I want to discuss the anthropic principle in more detail. It might
seem in contradiction with the Copernican principle, which says that
we are typical observers. The anthropic principle says that we aren't
completely typical because we are in a time and place that life would
arise. Otherwise we wouldn't be here. For instance, if you chose a
point in the Universe at total random, it would be very unlikely to be
as close to a star as we are. However, it is not unlikely or
surprising that we are close to a star because life would have to
arise close to a star. In other ways, you can explain why we are at
the time and place we are on the grounds that life would be more
likely to arise at our time and place. For instance, if the Universe
will exist for infinite length of time into the future, then isn't it
surprising that we are only 13.7 billion years after the Big Bang
instead of a googol, 10^100 years, or a googolplex years? Not really,
because there is a window of time in the history of the Universe in
which life is possible. Life requires heavy elements that are made in
stars. Therefore, life could only arise after the first generation of
stars have gone supernova, and distributed the heavy elements into the
interstellar medium. If supernova are rare events in the Universe, you
might think it would be surprising if one occurred near us shortly
before the formation of the Solar System, but actually, that would not
be surprising since it would make it more likely that we would be
here. Similarly, in the deep future, all the stars will burn out,
leaving white dwarves, neutron stars, and black holes. There won't be
enough material to form new stars. According to thermodynamics, all
matter will eventually end up in giant black holes, which will
eventually evaporate. Eventually, the last protons will decay, and
baryonic matter will no longer exist. Life will be impossible in such
a universe. Life is only possible during a window in cosmological
history, when you have second generation stars like the Sun. It is
therefore hardly surprising that we are located at the time we are in
the history of the Universe.

You can use the anthropic principle to explain the cosmic coincidence
problem, which is why are we located at the time when the matter
density and vacuum density are of the same order of magnitude when
usually they are not. Life would arise after matter-domination so that
matter can self-gravitate into stars. The matter density has to be
dense enough that stars are likely to form. Like I said, it has to be
after the first generation of stars so there will be heavy elements
necessary for life. At the same time, life is unlikely to arise in a
universe dominated by vacuum energy. If the vacuum energy density is
too much larger than the matter density, the gravitational attraction
can't overcome the enormous repulsive effect of the vacuum, and it's
unlikely matter can collapse gravitationally to form stars. Therefore,
life will be most likely to arise when the matter density is
comparable to the vacuum energy density, which is when we are now. The
anthropic principle is actually important in our current view of the
Universe, which is M-theory. The most advanced physics is M-theory,
and we have recently expanded M-theory to allow for de Sitter space,
so you can then combine M-theory with inflationary cosmology. There
are an infinite number of points in the moduli space of M-theory, not
just the five superstring theories, which do not correspond to the
real Universe. The real Universe corresponds to an unknown point in
the non-perturbative regime of M-theory that is consistent with a
de-Sitter-like universe.

Now imagine that you have inflationary cosmology. You have chaotic
inflation. Some parts of the universe undergo rapid inflation, like
shortly after our Big Bang, and other parts have a more leisurely
expansion, like we're experiencing now. These different parts are not
casually connected. Now these different parts of the universe end up
with different types of vacuum, which correspond to different points
in the moduli space of M-theory. Therefore, all possible points in the
moduli space of M-theory are realized somewhere in the universe. You
could call these disconnected parts of the universe, different
universes. Most of these will give rise to universes where life is not
possible. We are in one of the few universes within which life is
possible. That explains why we are in the universe that we are in,
even if it might seem unlikely. Even if it seems that there are
unlikely things that are necessary for life to be possible, obviously
we are going to be in a universe that has those apparently unlikely
things, as opposed to a universe that doesn't. Therefore, if you
combine M-theory, inflationary cosmology, and the anthropic principle,
you get our view of the Universe. The anthropic principle is probably
true and necessary. Despite that, many cosmologists shy away from the
anthropic principle, or at least stating it explicitly, because many
people misuse it, or try to use it to explain anything we can't
explain. The anthropic principle can't be used to explain everything.

