P.S.  In case you were thinking of asking, neither “The Tao of Physics” or “What The Bleep Do We Know?” are ever going to be added.

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In the first foundations session, things got off to a good start with Rob Spekkens as the invited speaker explaining to us once again why quantum states are states of knowledge. OK, I’m biased because he’s a collaborator, but he did throw us a new tidbit on how to make an analog of the Elitzur Vaidman bomb experiment in his toy theory by constructing a version for field theory.

Next, there was a talk by some complete crackpot called Matt Leifer. He talked about this.

Frank Schroeck gave an overview of his formulation of quantum mechanics on phase space, which did pique my interest, but 10 minutes was really too short to do it justice. Someday I’ll read his book.

Chris Fuchs gave a talk which was surprisingly not the same as his usual quantum Bayesian propaganda speech. It contained some new results about Symmetric Informationally Complete POVMs, including the fact that the states the POVM elements are proportional to are minimum uncertainty states with respect to mutually unbiased bases. This should be hitting an arXiv near you very soon.

Caslav Brukner talked about his recent work on the emergence of classicality via coarse graining. I’ve mentioned it before on this blog, and it’s definitely a topic I’m becoming much more interested in.

Later on, Jeff Tollaksen talked about generalizing a theorem proved by Rob Spekkens and myself about pre- and post-selected quantum systems to the case of weak measurements. I’m not sure I agree with the particular spin he gives on it, especially his idea of “quantum contextuality”, but you can decide for yourself by reading this.

Jan-Ake Larrson gave a very comprehensible talk about a “loophole” (he prefers the term “experimental problem”) in Bell inequality tests to do with coincidence times of photon detection. You can deal with it by having a detection efficiency just a few percent higher than that needed to overcome the detection loophole. Read all about it here.

Most of the rest of the talks in this session were more quantum information oriented, but I suppose you can argue they were at the foundational end of quantum information. Animesh Datta talked about the role of entanglement in the Knill-Laflamme model of quantum computation with one pure qubit, Anil Shaji talked about using easily computable entanglement measures to put bounds on those that aren’t so easy to compute and finally Ian Durham made some interesting observations about the connections between entropy, information and Bell inequalities.

The second foundations session was more of a mixed bag, but let me just mention a couple of the talks that appealed to me. Marcello Sarandy Alioscia Hamma talked about generalizing the quantum adiabatic theorem to open systems, where you don’t necessarily have a Hamiltonian with well-defined eigenstates to talk about and Kicheon Kang talked about a proposal for a quantum eraser experiment with electrons.

On Tuesday, Bill Wootters won a prize for best research at an undergraduate teaching college. He gave a great talk about his discrete Wigner functions, which included some new stuff about minumum uncertainty states and analogs of coherent states.

That’s pretty much it for the foundations talks at APS this year. It’s all quantum information from here on in. That is unless you count Zeilinger, who is talking on Thursday. He’s supposed to be talking about quantum cryptography, but perhaps he will say something about the more foundationy experiments going on in his lab as well.

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1. Foundations at APS
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OK, let me start by defining two problems that I take to be at the heart of understanding quantum theory:

1) The Emergence of Classicality: Our most fundamental theories of the world are quantum mechanical, but the world appears classical to us at the everyday level. Explain why we do not find ourselves making mistakes in using classical theories to make predictions about the everyday world of experience. By this I mean not only classical dynamics, but also classical probability theory, information theory, computer science, etc.

2) The ontology problem: The mathematical formalism of quantum theory provides an algorithm for computing the probabilities of outcomes of measurements made in experiments. Explain what things exist in reality and what laws they obey in such a way as to account for the correctness of the predictions of the theory.

I take these to be the fundamental challenges of understanding quantum mechanics. You will note that I did not mention the measurement problem, Schroedinger’s cat, or the other conventional ways of expressing the foundational challenges of quantum theory. This is because, as I have argued before, these problems are not interpretation neutral. Instead, one begins with something like the orthodox interpretation and shows that unitary evolution and the measurement postulates are in apparent conflict within that interpretation depending on whether we choose to view the measuring apparatus as a physical system obeying quantum theory or to leave it unanalysed. The problems with this are twofold:

i) It is not the case that we cannot solve the measurement problem. Several solutions exist, such as the account given by Bohmian mechanics, that of Everett/many-worlds, etc. The fact that there is more than one solution, and that none of them have been found to be universally compelling, indicates that it is not solving the measurement problem per se that is the issue. You could say that it is solving the measurement problem in a compelling way that is the issue, but I would say it is better to formulate the problem in such a way that it is obvious how it applies to each of the different interpretations.

