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.

Copyright © 2006 Matthew Leifer. All Rights Reserved.

Koantum feedback: http://koantum.wordpress.com/2006/07/08/61/

May I quote here a big name, pointing to the _present_ formalism?

“This statistical interpretation is now universally accepted as the best possible interpretation for quantum mechanics, even

though many people are unhappy with it. People had got used to the determinism of the last century, where the present determines the future completely, and they now have to get used

to a different situation in which the present only gives one information of a statistical nature about the future. A good many people find this unpleasant; Einstein has always objected to it. The way he expressed it was: ‘The good God does not play with dice’. Schroedinger also did not like the statistical interpretation and tried for many years to find an interpretation

involving determinism for his waves. But it was not successful as a general method. I must say that I also do not like indeterminism. I have to accept it because it is certainly the best that we can do with our present knowledge. One can always hope that there will be future developments which will lead to a drastically different theory from the present quantum mechanics and for which there may be a partial return of determinism. However, so long as one keeps to the present formalism, one has to have this indeterminism.”

Oh, I forgot the reference, that is …

P.A.M. Dirac, ‘The Development Of Quantum Mechanics’, Conferenza Tenuta il 14 Aprile 1972, Roma, Accademia Nazionale dei Lincei, 1974, 11 pages.