Author Archives: mleifer

Reorganizing my web empire

I have been busy reorganizing my mini-web empire, as you can see if you look at my swanky new website. Part of this has to do with the fact that I occasionally want to write about things other than the foundations of quantum mechanics, but I don’t want to burden the loyal readers of Quantum Quandaries with such trivia. Therefore, I have started two new blogs.

The first is my announcements blog. This mainly exists to serve the news feed on my website, and it will contain announcements every time I submit a paper to the arXiv, update a paper, get published, visit somewhere for a long time, unify quantum theory with general relativity etc. I won’t announce the details of every paper I write on this blog as well, unless I think the paper is interesting for people into quantum foundations (actually, on that topic you might like this recent paper and also this one). I hope you will appreciate my goal of always keeping this blog strictly on topic, bucking the trend to use blogs mainly for shameless self promotion. Of course, you are welcome to become a regular reader of my announcements blog as well, but I am under no illusions that it will appeal to anyone except maybe my mother.

Secondly, I have started another blog called Academic Tech. This should satisfy my inner geek, as it is about the uses of computers, technology and the net in academia. If you want to know about software and web tools that you can do amazing things with then you might want to read it. However, quantum theory still holds the vast majority of my attention, so articles for this blog will probably be posted much more frequently.

New Papers

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.

Quantum Physics at the Crossroads

FOLKLORE:

When I was but a young undergrad student, I read some interesting books about the history and foundations of quantum theory. In those books the Solvay conferences played a major role, particularly the 5th conference in 1927. I was informed that the official part of the proceedings was largely insignificant, and that all the action centred around the debates that took place between Bohr and Einstein, in which Einstein repeatedly tried to undermine the uncertainty principle via a series of thought experiments, but Bohr was always quick to respond with a correct analysis of the experiment that showed uncertainty to be triumphant. This always put in my mind a picture similar to da Vinci’s “Last Supper”, with Bohr playing the role of Jesus, regailaing his many disciples with the moral parable of the day over dinner.

Another piece of folklore concerns the Ph.D. thesis of one Prince Louis de Broglie. This contained the famous de Broglie relation that gives the wavelength of the waves to be associated with matter particles. The story goes that the thesis was on the verge of being rejected, but was saved by Einstein’s recommendation, who was the only person to recognize the deep significance of the relation. As the story is told, it is hardly surprising, because the contents of the rest of the thesis is never explained. One is left to imagine a document that could only have been about 10 pages long, which intrroduces the relation and then explains some of its consequences. That may seem stong enough for a very good Phys. Rev. article, but is hardly enough to warrant a Ph.D.

LIFE:

Since those distant days of my youth, I have attended many a physics conference myself. I now recognise that it is the general rule, almost without exception, that the participants regard the discussions they have outside the talks as being much more important and interesting than anything that was said in the talks themselves. This rule holds regardless of the actual inherent interest of the topics under discussion. In fact, it is quite common to find some of the older participants banging on about some Hamiltonian they wrote down in the 1970s, whereas the young guns are talking about something genuinely new and interesting, the significance of which is not understood by the older guys yet. It is also extremely unlikely to find the entire group of conference participants, however small that group may be, listening in rapt attention to the discussion of just two people over dinner (if only because there are simply some groups of people who don’t get on with each other, and others who are more interested in going to the pub), and it is equally unlikely that that conversation represents the only interesting thing going on at the conference.

Also, it goes without saying really that I don’t know of anyone who got their Ph.D. for a 10 page paper, however great the idea contained therein happens to be.
REALITY:

Currently, I am about half way through reading “Quantum Theory at the Crossroads”, the new book by Bacciagaluppi and Valentini about the 1927 Solvay conference. The second half of the book is an English translation of the proceedings, but equally interesting is the new analysis of the conference discussions from a modern point of view, contained in the first half. Here are some things I found particularly interesting.

– The only witnesses to the famous Bohr-Einstein debates were Heisenberg and Ehrenfest. The usuall account of these debates comes directly from an article written by Bohr many years after the conference took place. Heisenberg roughly confirms the account, also in recollections written many years later. The only account written shortly after the conference is a letter written by Ehrenfest, which seems to confirm that Bohr was triumphant in the debates, but gives no details.

