If, by “hidden variable” you mean something akin to lambda as it is used in Bell’s theorem, i.e. a complete description of the state of reality, then yes it is essentially the same thing.

However, some authors use “hidden variable” to mean any variables that exist in addition to the quantum state, which is assumed to be real at the outset and is not itself classed as a hidden variable. Obviously, this use of terminology rules out psi-epistemic theories a priori. If the quantum state is real then it is part of the ontic state on my usage. This allows us to consider realist theories in which the quantum state is not part of the ontic state. This difference of terminology has lead to some confusion in the literature, with some authors claiming that Bohmian mechanics is psi-epistemic because the particle positions do not uniquely determine the quantum state. However, in my usage, the quantum state is ontic in Bohmian mechanics because it is needed to determine how a measurement device will respond to the system. Basically, the ontic state should screen off the preparation from the measurement. That is just part of what it means to ascribe properties to the system. We want to be able to say that we are doing an experiment on the properties of the system itself, not on the system plus other external mechanisms for correlating preparation and measurement.

Using the term “ontic state” rather than “hidden variable” is also a bit of a re-branding exercise. As Bell pointed out, quantum states cannot be directly measured, so in some sense they are “hidden” variables, whereas in most ontological models it is the other variables that are more closely related to what we directly observe. Some people are also under the impression that “hidden variable” theories are necessarily different from orthodox quantum mechanics, so no-go theorems do not apply unless you add extra variables. However, you can have an, admittedly absurd, ontological model in which the ontic state is just the quantum state and collapse is a real physical phenomenon that occurs upon measurement (in an unspecified way). This is so close to what is written in many textbooks (but very different to what the Copenhagen founders believed) that we should be clear that the theorems apply to orthodox quantum mechanics in this sense, and not just theories like Bohmian mechanics that add extra variables.

]]>I appreciate what you say. First, sorry to land here, the previous post made me start off thinking the thread was a recent one.

I take the point about Occam’s razor, in fact it would be a blunt instrument even if simplicity wasn’t in the eye of the beholder, because it only says that a simpler explanation is more likely, or preferable, not that the more complicated one can’t be true.

About QM interpretations, to me if the mathematics is describing something we have analogies for, then we might find it by conceptual thinking. If it isn’t, then we might never get significantly nearer to understanding QM than we are now anyway.

I agree very much with your points made here:

http://mattleifer.info/2006/07/06/more-on-criteria-for-interpretations

You say “the most likely way that the debate on interpretations can be closed is if one interpretation makes itself indispensable for understanding quantum theory”, and you draw an analogy with SR, and how it leads directly to the main phenomena of the theory without having to posit the Lorentz transformations, just from a set of postulates. In other words, we need something that initially can bypass the mathematics.

Fuchs said something similar:

‘…no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance.’

Anyway, that’s what I look for, because we might only be able to get anywhere if it exists. If it doesn’t exist, it seems to me that we may just have to accept QM as it is, and say, ‘well, that’s just the way it is’.

]]>I don’t know why people have started commenting on this old post again, but my position on Everett has evolved considerably since I wrote this post, and indeed there has been some work explicitly addressing the problem that I was discussing, which is now called the “problem of evidence” in the Everett interpretation. I don’t think my post had anything to do with why people started looking at this, but anyway it is good to know that it is acknowledged as a problem and people have been trying to solve it. Whether or not those solutions are successful would require its own long discussion.

Please note that I NEVER invoked Occam’s razor against the MWI in the blog post. If I did so in the comments then I shouldn’t have. Occam’s razor is a blunt instrument and usually better replaced with other arguments. Simplicity is in the eye of the beholder. The naive Occam’s argument against MWI, that it postulates a vast number of unobservable worlds, can be countered with the idea that MWI is based on a small number of postulates (fewer than orthodox quantum mechanics). Arguably, a simple set of postulates is more important than the number of entities implied by a theory. Either way, it shows that the application of Occam’s razor is far from straightforward.

If I were arguing against MWI now, I would focus more on the principles behind it than on any of its implications. The idea that a quantum state, evolving unitarily in time, should be taken as a literal description of reality is, to my mind, far from natural. It pre-supposes a view that the Schrödinger equation has the same sort of status as a classical field equation, which, for one thing, introduces a prejudice towards a psi-ontic view. It is also not obvious to me that Schródinger evolution is innocent and easily understood whereas the measurement axioms are “bad”, which is the usual MWI narrative. I quite like the measurement axioms and think they form the core of the theory (i.e. you can derive most of the structure of QM by thinking of it as a generalized probability theory over a generalization of a classical measure space, which gets you the measurement axioms first and the Schrödinger equation later). This perspective is highly useful in a variety of fields, including quantum information, quantum statistical mechanics, quantum chaos, and algebraic quantum field theory. Unlike MWI, it has teeth in practical applications, which is why I think it has the ring of truth to it. From this perspective, Schrödinger evolution is not fundamental, but derived. Wigner’s theorem tells us that the automorphism group of QM consists of the unitary and anti-unitary operators on Hilbert space. Only the unitaries are continuously connected to the identity, so only they can represent continuous reversible dynamics. Then, the Schrödinger equation is just the derivative form of continuous evolution under a one-parameter unitary group.

]]>To me an important way to subdivide them is about what is thought to happen AFTER the apparent collapse of the wave function. In one group of interpretations the probabilities are about which of a number of possibilities somehow becomes promoted to reality. In that general approach, when one of them does, the other possibilities become irrelevant.

But in the second group, the possibilities all still exist somewhere. Of this group, the MWI was perhaps the founder member, and it inspired a lot of later similar ideas. To me the second group exists because the common sense first approach was difficult to interpret, and what was worse, it seemed to suggest the link with consciousness.

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