I’ve recently read another new popular book about quantum mechanics, Quantum Strangeness by George Greenstein. Before getting to saying something about the book, I need to get something off my chest: what’s all this nonsense about Bell’s theorem and supposed non-locality?

If I go to the Scholarpedia entry for Bell’s theorem, I’m told that:

Bell’s theorem asserts that if certain predictions of quantum theory are correct then our world is non-local.

but I don’t see this at all. As far as I can tell, for all the experiments that come up in discussions of Bell’s theorem, if you do a local measurement you get a local result, and only if you do a non-local measurement can you get a non-local result. Yes, Bell’s theorem tells you that if you try and replace the extremely simple quantum mechanical description of a spin 1/2 degree of freedom by a vastly more complicated and ugly description, it’s going to have to be non-local. But why would you want to do that anyway?

The Greenstein book is short, the author’s very personal take on the usual Bell’s inequality story, which you can read about many other places in great detail. What I like about the book though is the last part, in which the author has, at 11 am on Friday, July 10, 2015, an “Epiphany”. He realizes that his problem is that he had not been keeping separate two distinct things: the quantum mechanical description of a system, and the every-day description of physical objects in terms of approximate classical notions.

“How can a thing be in two places at once?” I had asked – but buried within that question is an assumption, the assumption that a thing can be in

oneplace at once. That is an example of doublethink, of importing into the world of quantum mechanics our normal conception of reality – for the location of an object is a hidden variable, a property of the object … and the new science of experimental metaphysics has taught us that hidden variables do not exist.

I think here Greenstein does an excellent job of pointing to the main source of confusion in “interpretations” of quantum mechanics. Given a simple QM system (say a fixed spin 1/2 degree of freedom, a vector in **C**^{2}), people want to argue about the relation of the QM state of the system to measurement results which can be expressed in classical terms (does the system move one way or the other in a classical magnetic field?) . But there is no relation at all between the two things until you couple your simple QM system to another (hugely complicated) system (the measurement device + environment). You will only get non-locality if you couple to a non-local such system. The interesting discussion generated by an earlier posting left me increasingly suspicious that the mystery of how probability comes into things is much like the “mystery” of non-locality in the Bell’s inequality experiment. Probability comes in because you only have a probabilistic (density matrix) description of the measurement device + environment.

For some other QM related links:

- Arnold Neumaier has posted a newer article about his “thermal interpretation” of quantum mechanics. He also has another interesting preprint, relating quantum mechanics to what he calls “coherent spaces”.
- Philip Ball at Quanta magazine explains a recent experiment that demonstrates some of the subtleties that occur in the quantum mechanical description of a transition between energy eigenstates (as opposed to the unrealistic cartoon of a “quantum jump”).
- There’s a relatively new John Bell Institute for the Foundations of Physics. I fear though that the kinds of “foundations” of interest to the organizers seem rather orthogonal to the “foundations” that most interest me.
- If you are really sympathetic to Einstein’s objections to quantum mechanics, and you have a lot of excess cash, you could bid tomorrow at Christie’s for some of Einstein’s letters on the topic, for instance this one.

Interesting, though hardly surprising, that comment count is proportional to how unknowable and controversial the topic.

Marko,

“You have to be careful not to mix the Lorentz-invariance of the theory with the invariance of its solutions. The preparation and measurement are technically understood as boundary conditions, which fix a particular solution of the equations of motion. There is nothing surprising in the fact that a particular solution is not Lorentz-invariant — this is common even in the classical theory, and not specific to the collapse postulate in QM. When we say that QFT is Lorentz-invariant, we mean that the *dynamics* (encoded in the action or EoMs) is invariant, and this is true regardless of the measurement.”

This might be true if the universe started with a measurement, and ended with one. Alas, this is not true, there are several measurements in between, that are part of the dynamics, not of boundary conditions. Technically speaking, while the dynamics between a given preparation and measurement can be well-described by a (unitary) S-matrix, if you want to talk about the future of a measurement or the past of a preparation, you’ll need to introduce a collapse that will break Lorenz-covariance. That is, if you don’t go Many-Worlds.

“Last time I checked with experimentalists, they did see a single outcome in every run of every experiment ever done. Do Everettians insist that these people are delusional? How do they explain any experimental results at all?”

I think you’re just trolling, but I’ll give a serious answer anyway. What Many-Worlds says that will happen in a measurement is that there will be several copies of the experimentalist, each observing a single outcome. And this is not postulated by fiat, it’s what the equations say. Do you think that anybody would take the theory seriously if this were not the case?

