Professional Jealousy

As some of you know, my alter ego works on quantum information and computation (I’ll leave you to decide which of us is Clark Kent and which is Superman). My foundations personality sometimes feels a twinge of professional jealousy and I’ll tell you why.

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.
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22 Comments on “Professional Jealousy”

  1. Torbjörn Larsson Says:

    Obviously this is thought through, and I’m merely a layman. But don’t we need a natural (or parsimonity) requirement also, to disallow interpretations that makes special pleadings and allow dualisms? There seems to be some interpretations that bases QM on consciousness and/or consciousness on QM.

    Or are they already ruled out by above criterias, such as “An interpretation should not conflict with any empirically established facts”?


  2. I don’t necessarily want to rule out such interpretations, but the onus is on advocates of such things to come up with viable scientific theories of conciousness that can establish their claim that conciousness can solve the problem.

    I may think they are on the wrong track, and unlikely to be sucessful, but I don’t want to stop anyone from trying.

  3. Torbjörn Larsson Says:

    I see. My idea was that they could make this claim unsubstantiated and that it was hard to rule out.

    The intent of your list could be to rule out interpretations as much as possible. It could of course also be used as a foundation to propose new interpretations, if one thinks they are necessary say for QG, as much as possible.

  4. DV8 2XL Says:

    An excellent list, and perhaps a bit overdue. I would submit that your last criterion be moved into the upper six. I honestly can’t see how a viable interpretation would not address this in light of what is now known.

  5. James Graber Says:

    I learned over forty years ago that an “interpretation”, by definition, was merely another way of talking about standard quantum mechanics, whereas any system which made different predictions was an “alternate theory”, *not* an “interpretation”. Therefore, “interpretations”, unlike “alternate theories”, can never be distinguished by experiment. Of course, calling something an “interpretation” does not make it an “interpretation”; for instance there are published papers arguing pro and con whether the Bohm “interpretation” makes predictions which differ from standard quantum mechanics I was shocked to find Google and Wikipedia offer little support for this important semantic distinction, which is also ignored or even contradicted in your second bonus point criterion. Regardless of how you choose to express it, I think it is crucially important to maintain a distinction between those systems which are merely alternate ways of expressing standard quantum mechanics, and those which actually propose observable new physics.
    Jim Graber


  6. I understand the distinction you make and indeed I have often made it myself in the past. However, I am beginning to think that it is not a particularly useful distinction to make in practice. I wanted the criteria to act as a guide for the kind of work on foundations of QM that people actually do, and so we should ask ourselves whether any interpretations in the more resticted sense actually exist. I think that the answer is no.

    Firstly, it should be noted that standard quantum mechanics is itself not completely unambiguous with respect to the predictions that it makes. This is because measurement is treated as an unanalysed primitive, and we need to use *good sense* to decide when and where to apply the measurement postulates. This hasn’t led to any great difficulty so far, and may never do so in the future, but it is conceivable that someone will think up an experiment where it really does matter and people will disagree about what QM actually predicts. Therefore, it is difficult to tell a priori whether a proposed interpretation is really 100% compatible with the predictions of QM because it is not clear what all of these are in the first place.

    Secondly, John Bell asked “What could be more practical than a good interpretation?”. I take this to mean that any interpretation worth its salt should have some input into physics, and not just stand as an elegant work of philosophy. This means that interpretations should suggest modes of explanation that were not previously available, and make it easier for us to discover and understand new aspects of the theory. To me this is much more than “another way of talking about standard quantum mechanics” and is an essential component of theory building.

    As I noted in the main post, even intepretations that seem to be 100% compatible with standard QM, as presently understood, may provide new ideas on how to modify quantum theory, or how to apply it to new areas where it is not clear how to proceed, like quantum gravity. If such a project ever meets with success, it will become less clear whether the original idea was really an “interpretation” or an “alternate theory”.

    After all is said and done, all this may just be a matter of semantics, since I intend the criteria to apply to a wide range of investigations in the foundations of quantum theory rather than to the narrowest definition of the word interpretation. Basically, any study aimed at addressing the conceptual difficulties of quantum theory is included. However, “Criteria for useful foundational studies” is considerably less catchy and many people wouldn’t have had a clue what I was talking about if I had used that title.