– Bacciagaluppi and Valentini argue that it is highly unlikely that Einstein’s main target was the uncertainty relations. This is because, outside of Bohr’s account of the conference discussions, Einstein hardly mentions the uncertainty relations as a point of concern in any of his correspondence or published works. Instead, they argue, it is likely that he was trying to get at the point that the concept of separability was incompatible with quantum theory, which was later crystallized in the EPR argument. In fact, Einstein gives an argument in this direction also in the published general discsussion at the conference. It seems likely that Bohr missed this point, just as he seemed to miss the point years later in his published response to the EPR argument.

– At the time of the conference, the consolidation of quantum theory was far from complete. Three approaches were discussed in the talks: de Broglie’s pilot wave theory, Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics (with additions by Born). Despite the fact that “equivalence proofs” between wave and matrix mechanics had been published at the time of the conference, they were treated as distinct theories, which could potentially make different predictions. This is because, at the time, Schrödinger did not accept Born’s statistical hypothesis for wave mechanics, which was not yet formulated for arbitrary observables in any case. Also, Heisenberg and Born did not accept the fundamental significance of the time-dependent Schrödinger equation, and still clung to a view of matrix meachanics as describing the transition probabilities for systems always to be thought of as being in definite stationary states. In fact, it seems that the only person at the conference who presented something that we would now regard as being empirically equivalent to modern quantum theory was de Broglie.
– This was not recognized at the conference, partly because de Broglie did not realize that one sometimes has to treat the apparatus as a quantum system in pilot wave theory in order to get equivalence with standard quantum theory. Also, there was as yet desciption of spin within de Broglie’s theory, but on the other hand this same objection could be levelled at wave mechanics. Finally, de Broglie himself regarded the theory as provisional, since it was not relativistic and involved waves in configuration space rather than ordinary 3d space. He placed great significance on ideas for a better theory, which were far from complete at the time of the presentation.

– Schrödinger emphasizes that de Broglie’s work was a major inspiration for his wave equation. In particular, de Broglie’s idea of unifying the variational principles of Newtonian mechanics with those of geometrical optics, was used in the derivation of the equation.

– de Broglie presented his pilot-wave theory for multiparticle systems, not just for single particles as is commonly thought.

In light of this and other arguments, Bacciagaluppi and Valentini argue that the time is ripe for a revision of the usual textbook history of quantum mechanics, and in particular of de Broglie’s contribution . Those who believe that the history of science should be written with the same objective standards that we hope to uphold for science itself, rather than simply being written by the victors, are well-advised to read this book.

The Cambridgeshire Cat

I have left the sunny climbs of Canada for a few months, in favor of the eternally sweltering UK.

In fact, I am visiting the University of Cambridge, which reminds me of the following quote from Stephen Hawking:

“When I hear of Schrödinger’s cat, I reach for my gun.”

Although attributed to him, I wasn’t able to find the source, so if anyone knows it then please let me know.

The quote has 3 possible interpretations (at least that’s less than quantum theory):

  • Prof. Hawking intends to shoot the cat, thus demonstrating that it is dead without a doubt and not in any kind of quantum superposition.
  • Prof. Hawking intends to shoot the bore who is bringing up this hoary old issue once again.
  • Prof. Hawking intends to shoot himself because he is so fed up of hearing about the apocryphal cat.

Whichever meaning is intended, I think I ought to be careful what I talk about in public around here.

Why not von Neumann?

Anyone who read the comments on my last post will know that von Neumann is something of a hero of mine. Here’s a question that sometimes bothers me – why didn’t von Neumann think of quantum computing? Compare his profile with that of Feynman, who did think up quantum computing, and then ask yourself which one of them you would have bet on to come up with the idea.

  • von Neumann: Worked on a variety of different subjects thoughout his career, including interdisciplinary ones. Was well aware of the work by Turing, Church, Post and others that later became the foundation for computer science and of the role of logic in this work. Is credited with the design of the basic architechture of modern computers. Worked on the mathematical and conceptual foundations of quantum mechanics and is responsible for the separable Hilbert space formulation of quantum theory that we still use today. Finally, at some point he was convinced that the best way to understand quantum theory was as a probability theory over logical structures (lattices) that generalize some of those from classical logic.
  • Feynmann: Spent most of his career working on mainstream topics in quantum field theory and high energy physics. Only towards the end of his career did his interests significantly diversify to include the theories of computation, quantum gravity and the foundations of quantum theory. Conceived of quantum theory mainly in the “sum over paths” formalism, where one looks at quantum theory as a rule for attaching amplitudes to possible histories as opposed to the probabilities used in classical theories.

