But that was the only time you have ventured to actually discuss the subject itself, and you don't seem to have modified your views based on what you learned from that exchange.

Einstein biographers seem to agree that he was so firm a believer in determinism that he rejected free will. See these Einstein quotes:

ReplyDelete“Everything is determined, the beginning as well as the end, by forces over which we have no control. It is determined for the insect, as well as for the star. Human beings, vegetables, or cosmic dust, we all dance to a mysterious tune, intoned in the distance by an invisible piper.”

“Human beings in their thinking, feeling and acting are not free but are as causally bound as the stars in their motions.”

“I do not believe in freedom of the will.”

“In human freedom in the philosophical sense I am definitely a disbeliever. Everybody acts not only under external compulsion but also in accordance with inner necessity.”

I can believe that Einstein told Pauli that he does not reject a theory because it is not rigorously deterministic. After all, Einstein's early expertise was in statistical mechanics, a stochastic theory. But it is still possible to believe that a deterministic theory underlies statistical mechanics.

I do not agree that I have avoided the Bell issues here. I will post another essay next week where I will attempt to address your issues more directly.

Those quotes come from the cloying 1929 interview in The Saturday Evening Post, "What Life Means to Einstein", by George Sylvester Viereck. As Einstein said, he was speaking (literally in his bath robe) "in the philosophical sense" about life, and in particular about things like the guilt of the Kaiser, etc. To the extent that the fawning Viereck quoted him accurately, and to the extent that these sentiments apply to the physics of quantum mechanics, it basically amounts to what people today call super-determinism, but (oddly enough) Einstein didn't invoke these ideas in his thinking about the EPR phenomena.

ReplyDeleteLook, there's no doubt that Einstein was strongly inclined to seek for causal and deterministic theories - and he often conflated the two, and they are certainly closely related concepts. He continued to hope for causality (in space and time), even in the face of Bohr, Heisenberg, Born, etc., categorically rejecting this. In response, Einstein argued that we can never decide with certainty if the world is causal or not. The puzzle here is that you began by defending determinism, then switched to rejecting it as meaningless, and now you now say you believe firmly in causality (the archtypical positivistically meaningless concept) as not only meaningful but indeed the bedrock of science, and yet you castigate Einstein (who explicitly agreed with you) and laud Bohr and Heisenberg (who vehemently disagreed with you). Very strange.