Quantization of energy in the very early universe

If the early universe was finite would not there be cancellation of the wave functions of what is in it except at discrete frequencies where reinforcement occurs?

You do not need to postulate a finite universe, wave mechanics works on open (Lobachevsky) geometry.

If there was such canceling could not there have been some principle similar to the Pauli exclusion principle that excludes multiple particles from being in the same orbital. So isn't it possible that in the early universe there was only one particle and the universe expanded in jumps?

It is unlikely that an exclusion principle worked at that time. The energy was so high that particles could transform into other particles including going from fermions to bosons and back. The exclusion principle doesn’t work on bosons. There are other reasons for a lack of uncertainty principle but that will do for now.

Is it possible that in the current universe all particles exist in orbits that transit the whole universe and that the number of particles that can be in a given orbit is limited?

Only electrons and nucleons exist in “orbitals” free particles do not. Also particles like the weak particles have an ultra-short range so that range certainly does not “transit the whole universe”. Only bosons have an infinite range.

Did the early universe in some ways resemble an atom. Can a wave function be written for its state?

See next answer.

It seems that if I take Planks constant times the speed of light and divide by the total energy of the universe that I get a wavelength. What happens if the size of the universe is less than that length?

I don’t know what you are trying to do with your plank equation but you have one HUGE problem. The universe is mass-energy invariant. You seem to be stating that you are (or should be) able to write a Hamiltonian for the universe. Because of the invariance noted above this is impossible. All we can ever know are energy differences.

How do you deal with harmonics in four dimensions?

To deal with a harmonic in the fourth dimension you just (basically) add one to the super/sub scripts of your three dimensional metric tensor.

Is the cosmic reality fractal in nature escaping the cancellation while maintaining its finite size in the way a perimeter can be infinite even though the area it bounds is finite? Can this be the origins of anisotropy? As the universe gets very small could anisotropy be generated in the way that a wave function generates the appearance of a particle?

The fractal and anisotropy stuff and what you are trying to postulate I cannot make any sense out of. So I’ll pass.

If the energy of the universe is constant and I shrink it don't I violate the uncertainty principle at some point since I know its "location" must be in the universe and I know the energy? Conversely does the energy of the early universe become uncertain as the size of the universe shrinks?

Positioning the shrunken you “somewhere” in the universe is not knowing your location.

Total energy is total energy no matter the universe’s size. As I noted we have no way of writing the Hamiltonian for the universe so the question in moot. If we cannot know the total energy how do we determine the change?

Interesting stuff to think about but a lot of your statements, in my opinion, are well off the mark.

Thanks for the response. I suspected I was way off the mark. Would have bet on it actually.

I thought that a free particles in a finite universe would interfere with itself unless the distance around the universe was an integer number of wavelengths? How do you construct a non-interfering wave on a closed universe? I thought the thing that caused interference was the topology of the path not the fact of the binding that caused it.

Thanks for the info on Pauli. I didn't know that.

Wald in his book General Relativity claims the there is no global conservation of energy. But that aside your comment on the need for an energy difference in order to write the Hamiltonian is interesting. Assuming the particle is not bound can I just use T=1/2 mv^2? That is not and energy difference and I thought that you could then get a plane wave from Schrod equation?

Also your comment on "not knowing your location". Does not a finite universe that is very small mean that everywhere in the universe is small distance from anywhere else? So if I say the particle is in the universe have I not bounded the uncertainty in its position? I know that on a 2 sphere the farthest you can get away from any point is half the circumfrence of a great circle. That works in higher dimensions to no?