Friday, June 08, 2018

Myths of Copenhagen

Discussing the Copenhagen interpretation of quantum mechanics with Adam Becker and Jim Baggott makes me think it would be worthwhile setting down how I see it. I don’t claim that this is necessarily the “right” way to look at Copenhagen (there probably isn’t a right way), and I’m conscious that what Bohr wrote and said is often hard to fathom – not, I think, because his thinking was vague, but because he struggled to express it through the limited medium of language. Many people have pored over Bohr’s words more closely than I have, and they might find different interpretations. So if anyone takes issue with what I say here, please do tell me.

Part of the problem too, as Adam said (and reiterates in his excellent new book What is Real?, is that there isn’t really a “Copenhagen interpretation”. I think James Cushing makes a good case that it was largely a retrospective invention of Heisenberg’s, quite possibly as an attempt to rehabilitate himself into the physics community after the war. As I say in Beyond Weird, my feeling is that when we talk about “Copenhagen”, we ought really to stick as close as we can to Bohr – not just for consistency but also because he was the most careful of the Copenhagenist thinkers.

It’s perhaps for this reason too that I think there are misconceptions about the Copenhagen interpretation. The first is that it denies any reality beyond what we can measure: that it is anti-realist. I see no reason to think this. People might read that into Bohr’s famous words: “There is no quantum world. There is only an abstract quantum physical description.” But it seems to me that the meaning here is quite clear: quantum mechanics does not describe a physical reality. We cannot mine it to discover “bits of the world”, nor “histories of the world”. Quantum mechanics is the formal apparatus that allows us to make predictions about the world. There is nothing in that formulation, however, that denies the existence of some underlying stratum in which phenomena take place that produce the outcomes quantum mechanics enables us to predict.

Indeed, what Bohr goes on to say makes this perfectly clear: “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” (Here you can see the influence of Kant on Bohr, who read him.) Here Bohr explicitly acknowledges the existence of “nature” – an underlying reality – but doesn’t think we can get at it, beyond what we can observe.

This is what I like about Copenhagen. I don’t think that Bohr is necessarily right to abandon a quest to probe beneath the theory’s capacity to predict, but I think he is right to caution that nothing in quantum mechanics obviously permits us to make assumptions about that. Once we accept the Born rule, which makes the wavefunction a probability density distribution, we are forced to recognize that.

Here’s the next fallacy about the Copenhagen interpretation: that it insists classical physics, such as governs measuring apparatus, works according to fundamentally different rules from quantum physics, and we just have to accept that sharp division.

Again, I understand why it looks as though Bohr might be saying that. But what he’s really saying is that measurements exist only in the classical realm. Only there can we claim definitive knowledge of some quantum state of affairs – what the position of an electron “is”, say. This split, then, is epistemic: knowledge is classical (because we are).

Bohr didn’t see any prospect of that ever being otherwise. What’s often forgotten is how absolute the distinction seemed in Bohr’s day between the atomic/microscopic and the macroscopic. Schrödinger, who was of course no Copenhagenist, made that clear in What Is Life?, which expresses not the slightest notion that we could ever see individual molecules and follow their behaviour. To him, as to Bohr, we must describe the microscopic world in necessarily statistical terms, and it would have seemed absurd to imagine we would ever point to this or that molecule.

Bohr’s comments about the quantum/classical divide reflect this mindset. It’s a great shame he hasn’t been around to see it dissolve – to see us probe the mesoscale and even manipulate single atoms and photons. It would have been great to know what he would have made of it.

But I don’t believe there is any reason to suppose that, as is sometimes said, he felt that quantum mechanics just had to “stop working” at some particular scale, and classical physics take over. And of course today we have absolutely no reason to suppose that happens. On the contrary, the theory of decoherence (pioneered by the late Dieter Zeh) can go an awfully long way to deconstructing and demystifying measurement. It’s enabled us to chip away at Bohr’s overly pessimistic epistemological quantum-classical divide, both theoretically and experimentally, and understand a great deal about how classical rules emerge from quantum. Some think it has in fact pretty much solved the “measurement problem”, but I think that’s too optimistic, for the reasons below.

But I don’t see anything in those developments that conflicts with Copenhagen. After all, one of the pioneers of such developments, Anton Zeilinger, would describe himself (I’m reliably told) as basically a Copenhagenist. Some will object to this that Bohr was so vague that his ideas can be made to fit anything. But I believe that, in this much at least, apparent conflicts with work on decoherence come from not attending carefully enough to what Bohr said. (I think Henrik Zinkernagel’s discussions of “what Bohr said” are useful here and here.)