None of this is meant as a slight against Feynman – he was certainly brilliant at everything he did scientifically – but it is clear that von Neumann was better positioned to come up with the idea much earlier on. Here are some possible explanations that I can think of:

  • The idea of connecting quantum mechanics to computing just never occurred to von Neumann. They occupied disjoint portions of his brain. Ideas that seem simple in hindsight are really not so obvious, and even the greatest minds miss them all the time.
  • von Neumann did think of something like quantum computing, but it was not obvious that it was interesting, since the science of computational complexity had not been developed yet. Without the distinction between exponential and polynomial time, there is no way to identify the potential advantage that quantum computers might offer over their classical counterparts.
  • The idea of some sort of difference in computing when quantum mechanics is thrown into the mix did occur to von Neumann, but he was unable to come up with a relevant model of computing because he was working with the wrong concepts. As alluded to in a paper of mine, Birkhoff-von Neumann quantum logic is definitely the wrong logic for thinking about quantum computing because the truth of quantum logic propositions on finite Hilbert spaces may be verified on a classical computer in polynomial time. The basic observation was pointed out to me by Scott Aaronson, but one needs to set up the model quite carefully to make it rigorous. I might write this up at some point, especially if people continue to produce papers that use quantum computing as a motivation for studying concrete BvN quantum logic on Hilbert spaces. Anyway, the point is that if von Neumann thought that replacing classical logic with his notion quantum logic was the way to come up with a model of quantum computing, then he would not have arrived at anything useful.
  • As a mathematician, von Neumann was not able to think of any practical problem to do with quantum mechanics that looks hard to do on a classical computer, but could be done efficiently in the quantum world. As a physicist, Feynman was much better placed to realize that simulating quantum dynamics was a useful thing to do, and that it might require exponential resources on a classical computer.

As a von Neumann fan, I’d like to think that something other than the first explanation is true, but I am prepared to admit that he might have missed something that ought to have been obvious to him. Hopefully, someday a historian of science will take it upon themselves to trawl the von Neumann archives looking for the answer.

Conferences

Here’s what this year’s foundational conference calendar looks like at the moment:

  • November 2-5: PSA 2006, Vancouver, Canada. This is the Biennial meeting of the Philosophy of Science Association and there are a few sessions on quantum theory.
  • November 28 – December 3: QCMC 2006, Tsukuba, Japan.  This is really a quantum information, computation and optics meeting, but there are often a few talks relevant to foundations.
  • March 5-9: APS March Meeting 2007, Denver, Colorado.  The Topical Group in Quantum Information organized special sessions on the foundations of quantum theory last year, so I imagine it won’t be a major focus this time round.  However, I haven’t seen the list of sessions for this year yet, it’s a good opportunity to find out what’s going on in the rest of physics, and at least there will be some quantum information.
  • March 26-28: Quantum Interaction, Stanford, USA.  This is a bit of an oddball meeting aimed at applying ideas from QM to Artificial Intelligence.
  • March 29-31: 15th UK and European Meeting on the Foundations of Physics, Leeds, UK.  With a special session on quantum information.
  • April: Operational Probabilistic Theories as Foils to Quantum Theory, Cambridge, UK.  This one is an invitation only 2-week event, so please don’t write to the organizers asking to come or they will get very annoyed with me.
  • June 11-16: Quantum Theory: reconsideration of foundations-4: The 80 years of the Copenhagen Interpretation, Vaxjo, Sweden.  This will be the last in this conference series.  Apparently, you can only reconsider the foundations so many times.  No info on the website yet, but it will probably appear soon.
  • I haven’t seen any official announcements yet, but apparently there will be TWO meetings in celebration of 50 years since the publication of Everett’s paper on the relative state interpretation of QM, better known as many-worlds, one at Perimeter Institute and one at Oxford University.

If anyone knows of any other relevant meetings then please let me know and I’ll post an update.

Quantum foundations before WWII

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.

