Tag Archives: foundations

Against Interpretation

Posted on 14 December, 2006 by | 4 comments

It appears that I haven’t had a good rant on this blog for some time, but I have been stimulated into doing so by some of the discussion following the Quantum Pontiff‘s recent post about Bohmian Mechanics. I don’t want to talk about Bohm theory in particular, but to answer the following general question:

  • 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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New Papers

Posted on 20 November, 2006 by | 1 comment

I don’t normally like to just list new papers without commenting on them, but I don’t have much reading time at the moment so here are two that look interesting.

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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Quantum foundations before WWII

Posted on 24 September, 2006 by | 8 comments

The Shtetl Optimizer informs me that there has not been enough contemplation of Quantum Quandaries for his taste recently. Since there has not been a lot of interesting foundational news, the only sensible thing to do is to employ the usual blogger’s trick of cut, paste, link and plagiarize other blogs for ideas.

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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More on criteria for interpretations

Posted on 6 July, 2006 by | 3 comments

Well, my “big list” has proved to be my most popular blog post to date, thanks in no small part to a mention over at Uncertain Principles and a n u mber of other blogs. I know when I’m on to a good thing, so let’s stick with the topic for one more post.

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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Professional Jealousy

Posted on 28 June, 2006 by | 22 comments

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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Vaxjo Meeting

Posted on 13 June, 2006 by | Leave a comment

I returned this weekend from the meeting on Foundations of Probability and Physics at the University of Vaxjo in Sweden. There were many interesting talks, so I'll just mention a few of them that I found particularly inspiring.

– Giacomo Mauro d'Ariano explained his axiomatization of quantum theory, inspired by observations from quantum state and process tomography. One of the nice features of this is that he gives an operational definition of the adjoint. Why the observables of QM should form an algebra from an operational point of view has been a topic of recent debate amongst foundational people here at Perimeter, so this could be a piece of the puzzle.

– Rüdiger Schack explained what it might mean for quantum randomness to be "truly random" from a Bayesian point of view, using the concept of "inside information" that he has developed with Carlton Caves.

– Philip Goyal gave another axiomatization of quantum theory. I'm not sure whether the framework he uses is that well-motivated (especially the sneaky way that complex numbers are introduced). On the other hand, one of his axioms has the flavor of an "epistemic constraint", which gels nicely with ideas that have been expressed earlier by Chris Fuchs and Rob Spekkens.

– Joseph Altepeter gave another excellent talk about the state of the art Bell inequality experiments currently going on in Paul Kwiat's group.

– John Smolin outlined speculative ideas that he and Jonathan Oppenheim have developed that applies the concept of locking quantum information to solve the black hole information loss problem. 

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Realists on the counter attack

Posted on 25 April, 2006 by | 7 comments

Martin Daumer, Detlef Duerr, Sheldon Goldstein, Tim Maudlin, Roderich Tumulka and Nino Zanghi, a collection of scholars noted for their advocacy or realist interpretations of quantum mechanics, and Bohmian mechanics in particular, have posted an article on quant-ph that attacks the idea that quantum theory is “fundamentally about information”. The article is a response to a recent essay in Nature by Anton Zeilinger, and is mainly a criticism of his particular viewpoint.

Most of their argument is based on the fact that interpretations like Bohmian mechanics offer a clear counterexample to various claims, such as that QM shows nature is fundamentally indeterministic and that the Bell and Kochen-Specker no-go theorems rule out realism. I think this is all fair enough, and I agree that it is well worth taking the time to become familiar with the Bohm interpretation if one is at all interested in foundations. It is quite amazing how often it can be used as an example to clear up confusion and misunderstandings about what we can infer from QM. On the other hand, this is a far cry from saying that Bohmian mechanics should be taken seriously as a description of reality. There are several arguments against doing so, which would take too long to go into right now. Perhaps I will do so in another post when I have more free time.

In any case, Zeilinger’s Nature essay seems a rather easy target to me. It was a short article, and there was clearly not enough space for any detailed arguments. Whether or not you think that Zeilinger in fact has any compelling arguments, there are many other contemporary approaches that also claim QM is about “information” in some sense, and it would be good to see a more in depth response to all of these from the realist camp. Examples include the quantum Bayesianism of Caves, Fuchs and Schack; the axiomatic approach of Bub, Clifton and Halvorson; and Hardy’s axiomatics.

Those of you who are waiting for Rovellifest 2 – fear not, for it is coming within the next week or so. For now, I feel like I need to write something on a topic I feel positive about, to aviod this blog descending into a sea of negative criticisms.

