Bohr's Reply to EPR (Part II)

In Part I, I claimed that Bohr simply took for granted the conclusion that EPR argue for, namely, that quantum mechanics does not yield a complete description of physical reality,  and that where they part ways is the unargued-for suggestion that a more complete theory is possible.

If this is right, why isn't it clear to every reader of Bohr's reply to EPR?

The reason, I think, is that it wasn't clear in Bohr's own mind.  When I read Bohr, it often seems to me that he is conflating two distinct questions.  One is the question of whether there could be a theory whose state-descriptions go beyond what is allowed by quantum mechanics.  The other is whether we might ever be in a position to know more about the state of a quantum system than is allowed by the uncertainty relations.

They aren't the same question. Think of classical mechanics.  In classical mechanics, a complete state-description is a specification of precise values of all the system's dynamical variables.  For systems composed of many molecules, it would be hopeless to even come close to knowing the precise state of the system, and so we resort to probability distributions over the set of precise states.  It is irrelevant, for the way the theory is used, whether these limitations on knowledge of the precise state are pragmatic limitations, or limitations in principle.

Einstein's view was that quantum wave functions had a status similar to the probability distributions used in classical statistical mechanics; they represented incomplete knowledge of a precise state that would occur in some other theory (not necessarily classical).   If anyone, prior to Einstein's death, presented a good argument for why one shouldn't think of quantum states in this way, I haven't seen it.  No such argument is found in Bohr's reply to EPR.

Though I don't understand Bohr's response to Einstein, I do understand what Einstein attributes to Bohr as a reply, in his Replies to Critics in the Schilpp volume.  There are two ways to reject the conclusion of an argument. One is to find a flaw in the reasoning; the other is to accept the reasoning that leads from premises to conclusion, and to reject one or more of the premises.  Bohr's reply to EPR reads as if he thinks he's found a flaw in the reasoning; he says he's detected an ambiguity in the EPR reality criterion, an ambiguity fatal to the argument.  But in the Replies, Einstein has Bohr reject a premise of the argument.

Of the "orthodox" quantum theoreticians whose positions I know, Niels Bohr's seems to me to come nearest to doing justice to the problem.  Translated into my own way of putting it, he argues as follows:

If the partial systems A and B form a total system which is described by its ψ-function ψ/(AB), there is no reason why any mutually independent existence (state of reality) should be ascribed to the partial systems A and B viewed separately, not even if the partial systems are spatially separated from each other at the particular time under consideration.

So: I understand that as a potential reply to EPR, though I also think that it would be incumbent on someone who replied that way to answer Einstein's challenge, at the end of the Dialectica article, to point to some phenomenon that suggests that we should reject the premise.

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. (Einstein 1948, translation in Howard 1985)

I don't think that Bohr, or anyone else, answered that challenge in Einstein's lifetime.

References

Einstein, Albert (1948). Quanten-mechanik und wirklichkeit. Dialectica 2, 320–324

Einstein, Albert (1949).  Remarks concerning the essays brought together in this co-operative volume, in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Chicago: Open Court Press), 665–688.

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

Bohr’s reply to EPR (Part I)

80 years ago today, on October 15, 1935, Niels Bohr’s reply to “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” was published in Physical Review.

It is a deeply puzzling document.

One puzzle is why it exists at all.  EPR’s argument is addressed to physicists who regard quantum mechanics as yielding, in principle, a complete description of physical reality.  That’s not Bohr.  For Bohr, QM doesn’t provide a complete description of physical reality because it doesn’t provide a description of physical reality at all.  It was an integral part of Bohr’s philosophy of quantum mechanics that any description of reality had to be in classical terms.  This meant, for instance, that, because, classically, electrons are particles and light is a wave, any talk of matter waves or  light quanta is only a symbolic expedient, not to be taken literally (see, e.g., Bohr 1929, p. 17). The lesson of quantum mechanics, according to Bohr, it that we must give up the quest for a complete description of reality, and settle for partial descriptions in terms of complementary classical concepts.  EPR conclude, in their last paragraph, that the “wave function does not provide a complete description of the physical reality.”  This is something that Bohr takes for granted; for him wave-functions are not descriptions of physical reality at all.

Another source of puzzlement is why, if a reply were needed, a single sentence would not have sufficed.

