Saturday, 5 September 2015

Talking about Bell

On August 24, a paper was posted on the physics ArXiV (Hensen et al,, announcing  achievement of what has been a long-standing goal in experimental work testing the Bell Inequalities: an experiment that closes both the locality loophole and the detector efficiency loophole at the same time.This was a bit poignant for me, as my teacher and mentor, Abner Shimony, who had taken a keen interest in experimental tests of Bell Inequalities (and one of the authors of the CHSH inequality, which is the one used in this experiment), and who was a keen advocate of attempts to close both loopholes, had passed away just two weeks earlier, on August 8 (obituary here).

The paper has attracted well-deserved attention: it is the subject of write-ups in NatureForbes,   ScienceNew Scientist, and in Physics World, among other places.

I think it’s great that people are talking about Bell’s theorem.  But I want to advocate for a change in how we talk about Bell’s theorem, because I think some of the standard ways  of talking are misleading.  (And I want to emphasize that I don’t mean to single out the authors of the above-mentioned articles for criticism; I am impressed at the overall clarity of the accounts, and the complaints I’m making about how people talk about Bell’s theorem have to do with things that are very commonly said).

Here are some of things I'd like to see change in the way Bell’s theorem is talked about.

1. Hidden variables. Bell’s theorem is often glossed as a no-go theorem for hidden-variables theories; this is suggested by both the Nature and Science articles (though, to be fair, the Nature article talks about “Einstein’s hidden variables,” by which might be meant a local hidden variable theory, which is what Einstein sought).

As Bell himself often stressed, Bell’s theorem is not a no-go theorem for hidden variables.

A hidden-variables theory is one that supplements the quantum state with extra structure, enough so that, for experiments (and other events) in which unitary quantum state evolution leads to a superposition of macroscopically distinct terms, the extra structure picks out one of the terms as the way things are.  The best-known of these is the de Broglie-Bohm pilot-wave theory, presented by de Broglie at the 1927 Solvay conference  (see Bacciagaluppi and Valentini 2009) and revived by Bohm in 1952.  Bell’s theorem does not rule out the de Broglie-Bohm theory!  In fact, the theory served as an inspiration for it.

If you look at the essays in Bell’s Speakable and Unspeakable in Quantum Mechanics, there’s a recurring theme: there can be no no-go theorem for hidden-variables theories, because we actually have one (see, in particular, “On the impossible pilot wave”).  In the first essay in the collection (written before, but published after, the second), Bell goes through several purported no-go theorems, and finds each of them wanting.  He has an ace up his sleeve, which he reveals in the last section; he knows that any such proof must rest on an assumption that is violated by the pilot-wave theory; his strategy is to identify the premise and ask whether it’s physically well-motivated.

2. Local realism. It is commonly said that “local realism” is what is ruled out by violation of the Bell Inequalities, where
  • Realism is the assertion that the outcomes of any experiment are predetermined by the complete physical state of the system, and
  • Locality means absence of action at a distance.
(The terminology of “realism,” which can be traced back to Clauser & Shimony (1978), is a bit misleading, as one can be a realist in the sense of thinking that the physical world exists independently of us and doesn’t depend on our observation for its existence, while holding that some experimental outcomes are genuinely chancy events, not predetermined by even a complete description of the state of things.  I note that the New Scientist article is misled by the terminology, glossing realism as the claim that “the universe is ‘real’ – our observing it doesn’t bring it into existence by crystallising vague probabilities.”)

It's true that the conjunction of “realism,” understood as above, and the absence of action-at-a-distance, entails the Bell Inequalities. But if that’s all you say about the conditions that imply the Bell Inequalities, then you might mislead the reader into thinking that, if you just abandon realism, you can have a theory that eliminates any sort of nonlocality.  And that’s not right.  There’s a locality condition, weaker than local realism, that is enough to entail the Bell inequalities; this is, roughly, the condition that all correlations be locally explicable, perhaps involving fundamentally chancy events, but with no correlations between distant events that aren’t explained in terms of conditions in the past.  That locality condition is violated by quantum mechanics and any theory that violates the Bell Inequalities.

3. Spooky action at a distance.  So, there’s something nonlocal about a theory that violates the Bell Inequalities.  And, if it’s a deterministic theory, the outcome of an experiment at Bob’s end of things can depend on Alice’s parameter setting, which is clearly a case of action at a distance.

But, can we conclude, straight away, that any theory that violates the Bell Inequalities involves action at a distance?