  7. Moshe Says:

    Nice list and nice blog, interpretation definitely is blog-worthy…

    To pick on one of your points that resonates with me, is there great deal of work on intepretation of QFT? it always seems curious to me that with so much attention paid to locality, causality and relativity (sometimes even the general one…), the default language is that of single particle QM and *not* that of QFT (of course I may be wrong…).

  8. Jim Graber Says:

    I agree that “interpretations” can suggest “new theories”. I also believe that is their most useful contribution. Otherwise, the “That’s philosophy, not physics” criticism applies.

    As a very practical example of something I think has been treated as an interpretational question, but is really a physical one, is the onset of decoherence. Now that we are trying to build quantum computers, we can measure and perhaps even engineer the occurrence of decoherence. To me, this seems to be a precise and measurable phenomenon which “defines the Heisenberg Boundary” or “solves the Problem of Measurement.” While measuring decoherence times does not prevent someone from believing in e.g. a many-worlds interpretation, it certainly seems to answer the question “When does the collapse occur?” in a very practical way. To me, it also seems to more directly contradict Bohr’s idea that 1927 quantum mechanics was “complete”, which I think of as a dead horse anyway, given QED, QFT and the standard model, etc. I realize most philosophers would disagree with this last assessment, and think I was missing the point.


  9. Moshe,

    Part of the reason why nonlocality etc. is not often discussed in terms of QFT is that it is difficult to identify localized subsystems in conventional approaches to QFT. On the other hand, Algebraic Quantum Field Theory is a different matter because there one can easily describe localized regions of spacetime. There has been a lot of work on Bell violations in AQFT, with particular emphasis on violations in the vacuum state of the theory, by Reinhardt Werner, the late Rob Clifton and others. Recently, some people have been working on how to extract entanglement from the vacuum in more conventional approaches to QFT.

    However, the main conclusions at the conceptual level are not really any different than in the nonrelativistic case.


  10. I should also note that there is quite a substantial literature on the philosophy of QFT that addresses quite different issues than the usual questions in the interpretation of QM. Things like whether one should adopt a field or particle ontology, the meaning of virtual parrticles and gaugue invariance have been discussed.

    There is a collection of papers edited by Brown and Harre called “Philosophical Foundations of Quantum Field Theory”, which is a good starting point for anyone interested in this.

    For the nonlocality in AQFT stuff, a good starting point is the AQFT section of “Quantum Entanglements” – the collected papers of Rob Clifton. From there you can find most of the relevant papers by following references.


  11. Jim,

    I more or less agree with your last comment, but I would add John Bell’s phrase FAPP (For All Practical Purposes) to the end of almost every sentence. Whilst it’s true that decoherence is the best developed explanation that we have for the “emergence of the classical from the quantum”, that is only one aspect of the complicated set of interrelated issues known as the “measurement problem”.

  12. Moshe Says:

    Excellent, I will take a look, thanks.


  13. An interpretation should have a well-defined ontology.

    This is the only criterion I strongly disagree with. It is perfectly reasonable for an interpretation to be totally agnostic about what “actually exists in reality”.

    For example an interpretation can be based purely on epistemology. “These are the things you can measure. Which (if any) of them ‘actually exist in reality’ is not a meaningful question”.

    A less extreme example is an interpretation that states that something (e.g. the state vector or the operators) is real, but the question of which has no real meaning. Given that there are multiple mathematical formulations of QM that are physically equivalent, it is unreasonable to demand that an interpretation must state that one of them is correct, and that the others only work because they give the same answers as the “true” formulation.

    Stripped of their ontological baggage, many interpretations are equivalent. Requiring that an interpretation must answer questions to which QM, by its construction, does not permit experimental answers is what makes the interpretation question seem so much harder than it really is.

    Demanding that an interpretation of QM have a well defined ontology is like demanding that an interpretation of a play must answer questions about what “really” happened off stage.