I think that in fact these recent developments have helped to refine Bohr’s picture until we can see more clearly what it really boils down to. Bohr saw measurement as an irreversible process, in the sense that once you had classical knowledge about an outcome, that outcome could not be undone. From the perspective of decoherence, this is now viewed in terms that sound a little like the Second Law: measurement entails the entanglement of quantum object and environment, which, as it proceeds and spreads, becomes for all practical purposes irreversible because you can’t hope to untangle it again. (We know that in some special cases where you can keep track, recoherence is possible, much as it is possible in principle to “undo” the Second Law if you keep track of all the interactions and collisions.)

This decoherence remains a “fully quantum” process, even while we can see how it gives rise to classical-like behaviour (via Zurek’s quantum Darwinism, for example). But what the theory can’t then do, as Roland Omnès has pointed out, is explain uniqueness of outcomes: why only one particular outcome is (classically) observed. In my view, that is the right way to put into more specific and updated language what Bohr was driving at with his insistence on the classicality of measurement. Omnès is content to posit uniqueness of outcomes as an axiom: he thinks we have a complete theory of measurement that amounts to “decoherence + uniqueness”. The Everett interpretation, of course, ditches uniqueness, on the grounds of “why add an extra, arbitrary axiom?” To my mind, and for the reasons explained in my book, I think this leads to a “cognitive instability”, to purloin Sean Carroll’s useful phrase, in our ability to explain the world. So the incoherence that Adam sees in Copenhagen, I see in the Everett view (albeit for different reasons).

But this then is the value I see in Copenhagen: if we stick with it through the theory of decoherence, it takes us to the crux of the matter: the part it just can’t explain, which is uniqueness of outcomes. And by that I mean (irreversible) uniqueness of our knowledge – better known as facts. What the Copenhagenists called collapse or reduction of the wavefunction boils down to the emergence of facts about the world. And because I think they – at least, Bohr – always saw wavefunction collapse in epistemic terms, there is a consistency to this. So Copenhagen doesn’t solve the problem, but it leads us to the right question (indeed, the question that confronts the Everettian view too).

One might say that the Bohmian interpretation solves that issue, because it is a realist model: the facts are there all along, albeit hidden from us. I can see the attraction of that. My problem with it is that the solution comes by fiat – one puts in the hidden facts from the outset, and then explains all the potential problems with that by fiat too: by devising a form of nonlocality that does everything you need it to, without any real physical basis, and insisting that this type of nonlocality just – well, just is. It is ingenious, and sometimes useful, but it doesn’t seem to me that you satisfactorily solve a problem by building the solution into the axioms. I don’t understand the Bohmian model well enough to know how it deals with issues of contextuality and the apparent “non-universality of facts” (as this paper by Caslav Brukner points out), but on the face of it those seem to pose problems for a realist viewpoint too.

It seems to me that a currently very fruitful way to approach quantum mechanics is to think about the issue of why the answers the world gives us seem to depend on the questions we ask (à la John Wheeler’s “20 Questions” analogy). And I feel that Bohr helps point us in that direction, and without any need to suppose some mystical “effect of consciousness on physical reality”. He didn’t have all the answers – but we do him no favours by misrepresenting his questions. A tyrannical imposition of the Copenhagen position is bad for quantum mechanics, but Copenhagen itself is not the problem.

10 comments:

Adam Becker said...

Hi Philip,

I like this, but I don't agree with everything you've said here.

On the issue of contextuality, which you're right to emphasize, I think that Bohr himself gives one possible good answer: he talked about "the impossibility of any sharp distinction between the behaviour of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear." When dealing with very small objects, our large measurement devices are necessarily clumsy, by virtue of their largeness. So contextuality can be seen as a purely mechanical effect. This is, for example, how it works in the Bohmian interpretation: there, contextuality is guaranteed by the interaction between a measurement device and the thing it's measuring.

But more generally, I am loath to ascribe positions to Bohr. He really was unclear. His students said he spoke of a complementarity between clarity and truth, and thus Bohr's seeming incomprehensibility was merely the result of his concern for the truth. I think that you're giving one possible reading of Bohr, but it's certainly not clear that this is the single best way to read Bohr. Another possible reading is that he really did see a divide between the world of the classical and the world of the quantum, and was simply unclear about where that divide might lie. And another possibility is that he changed his mind a lot, or was simply (and understandably) confused. As Jim said on Twitter, Mara Beller's Quantum Dialogue is particularly good on this subject.

