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Does universal wave function exist?

What the science tells us?

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I'm not sure why you're being downvoted, because it's actually a good question (perhaps a little short, but nevertheless important). A wavefunction is inherently multi-particle. I had a professor once who got this wrong and said that the single-particle wavefunction was more fundamental, but in reality, effects such as quantum entanglement can only be explained by multi-particle wavefunctions. These also account for electron-electron correlation, something that is left out of many quantum chemistry calculations at the expense of accuracy. – Nick Mar 17 '13 at 3:48
"A wavefunction is inherently multiparticle" is certainly not a correct statement. Only in relativistic theory, when the particle number is not fixed, would this be true. Hilbert space isomorphisms aside, what "the wavefunction" represents is very different for different physical systems. It is a solution to a differential equation; the differential equation contains the physics, and is the fundamental concept. – levitopher Mar 17 '13 at 3:56
Huh? If I have a wavefunction for helium, it needs to be a function of 2 electrons and 2 protons. Ψ ≠ ψ(x1)ψ(x2)ψ(x3)ψ(x4); you can't separate it like that. – Nick Mar 17 '13 at 4:02
@Nick we seem to have people lurking in the background who downvote capriciously and without comment for no good (physics) reason these days ...Obviously one has to live with this ... – Dilaton Mar 17 '13 at 8:31
@Nick I'd hazard a guess that it's being downvoted because it's not really clear. Anixx, could you elaborate your question? It's rather broad/unclear at the moment. – Manishearth Mar 17 '13 at 9:05

Wavefunctions live on configuration spaces. A configuration space is (not surprisingly) the space of configurations of the system in question. In elementary quantum mechanics with several particles, it's the space of configurations of those particles.

In a more field theoretic scenario, the functional Schroedinger picture, you have wavefunctions (strictly wavefunction als) on the configuration space of classical fields.

So the meaning of a wavefunction depends on the elements in your model (particles in QM, classical fields in field theory). I guess by "universal wavefunction" you mean a wavefunction which describes everything in the universe? If the principles of quantum mechanics are correct and universal, then once you have identified the ingredients of a theory of everything, then there will be a wavefunction to describe its quantum mechanical states.

A note of caution: when you hear people (e.g. Hartle and Hawking) refer to "the wave function of the universe", they're not referring to this ultimate entity, but rather to a wavefunction which describes the large scale structure of a highly symmetric model of the universe. Their configuration space is minisuperspace, and their wavefunction usually refers to just the allowed values of a single parameter!

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Reading the question, I immediadely thought about the Hartle-Hawking wave function :-). Maybe you can extend this point a bit? However, I already like and +1ed your answer. – Dilaton Mar 17 '13 at 8:15
@Dilaton I got the slight impression that Anixx was asking about something more general than the HH wavefunction, so I kept it very general. A description of the HH argument would be a different question, and it may already exist here somewhere (?) – twistor59 Mar 17 '13 at 9:31
I have just searched for hartle-hawking, but there seems to be no question directly asking for a more general description of it ... – Dilaton Mar 17 '13 at 9:51

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