Would it be possible to come up with the Universe’s Wave-function 1 planck after the BB when the Universe was as large as a marble?
What about the wave function that set off the Big Bang in the first place?
Well, yeah, sure, you could calculate the wave function for the young universe. Study “deBroglie waves” to find out how.
But as far as the function that set off the BB, it isn’t accepted as understood what the situation was just before the BB (though an interesting theory on this is getting some good press just now).
Napier are you the sort of person that could calculate the wave function for the young universe? And do you have a cite for the pre-BB theory? I really want to read about it.
I think I’m the sort of person who could calculate the wave function for anything of known mass - I have a degree in Physics and studied this subject 25 years ago; I have forgotten exactly how but could look it up in a textbook. As I recall the basic principle is that the wavelength is proportional to Planck’s constant and inversely the mass. No question, the wavelength for something this massive would be so vanishingly small that it would be hard to find some physical significance (such as scattering or tunneling or interference) to it. But why do you want to calculate this?
A cite for recent pre-BB theories? It was either in the latest Scientific American, or in an issue of the Economist a few weeks ago with a big feature on cosmology, I think. If you give me a sufficiently motivating reason I will go scurrying around trying to find whatever it was I read.
But, again, why? This is really somewhat obscure stuff.
Is it possible that part of the universe’s probability density fell outside the universe. Could the universe have existed outside itself?
And don’t you calculate wave-functions based on momentum? How do you obtain data for the momentum of the universe, would this be the expansion momentum or is the universe moving through a metaverse?
Do wave-functions change in an isolated system like the universe? And if the universe’s wave-function is based on it’s expansion momentum how is it explained when the expansion is accelerating? Wouldn’t this mean that the wave-equation for the universe would have to have time in it… and this could inturn be inversed to say that the speed of time is changing not the expansion rate of the universe nor the momentum of the universe?
This has certainly been discussed: see Hartle and Hawking, *Phys.Rev * D28 (1983) 2960. No physicist will take this as the final answer, but most are likely to regard this as legiminate speculation.
I don’t know what about this thread interests me more: The questions being asked, or the fact that there is a good chance of them being addressed, if not answered, here.
Derleth, eagerly awaiting the arrival of the local physicists. 
A wave function describes a collection of experiments. The Universe is unique (AFAWK) and so any talk of a wave function of the Universe is pure speculation.
This is my professional opinion. Your physicist may differ.
If we were to talk of the BB in terms of QM nonetheless, we would need a density matrix, not a wavefunction. This is the description appropriate for systems at high temperature, or those interacting with other unknown systems. The density matrix of the Universe is easy to write down:
exp(-H/kT)/Tr(exp(-H/kT));
where k=Boltzmann constant, T=temperature of the Universe, and H= Hamiltonian of the Universe.
Of course, it’s that H that’s the tricky part. All of the stuff having to do with elementary particles can be handled just fine using the Standard Model. But what to use for the Hamiltonian for gravity? Until we have a real quantum theory of gravity, this part is a mystery.
What (astro)physicists do is to treat gravity non-quantum mechanically, and deal with the particle stuff quantum-mechanically. This is how you get predictions like the primordial abundance of Helium and Lithium, etc. The expansion of the Universe goes on according to General Relativity, ignoring any quantum effects.
The other stuff about pre-BB wave functions and creation of the Universe from a quantum fluctuation in nothingness I regard as futile speculation - how could it ever be tested? Destroy the Universe and see if another one arises? I’m not the only one: Howard Georgi (IIRC) called string theory “advanced recreational theology”, or something like that.
“Could the universe have existed outside itself?”
This depends on your definitions of several things and on the question of what’s beyond the edge of the universe, which in itself may well sound like more of a question than it really is because of the incorrect physical assumptions that are built into language. But if you are imagining some gigantically long wavelength probability function, you’re barking up the wrong tree - deBroglie waves get shorter for things that are more massive. Even for a penny, the wavelength is so unimaginably small as to have no physical significance for us.
“And don’t you calculate wave-functions based on momentum?”
What? No, no, the wave function is better thought of as an intrinsic property of the thing itself, not dependant on its observer. For a practical example (of which there are few in quantum mechanics), when the wave function of an electron spills sufficiently far over into the other side of a tunnel diode, the electron disappears and reappears on the other side of an impenetrable barrier, and it appears that the diode conducts a little bit. This is true no matter what distant being is observing the diode at an enormous relative velocity.
FriendRob check this out http://www.geocities.com/capecanaveral/hangar/6929/h_kaku2.html
Alright ignore the first question about the universe existing outside itself ( I just read that it would be all possible universes outside, how stupid of me :rolleyes: ).
But can anyone answer some of my other questions please, I can’t afford to buy Hawking’s book I am just a poor college student.
Moderator’s Note: Woo-hoo! It worked!
Note: A reply to this thread accidentally got put into its own thread, but I “merged” the two threads. Achernar’s post was on the orphaned thread; at the time, it made sense.
Well, most colleges have a big building with books that you can check out without buying them… it’s called a “library”… 
Kaku likes the speculative stuff - some of what he says on the site you pointed to is pretty far off, tho:
Well, there are infinitely many other universes, not mere “billions”, and so presumably infinitely many that have conditions similar to ours.
Here’s a site that has some more discussion of these things (especially near the bottom of the page):
http://dhushara.tripod.com/book/upd/umar99/cosinf/hyp2.htm
These are tough questions, and not easily summarized in a few short paragraphs!