w
ould be a plasma. Furthermore, since particle number is not conserved in relativistic collisions,
particles and their antiparticles can be produced and destroyed. So for example, while it seems that
in the universe today, there are a lot more electrons than there were positrons, long ago when the
universe was less than a millionth its current size, there almost as many positrons as electrons. The
small excess of electrons that eventually became the electrons in our atoms was quite unimportant
at early times. For the same reason, at even earlier times, there was a lot of other stuff around in
the early moments of the universe that we don’t see much of today — heavy unstable particles
which today we can make only at large accelerator laboratories and which quickly decay back
into ordinary stuff were as common in the very early universe as electrons. These heavy particles
disappear when the universe cools to a temperature such that the typical particle energy is below
their mass. It is all quite strange — but simple, in a funny way, because everything is more or less
fixed just by the temperature.
Now why would anyone believe this? We cannot, after all, go back and do experiments on the
early universe. Why is this discussion science? The answer is that we can almost see it! At least we
can look back toward the beginning of the universe by looking far away in the universe, because the
light from far away regions of the universe has taken a long time to get to us. But we can’t look back
all the way. Once the universe gets so hot that atoms dissociate into ions, photons cannot go very
far without colliding with electrons — the universe becomes opaque. Thinking about this in the
other direction is even more interesting. As the universe cools to below the temperature at which
atoms dissociate (a few thousand degrees C), it becomes transparent to photons, which means
that photons fall out of thermal equilibrium. From then on, most of the photons just move freely,
never colliding with anything again. This “gas” of photons continues to behave like relativistic
stuff, while the atoms are nonrelativistic. Thus as the universe continues to expand, the energy
density in the photons gets less and less important to the overall Hubble evolution, but the photons
are still there, getting more and more red shifted as time goes on. This gas of photons from the
formation of atoms, a few hundred thousand years after the big bang, is the Cosmic Microwave
Background Radiation (CMBR). A tiny fraction of these photons hit the earth and can be detected.
Much of what we actually know about the early universe comes from studies of the CMBR. The
first obvious thing to do is to measure the temperature, which turns out to be about 2.7
◦
C, which is
about 1000 times smaller than the temperature at which atoms come apart into ions. This means,
since photon temperature and energy is inversely proportional to a, means that the universe today
is about 1000 times bigger today than it was when atoms first formed. There is actually much more
to this statement than meets the eye. It is an important prediction of the hot big bang model that
CMBR looks like it has a temperature at all. The reason it does, even though the photons are no
longer colliding very much, and are not in thermal equilibrium, is that the random distribution of
photon energies that was present when the universe first became transparent is still there — just all
the energies have been scaled down. This prediction has been confirmed by looking at the CMBR
in many different regions of photon energy, and checking that the distribution of energies is what
one would expect in a thermal distribution.
We cannot directly see the universe at scales smaller than 1/1000 the current scale. However,
we can use the tools we have discussed to follow the universe back to small sizes and higher
temperatures and energies. We can go back about a factor of a trillion (10
12
) before we get to
such high energies that have not directly seen the physics in laboratory experiments, so we are
reasonably confident that we have the picture right back that far. And there are some observable
consequences. For example, most of the nuclei of light elements (deuterium, helium, etc) were
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