André,

“This is IMHO the main point that Everettians are missing: While it is mathematically perfectly consistent as a theory – and it looks like physics because the unitary dynamics has the same description as in standard QM (with ill-defined projection postulate) – the “anything goes” approach of Many Worlds is not a scientific theory, it is just a mathematical construct.”

Even if you don’t buy the Everettian approach to probability, this is not true. The theory makes many deterministic predictions: there will be no violation of conservation of energy, there will be no break of Lorenz-covariance, there will be no superposition of charges, etc.

And I don’t think probability is a weak point of Many-Worlds, rather it is a strength (I’m aware that this statement is controversial). Standard QM cannot make sense of objective probability, but Many-Worlds can.

“In this regard, an Everettian standpoint on QM is in no way better than the String Theory Landscape.”

This is just an empty insult.

I don’t know how anyone who is a “realist” and has taken the time to understand Bell’s theorem and its experimental tests (and examination of its experimental loopholes, most of them implausible) can not be really, really disturbed by the consistent observation of violations of the theorem under a variety of increasingly stringent tests. It certainly freaked me out when I learned about it in grad school. Of course, as Lee noted above, this is only a problem for those who look for deeper meaning from theories and experiments; instrumentalists and those whose interest in QM is for practical ends can freely ignore the conceptual issues, and there is certainly nothing wrong with that.

Tim Maudlin (a philosopher of physics who has deeply studied Bell’s theorem and articulated much on it) has argued Bell made two key assumptions:

localityand the experimenter’sfreedom to choose experimental settings. Determinism is not an assumption. Hence, since all known experimental loopholes (like detector inefficiency) are now closed, violations of Bell’s inequality imply either locality or freedom of choice is false. Bell noted that the latter is possible if nature is “superdeterministic” in Bell’s sense. Since most people don’t take his superdeterminism too seriously (and he didn’t either), and experimenters at least seem to believe they can freely manipulate the settings, it is usual to conclude that non-locality is a fact of nature.While I may understand their rationale, it still dismays me that so many people have thrown locality “under the bus” (so to speak). Locality isn’t like the 19th century ether that was invented to explain certain physical phenomena; it’s at the core of relativity, electromagnetism, classical mechanics, and even QM evolution up to the time of measurement. I can’t think of anywhere else in all of fundamental physics–outside QM entanglement–where locality is in question. Moreover, there are obvious conceptual issues with non-local influences/communication between entangled particles at space-like separation: How do the particles “find” each other within the entire universe, so they can “communicate” (other than tautalogically or some other version of “it just happens; don’t ask how”); and why don’t we see nonlocality in other contexts if it’s a truly fundamental aspect of nature?

I think there might be other viable alternatives besides the unpalatable choice between superdeterminism and non-locality. Concretely, one question stands out: What if experimental tests are

notactually testing Bell’s theorem the way it seems they are, so that the relevance we assign to the observed violations is an artifact of our ignorance of the “construction” (incomplete modeling) of the particles we employ, and of their interaction with the experimental apparatus, rather than an actual demonstration of non-locality? Stated differently, what if the change of basis (e.g., polarization basis for photons) that is central to Bell tests does not actually cause a particle to fully “forget” its original basis, and furthermore the memory of its original basis subsequently affects its path through the apparatus even though the particle by itselfstatisticallyrespects its new basis in all ways? I’m thinking of something analogous to the phase of the wave function, but which corresponds to an actual attribute (or “hidden variable”, to use that awful term) of the test particles.In a meaningful sense this alternative violates the “freedom of choice” assumption if the nature of the particle is such that an apparatus cannot effect an irreversible change of basis without destroying the original entanglement. It would mean a photon is not completely characterized by its spin, frequency, helicity/polarization, electromagnetic coupling, and of course Poincaré symmetry; something more is present.

I don’t think this idea can be dismissed out of hand. Abstractly, particles are representations of the Poincaré group and an internal symmetry group which are characterized by spin, mass, angular momentum, charge, etc., the origins of which remain unexplained. Given this lack of explanation/understanding there is no empirical reason–only historical or philosophical prejudice–for assuming we possess a complete characterization of the properties and behavior of the known particles. We can reliably model only what we observe, but our ability to test those models is constrained by what we know we should look for (ignoring serendiptous discoveries).