I don’t think so.  For a chancy theory, it’s not so clear that the nonlocality involved counts as action at a distance.  This isn’t just because it can’t be used for signalling; there are theories, such as the pilot-wave theory, that have action-at-a-distance that can’t be exploited for signalling.

A number of people have argued that  the sorts of correlations between distant events involved in a theory that takes quantum state collapse to be a chancy event ought not be thought of as involving action at a distance.  For my take on the argument, see my "Lessons of Bell's Theorem," forthcoming in a volume on Bell.   Not everyone agrees with this; see my back-and-forth with Travis Norsen on that site.  But I think that, at the very least, one should not take for granted that every sort of nonlocality involves spooky action at a distance.

This is connected with the compatibility of Bell-Inequality violations with relativity; the key point is that, unlike cause-and effect relations as usually conceived, the relation between the events at Alice and Bob's wings of the experiment is symmetric, and, unlike cause-and-effect relations as usually conceived, does not require a temporal order between two events.  And that means that theories that have that sort of relation, unlike theories that have action at a distance, can respect a relativistic causal structure, which requires that  there be no temporal order between spacelike-separated events.

4. The Great Einstein Verb Shift.  Something funny happens when people start talking and writing about Albert Einstein’s thoughts on quantum mechanics: the thoughts turn into feelings, and the verbs used in sentences about Einstein  become emotive words.  We are told (by Brian Greene and Alan Alda, no less!) that Einstein “hated” quantum mechanics.  In the Nature article, there’s talk of “Einstein’s annoyance” and it is said that entanglement “galled” Einstein.  In the Science article spooky action at a distance “bothered” Einstein, and it is said that he found wave-function collapse “unpalatable.”

This is unfairly dismissive, I think. Einstein spent a lot of time thinking about quantum mechanics, and he concluded that the theory was incomplete.  But this was not based on feelings about the theory; it was a reasoned judgment. He spelled out the argument in several places, most cleanly in an article published in Dialectica in 1948.

The argument rests on premises of locality, that is, absence of action at a distance, and separability, which says the physical state of a system that has two spatially separated parts can be specified by completely specifying the states of their parts.

His attitude towards these principles was:  first, that they are well-entrenched principles of physics, second, though they need not be regarded as immutable, they ought not to be abandoned without a good reason, and third, that nobody—not Bohr, not Heisenberg, or anyone else—had provided good reason. 
Here’s what he said, at the end of the Dialectica article.
As it appears to me, there can be no doubt that the physicists who hold the quantum mechanical manner of description to be, in principle, definitive, will react to these considerations as follows: They will drop requirement II of the independent existence of the physical realities which are present in different portions of space; they can rightly appeal to the fact that the quantum-theory nowhere makes explicit use of this requirement.

I grant this, but note: if I consider the physical phenomena with which I am acquainted, and especially those which are so successfully comprehended by means of quantum-mechanics, then, nevertheless, I nowhere find a fact which makes it appear to me probable that one has to give up requirement II. For that reason I am inclined to believe that the description afforded by quantum-mechanics is to be viewed …  as an incomplete and indirect description of reality, that will again be replaced later by a complete and direct description.

In any case, one should be on guard, in my opinion, against committing oneself dogmatically to the schema of current theory in the search for a unified basis for the whole of physics. (Quoting from translation in Howard 1985).
I think he’s right about this; in 1948 nobody was able to point to a physical phenomenon that suggested that we would have to abandon the requirements of Locality and Separability.  Things are different now, and they are different because of Einstein’s reflections on quantum mechanics; Bell’s theorem, which arose from Bell thinking hard about the EPR argument,  and the subsequent experimental tests of the Bell Inequalities, do give us reason to think that an adequate physical theory will be, in some sense, nonlocal.  But we might not have learned this were it not for Einstein’s reflections on quantum mechanics.

Let’s not belittle Einstein’s considered judgments about quantum mechanics by using language that suggests that these judgments were gut feelings.

And, by the way, I think a case can be made that, though he thought it wasn’t the final story, Einstein did, indeed, appreciate what an advance in understanding quantum mechanics was, and that he liked it very much.  See my earlier blog post, “Einstein liked quantum mechanics.”


News articles reporting the experiment:
Zeeya Merali, Quantum ‘spookiness’ passes toughest test yet Nature 525 (7567),  pp. 14-15.  Online 27 August 2015.

Chad Orzel, New Experiment Closes Quantum Loopholes, Confirms Spookiness Forbes.  Online 27 August 2015.

Adrian Cho,  More evidence to support quantum theory’s ‘spooky action at a distance’ Science News. Online 28 August 2015.

Jacob Aron, “Quantum weirdness proved real in first loophole-free experimentNew Scientist. Online 28 August 2015.