ii) The standard way of describing the problems essentially assumes that the quantum state-vector corresponds more or less directly to whatever exists in reality, and that it is in fact all that exists in reality. This is an assumption of the orthodox interpretation, so we are talking about a problem with the standard interpretation and not with quantum theory itself. Assuming the reality of the state-vector simply begs the question. What if it does not correspond to an element of reality, but is just an epistemic object with a status akin to a probability distribution in classical theories? This is an idea that I favor, but now is not the time to go into detailed arguments for it. The mere fact that it is a possibility, and is taken seriously by a significant section of the foundations community, means that we should try to formulate the problems in a language that is independent of the ontological status of the state-vector.

Given this background viewpoint, we can now ask to what extent decoherence can help us with 1) and 2), i.e. the emergence and ontology problems. Let me begin with a very short description of what decoherence is in this context. The first point is that it takes seriously the idea that quantum systems, particularly the sort that we usually describe as “classical”, are open, i.e. interact strongly with a large environment. Correlations between system and environment are typically established very quickly in some particular basis, determined by the form of the system-environment interaction Hamiltonain, so that the density matrix of the system quickly becomes diagonal in that basis. Furthermore, the basis in which the correlations exist is stable over a very long period of time, which can typically be much longer than the lifetime of the universe. Finally, for many realistic Hamiltonians and a wide variety of systems, the decoherence basis corresponds very well to the kind of states we actually observe.

From my point of view, the short answer to the role of decoherence in foundations is that it provides a good framework for addressing emergence, but has almost nothing to say about ontology.  The reason for saying that should be clear:  we have a good correspondence with our observations, but at no point in my description of decoherence did I find it necessary to mention a reality underlying quantum mechanics.  Having said that, a couple of caveats are in order. Firstly, decoherence can do much more if it is placed within a framework with a well defined ontology. For example, in Everett/many-worlds, the ontology is the state-vector, which always evolves unitarily and never collapses. The trouble with this is that the ontology doesn’t correspond to our subjective experience, so we need to supplement it with some account of why we see collapses, definite measurement outcomes, etc. Decoherence theory does a pretty good job of this by providing us with rules to describe this subjective experience, i.e. we will experience the world relative to the basis that decoherence theory picks out. However, the point here is that the work is not being done by decoherence alone, as claimed by some physicists, but also by a nontrivial ontological assumption about the state-vector. As I remarked earlier, the latter is itself a point of contention, so it is clear that decoherence alone is not providing a complete solution.

The second caveat, is that some people, including Max Schlosshauer in his review, would argue for plausible denial of the need to answer the ontology question at all. So long as we can account for our subjective experience in a compelling manner then why should we demand any more of our theories? The idea is then that decoherence can solve the emergence problem, and then we are done because the ontology problem need not be solved at all. One could argue for this position, but to do so is thoroughly wrongheaded in my opinion, and this is so independently of my conviction that physics is about trying to describe a reality that goes beyond subjective experience. The simple point is that someone who takes this view seriously really has no need for decoherence theory at all. Firstly, given that we are not assigning ontological status to anything, let alone the state-vector, then you are free to collapse it, uncollapse it, evolve it, swing it around your head or do anything else you like with it. After all, if it is not supposed to represent anything existing in reality then there need not be any physical consequences for reality of any mathematical manipulation, such as a projection, that you might care to do. The second point is that if we are prepared to give a privelliged status to observers in our physical theories, by saying that physics needs to describe their experience and nothing more, then we can simply say that the collapse is a subjective property of the observer’s experience and leave it at that. We already have privelliged systems in our theory on this view, so what extra harm could that do?

Of course, I don’t subscribe to this viewpoint myself, but on both views described so far, decoherence theory either needs to be supplemented with an ontology, or is not needed at all for addressing foundational issues.

Finally, I want to make a couple of comments about how odd the decoherence solution looks from my particular point of view as a believer in the epistemic nature of wavefunctions. The first is that, from this point of view, the decoherence solution appears to have things backwards. When constructing a classical probabilistic theory, we first identify the ontological entities, e.g. particles that have definite trajectories, and describe their dynamics, e.g. Hamilton’s equations. Only then do we introduce probabilities and derive the corresponding probabilistic theory, e.g. Liouville mechanics. Decoherence theory does things in the other direction, starting from Schroedinger mechanics and then seeking to define the states of reality in terms of the probabilistic object, i.e. the state-vector. Whilst this is not obviously incorrect, since we don’t necessarily have to do things the same way in classical and quantum theories, it does seem a little perverse from my point of view. I’d rather start with an ontology and derive the fact that the state-vector is a good mathematical object for making probabilistic predictions, instead of the other way round.

