## Is there any reason the Universe must have a wave function?

I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me? Super newb btw.

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 Quote by C Rob I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me? Super newb btw.
Hawking popularized the phrase "the wave function of the universe".
What was usually meant was merely a quantum wavefunction for the SCALEFACTOR or roughly speaking the size of the universe.
I don't know what you and your fellow debater mean by the phrase. How to answer would depend on what you mean by it.

In cosmology there is a quantity called the scalefactor which intuitively is the average distance between galaxies. The symbol is a(t). The function a(t) is increasing with time.

a(t) is not the size of the universe, nor is it the size of the observable universe---we don't know what the size of the universe is, it might not even be well-defined, it might be infinite. So a(t) is just CALLED the size of the universe in popular books.
a(t) is well-defined mathematically in the context of the Friedmann metric and the Friedmann equations tell you how it evolves with time.

Naturally you can QUANTIZE the Friedmann equation and then instead of a normalized classical length observable a(t) you get a wavefunction describing our information about that length.

It is very modest and low-key. That is what Hawking and buddies usually meant when they wrote about "the wave function of the universe". No big deal. Not grandiose at all.
The actual reality of it is plain and simple. Universe expanding means the scalefactor is increasing and we have a wavefunction for that.

The quantum wavefunction version works a little bit better than the classical version when you get back near the big bang and want to push on to before the big bang.

Nowadays, the quantum cosmology people like Ashtekar and Bojowald do not talk about
"the wave function of the universe" because it sounds self-important and it's misleading. They talk about the wavefunction of the scalefactor, or the wavefunction of the inverse scalefactor. Sounds more dry and technical. Basically the same thing with less hype.

 Recognitions: Science Advisor As often the case, people have different usage for the word. The simplest concept for the "wavefunction of the universe" is the idea that you take the normal wave function of a particle, and then add every particle in the universe to it, probably in some uber complicated superposition. Presto, wave function of the universe. Obviously the states lives in a Hilbert space that is huge, poorly understood and probably illdefined mathematically. In some sense something like it is probably trivially true, but not particularly informative as it doesnt really tell you anything. The above version is often truncated down to something that fits into a cosmological model, like the FRW metric. Obviously in this new context we are talking about tiny portions of the 'wave function of the universe', but this too is sometimes called 'the wave function of the universe'. Slightly different but related in principle is the wave functional defined in the Wheeler De Witt equation, which encodes all the information about matter, geometry and field configurations over *the* spacetime of the universe (whatever that is). The hamiltonian constraint annihilates this wave functional in this picture. This is a slightly more interesting, and arguably deeper concept and relates to recent work Hawking and others did, and is amongst the foundations of quantum gravity. Yet another version relates to the Many World interpretation of QM, about which I don't know much about. You should come away with the feeling that these concepts are vague and have a good likelihood of being theoretical fictions. We are very far away from concrete statements about testable or observable parts of nature.

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## Is there any reason the Universe must have a wave function?

A mathematical artifact, IMO. How big would the detector need to be? It's the sort of thing physicist probably joke about at the local pub.

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 Quote by C Rob I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me? Super newb btw.
If QM is the fundamental theory describing everything, then Universe must have a wave function.
If QM is not so universal theory but applicable only as an effective description of micro phenomena, then the wave function of the Universe is meaningless.

Personally, I think the former is the correct view.

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 Quote by Demystifier If QM is the fundamental theory ... then Universe must have a wave function. If QM is not so universal theory ... then the wave function of the Universe is meaningless. ...
Demy,
how about a third possibility. The QM setup involves a system, and an observer outside the system who can make observations. QM accurately describes what the observer can know. The wave function represents the observer's information.

But this setup doesn't work with the universe.

The logical difficulty with supposing a quantum state of the universe is that the universe is all-inclusive. There is no room for a classical outside observer. Because any wanna-be observer is just another piece of the universe.

QM is not about Nature it is about what we can say about Nature, according to the ancient Bohrish wisdom.

And traditionally the observer who is saying things is supposed to be outside of the box.