In his contribution to the volume, Albert Einstein: Philosopher-Scientist, Bohr wrote, in connection with a precursor to the EPR argument,

In my opinion, there could be no other way to deem a logically consistent mathematical formalism as inadequate than by demonstrating the departure of its consequences from experience or by proving that its predictions did not exhaust the possibilities of observation, and Einstein’s argument could be directed to neither of these ends (p. 229).

The same goes for the EPR argument. EPR did not attempt to show that the mathematical formalism of QM is inconsistent.  They did not attempt to show that its predictions depart from what is observed, and they did not attempt to show that there are predictions that can be made about the results of observation that go beyond what one can get from QM.   That is, they did not attempt to show that QM was inadequate, in any sense recognized by Bohr. Why, then, would the above-quoted sentence not suffice as a reply to EPR?

Here’s my conjecture about what troubled Bohr about the EPR paper.  Though he takes for granted what they strive to argue for, that QM cannot yield a complete description of physical reality, where he departs from EPR is in the last line of their paper.  They write, in conclusion,

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

That’s where Bohr and EPR part ways.  Bohr accepts the conclusion that EPR argue for, that QM cannot yield a complete description of physical reality; what he does not accept is the suggestion (not argued for by EPR) that a more complete description is possible.

References

Bohr, Niels (1929).  Introductory Survey.  In Atomic Theory and the Description of Nature (Cambridge University Press, 1934), 

(1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 48, 696-702.

——— (1949).  Discussions with Einstein on Epistemological Problems in Atomic Physics, in P.A. Schilpp, ed., Albert Einstein: Philosopher-Scientist (Chicago: Open Court Press), 199–241.

Einstein, Albert, Boris Podolsky, and Nathan Rosen (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review 47, 777-780.

 

Talking about Bell

On August 24, a paper was posted on the physics ArXiV (Hensen et al, http://arxiv.org/abs/1508.05949), 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 Nature,  Forbes,   Science,  New 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.”

References

The preprint:  Hensen et al, “Experimental loophole-free violation of a Bell inequality using entangled electrons spins separated by 1.3 km.” Posted 24  August 2015.  .

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 experiment” New Scientist. Online 28 August 2015.

Hamish Johnson, “Physicists claim 'loophole-free' Bell-violation experiment” Physics 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.

Lynch mobs, real and imagined

Today, of all days, with the horrible massacre in the Emanuel African Methodist Church in Charleston fresh in our minds, The Times published an article in which the folks who mocked Tim Hunt on the #distractinglysexy hashtag were referred to as a "lynch mob."  (I think; it's not clear who, exactly, the lynch mob is meant to be; perhaps the editors of Nature, who ran an editorial urging that all involved in science condemn Hunt's comments, are to be counted as part of the mob, as well.)

Hunt is a retired scientist who was asked by University College London to resign from an honorary position that carries no salary.   He has also resigned from the Royal Society's awards committee, though he remains a Fellow of the Royal Society, despite what Boris Johnson might think.  And though he claimed "I'm finished," in a plea for pity in The Guardian , it seems to me that, if he chose to, he could continue doing what he has been doing in the five years since his retirement, that is, public outreach for science.  If, tomorrow, he issued a statement announcing that he's seen the error of his ways and offered to partner with some organization promoting the position of women in science (e.g. the WISE campaign), people would eat that up, I think.  Or, if he wanted to do a lecture tour picturing himself as victim of Political Correctness, there are organizations that would eat that up, too.

He has not been lynched.  He hasn't even been sacked, in any serious sense of the word.  Being sacked, for most people, would mean loss of livelihood.  He has been mocked, and UCL has acted to distance himself from his remarks, after Hunt himself made it clear that he wasn't going to do so. And what he's doing these days, as reported in the Guardian today, is relaxing and looking forward to watching Wimbledon.

Shall we recall what lynching is?

Lynch mobs murdered people, mostly African Americans, brutally, and left their bodies hanging on trees as a warming to others that it could happen to them. A few months ago the nonprofit organization Equal Justice Initiative released a report, Lynching in America: Confronting the Legacy of Racial Terror.   The report documents nearly 4,000 lynchings in the southern United States between 1877 and 1950, and "makes the case that lynching of African Americans was terrorism, a widely supported phenomenon used to enforce racial subordination and segregation."

The massacre in Charleston reminds us that the hatred that fueled lynch mobs is still alive.