The second comment concerns an analogy between the emergence of classicality in QM and the emergence of the second law of thermodynamics from statistical mechanics. For the latter, we have a multitude of conceptually different approaches, which all arrive at somewhat similar results from a practical point of view. For a state-vector epistemist like myself, the interventionist approach to statistical mechanics seems very similar to the decoherence approach to the emergence problem in QM. Both say that the respective problems cannot be solved by looking at a closed Hamiltonian system, but only by considering interaction with a somewhat uncontrollable environment. In the case of stat-mech, this is used to explain the statistical fluctuations observed in what would be an otherwise deterministic system. The introduction of correlations between system and environment is the mechanism behind both processes. Somewhat bizzarely, most physicists currently prefer closed-system approaches to the derivation of the second law, based on coarse-graining, but prefer the decoherence approach when it comes to the emergence of classicality from quantum theory. Closed system approaches have the advantage of being applicable to the universe as a whole, where there is no external environment to rely on. However, apart from special cases like this, one can broadly say that the two types of approach are complimentary for stat mech, and neither has a monopoly on explaining the second law. It is then natural to ask whether closed system approaches to emergence in QM are available making use of coarse graining, and whether they ought to be given equal weight to the decoherence explanation. Indeed, such arguments have been given – here is a recent example, which has many precursors too numerous to go through in detail. I myself am thinking about a similar kind of approach at the moment. Right now, such arguments have a disadvantage over decoherence in that the “measurement basis” has to be put in by hand, rather than emerging from the physics as in decoherence. However, further work is needed to determine whether this is an insurmountable obstacle.

In conclusion, decoherence theory has done a lot for our understanding of the emergence of classicality from quantum theory. However, it does not solve all the foundational queations about quantum theory, at least not on it’s own. Further, its importance may have been overemphasized by the physics community because other less-developed approaches to emergence could turn out to be of equal importance.

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• Firstly, he does believe that the whole universe obeys the laws of quantum mechanics, which are not required to be generalized.
• Secondly, he does not think that Everett/Many-Worlds is a good way to go because it doesn’t give a well-defined rule for when we see one particular outcome of a measurement in one particular basis.
• He believes that collapse is a real phenomenon and so the problem is to come up with a rule for assigning a basis in which the wavefunction collapses, as well as, roughly speaking, a spacetime location at which it occurs.
• For now, he describes collapse as an unanalysed fundamenally stochastic process that achieves this, but he recognizes that it might be useful to come up with a more detailed mechanism by which this occurs.

Steane’s problem therefore reduces to picking a basis and a spacetime location. For the former, he uses the standard ideas from decoherence theory, i.e. the basis in which collapse occurs is the basis in which the reduced state of the system is diagonal. However, the location of collapse is what is really interesting about the proposal, and makes it more interesting and more bizzare than most of the proposals I have seen so far.

Firstly, note that the process of collapse destroys the phase information between the system and the environment. Therefore, if the environmental degrees of freedom could ever be gathered together and re-interacted with the system, then QM would predict interference effects that would not be present if a genuine collapse had occurred. Since Steane believes in the universal validity of QM, he has to come up with a way of having a genuine collapse without getting into a contradiction with this possibility.

His first innovation is to assert that the collapse need not be associated to an exactly precise location in spacetime. Instead, it can be a function of what is going on in a larger region of spacetime. Presumably, for events that we would normally regard as “classical” this region is supposed to be rather small, but for coherent evolutions it could be quite large.

The rule is easiest to state for special cases, so for now we will assume that we are talking about particles with a discrete quantum degree of freedom, e.g. spin, but that the position and momentum can be treated classically. Now, suppose we have 3 qubits and that they are in the state |000> + e^i phi |111>. The state of the first two qubits is a density operator, diagonal in the basis {|00>, |11>}, with a probability 1/2 for each of the two states. The phase e^i phi will only ever be detectable if the third qubit re-interacts with the first two. Whether or not this can happen is determined by the relative locations of the qubits, since the interaction Hamiltonias in nature are local. Since we are treating position and momentum classically at the moment, there is a matter of fact about whether this will occur and Steane’s rule is simple: if the qubits re-interact in the future then there is no collapse, but if they don’t then the then the first two qubits have collapsed into the state |00> or the state |11> with probability 1/2 for each one.