James Hartle (among others) has thought about this and other fundamental difficulties with defining a quantum state of the universe, I believe, and has concluded that some modification of QM is needed to handle the problem. You may have read what Hartle has proposed, or perhaps you have some ideas of your own.

Personally I don't take a position on this. In the research that I'm familiar with, the wavefunction of the universe is simply the quantum state of the SIZE, which you need to run a quantum model of the big bang which goes back in time to before the big bang---quantizing the Friedmann equation of cosmology. In that sense, it is routine for people to plot the wavefunction of the size and calculate with it.

 An isolated physical system will have a wavefunction. So particle-in-a-box has a wavefunction. Now make it two-particles-in-a-box. The wavefunction of that system is distinct from that of the first system. Same goes for many-particles-a-box; distinct wavefunction from that of the previous two systems. Now let our isolated system be the universe. Therefore, by the same reasoning, the universe has a wavefunction. Disclaimer: I feel that decoherence makes the above argument invalid for macroscopic systems. Maybe someone else can shed some more light on this.

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 Quote by C Rob I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me?
That depends on whether you think quantum mechanics is applicable to the universe or not.

 Recognitions: Science Advisor There are many proposals to get semi tractable notions of a 'wave function of the universe'. In fact most of quantum cosmology research is about that question in one guise or the other (for instance common calculations are done in mini superspace +wkb approximations + choice of boundary conditions). Alas the state of the art is far from satisfying. People are very far from a realistic calculation.
 "The logical difficulty with supposing a quantum state of the universe is that the universe is all-inclusive. There is no room for a classical outside observer. Because any wanna-be observer is just another piece of the universe"-Marcus So....we don't know if the universe has a wave function. Assuming it does, since it's in a definite state, the wave has been narrowed, right? An observer(or interaction) is necessary. Marcus is this why you don't like it, because it implies an observer(God)? I'm am not versed in physics, so please don't destroy me too thoroughly.

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 Quote by C Rob "The logical difficulty with supposing a quantum state of the universe is that the universe is all-inclusive. There is no room for a classical outside observer. Because any wanna-be observer is just another piece of the universe"-Marcus So....we don't know if the universe has a wave function. Assuming it does, since it's in a definite state, the wave has been narrowed, right? An observer(or interaction) is necessary. Marcus is this why you don't like it, because it implies an observer(God)? I'm am not versed in physics, so please don't destroy me too thoroughly.
why should I want to scold you? and on what grounds?
I dont study up on questions like this.
As I said in my first post#2, I think, the research I read just deals with a wave function for the SIZE (or a scalefactor that plays the role of the size)
nobody I'm aware of worries about some kind of all-describing wavefunction

Jim Hartle would be the closest---I mean of people who are still active in research. Maybe the others know some besides.

Unless you can construct the quantum state and calculate with it, I don't see the point.
But you are welcome to speculate as far as I'm concerned. (might be more appropriate in philosophy forum if it is not an empirical line of thought you are pursuing however)

 Recognitions: Science Advisor The holy grail of quantum cosmology is in fact to find such a beast in the full superspace, and uniquely pick out the initial conditions and the boundary conditions. But it probably won't happen until a full microscopic description exists of quantum gravity. So people are content with doing various surgeries and approximations to the full wavefunction to get some sort of analytic control (see the no boundary proposal by Hawkings et al, or the tunneling universe by Vilenkin). Those two are probably the most intensely studied ones in recent years.

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 Quote by vanesch That depends on whether you think quantum mechanics is applicable to the universe or not.
The standard position in cosmology today is that quantum fluctuations early in the universe produced the clusters of galaxies which we see in pictures from Hubble and other telescopes. Many cosmology books mention this, but not all books mention the interpretational difficulties that this entails. For example a superposition of fields seems to lead, via Einstein's GR equation, to a superposition of spacetime geometries.

My paragraph on decoherence is probably too short or just plain wrong. Elaborations and corrections are most welcome, as are answers to chronnox's questions. I have been meaning to read Schlosser's Reviews of Modern Physics paper

http://arxiv.org/abs/quant-ph/0312059

on decoherence, but I have not gotten around to it.

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