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The Church of the Smaller Hilbert Space

Posted on 13 April, 2006 by | 6 comments

This is supposed to be a balanced blog, but my nonexistent readership may wish to know exactly what I do believe about quantum mechanics. The document below explains everything.

WARNING: The document below contains geek humor that also parodies the style of a certain well-known religious text. If you don't find jokes about density operators funny and/or you are a devout religious person then you may find its contents offensive. The document below does not necessarily represent the opinions of its author, or indeed any person, animal, alien or sentient artificial intelligence, living, dead or yet to be born.

Ten Commandments of the Church of the Smaller Hilbert Space
Update:  The link is now working.  Apologies for the delay.

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The Free Will Theorem

Posted on 13 April, 2006 by | 2 comments

Michael Nielsen recently posted a comment by John Sidles about a preprint by Kochen and Conway that was posted on the quant-ph arXiv yesterday. It's called "The Free Will Theorem", which is certainly a provocative title. Here's my comment on the paper that I left on Mike's blog.

Hmm… I had a look at this paper. The title sounds a bit crackpot, but given the status of the authors I was willing to give it a chance.

First of all the name “Free Will Theorem” opens a whole can of worms, which we probably don’t want to get into. Suffice to say, what they actually prove is an “indeterminism theorem”, i.e. they use a Bell-type argument + a no-signalling requirement to prove that nature must be indeterministic. I have heard similar arguments before, in particular Y. Aharonov and D. Rohlich mention it in their book, although I’ve never seen it written down formally before.

To call this a “free will theorem” one has to get into the debates about whether free will is compatible with determinism and, if not, whether indeterminism even solves the problem. Most contemporary philosophers seem to answer yes and no respectively, so I don’t think this theorem has much to do with free will, although it would take a lot more space to go through the arguments for and against thoroughly.

However, what I did think was interesting about the paper was the “hexagon universe” toy-model that they introduced in the second half of the paper. Given the current interest in understanding aspects of QM via simpler toy theories, e.g. nonlocal boxes and Spekkens toy theory, this might be a useful addition to the canon. I haven’t managed to decipher all the details of this model yet, so I’ll have to defer judgement on that.

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Foundations at APS

Posted on 14 March, 2006 by | 1 comment

I’m currently at the APS March Meeting, where there were two sessions on Quantum Foundations on Monday. I am pleased to report that they were well attended. Hopefully, this marks the start of an increased involvement of the APS in the field.

The second session was particularly interesting, so here’s a short summary of what we heard:

  • Invited speaker Lucien Hardy outlined his Causaloid framework for general probabilistic theories without a fixed background causal structure. It is hoped that this might lead to a new path for developing a theory of quantum gravity.
  • Chris Fuchs gave a shortened version of his usual talk, focussing on the role of symmetric informationally complete POVMs in his approach to quantum foundations.
  • Terry Rudolph presented an extension of Rob Spekkens’ toy theory for dealing with continuous variable theories. This has lots of features in common with QM, but has a natural hidden variable interpretation, being a resticted version of Liouville mechanics.
  • Rob Spekkens showed how two seemingly different notions of “nonclassicallity”, nalely negativity of peseudo-probability distributions and the impossibility of a noncontextual hidden variable theory, are actually the same within the new approach to contextuality that he has developed.
  • Nicholas Harrigan outlined an approach to quantifying contextuality that he has been developing with Terry Rudolph.
  • Joseph Altepeter, from Kwiat’s group, gave an interesting presentation on their current state of the art photonic Bell inequality experiments.
  • OK, I have to admit that I was getting tired at this point and skipped out for a talk, so I have no idea about the next talk. Apologies to Giuliano Scarcelli.
  • There then followed two talks about decoherence from Diego Dalvit and Fernando Cucchietti, collaborators of Zurek and Paz respectively. This is an important topic for many interpretations of QM and the results looked solid. However, I’m not an expert on this stuff.
  • Ruth Kastner, who was due to deconstruct the now famous Ashfar experiment, was unfortunately unable to attend due to illness, but Ashfar was here to give his side of the story instead. The experiment is interesting at least because it has made quite a few physicists think about complimentarity and foundations in general a bit more deeply. Personally, I agree with Kastner’s analysis, but Ashfar disputes it.
  • Jeff Tollaksen outlined a new way of measuring the “weak values” introduced by Aharonov and collaborators. I didn’t follow the details of the construction, but look forward to reading the paper.
  • Caslav Brukner outlined his work with Zeilinger on an “information based” approach to quantum foundations. It’s not my personal favourite amongst such approaches, but gave plenty of food for thought.

Well, foundations at this meeting are pretty much finished after that. There are still a few interesting quantum information sessions before the end of the week, but I can leave other bloggeurs to deal with that.

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