Things are going to get more complicated if we quantize the position and momentum, or indeed if we move to quantum field theory, since then we don’t have definite particle trajectories to work with. It is not entirely clear to me whether Steane’s proposal can be made to work in the general case, and he does admit that further technical work is needed. However, he still asserts that whether or not a system has collapsed at a given point is spacetime is in principle a function of its entire future, i.e. whether or not it will eventually re-interact with the environment it has decohered with respect to.

At this point, I want to highlight a bizzare physical prediction that can be made if you believe Steane’s point of view. Really, it is metaphysics, since the experiment is not at all practical. For starters, the fact that I experience myself being in a definite state rather than a superposition means that there are environmental degrees of freedom that I have interacted with in the past that have decohered me into a particular basis. We can in principle imagine an omnipotent “Maxwell’s demon” type character, who can collect up every degree of freedom I have ever interacted with, bring it all together and reverse the evolution, eliminating me in the process. Whilst this is impractical, there is nothing in principle to stop it happening if we believe that QM applies to the entire universe. However, according to Steane, the very fact that I have a definite experience means that we can predict with certainty that no such interaction happens in the future. If it did, there would be no basis for my definite experience at the moment.

Contrast this with a many-worlds account a la David Wallace. There, the entire global wavefunction still exists, and the fact that I experience the world in a particular basis is due to the fact that only certain special bases, the ones in which decoherence occurs, are capable of supporting systems complex enough to achieve conciousness. There is nothing in this view to rule out the Maxwell’s demon conclusively, although we may note that he is very unlikely to be generated by a natural process due to the second law of thermodynamics.

Therefore, there is something comforting about Steane’s proposal. If true, my very existence can be used to infer that I will never be wiped out by a Maxwell’s demon. All we need to do to test the theory is to try and wipe out a conscious being by constructing such a demon, which is obviously impractical and also unethical. Needless to say, there is something troubling about drawing such a strong metaphysical conclusion from quantum theory, which is why I still prefer the many-worlds account over Steane’s proposal at the moment. (That’s not to say that I agree with the former either though.)

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• Just what is the goal of studying the foundations of quantum mechanics?

Before answering this question, note that its answer depends on whether you are approaching it as a physicist, mathematician, philosopher, or religious crank trying to seek justification for your outlandish worldview. I’m approaching the question as a physicist and to a lesser extent as a mathematician, but philosophers may have legitimate alternative answers. Since the current increase of interest in foundations is primarily amongst physicists and mathematicians, this seems like a natural viewpoint to take.

Let me begin by stating some common answers to the question:

1. To provide an interpretation of quantum theory, consistent with all its possible predictions, but free of the conceptual problems associated with orthodox and Copenhagen interpretations.

2. To discover a successor to quantum theory, consistent with the empirical facts known to date, but making new predictions in untested regimes as well as resolving the conceptual difficulties.

Now, let me give my proposed answer:

• To provide a clear path for the future development of physics, and possibly to take a few steps along that path.

To me, this statement applies to the study of the foundations of any physical theory, not just quantum mechanics, and the success of the strategy has been born out in practice. For example, consider thermodynamics. The earliest complete statements of the principles of thermodynamics were in terms of heat engines. If you wanted to apply the theory to some physical system, you first had to work out how to think of it as a kind of heat engine before you started. This was often possible, but a rather unnatural thing to do in many cases. The introduction of the concept of entropy eliminated the need to talk about heat engines and allowed the theory to be applied to virtually any macroscopic system. Further, it facilitated the discovery of statistical mechanics. The formulation in terms of entropy is formally mathematically equivalent to the earlier formulations, and thus it might be thought superfluous to requirements, but in hindsight it is abundantly clear that it was the best way of looking at things for the progress of physics.

Let’s accept my answer to the foundational question for now and examine what becomes of the earlier answers. I think it is clear that answer 2 is consistent with my proposal, and is a legitimate task for a physicist to undertake. For those who wish to take that road, I wish you the best of luck. On the other hand, answer 1 is problematic.

Earlier, I wrote a post about criteria that a good interpretation should satisfy. Now I would like to take a step back from that and urge the banishment of the word interpretation entirely. The problem with 1 is that it ring-fences the experimental predictions of quantum theory, so that the foundational debate has no impact on them at all. This is the antithesis of the approach I advocate, since on my view foundational studies are supposed to feed back into improved practice of the theory. I think that the separation of foundations and practice did serve a useful role in the historical development of quantum theory, since rapid progress required focussing attention on practical matters, and the time was not ripe for detailed foundational investigations. For one thing, experiments that probe the weirder aspects of quantum theory were not possible until the last couple of decades. It can also serve a useful role for a subsection of the philosophy community, who may wish to focus on interpretation without having to keep track of modern developments in the physics. However, the view is simply a hangover from an earlier age, and should be abandoned as quickly as possible. It is a debate that can never be resolved, since how can physicists be convinced to adopt one interpretation over another if it makes no difference at all to how they understand the phenomenology of the theory?