I also don't think it's right to say that knowledge is classical. (I see the connection to Kant, but I don't think that helps much.) It's simply not true that human experience of the everyday world is necessarily classical, any more than it's necessarily Aristotelian or necessarily astrological. Classical physics has plenty of profoundly counterintuitive consequences. Think of the first time you held a spinning bicycle wheel and tried to move its axis, the way it kicked back at you in an unexpected way. Or, even more fundamental, the idea that an object in motion tends to stay in motion -- certainly not an idea that lines up with everyday experience on Earth! If there's a way that all human minds universally organize perceptions (a thesis I'm somewhat skeptical of to begin with), it sure ain't classical. This is a great deal of what was at stake in the debates between Einstein and Bohr: Bohr (the conservative) insisted that classical concepts like energy and momentum were required for thinking about the outcomes of experiments, whereas Einstein (the radical, as always) insisted that we could develop new concepts that would give a greater understanding of what was actually happening in the quantum realm, just as spacetime replaced the concepts of individual space and time.

(to be continued, I hit the character limit for comments...)

Adam Becker said...

(Continuing where I left off in my previous comment.)

I'll end with a question: it sounds to me like what you're really defending here, aside from a particular reading of Bohr, is the idea that a psi-epistemic viewpoint (the wave function is knowledge about something, rather than a real thing in the world) is not incompatible with a broadly realist stance about the world, including the world of very small things. Is that your position? If so, I agree with you! But I am somewhat more sympathetic to psi-ontic views (the wave function is something real, be it physical or lawlike). This is, in part, because the PBR theorem is a problem for the most straightforward kinds of psi-epistemic positions. (Matt Leifer, a psi-epistemicist and realist, has a good post on this here.) Furthermore, being psi-epistemic doesn't automatically give you a way out of the kind of nonlocality that Bell's theorem demands, especially if you still want to be a realist of some stripe. So given the choice between "the wave function is my information about something, I don't know what that something is, but that something is nonlocal" and "the wave function is a thing, I know what it is, and it's nonlocal," I'll probably choose the latter. (That's not the choice, and there are both psi-epistemic and psi-ontic ways to avoid nonlocality. But those ways out have other unpleasant consequences of their own.)

Philip Ball said...

Thanks so much for these comments Adam.

Clearly it's not possible to say for sure which of us is right about Bohr; mine is just the generous interpretation. I do agree that it would seem unwise to regard his writings as monolithic and consistent.

I'm not sure what you mean by saying that human experience is not necessarily classical. By that I certainly didn't mean that human intuitions must fit with what classical physics tells us, because as you say there can be plenty that is counter-intuitive about classical physics too. I mean that all perception, and thus measurement in Bohr's sense, ultimately takes place at the classical, macroscopic limit, where decoherence has kicked in. This is, I think, what Bohr was saying, though now our understanding of decoherence allows us to express it in clearer terms.

I'm surprised to find that there are notions that quantum contextuality can be explained as a purely mechanical effect. To me that smacks of Heisenberg's (misconceived) gamma-ray microscope. My understanding is that Kochen and Specker (and indeed Bell, though he published it later than them) established that contextuality is as fundamental as nonlocality: just as we can be confident that any "deeper" theory below QM will have to be nonlocal, it will have to be contextual.

Your phrasing "the wave function is my information about something, I don't know what that something is, but that something is nonlocal" actually sums up very nicely the way I tend to lean, though I wouldn't be dogmatic about it. To my mind, that encapsulates what we can currently say with confidence about QM (and you can probably see why I think Copenhagen at least starts us, imperfectly, down that road). In contrast, to say "The wave function is a thing, I know what it is" strikes me as an article of faith right now - it may turn out to be true, but we can't be sure about that right now. Perhaps I'm just more conservative!

I do like it that you make Einstein the radical! It's so tiresome how he is so often portrayed as the stick-in-the-mud about QM.

C Adams said...

Thanks for your interesting piece and opening a discussion. A couple of comments.

“to “undo” the Second Law if you keep track of all the interactions and collisions”

You do not undo the 2nd law. The second law (increase in entropy) only kicks in if you throw the information away, but if you can recover it, then you have not really thrown it away.

“But what the theory can’t then do, as Roland Omnès has pointed out, is explain uniqueness of outcomes”

One way to view this is that there was only ever going to be one outcome, it is just that we did not know which. Classical physics says we do not know if because we do not have sufficient information. Quantum mechanics says that we still do not know, even if we have all the information that it is possible to have.

In summary, quantum mechanics is simply a formulation of what we can say about the World, it does make any claims on whether the World exists.

Clara, once known as Nemo said...