Hamish Johnson, “Physicists claim 'loophole-free' Bell-violation experimentPhysics World. Online 2 September 2015.

Other references

Bacciagaluppi, Guido, and Antony Valentini. (2009). Quantum Theory at the Crossroads:
Reconsidering the 1927 Solvay Conference
. Cambridge: Cambridge University Press.

Bell, John S.  (1987, 2004).  Speakable and Unspeakable in Quantum Mechanics.  Cambridge University Press.

Clauser, John F., and Abner Shimony.  Bell’s theorem : experimental tests and implications. Reports on Progress in Physics 41 (1978), 1881-1927.

Howard, Don (1985). Einstein on Locality and Separability. Studies in History and Philosophy of Science  16, 171-201.


  1. Nice post Wayne. In this instance I don't think I can be accused of anything untoward, because my quoted comments in Science were so brief. However if I had been quoted at greater length, you would have seen this: "This [the significance of the result] can be explained in different ways, but in the terms the authors choose: nature cannot be both local and realistic. That is, either the physical influence of an action can travel faster than the speed of light, or the physical properties of a system do not exist prior to measurement." In other words, I thought about trying to change the terms of the conversation but in the end decided that the terminology of hidden variables or realism is so entrenched amongst physicists that this was not the time to attempt such a change. One can hope that a change will spread from more philosophically minded physicists outwards, but since there are radical disagreements among philosophically minded physicists (e.g. me vs Travis Norsen) it's hard to see how that will happen smoothly. In my own papers these days I generally use "local causality", and I try to persuade my co-authors in co-authored papers to accept this too.

    Regarding Bell's theorem being a no-go theorem for hidden variables, you point to Bell's writings as if they are monolithic which (as I'm always stressing) they are not. In Bell's 1966 paper, which wrote before his "1964" paper, he presents (see even the abstract) the idea of proving a better (than von Neumann's) no-go theorem by adding the "axiom" of distant systems being independent of one another.

    Similarly, I think it would be acceptable to talk about spooky action at a distance *if* one makes clear that it is in the context where other assumptions have been made, about causality, or realism, or quantum-state-realism. But I would have to admit that I probably am guilty of using this phrase with science communicators without being careful in this way.

  2. You're right that, in the 1966 paper, Bell talks about the project of pursuing "further 'impossibility proofs,' replacing the arbitrary axioms objected to above by some condition of locality, or of separability of distant systems." And adds the note in press that, since the completion of the paper, such a proof has been found.

    Does that mean that at the time he thought of the 1964 proof as a no-go theorem for hidden-variables? Here's how I read it: that proof, like those of von Neumann and others, is an 'impossibillity' proof, not an impossibility proof. That is, I read the quotes around the word as scare quotes, used in the same sense in the 1966 paper as they are in the "On the impossible pilot wave" and in the Preface to the 1st edition.

  3. But maybe I'm reading early Bell through the eyes of later Bell! ;-)

  4. On spooky action at a distance: in your last paragraph, are you saying that, if one makes the assumption of quantum state realism, then we have action at a distance?

    If that's what you mean, I'm not convinced. The line I take in the sections 6 and 7 of my paper for the Gao Bell volume is a quantum state realist one, but I don't think it involves any action at a distance.

  5. It's hard to know exactly how to read Bell in the 1966 paper, but I don't think he would have put scare quotes around his "impossibility" proof, because I think he thought he had found a reasonable axiom, unlike the earlier, unreasonable, ones.

    On your paper I don't know it to comment. By that comment all I meant was that I have used the term "spooky action at a distance" in the context of an EPR-style experiment, where it only makes sense if one thinks of the collapse of the distant quantum state as a real phenomenon.

    1. Yes, but I think that one can think of collapse of the quantum state as a real phenomenon, as in a dynamical collapse theory, without there being any action at a distance.

      The paper's at if you want to take a look at it.

  6. The paper has been published in Nature: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres.

    We'll probably see some more news stories about it; let's see how they score. This one, in The New York Times, scores 3 out of 4 (points 1, 3, and 4):
    “Quantum Theory Experiment Said to Prove ‘Spooky’ Interactions”

  7. Another one that hits 1, 3, and 4.

    The Economist, Hidden no more.

  8. In this one, Einstein "furiously disagreed"! The Express (UK)

    "Quantum effect once dismissed by Albert Einstein as 'spooky' is proved to be REAL"

    Also offers the curious opinion that "In 1964, scientist John Stewart Bell conducted an experiment to rule out hidden variables that could offer an explanation."