On the other hand, if one looks closely it is evident that many “interpretations” that are supposedly of this type are not mere interpretations at all. For example, although Bohmian Mechanics is equivalent to standard quantum theory in its predictions, it immediately suggests a generalization to a “nonequilibrium” hidden variable theory, which would make new predictions not possible within the standard theory. Similar remarks can be made about other interpretations. For example, many-worlds, despite not being a favorite of mine, does suggest that it is perfectly fine to apply standard quantum theory to the entire universe. In Copenhagen this is not possible in any straightforward way, since there is always supposed to be a “classical” world out there at some level, which the state of the quantum system is referred to. In short, the distinction between “the physics” and “the interpretation” often disappears on close inspection, so we are better off abandoning the word “interpretation” and instead viewing the project as providing alternatives frameworks for the future progress of physics.

Finally, the more observant amongst you will have noticed that I did not include “solving the measurement problem” as a possible major goal of quantum foundations, despite its frequent appearance in this context. Deconstructing the measurement problem requires it’s own special rant, so I’m saving it for a future occasion.

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Firstly, Andrew Steane has a new paper entitled “Context, spacetime loops, and the interpretation of quantum mechanics”, which was written for the Ghirardi festschrift. Steane is best known for his work on quantum error correction, fault tolerance and ion trap quantum computing, which may not engender a lot of confidence in his foundational speculations. However, the abstract looks interesting and the final sentence: “A single universe undergoing non-unitary evolution is a viable interpretation.” would seem to fit with my “Church of the smaller Hilbert space” point of view. Steane has also addressed foundational issues before in his paper “A quantum computer only needs one universe”, and I like the title even if I am not familiar with the contents. Both of these are on my reading list, so expect further comments in the coming weeks.

The second paper is a survey entitled “Philosophical Aspects of Quantum Information Theory” by Chris Timpson. The abstract makes it seem like it would be a good starting point for philosophers interested in the subject. Timpson is one of the most careful analysers of quantum information on the philosophy side of things, so it should be an interesting read.

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Scott recently posted a list of papers on quantum computation that a computer science student should read in order to prepare themselves for research in quantum complexity. Now, so far, nobody has asked me for a list of essential readings in the Foundations of Quantum Theory, which is incredibly surprising given the vast numbers of eager grad students who are entering the subject these days. In a way, I am quite glad about this, since there is no equivalent of “Mike and Ike” to point them towards. We are still waiting for a balanced textbook that gives each interpretation a fair hearing to appear. For now, we are stuck trawling the voluminous literature that has appeared on the subject since QM cohered into its present form in the 1920′s. Still, it might be useful to compile a list of essential readings that any foundational researcher worth their salt should have read.

Since this list is bound to be several pages long, today we will stick to those papers written before the outbreak of WWII, when physicists switched from debating foundational questions to the more nefarious applications of their subject. This is not enough to get you up to the cutting edge of modern research, so more specialized lists on particular topics will be compiled when I get around to it. I have tried to focus on texts that are still relevant to the debates going on today, so many papers that were important in their time but fairly uncontroversial today, such as Born’s introduction of the probability rule, have been omitted. Still, it is likely that I have missed something important, so feel free to add your favourites in the comments with the proviso that it must have been published before WWII.

• P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1930).
• J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press (1955). This is the first English translation, but I believe the original German version was published prior to WWII.
• W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik, 43, 172-198 (1927). The original uncertainty principle paper.
• A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935).
• N. Bohr, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 48, 696 (1935).
• N. Bohr, The Philosophical Writings of Niels Bohr (vols. I and II), Oxbow Press (1987). It is a brave soul who can take this much Bohrdom in one sitting. All papers in vol. I and about half of vol. II were written prior to WWII. There is also a vol. III, but that contains post 1958 papers.
• E. Schrödinger, Discussion of probability relations between separated systems, Proceedings of the Cambridge Philosophical Society. 31, 555-562 (1935).
• E. Schrödinger, Die Gegenwärtige Situation in der Quantenmechanik, Die Naturwissenschaften. 23, 807-812; 824-828; 844-849 (1935). Translated here.
• Birkhoff, G., and von Neumann, J., The Logic of Quantum Mechanics, Annals of Mathematics 37, 823-843 (1936).