Philip, Adam,

you speculate about a possible deeper theory for the wave function, one that is nonlocal and contextual. For a number of years, I have followed what Schiller proposes on this topic at http://www.motionmountain.net/research.html . In his talk slides, he indeed presents a deeper theory, where psi is an average of a crossing density due to fluctuating strands. That model for psi is nonlocal and it is contextual, following Bohr, Copenhagen and decoherence rather closely. My own view is somewhat different - I do not think that psi is a "thing" - but the proposal keeps me wondering whether Bohr might have been right after all.

Jim said...

If it's not too late... I think it's important to be clear on what the PBR theorem is saying (and, indeed, Matt Leifer's blog post and subsequent paper on this are models of clarity). PBR's no-go theorem does not (it cannot) rule out 'pure' psi-epistemic interpretations of the wavefunction. It does rule out epistemic interpretations in which what we see is presumed to result from the statistical behaviour of underlying real (ontic) physical states. And, whilst a pure psi-epistemic interpretation is anti-realist, this shouldn't be taken to imply that advocates of such an interpretation are out-and-out empiricists or deny at least some aspects of scientific realism. I believe it is possible to hold to a position which accepts objective reality (the Moon is still there when nobody looks); entity realism ("if you can spray them then they are real"); and yet still question whether the QM *representation* and particularly the wavefunction corresponds (directly or statistically) with the real physical states of such entities. This, I believe, is essentially Carlo Rovelli's position. Then, as I said in a tweet, once you start doubting the QM representation, you can't help but wonder if we've been kidding ourselves all these years with classical mechanics...

Chris Dewdney said...

I don’t agree that the “solution comes by fiat”. In deBB theory, as Bohm presented it in 1952, one reformulates the quantum theory, in a form as close as possible to classical theory, by simply rewriting the complex Schrödinger equation as two, real equations. One of these equations is similar to a classical Hamilton-Jacobi equation (with an extra quantum potential) and the other to a continuity equation for the probability density. The pair of equations is just quantum theory rewritten in a pseudo-classical form, a form that allows one to maintain a very natural definition of particle trajectories. Every particle has a definite (but unknown and uncontrollable) trajectory and the trajectories accounts for the definite results of measurement.

Regarding nonlocality, the essential point is that it concerns many particles (there is no non locality for a single particle) - for which the Schrödinger equation determines the evolution of a configuration space wave function. This is often overlooked when the emphasis of discussion is on single particle quantum mechanics (it might be said to be deceptively spacious). In deBB theory the velocity of the individual particles depends on the multi-particle configuration space wave function and hence on all of the particle coordinates at once. In the Hamilton-Jacobi form of this configuration space description one naturally finds nonlocal quantum forces - without adding them artificially.

So, in deBB theory one does not proceed by “devising a form of nonlocality ….without any real physical basis…” instead, nonlocality arises naturally within the simple mathematical reformulation of the theory. I saw this amazingly clearly when, working in JP Vigier’s lab in the Institut Henri Poincaré in Paris and sitting at what had been de Broglie’s desk, I first calculated the trajectories of a pair of spin one-half particles, in a spin zero singlet state, undergoing spin measurements in Bohm’s version of the EPR experiment (see the 1986 paper - Spin and non-locality in quantum mechanics C Dewdney, PR Holland, A Kyprianidis, JP Vigier Nature 336 (6199), 536). It became very clear from these calculations that what happened to one of the particles depended not only on where the other particle was, but also on which measurements were carried out at the location of the distant particle. Contextuality is also a natural part of deBB theory. In deBB theory the value assigned to an individual physical observable depends not only on the set of hidden variables but also on the wave function. Consequently, the value revealed by a measurement depends on the hidden variables, the initial wave function and the measurement Hamiltonian (describing all of the measurements taking place). (see Constraints on quantum hidden-variables and the Bohm theory. C Dewdney 1992 J. Phys. A: Math. Gen. 25 3615).

When I was a PhD student at Birkbeck in the late 70’s, I remember Bohm saying to me in discussion, that one could imagine the counterfactual historical scenario in which de Broglie’s theory had been accepted at the outset (there were no conclusive arguments against it). Nonlocally correlated particle trajectories would then have been recognised as a natural and irreducible aspect of quantum theory from the beginning and there would have been no measurement problem relying on observers for its “resolution”. Further imagine, he said, that after some 25 years it was suggested that one should remove “by fiat” the idea of particle trajectories from quantum theory, this would have looked very strange indeed, and would have been rejected by the physics community, as it would immediately have given rise to the host of interpretational difficulties with which we all too familiar today.
From this point of view, one could argue that all of the interpretational difficulties within quantum theory arise as a result of the removal from physics of the idea of particle trajectories – “by fiat”.