Nonetheless, first reactions to this alternative may be something like “Yuck, that’s really ad hoc and contrived” or “Yeah right, and why exactly haven’t we detected this attribute in other kinds of experiments?” But the Aharonov-Bohm effect can be interpreted as demonstrating the reality of the phase of the wave function, even though (as in the second objection) this phase is generally unobservable. And at least in my own research, much of it currently related to dynamical, geometric models of electrons and photons, the alternative scenario outlined above is

notad hoc; it actually appears plausible.*Given the centrality of locality in physics, I think we should “fight to the death” to preserve it in a fundamental theory. That presumably requires considering alternative possibilities besides superdeterminism or giving up.

* [The reason you won’t find papers on these models (yet) is straightforward. Any proposal of a concrete, mathematical yet explanatory dynamical model is automatically faced with the highly nontrivial task of ensuring empirical and theoretic consistency with all known phenomena and established theory of the modeled particle; or at least enough consistency must be demonstrated to make the model interesting, especially with QM/QFT and electromagnetism. That effort is ongoing…]

I’ve seen a lot of debate on this comment section on traditional interpretations of quantum mechanics, but nobody seems to have taken a look at Neumaier’s interpretation yet.

Mateus Araújo,

“And I don’t think probability is a weak point of Many-Worlds, rather it is a strength (I’m aware that this statement is controversial). Standard QM cannot make sense of objective probability, but Many-Worlds can.”

And Neumaier in his thermal interpretation of quantum mechanics states that the probability found in quantum mechanics is not objective, but is emergent from the fact that we only have incomplete knowledge of the state of the system:

https://arxiv.org/pdf/1902.10779.pdf

Peter,

Neumaier says something similar to what the Scholarpedia article said about Bell’s Theorem in section 4.5 of his 2nd paper on his thermal interpretation:

“Bell’s theorem, together with experiments that prove that Bell inequalities are violated imply that reality modeled by deterministic process variables is intrinsically nonlocal. The thermal interpretation explicitly acknowledges that all quantum objects (systems and sub-systems) have an uncertain, not sharply definable (and sometimes extremely extended) position, hence are intrinsically nonlocal. Thus it violates the assumptions of Bell’s theorem and its variations.”

https://arxiv.org/pdf/1902.10779.pdf

compare with Scholarpedia:

“Bell’s theorem asserts that if certain predictions of quantum theory are correct then our world is non-local.”

Mateus,

“Technically speaking, while the dynamics between a given preparation and measurement can be well-described by a (unitary) S-matrix, if you want to talk about the future of a measurement or the past of a preparation, you’ll need to introduce a collapse that will break Lorenz-covariance.”

I agree, concatenation of two solutions along a “measurement boundary” (past for one, future for the other) is not itself a solution. But note that QFT is usually always applied precisely in the sense that preparation happened in t=-oo, while the measurement happens at t=+oo. Of course, this is an approximation, but works well enough for events in the LHC and such, a context most common for QFT.

“What Many-Worlds says that will happen in a measurement is that there will be several copies of the experimentalist, each observing a single outcome. And this is not postulated by fiat, it’s what the equations say.”

Not really. The equations fail to say why the experimentalist always observes a single outcome in the computational (0/1) basis, and never observes a single outcome in the superposition (+/-) basis. There is nothing in unitary dynamics that could distinguish between the two bases. In order to work around that, MW has to resort to postulating a preferred basis — and this is postulated by fiat. The preferred basis postulate (a) breaks unitarity, and (b) it is essentially equivalent (in predictive power) to the collapse postulate, because otherwise MW would be a different theory, rather than just an interpretation of QM.

I’ve seen various attempts to single out a particular preferred basis using various arguments and handwaving, but they all fall short of being successful, as long as MW holds up to strict unitary evolution.

Best, 🙂

Marko

“As far as I can tell, for all the experiments that come up in discussions of Bell’s theorem, if you do a local measurement you get a local result, and only if you do a non-local measurement can you get a non-local result.”

This is about as embarrassing and revelatory a sentence as could be written. What in the world could a “non-local result” mean?

You do experiments in two (or three: GHZ) labs. You get results of those experiments. Those results display correlations that no local theory (in the precise sense defined by Bell) can predict. Ergo, no local theory can be the correct theory of the actual universe. I.e. actual physics is not local (in Bell’s sense).

This is the sort of thing that can be explained in 20 minutes to undergrads, and they understand it. Woit is clearly intelligent enough to understand it, and his lack of comprehension is indicative of some weird refusal to pay attention to what Bell did.