    Sometimes ambiguity is real.


  14. I disagree. Every interpretation has to make some ontological committment, although this may be very weak, otherwise there is no way at all of hooking up the theory to what goes on in reality, i.e. no way of connecting it to experiments. This committment could be as weak as “the results of experiments are real”, as I mentioned in the commentry to the criteria, but even this needs to be said because it is not straightforwardly true in all interpretations, e.g. many-worlds.


  15. Nice article. There’s always room for interpretation when we only have access to quantum behaviour but not the underlying mechanism. The key thing: as long as your interpretation fits the facts, it’s a valid interpretation. And no one can tell you otherwise.

    “An interpretation should have a well-defined ontology.”

    I would tend to agree. But then you have to clearly define what constitutes “reality”, and we seem to only have very loose definitions. Are only elementary particles real? Photons and electrons? Or do we extend the definition of reality to cover everything which is “more than just a mathematical formula”. I would say, yes, extend the definition.

    “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.” In my blog, I consider the wavefunction as “reality before observation”, which seems to fit quite well. I don’t have a fixation with the wavefunction, but there’s some reality out there which we don’t seem to have access to. How can the particle go through two slits at once in the double-slit experiment? Surely just considering it to be a point particle is not a full description of its “reality”. And the wavefunction appears to represent its behaviour – its reality – more accurately. See the section on “Veiled Reality” on my blog for more.

    You don’t mention quantum decoherence anywhere. I think the discoveries of quantum decoherence give great insights into the true nature of quantum reality (for example, getting an electric current to flow in two directions at once: http://physicsweb.org/articles/world/13/8/3

    Here’s my blog for my personal ideas: http://www.ipod.org.uk/reality/


  16. “You don’t mention quantum decoherence anywhere. I think the discoveries of quantum decoherence give great insights into the true nature of quantum reality”

    I don’t. They are important to understand the emergence of classicality, but they give no clues for ontology, which is the main problem.

    I am not even convinced that decoherence is the only way to explain emergent classicality, but that’s a work in progress at the moment. For sure, it is ONE way to understand it, but just as with the emergence of the second law of thermodynamics, I think there will eventually be several inequivalent explanations that are more or less the same in terms of practical consequences. In short, I think decoherence is oversold, but that’s a battle I have to fight another day after doing some more technical work.


  17. “I think decoherence is oversold”

    I don’t agree. The way I see decoherence is that it may not be a perfect explanation of what happens during state vector reduction, but I classify it as “not perfect, but pretty close to what happens”. I don’t think it’s oversold at all when you look at the pretty stunning results of experiments such as that Physicsweb link I posted.

    I think I would disagree with you that decoherence is not an important pointer towards ontology – underlying reality. Especially when interpretations which include decoherence have experimental evidence – unlike pie in the sky interpretations, which people have conjured out of the air. I think Bohm’s pilot wave interpretation, as a good example, is rendered obsolete when you realise that any interaction with the enviroment (e.g., a photon entering the double-slit experiment) can destroy interference effects.


  18. Just following up my last posting, if decoherence experiments can show a particle in two places at once (such as experimenters at NIST did “In effect, the atom was in two different places at the same time”: see here) then that kills Bohm’s Pilot Wave interpretation (never more than just one electron following a wave). So I think decoherence definitely has a role in understanding ontology.

    Relevant page on my blog: http://www.ipod.org.uk/reality/reality_veiled_reality.asp

  19. John Sidles Says:

    I would add, the interpretation should be extensible, noting that historically, such extensions obey the heuristic principle that “everything that exists is dynamical”.

    An example: by making particle number dynamical, quantum mechanics extends to field theory.

    Another example: making Cartesian state-space dynamical, Newtonian mechanics extends to general relativity mechanics.

    An emerging example: the program of geometric quantum mechanics (e.g., Ashtekar and Schilling) extends Hilbert space to dynamical Kahler manifolds.

    Another way of saying this is, the foundations of quantum mechanics should not be fixed, but rather, should be themselves be comprised of dynamical entities.


  20. [...] 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 [...]


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