Many of the important papers are translated and reproduced in:

• J. A. Wheeler and W.H. Zurek (eds.), Quantum Theory and Measurement, Princeton University Press (1983).

Somewhat bizzarely it is out of print, but you should find a copy in your local university library.

I am also informed that Anthony Valentini and Guido Bacciagaluppi have recently finished translating the proceedings of the 5th Solvay conference (1927), which is famous for the Bohr-Einstein debates, and produced one of the most well-known photos in physics. It should be worth a read when it comes out. A short video showing many of the major players at the 1927 Solvay conference is available here.

Update: A draft of the Valentini & Bacciagaluppi book has just appeared here.

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The big news is that we have the first response to the criteria from an interpreter of quantum theory over at koantum matters. I would love to see responses from advocates of other interpretations, not because I expect many surprises, but more because it would help me to improve the criteria. I’d like to know if interpreters interpret the criteria in the way I intended.

One of the reasons for engaging in a project like this is that I personally don’t find any of the contemporary interpretations all that compelling. Advocates are often fairly good at arguing their case, so it can be hard to express exactly why a given interpretation makes me uneasy. It is fairly clear that, rightly or wrongly, most of the physics community agrees with me on this, since otherwise there would not be such an emphasis on Copenhagen and Orthodox Dirac-von Neumann ideas in undergraduate quantum mechanics courses. Other interpretations are usually dealt with in one or two lectures at the end of a course, if they are mentioned at all.

In my opinion, the most likely way that the debate on interpretations can be closed is if one interpretation makes itself indespensible for understanding quantum theory. This could be because it leads to new physics, but alternatively it could just lead to a far better way of explaining the phenomena of quantum theory to both students and the general public.

A useful comparison here is to Einstein’s approach to special relativity. In fact, the postulates of quantum theory have been compared to Einstein’s postulates by a variety of authors (e.g. see here and here). Despite Einstein’s insights, the plain fact of the matter is that almost all of the predicitive content of special relativity is contained in the Lorentz transformations, and their extension to the Lorentz and Poincare groups. Especially when doing quantum field theory, special relativity is almost always reduced to just this in modern applications. We could then contemplate starting with a mathematical axiomatization of the Lorentz group and never bother to teach students about Einstein’s postulates at all. This is supposed to be analogous to the current situation in quantum theory, where we cannot derive the whole theory from postulates that are explicitly physical in nature, but are ultimately forced to thinking in terms of abstract Hilbert spaces and the like.

In my view, the main advantage of Einstein’s approach is that it leads directly to the main phenomena of the theory without having to posit the Lorentz transformations to begin with. For example, by considering Einstein’s train thought experiments, we can understand why there is length contraction, time dilation and relativity of simultanaeity directly from the postulates themselves. We would consider a student ill equipped to study relativity if these arguments were not understood before diving into the derivation of the Lorentz transofrmations. In my opinion, it is this that makes relativity more easily understandable than quantum theory.

Therefore, I would argue that to replace orthodoxy in the classroom, an interpretation will have to provide a direct route to some of the main phenomena of quantum theory, as well as facilitating an elegant route to the full mathematical formalism. If not, the interpretation is always likely to remain interesting to only a small band of specialists. Part of the aim of the criteria is to try and make interpreters think about these sort of issues, and that was in particular the point of the “principles” criterion.

Another aim, and perhaps the main one, is to try and move the debate about interpretations forward a little bit. Currently, interpretaions are usually understood as counterpoints to Copenhagen/Orthodoxy. That is, we first explain these ideas, then poke holes in them by discussing the measurement problem, and finally introduce a new interpretation that is supposed to fix the problem. However, we now know that Copenhagen/Orthodoxy is just a small corner in a large space of possibilities, and not necessarily the most convincing of the possibilities at that. Therefore, it seems silly to focus exclusively on these ideas as the starting point. However, once we recognise this, it becomes difficult to formulate the conceptual problems of quantum theory in an interpretationally neutral way, since the measurement problem cannot even be formulated precisely unless we have already taken some stand on the meaning of the wavefunction. Nevertheless, unease about interpretations persists, so the criteria are partly designed to give interpreters a hard time by identifying the weaknesses in their proposals in a more neutral way. This is problematic because there are a number of known issues that only seem to apply to particular interpretations, e.g. it would be nice if the criteria forced many-worlds advocates to discuss the basis problem and the meaning of probability, which may not have analogs in other interpretations. One way of doing this would be to introduce a series of if … then … clauses into the criteria, e.g. if you take an ontological view of the wavefunction then explain the Born rule. However, this is obviously very inelegant and it would be nicer to capture the problems with all interpretations in a short simple set of criteria that applies to every interpretation equally.

