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

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.

marcus

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.

Haelfix

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.

Chronos

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.

Demystifier

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.

marcus

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.

cmos

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.

vanesch

That depends on whether you think quantum mechanics is applicable to the universe or not.

Haelfix

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.

Fra

My choice of conceptual associations are along these lines.

Bohr's idea
- The wave function represents the observer's information.
- Information about what? - About the system!

If the systems is a box in a lab, this can be handled. But what if the box is the entire universe?

If we consider the idea of "the screen", then the screen is somehow the communication channel between observer and the unknown. Wether the outside is finite, or infinite is for the observer to try to figure out, if possible.

Do we even have to answer a priori what is on the other side of the screen? Isn't the whole point that that is part of this "information".

Lets say the wavefunction represents the information of one side of the screen, relative to the other side.

Then it seems the wavefunction of "the universe", relative to any choice of system/observer is different for each observer, and the world universe have no other meaning than the wavefunction of the observers environment (ie. what can be seen through "the screen"), and to me it's sound that there are no a priori structures here. These structures should be part of the information.

But like Rovelli argues in his relational QM, this doesn't prevent them from trying to communicate their views. And this very process results in a physical interaction. This means that due to the physical interactions, this subjectivity doesn't imply any inconsistencies no more than the stick and clock readings of different SR observers differ.

It seems the problems start when we presuppose universal a priori structure of the universe, on which we define the information.

So, when we ask what is the "wavefunction of the universe" what strikes me first is the preimposed structure implied in the world universe. How about instead asking what is the "wavefuncion" or "state of information" of an observer. And let the information itself, describe this "universe".

Something doesn't smell right to me, when one asks a seemingly innocent quesiton like what do you know about A. The structure implicit in A is hidden structure. Instead just ask "what do you know". (implicitly meaning about whatever you know anything about).

The observer seeing the world through the screen is IMO a nice abstraction here. The observer tries to make sense of whatever comes through the screen, without preconceptions about what's on the other side.

/Fredrik

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.

marcus

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)

Haelfix

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.

George Jones

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.

See the thread

http://www.physicsforums.com/showthread.php?t=246423

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.

marcus

Parts of the Schlosshauer paper were very helpful. It's a well written review---he was careful to be clear and accessible.

I see the point you emphasize here. If decoherence of a quantum state happens by interaction with the environment, and we consider the state of the whole shebang, then what is the environment?

Does a path integral, or sum over histories, approach sidestep such difficulties?

marcus

C Rob asked if the Universe must have one grand all-encompassing all-describing wavefunction. I think that's the drift. At first I wasn't sure what was meant (a lot of quantum cosmology deals with socalled minisuperspace models, reduced down to a few parameters---indeed classical cosmology focusses a lot on reduced models).

but I think here the issue is the necessity of one grand comprehensive quantum state.

Must there be one? Rovelli argues there need not be:
http://arxiv.org/abs/quant-ph/0604064
Relational EPR
Authors: Matteo Smerlak, Carlo Rovelli
Foundations of Physics 37 (2007) 427-445
(Submitted on 10 Apr 2006)

"We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of 'non-locality', when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality."

The quantum state (technically a vector in a Hilbertspace) represents an observer's information about the world. Experience has shown it is an excellent way of representing uncertainties as well as knowledge, and the difficulties of determining various things at once---the limitations of a real observer. So good.

Rovelli says there doesnt have to be a single unique overall correct state. He says let every real observer have his own separate Hilbertspace and his own current idea of what the state vector (wavefunction) is. And let the observer keep track of how that changes as he makes measurments and determines more about the world. then observers can consult and find out what facts they can agree on.

Fra brought this up in an earlier post. So anyway Rovelli's is one possible view.

I see this as a question in the foundations of quantum mechanics, or foundations in general.
I tend to agree with Rovelli. I don't think Hilbertspaces and wavefunctions are physically real. I think they are manmade devices for describing the behavior of information. Wavefunction QM is about the observer and his information. It doesn't have some ultimate objective reality like it's the ground of existence. So there doesnt have to be One Big wavefunction. But others certainly differ on that score.
==========================

The practical issue in quantum cosmology, I think, is not to solve foundational or interpretational problems once and for all, but something quite different. Namely to get a mathematical formalism that joins largescale General Relativity geometry with extreme geometry of high curvature, very small scale, very high density matter.

In other words the practical problem is to remove the singularities of General Relativity in an expanded framework and be able to smoothly relate largescale geometry to smallscale (probably chaotic fluctuating) quantum geometry. And to find matter in the picture.

So from my perspective about the most advanced effort in this direction currently is what Ambjorn and Loll discuss in their July 2008 SciAm article. The link is in my signature. That is one way that quantum cosmology could turn out looking----if they can work matter into the picture successfully.

the quantum average of all the fluctuationg geometies turns out to be a smooth classical one. And it is a model that you can compute with----get numbers out of----suggesting the possibility of eventually testing predictions.

I see an effective quantum cosmology taking shape there which does NOT require postulating the existence of some single Overall wavefunction. (at least I don't think it does, please let me know if you think a big overall quantum state is required by the Ambjorn Loll approach.)

Chronos

Sounds stringy to me, marcus.