” The equations fail to say why the experimentalist always observes a single outcome in the computational (0/1) basis, and never observes a single outcome in the superposition (+/-) basis.”

There is always a single outcome in the diagonal basis that was actually measured. You can measure the spin on an electron in any direction you like and you will always get a definite result.

Marko,

You are silently moving the goalposts from “experimentalists should observe multiple outcomes” to the preferred basis problem. You seem, however, to not understand what the problem is (was, actually). You write:

“The equations fail to say why the experimentalist always observes a single outcome in the computational (0/1) basis, and never observes a single outcome in the superposition (+/-) basis. There is nothing in unitary dynamics that could distinguish between the two bases.”

Actually, an experimental apparatus that makes a measurement in the 0/1 basis is different from an apparatus that makes a measurement in the +/- basis. There is no difficulty in capturing this difference in the unitary dynamics, it is really a different unitary transformation.

Rather, the problem was that given a unitary that makes the measurement in the 0/1 basis, ending up with a state like |0>|M_0> + |1>|M_1>, why should we interpret this state as representing a superposition of quasi-classical worlds |0>|M_0> and |1>|M_1>, instead of some other superposition of worlds, or even a single world with some other result? Historically it was simply postulated to be so: an apparatus that measures in the 0/1 basis creates quasi-classical worlds in the 0/1 basis. This is obviously rather unsatisfactory, and people moved on to trying to determine what the quasi-classical worlds are via the Schmidt decomposition, which doesn’t really work (and it is anyway rather weird to postulate that the Schmidt decomposition has some special role).

The problem was solved via decoherence. People realised that an apparatus that measures in the 0/1 basis makes the system

decoherein this basis. This has two effects: the quasi-classical worlds |0>|M_0> and |1>|M_1> are single out by being stable under decoherence, and also they become dynamically decoupled, which justifies thinking of them as separate worlds in the first place.For a historical account of the preferred basis problem, I’d recommend Saunders’ introduction to the “Many Worlds?” book, available here. For a pedagogical take on how decoherence gives rise to the quasi-classical worlds, I’d recommend Wallace’s Decoherence and Ontology.

Mateus,

“You are silently moving the goalposts from “experimentalists should observe multiple outcomes” to the preferred basis problem.”

I’m not trying to move the goalposts — these two things are related. Let me put it this way. You split the Universe into three subsystems: the spin, the apparatus (including us), and the environment (rest of the Universe). Then you trace over the environment, and obtain a density matrix which is almost-block-diagonal in the computational basis, courtesy of (handwavingly specified) interaction with the environment. Say this density matrix looks like diag(1/2,1/2) [here each entry is actually a submatrix describing the detailed state of the apparatus]. The collapse postulate is a further (nonunitary) transformation of the matrix into a form like diag(1,0), encoding the statement “result ‘0’ was observed”. In MW you refuse to make that additional step, and instead interpret the non-collapsed density matrix as “in one branch I see diag(1,0), in the other branch the other me sees diag(0,1), and the two branches are weighted with probability 1/2 each”. This interpretation makes sense only if you *prove* that the density matrix is really almost-diagonal in the computational basis, as opposed to some other basis. I’ve never seen this proof, only qualitative handwaving arguments that the interaction with the environment has precisely the right properties to single out a computational basis. So I wouldn’t call this problem “solved” by decoherence.

Regarding decoherence itself, of course you can always describe nonunitary dynamics of a system as unitary dynamics of a larger system, by tracing over the ancilla. That’s basically a theorem. Nevertheless, this relies on the assumption that the appropriate ancilla physically exists, i.e. that your physical system does have an environment with appropriate interactions. In other words, decoherence may work only for open quantum systems, but not for isolated systems. I find the “environment assumption” ontologically unsatisfactory, since the Universe as a whole is an isolated system, with no environment to fix a preferred basis. For a serious analysis of this issue, see for example arXiv:1105.3796.

I asked the same question to John Preskill a while ago (https://quantumfrontiers.com/2013/01/10/a-poll-on-the-foundations-of-quantum-theory/#comment-2823), and his reply was basically that we should always trace out the part of the Universe which is outside our observable horizon. I find this unsatisfactory, just like Bousso and Susskind do in the arXiv paper.

Best, 🙂

Marko

All,

I’m closing comments on this posting. This has gotten to the point where zero light is being shed on the Bell-nonlocality issue, and I’ve lost the patience needed to try and sensibly moderate a general discussion that people want to take in other directions.