A big and important argument about religion and science has flared up again on Twittter. It occurs to me, though, that nobody has taken the obvious step of polling people about their actual beliefs, so let's see if we can't settle this question with (social) SCIENCE!:

What? It's not like this is any more pointless than the *actual* science-and-religion argument that's going on in blogdom.

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To those of us in the Church of the Larger Hilbert Space, we need not concern ourselves with "measurement," but merely need to look an entangling gate in a larger space. Of course, this viewpoint only is attractive to the Î¨-ontologists amongst us, I think, and many people much smarter than me find that Î¨-epistemic frameworks make more sense, so I'm glad for my friends in the Smaller Spaces.

Which one takes the Axiom of Choice as apocryphal?

Well, obviously I voted for the Smaller Church, but I don't really believe in either the Church of the Larger Hilbert Space or the Church of the Smaller Hilbert Space at the moment. They both have their uses and give different insights into the nature of quantum theory, but to date neither of them has been completely successful in giving a full account of the foundations of quantum theory without having to resort, at some point, to concepts that are only acceptable to the other church. The real answer is likely to involve concepts that are alien to both churches.

To be clear, I don't actually think that the ten commandments thing that I wrote is properly representative of the Church of the Smaller Hilbert Space any more. Obviously, it was meant to be humorous, but I was also much more young, naive and idealistic when I wrote it. In particular, I now think that the Smaller church is largely independent of all the quantum Bayesian stuff, i.e. there are realist interpretational programs, such as epistemic hidden variable theories, that are compatible with the Smaller church and don't commit you to any particular view on the nature of probability.

The basic issue of conflict between the two churches goes all the way back to Schroedinger vs Heisenberg. On the Larger view, quantum theory is thought of as a dynamical theory, much like a classical field theory, but involving a much weirder object, the quantum state, that has all kinds of crazy features like entanglement. Nevertheless, advocates of the Larger church see the Schroedinger equation as the central actor in quantum theory, and in principle all other aspects of the quantum formalism, such as the measurement postulates, should be derived from it (a la Zurek for example). Basically, the Larger church takes the idea that the universe is in a global pure state that is evolving unitarily seriously as a description of reality.

On the other hand, the Smaller church is more closely allied with Heisenberg, i.e. quantum theory is a theory wherein something weird happened to the dynamical variables: they became noncommutative. The quantum formalism is then just the only probabilistic theory of such variables that makes sense. Smaller churchgoers are likely to see the structure of quantum states as derived, by Gleason's theorem for example, and similarly for unitary dynamics, e.g. by Wigner's theorem. The basic structures of the theory have to do with the observables rather than states and the distinction between pure and mixed states is no big deal, at least no bigger than the distinction between generic probability distributions and point measures in classical probability theory.

I don't think this is just an issue of whether you are a psi-ontologist or a psi-epistemicist, although obviously being a psi-ontologist is much more likely to put you in the Larger church. Rather, I think the issue is prior to such debates about the status of the wavefunction. It is about how you think the quantum formalism should be built up from its basic features. Obviously, which story you find the most plausible strongly colors the attitude you are likely to take to the various interpretations of quantum theory and, indeed, I think it is the main source of the violent disagreements over them. Therefore, I think it is more important to sort this stuff out than to argue about questions that are further down the line, like the correct interpretation.

In any case, as you can see, I take this topic very seriously; perhaps more seriously than is good for my health, but it is too late to stop now.

in hilbert space, no one can hear you scream.

It's far from pointless. Remember, your finite but unbounded life depends on giving the correct answer.

I belong to the Church of Spacetime.

Spacetime is the only ontic entity I accept, I believe it is more then enough to explain everything else.

Do not do anything that attaches meaning to the arbitrary tools you choose to work with.is a good commandment.