With this in mind, it should be clear that the current list is far from final, and I would welcome any ideas on how to improve it.

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In quantum computation we have a set of criteria for evaluating proposed experimental implementations, known as the diVincenzo criteria. These tell you what is required to implement the circuit model of quantum computation, and include things like the ability to prepare pure input states and the ability to perform a universal gate set. Of course, you might choose to implement an alternative model of computation, such as the measurement based models, and then a different set of criteria are applicable. Nevertheless, talks about proposed implementations often proceed by explaining how each of the criteria is to be met in turn. This makes it very clear what the weak and strong points of the implementation are, since there are usually one or two criteria that present a significant experimental challenge.

In contrast, there is no universally accepted set of criteria that an interpretation of quantum mechanics is supposed to meet. They are usually envisioned as attempts to solve the nefarious “measurement problem”, which is actually a catch-all term for a bunch of related difficulties to which different researchers attach different degrees of significance. The question of exactly what an interpretation is supposed to do also varies according to where one is planning to apply it. Is it supposed to explain the emergence of classical mechanics, help us understand why quantum computation works, give us some clues as to how to construct quantum gravity, or simply stand as a work of philosophical elegance?

It seems to me that the foundations community should have, by now, cracked their heads together and come up with a definitive list of issues on which an interpretation has to make a stand, before we are prepared to accept it as a viable contender. Then, instead of reading lots of lengthy papers and spending a lot of time trying to work out exactly where the wool has been pulled out from under our eyes, we can simply send each new interpreter a form to fill in and be done with it. Of course, this is bound to be slightly more subjective than the di Vincenzo criteria, but hopefully not by all that much. For what it’s worth here is my attempt at the big list.

The first six criteria would probably be agreed upon by most people who think seriously about foundations.

• An interpretation should have a well-defined ontology.
  • To begin with, you need to tell me which things are supposed to correspond to the stuff that actually exists in reality. This can be some element of the quantum formalism, e.g. the state vector, something you have added to it, e.g. hidden variables, or something much more exotic, e.g. relations between things without any definite state for the things that are related, correlations without correlata etc. This is all fine at this stage, but of course the more exotic possibilities are going to get into trouble with the later criteria.
  • At this stage, I am even prepared to allow you to say that only detector clicks exist in reality, so long as you are clear about this and are prepared to face the later challenges.
  • As a side note, some people might want to add that the interpretation should explicitly state whether the quantum state vector is ontological, i.e. corresponds to something in reality, or epistemic, i.e. something more like a probability distribution. I am inclined to believe that if you have a clear ontology then it should also be clear what the answer to this question is without any need for further comment. I am also inclined to believe that this fixation on the role of the state vector is an artifact of taking the Schroedinger picture deadly seriously, and ignoring other formalisms in which it plays a lesser role. For instance, why don’t we ask whether operators or Wigner functions are ontological or epistemic instead?

• An interpretation should not conflict with my direct everyday experience.
  • In everyday life, objects appear to be in one definite place and I have one unique conscious experience. If you have adopted a bizarre ontology, wherein this is not the case at the quantum level, you have to explain why it appears that it is the case to me. This is a particularly relevant question for relationalists, Everettistas and correlationalists of course. It is also not the same thing as…

• An interpretation should explain how classical mechanics emerges from quantum theory.
  • Why do systems exist that appear to have states represented by points in phase space, evolving according to the classical evolution equations?
  • Note that it is not enough to give some phase space description. It must correspond to the description that we actually use to describe classical systems.
  • Some people might want to phrase this as “Why don’t we see macroscopic superpositions?”. I’m not quite sure what it would mean to “see” a macroscopic superposition, and I think that this is the more general issue in any case.
  • Similarly, you may be bothered by the fact that I haven’t mentioned the “collapse of the wavefunction” or the “reduction of the wavevector”. Your solution to that ought to be immediately apparent from combining your ontology with the answer to the present issue.
  • Some physicists seem to think that the whole question of interpretation can be boiled down to this one point, or that it is identical with the measurement problem. I hope you are convinced that this is not the case by now.

• An interpretation should not conflict with any empirically established facts.
  • For example, I don’t mind if you believe that wavefunction collapse is a real physical process, but your theory should be compatible with all the systems that have been observed in superposition to date.