Temperamental Physicists

The other day I was surfing on Chris Fuchs’ website, looking for a journal reference to one of his papers. I noticed that there is a new addition to his compendia of emails about the foundations of quantum mechanics. Now, depending on your temperament, you either love or hate reading such things. Certainly, the ideas are not as carefully formulated as they would be in a scientific paper, and some might find this annoying. Also, if you get annoyed by reading things that you don’t agree with, and you are bound to find at least something you don’t agree with unless your name is Chris Fuchs, then this is not for you. On the other hand, it does give some insight into how a fellow thinker about foundations formulates, develops and changes his ideas, which is something that most scientists go to great lengths to hide from public view. It also gives you an idea of his influences, and it is the reactions of other people to the emails and the quotes from philosophers that I will never be motivated to read myself, that really bring the thing to life. Speaking of the latter, I liked this quotation from William James – if anyone knows the source then please let me know:

The history of philosophy is to a great extent that of a certain clash of human
temperaments. Undignified as such a treatment may seem to some of my colleagues,
I shall have to take account of this clash and explain a good many of the divergencies
of philosophies by it. Of whatever temperament a professional philosopher is, he tries,
when philosophizing, to sink the fact of his temperament. Temperament is no conventionally
recognized reason, so he urges impersonal reasons only for his conclusions. Yet
his temperament really gives him a stronger bias than any of his more strictly objective
premises. It loads the evidence for him one way or the other, making a more sentimental
or more hard-hearted view of the universe, just as this fact or that principle would. He
trusts his temperament. Wanting a universe that suits it, he believes in any representation
of the universe that does suit it. He feels men of opposite temper to be out of key
with the world’s character, and in his heart considers them incompetent and ‘not in it,’
in the philosophic business, even though they may far excel him in dialectical ability.
Yet in the forum he can make no claim, on the bare ground of his temperament,
to superior discernment or authority. There arises thus a certain insincerity in our
philosophic discussions: the potentest of all our premises is never mentioned. I am
sure it would contribute to clearness if in these lectures we should break this rule and
mention it, and I accordingly feel free to do so.

It seems to me that the quote would still make sense if one replaced “philosophy” by “theoretical physics”. Now, before I get accused of being on the loony left of postmodernism and sociology of science, let me clarify that I do believe that the role of experiment is a big difference between the two subjects, and it is capable of resolving issues much more conclusively than argument alone. However, each physicist has to choose what topic to work on and which ideas and methods are most likely to lead to success. Despite the successes of the great edifice of modern theoretical physics, there are still dozens of possible views on which aspects of it are the most important and on why it all works in the first place. The temperament of the physicist plays a large role in coloring her/his attitude to such issues. For example, something as simple as the level of respect for authority can play an enormous role. This is evident in the currently ongoing debate about the success/failure of string theory (which I don’t claim to have enough expertise to say anything sensible about by the way) and in differing attitudes to whether the foundations of quantum mechanics is an important subject for a physicist to understand, or a load of metaphysical hogwash.

It takes all types to make the subject go forward, and it would be a boring life if we all agreed exactly what needed doing and how to go about doin it. However, I do think that if we paid greater attention to the fact that there need not be entirely scientific reasoning behind our differing points of view, and that this is OK – even normal – then that would help to diffuse some of the great controversies of modern science.

fqxi award announcements

There has been quite a bit of discussion on physics blogs recently about the announcement of the Foundational Questions Institute grants a couple of days ago. The stated aim of the institute is:

To catalyze, support, and disseminate research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality but unlikely to be supported by conventional funding sources.

In the blogs and comments, some have praised the choice of grantees, whilst others have criticized it for being too conservative, a waste of time, or for not including grants for some particular foundational topics that they think are important. The connection of fqxi to the Templeton foundation has also been extensively debated. Being a recipient of a grant myself, I obviously think they made at least some good choices, and am looking forward to being able to do some foundational work without having to pretend it has any practical applications in quantum information.

For those who complained about the choice of topics, I would just say that they can only work with the proposals they actually receive, so if people want to change the range of topics that are supported then I think the best way to do so is to submit a strong proposal to the next call.  To other critics, I would say that the worth of fqxi should ultimately be judged by the quality of research that is produced, rather than any predjudices one might have about what makes good foundational research, and this will become clear over the next couple of years.

More on criteria for interpretations

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.