I get email: How could everything be packed into an infinitesmal universe?

A few days ago, I posted my first io9 column in quite a while, and it seems like there was substantial pent-up demand to ask a real, live physicist questions about the universe. I apologize for my neglect. While the regular column will ramp-up again, I figured I’d do a few quickies here on the blog.

I got a very interesting query from a very nice Canadian named Lawrie posed the following question:

If the universe did indeed begin from a big bang, that would mean all the mass and energy we now see was concentrated in a tiny area. Let’s leave aside the idea of a geometric point. Even after that starting point, and for some measurable period of time, the universe was still tiny. I understand subatomic particles are small. But presumably they have some dimension. So how could such a huge number fit in so small a space? I would have thought there must be some physical limit to the amount of space a given number of particles can be crammed into?

So first off, kudos to her for not trying to figure out what’s going on when the universe was a literal point. After all, at some point, the energy density was so dense that gravity was strong enough to make the entire horizon scale of the universe seem like a black hole. At that point, quantum mechanics and general relativity were in severe conflict and we simply don’t know how to do deal with it. So we don’t (at least not yet), and instead start the clock at around 10^{-44} seconds afterwards, the so-called Planck time (though I would love to hear a well-posed question about what we do know about the Planck time).

But here’s where we bump up against your first misconception: particles literally are a pointlike. The only thing that prevents us from confining a particle to infinitely small space is quantum mechanics and the Heisenberg Uncertainty Principle. Confining a particle to a tiny box (if you want to think of it that way) gives it a huge uncertainty in momentum, essentially guaranteeing that they have a huge energy — which is kind of what happens. The energy of the individual particles in the very early universe (photons, really) are tremendously energetic (aka hot).

What’s more, photons really can overlap. That is, in fact, how a laser works — you have a bunch of photons at the same energy in the same place moving in the same direction. Photons, and other bosons (integer spin particles) are statistically _more_ likely to be in the same place than otherwise.

Fermions (like electrons, quarks and protons), on the other hand, obey the Pauli Exclusion Principle which means that they can only be packed so tight. However, there are two escape hatches: One is that the electrons in the very early universe were massless (no massive Higgs field yet) and so energetic electrons (and quarks) could occupy lots of possible energy states, and thus could be packed quite tightly. Two is that electrons and positrons could be shoved close enough together to make a photon-photon pair, which again, can be packed arbitrarily tight.

But as to why Fermions behave the way that they do and Bosons behave that they do, that’s a question for another day. But sufficed to say, it involves symmetry.

-Dave

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