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.

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

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.

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.

“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/

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.

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”.