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I have heard couple of times about the concept of wave function of the universe, an object that would capture every degrees of freedom inside it (every particle, me, even you dear reader, etc...) and it always sounded fallacious or at least non pertinent, what would be the point of using that gigantic object to describe our universe. From my first classes of statistical mechanics, I learned that there is no point in trying to monitor $10^{23}$ and more degrees of freedom, that we need to look for emergent pertinent quantities (pressure, temperature, etc...). Even more, I am know reading an article where the author (there is no point in giving you the title/name) takes the example of a local QFT completely describing the Solar system, so roughly $10^{60}$ degrees of freedom, plus the possibility that an observer could be monitoring all those in real time, which is totally unrealistic. Does this make sense to you?

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Yes, it is a logically positivistically meaningless notion, so in an absolute sense it is complete bullshit--- you can't measure the wavefunction of the universe, nor give a sense to the idea that it is A and not B when the overlap of A and B is nonzero. But it is useful bullshit, as a figure of speech, used as a conceptual aid, to get you to understand how the Everett interpretation works, how cosmology can give a complete description, how the dynamics of vacuum selection could be working, and how a nonsymmetric universe can emerge from a symmetric initial conditions. The point is that it is an imprecise but good crutch for the intuition, like the idea of an infinitesimal quantity in mathematics, or the idea of negative coupling phi-4 theory in quantum field theory, or a bazillion other things which have precise analogs, but don't need precise analogs to be useful as figures of speech.

Here is a question which is clarified by considering the wavefunction of the universe. Suppose the laws of physics are rotationally invariant, and the universe started out completely rotationally symmetric. Would we observe a symmetric state?

The answer is no, because the wavefunction of the universe would be in a superposition of states which would be symmetric, but no observer's perception would be symmetric. Now to make this precise, you could go to an observer's point of view, and consider the universe relative to this observer, and see that it is not symmetric. Or you could say that you collapsed the wavefunction of the universe by looking around, or whatever you prefer. The end result is talking about sense-impressions, but the philosophical crutch allows you to understand that this does not require a breaking of symmetry in any fundamental law or initial condition.

The wavefunction of the universe is also used to give predictions on the likelihood of different states in quantum gravity. Here the point is to make sure that we are not making models whose a-priori probability is too low to be plausible. In this context, the wavefunction of the universe is a useful figure of speech.

It is not a mistake to use positivistically unverifiable notions, so long as you always know how to translate this into sense impressions at the end, so that you eliminate the metaphysical looking things.

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