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For all matter to have been occupying the same point in space, this would violate the Pauli exclusion principle. Since fermions cannot occupy the same quantum state, the particles that are now fermions could not have been fermions at the point in the evolution of the universe where all particles occupied the same quantum state.

But, as I understand it, this would not be a problem for bosons. Bosons can basically superimpose upon each other, infinitely.

So my question is, if the Pauli exclusion principle was constant, then wouldn't it stand to reason that all particles that are now fermions started out as bosons, and that the very first symmetry breaking event, in fact the catalyst to the evolving quantum reaction that this universe is, was the spontaneous differentiation of "non-stackable" particles with odd half-integer spin out of the set of particles that have integer spin? Did bosons come first, begining the universe in a state of bosons that were perfectly symmetrical in time and space and all quantum numbers, and then the big bang was the shift in spin of a large percentage of those bosons, a shift in spin that caused those, now fermions, to be, in a way, "out-of-phase," with the whole-integer bosons? And this phase differential was the ever-evolving niche that determined the survivability conditions for the different species of particle that would survive the annihilations that would have to take place for any sort of universe to come into exostence and evolve? And since fermions cannot occupy the same quantum state, was the force that excludes this the energy source of the unfathomable, exponential inflation of the universe?

Let me try to whittle my question down again. I'm very sorry for my illeteracy in being able to ask my questions succinctly.

Does the big bang and the subsequent inflation fit into an "oil-and-water" model of our universe, with bosons being the water, and suddenly, some of those bosons breaking symmetry and becoming oil (fermions in this model), and that "fermionic oil" blasting and fragmenting away from each other because of their "hydrophobia-like-repulsion" of each other (Pauli exclusion)?

I'm not asking if this is a valid technical explanation, but if it is a valid mental model, that coincides with what we know about how the early universe was.

I appreciate your understanding and patience. I know my way of communicating is clunky and awkward.

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  • $\begingroup$ Related: en.wikipedia.org/wiki/X_and_Y_bosons $\endgroup$
    – PM 2Ring
    Apr 16 at 14:42
  • $\begingroup$ There are no particles to begin with. There are only quanta of energy. What the Pauli exclusion principle says is that one can not have two identical fermionic states, but that describes spatially extended states, which mostly applies to bound states which the universe is not. One can have an arbitrary number of fermionic quanta with different momenta occupying the same spatial volume. I think this is, again, just a poor mental model for quantum mechanics reeking havoc. $\endgroup$
    – FlatterMann
    May 25 at 20:49
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    $\begingroup$ @FlatterMann Please stop posting answers in comments. $\endgroup$
    – PM 2Ring
    May 26 at 5:08

2 Answers 2

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A particle's quantum state is described by its position and momentum together. In the early universe, particles were very tightly packed in space, but they were very spread out in momentum! Thus, no large occupation numbers are required.

In fact, as the universe expands, distances between particles scale as $a$ while (peculiar) momenta scale as $1/a$, where $a$ is the cosmic expansion factor. Thus their product is constant, implying that a system's density in position-momentum phase space is conserved.

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  • $\begingroup$ "tightly packed in space, but very spread out in momentum." Please help me understand this point, as it is not intuitive to me, but I feel like it may be critical to something I am not understanding. $\endgroup$
    – blacktopshaman
    May 28 at 14:26
  • $\begingroup$ @blacktopshaman The expansion rate was much higher in the past, so particles were moving away from each other much faster. If you consider two neighboring particles, in the early universe their spatial separation was much lower but their momentum difference was much higher. $\endgroup$
    – Sten
    May 29 at 12:31
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You have made a fundamental mistake in your argument.

The big bang did not happen at the "same point", it happened everywhere. Therefore the Pauli exclusion principle does not apply.

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    $\begingroup$ Maybe at the time of the big bang "Everywhere" was all at one point. $\endgroup$
    – Bill Alsept
    May 26 at 1:00

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