Jayarava Attwood said...

Understanding quantum is a two-sided problem. Firstly there is the weirdness of quantum mechanics and secondly the weirdness of "understanding". Sometimes we focus on the quantum side of things without considering what knowledge even is. As you say Kant was entirely pessimistic about knowledge of reality. But Kant was writing before the development of modern science and I think we can safely say that he was not entirely right. We can infer a great deal about reality from comparing notes about how we experience it. On the scales of mass, length, and energy where classical physics is a good description, we understand reality quite well.

It so happens that we are somewhere in the middle of the scales of mass, length, and energy spanning 60-100 orders of magnitude. We experience about as much of reality as we see of the EM spectrum.

The quantum problem is that we cannot *experience* quantum phenomena. Thus knowledge about reality at the quantum level is always going to be abstract. The same is, less obviously, true on the largest scales.

I may grasp that there is EM radiation I cannot see or feel, but do I really understand the *reality* of radio waves or X-rays? I can probably with some revision cope with Maxwell's equations. But so what? I still have no experience of radio waves because none of my senses can detect them. When they X-rayed my broken wrist last year, it gave me no sense impressions that I might develop into knowledge.

Along with the breakdown of classical physics, there is a breakdown of the classical concept of knowledge at the scales where quantum descriptions rule. We talk about having images of atoms, for example, but there are many layers of technology between us and the object. If I see a static image of an atom, for example, I tacitly "translate" that into a classical object and believe I understand what I am seeing. But in many ways this picture is false. It tells me nothing about atoms generally if I measure the intensity of electric fields around an atom frozen close to absolute zero and plot them on a graph. The map is not the territory, let alone the pixelated image of the map.

Philip Ball said...

Thanks very much Chris for those very helpful comments. I don't by any means reject the deBB formalism, any more than I reject most of the other interpretations. Indeed, I can see that it has virtues. My impression is that many quantum physicists don't engage with it simply because it seems like a lot of effort for no real gain - they end up with exactly the same predictions as the standard quantum formalism (by design, of course!). I think that the two state vector formalism of Aharonov suffers from neglect for the same reasons, though I appreciate that both can, in certain circumstances, offer a useful way of looking at quantum problems that is not easily evident in other viewpoints. The question, of course, is whether one should deduce any actual ontology from these reformulations of quantum theory.

I don't understand the formalism well enough to be sure, but my understanding is that to connect with the standard quantum formalism you do need at least one extra assumption in the deBB approach (aside from those hidden variables) - the quantum equilibrium hypothesis. And the fact that nonlocality comes out quite naturally doesn't in itself seem an obvious gain over standard QM. I shouldn't say that this nonlocality is "put in by hand", but rather, that it seems to me the deBB formalism just ushers the nonlocality of standard QM into a particular place that then allows one to create a realist, deterministic description of the rest. That's an interesting way to do things, but I'm not convinced it is obviously an advance.

All the same, the counterfactual history you suggest is indeed an interesting one, and I fully buy James Cushing's argument that things could look very different now if the Copenhagen interpretation had not, for what ever reason, got in first. I suspect people would then just be railing against the "absurd Bohmian tyranny" and demanding that a Copenhagenist view be admitted to the textbooks too...

Nicophil said...

E.T. Jaynes wrote :
http://worrydream.com/refs/Jaynes%20-%20Probability%20in%20Quantum%20Theory.pdf

"" Although Bohr's whole way of thinking was very different from Einstein's, it does not follow that either was wrong.
Einstein's thinking is always on the ontological level traditional in physics; trying to describe the realities of Nature. Bohr's thinking is always on the epistemological level, describing not reality but only our information about reality.

The peculiar flavor of his language arises from the absence of all words with any ontological import. Those who, like Einstein, tried to read ontological meaning into Bohr's statements, were quite unable to comprehend his message. This applies not only to his critics but equally to his disciples, who undoubtedly embarrassed Bohr considerably by offering such ontological explanations as [...] the remark of Pauli quoted above, which might be rendered loosely as "Not only are you and I ignorant of x and p ; Nature herself does not know what they are" [or "Eine prinzipielle Unbestimmtheit, nicht nur Unbekanntheit"].

We routinely commit the Mind Projection Fallacy: supposing that creations of our own imagination are real properties of Nature, or that our own ignorance signifies some indecision on the part of Nature. It is then impossible to agree on the proper place of information in physics. This muddying up of the distinction between reality and our knowledge of reality is carried to the point where we find some otherwise rational physicists, on the basis of the Bell inequality experiments, asserting the objective reality of probabilities, while denying the objective reality of atoms !""