• An interpretation should provide a clear explanation of how it applies to the “no-go” theorems of Bell and Kochen Specker.
  • A simple answer would be to explain in what sense your interpretation is nonlocal and contextual. If you claim locality or noncontextuality for your interpretation then you need to give a clear explanation of which other premises of the theorems are violated by your interpretation. They are theorems, so some premise must be violated.

• An interpretation should be applicable to multiparticle systems in nonrelativistic quantum theory.
  • Some interpretations take the idea that the wavefunction is like a wave in real 3d space very seriously (the transactional interpretation comes to mind here). Often such ideas can only be worked out in detail for a single particle. However, the move to wavefunctions on multiparticle configuration space is very necessary and needs to be convincingly accomplished.

The next four criteria are things that I regard as important, but probably some people would not give them such great importance.

• An interpretation should provide a clear explanation of the principles it stands upon.
  • For example, if you claim that your interpretation is minimal in some sense (as many-worlds and modal advocates often do) then you need to make clear what the minimality assumption is and derive the interpretation from it if possible.
  • If you claim that “quantum theory is about X” then a full derivation of quantum theory from axioms about the properties that X should satisfy would be nice. Examples of X might be nonstandard logics, complimentarity, or information.
• No facticious sample spaces.
  • OK this is a bit of a personal bugbear of mine. Some interpretations introduce classical sample spaces (over hidden variable states for instance) or generalizations of the notion of a sample space (as in consistent histories). Quantum theory is then thought of as being a sort of probability theory over these spaces. Often, however, the “quantum states” on these sample spaces are a strict subset of the allowed measures on the sample space, and the question is why?
  • I allow the explanation to be dynamical, in analogy to statistical mechanics. There we tend to see equilibrium distributions even though many other distributions are possible. The dynamics ensures that “most” distributions tend to equilibrium ones. Of course, this gets into the thorny issues of the foundations of statistical mechanics, but provided you can do at least as good a job as is done there I am OK with it.
  • I also allow a principle explanation, e.g. some sort of fundamental uncertainty principle. However, unlike the standard uncertainty relations, you should actually be able to derive the set of allowed measures from the principle.

• An interpretation should not be ambiguous about whether it is consistent with the scientific method.
  • Some interpretations seem to undermine the very method that was used to discover quantum theory in the first place. For example, we assumed that experiments really had outcomes and that it was OK to reason about the world using ordinary deductive logic. If you deny any of these things then you need to explain why it was valid to use the scientific method to arrive at the theory in the first place. How do you know that an even more radical revision of these concepts isn’t in order, perhaps one that could never be arrived at by empirical means?

• An interpretation should take the great probability debate into account.
  • Quantum theory involves probabilities and some interpretations take a stand on the fundamental significance of these. Is the interpretation consistent with all the major schools of thought on the foundations of probability (propensities, frequentism and subjectivism), at least as far as these are themselves consistent? If not, you need to be clear on what notion of probability is actually needed and address the main arguments in the great probability debate. Good luck, because you could spend a whole career just doing this.

The final three criteria are not strictly required for me to take your interpretation seriously, but addressing them would score you extra bonus points.

• An interpretation should be consistent with relativistic quantum field theory and the standard model.
  • Obviously, you need to be consistent with the most fundamental theories of physics that we have at the moment. However, the conceptual leap from nonrelativistic to relativistic physics is nontrivial and it has implications for ontology even if we forget about quantum theory. Therefore, it is OK to just focus on the nonrelativistic case when developing an interpretation. QFT might require significant changes to the ontology of your interpretation, and this is something that should be addressed eventually.

• An interpretation should suggest experiments that might exhibit departures from quantum theory.
  • It’s good to have something which can be tested in the lab. Interpretations such as spontaneous collapse theories make predictions that depart from quantum theory and these should be investigated and tested.
  • However, even if your interpretation is entirely consistent with quantum theory, it might suggest novel ways in which the theory can be modified. We should be constantly on the lookout for such things and test them wherever possible.

• An interpretation should address the phenomenology of quantum information theory.
  • This reflects my personal interests quite a bit, but I think it is a worthwhile thing to mention. Several quantum protocols, such as teleportation, suggest a strong analogy between quantum states (even pure ones) and probability distributions. If your interpretation makes light of this analogy, e.g. the state is treated ontologically, then it would be nice to have an explanation of why the analogy is so effective in deriving new results.

Related posts:

1. More on criteria for interpretations
2. Against Interpretation
3. What can decoherence do for us?