Although the title of the Times article is "Eight Nobel scientists condemn ‘lynch mob’," it's not clear which, if any, of the scientists mentioned in it used the phrase "lynch mob."  The phrase doesn't, unless I've missed it, appear in the body of the article.  I hope that the scientists who are quoted in that article will step up to distance themselves from that characterization.

Einstein liked Quantum Mechanics

“In my opinion, this theory [quantum mechanics] contains without doubt a piece of the ultimate truth.“ Einstein, in 1931.

“Quantum Mechanics represents an important and in some sense even conclusive advance in physical knowledge.” Einstein, in 1948.

Follow-up to my blog post last month about the EPR paper, in which I griped about a pet peeve of mine, the persistent myth that Einstein disliked (sometimes it is said that he hated) quantum mechanics. Einstein disagreed with Bohr and Heisenberg and others about the conclusions one should draw from the success of quantum theory, and he disliked the Copenhagen philosophy (or philosophies), but that’s not the same as disliking quantum mechanics. All the evidence I know of indicates that he appreciated as much, or more, as anyone else what a significant advance in physics the theory was.

It is true that one can find some negative comments in some letters. For example, one finds, in a letter to Ehrenfest, in January 1927, “My heart does not warm to Schrödingerei—it is uncausal and altogether too primitive” (quoted by Fine 1986, p. 27). But to put this in perspective, this is mild compared to Heisenberg’s comment on Schrödinger: “The more I reflect on the physical content of Schrödinger’s theory, the more disgusting [abscheulich] I find it” (letter to Pauli, June 8 1926, in Pauli 1979, letter 136). 

In his Dialectica article (1948), Einstein wrote, “Quantum Mechanics represents an important and in some sense even conclusive advance in physical knowledge.” But perhaps this was a public pronouncement hiding private loathing?

One place to look for Einstein’s sincere attitude is in his recommendations for Nobel Prizes. These were confidential, to be seen only by the Nobel Prize committee, and they were influential; as we shall see below, the committee took Einstein’s recommendations very seriously. So, we can assume that Einstein is recommending for honours only the people that he really thinks deserve the honours. Abraham Pais, Einstein’s biographer, was given permission to see Einstein’s letters to the Nobel prize committee, and he reports what he found in an appendix of his biography, ‘Subtle is the Lord…’. 

Let us confine our attention to the recommendations made after the crucial period 1925-1927, which saw the genesis of quantum mechanics as we know it, primarily at the hands of Heisenberg and Schrödinger. Let us focus on his recommendations for theoretical physics, putting aside recommendations for experimental work and his numerous recommendations for Peace Prizes.

In 1928 he recommended that the prize be awarded either to de Broglie, Davisson, and Germer, for the proposal of electron waves and its experimental verification, or to Heisenberg and Schrödinger jointly. Other possibilities he floated were a prize to be shared between de Broglie and Schrödinger, for wave mechanics, or one to Heisenberg, Born, and Jordan, for matrix mechanics.The 1929 prize went to de Broglie.

In 1931 he recommended individual prizes for Schrödinger and Heisenberg. In his letter, he wrote,

“In my opinion, this theory contains without doubt a piece of the ultimate truth. The achievements of both men are independent of each other and so significant that it would not be appropriate to divide a Nobel prize between them.”

There was no prize awarded in 1931. In 1932 Einstein’s recommendation was a prize for Schrödinger. In 1932 the prize was awarded to Heisenberg, and in 1933, jointly to Schrödinger and Dirac.

His next recommendation for theoretical physics was in 1945, for Pauli, and in 1945 Pauli got his Nobel prize, for the exclusion principle.

And that’s it, in terms of recommendations for prizes in theoretical physics, after 1927. Once quantum mechanics existed, Einstein, in his recommendations for Nobel prizes in theoretical physics, had no other concern than to honour its founders.

References

Einstein, Albert (1948). Quanten-mechanik und wirklichkeit. Dialectica 2, 320–324. 

Fine, Arthur (1986). The Shaky Game: Einstein, Realism, and the Quantum Theory. University of Chicago Press.

Pais, Abraham (1982). ‘Subtle is the Lord…’: The Science and the Life of Albert Einstein. Oxford University Press.

Pauli, Wolfgang (1979).  Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg, u.a./Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein, Heisenberg, a.o.  A. Hermann, K. v. Meyenn, and V.F. Weisskopf, eds.  Springer.