When we observed the redshift of the galaxies, you could have
explained that by saying we were located at the center of the
Universe. We did not say that because that would violate the
Copernican principle. The anthropic principle does not offer any way
around the Copernican principle in this case because there is no
reason why life would be more likely to arise at the center of the
Universe. Some people have also used the phrase anthropic principle to
mean that the presence of life on Earth is itself a piece of
experimental data that you can take into account when building your
theories. Just as you observe data from telescopes and particle
accelerators, you can observe that life exists on Earth. In the 19th
Century, Lord Kelvin advocated that the Earth was 10sup7/sup years
old, based on its cooling time, Evolutionary biologists were able to
argue that this was not enough time for all species to evolve. They
were using the observation of life on Earth to disprove an estimate
for the age of the Earth. Their claim was vindicated by the discovery
of radioactivity which allowed both the dating of the Earth, and
showed the flaw in Kelvin's argument. This was an important
astronomical argument being drawn from the observation of life on
Earth.

The synthesis of the higher elements is rather difficult due to the
nonexistence of stable elements with atomic weights A = 5 or A = 8.
This makes it hard to build up nuclei by collisions of sup1/supH,
sup2/supD, sup3/supHe, and sup4/supHe nuclei. The only way
reason that heavier elements are produced at all is because of the
reaction

3^4He - ^12C

A three body process like this will only proceed at a reasonable rate
if the cross section for the process is resonant, if there is an
excited energy level of the carbon nucleus that matches the typical
energy of three alpha particles in a stellar interior. The lack of
such a level would lead to a negligible production of heavy elements,
and no carbon-based life. Recognizing this, Hoyle predicted that
carbon would display such a resonance, which was later found. Now, in
some ways this is like Lord Kelvin and the age of the Earth, where the
observation of life on Earth leads to a conclusion, in this case, that
there must exist such a resonance. Still, there is a feeling that we
are lucky that there is such a resonance since otherwise we wouldn't
be here. Maybe we are lucky. Maybe there is a large number of
universe, called an ensemble, or a large number of parts of the
universe, and we are in one of the few that have such a resonance. If
that's true, it would hardly be surprising that we would be located in
one of the few universes or parts of the universe that have such a
resonance.

Here's another example. We have three generations of fermions. Each
has two quarks, one with a charge of 2/3, and one with a charge of
-1/3. With the second and third generations, the quark with a charge
of 2/3 is heavier than the quark with a charge of -1/3. In the first
generation, the quark with a charge of -1/3, the down quark, is
heavier than the quark with a charge of 2/3, the up quark. For that
reason, a lone proton is stable, and a lone neutron is unstable. Let's
say instead, in the first generation, the 2/3 quark was heavier than
the -1/3 quark, like in the other two generations. Then a lone neutron
would be stable, and a lone proton would be unstable. Then in the
early universe, all the lone protons would decay, and the lone
neutrons would not. You could still have some atoms form with nuclei
that contain protons and neutrons in a bound state. However, if free
protons decay in a few minutes, there will be very little hydrogen in
the Universe. There would no stars, and no life in the universe. Life
would be impossible. Now what does this tell us? The masses of the
fermions are derived from interaction with the Higgs field, although
we can't calculate the values of the masses. You could imagine that in
different parts of the universe, the Higgs field is different, which
causes the values of the masses of the fermions to be different. Maybe
in most parts of the universe that have three generations of quarks
and leptons similar to ours, the up quark is heavier than the down
quark, and thus have no life. It would not be surprising that we are
in a part of the universe, or a universe, in which life is possible,
even if life is not possible on most parts of the universe, or most
universes.

Paul Dirac noticed the existence of large dimensionless numbers in
physics, which is called Dirac's large number hypothesis. Today, we
can explain it with anthropic arguments, such as pointing out that
life could not have arisen until heavy elements were produced in first
generation stars. Lastly, I just want to say that there are tons of
crackpots who know nothing about physics, but invoke the name
anthropic principle, but they are referring not to the real anthropic
principle, but instead to a garbled misunderstanding of it which I
won't dignify by repeating here. This might be part of the reason why
some in the physics community shy away from it. However, the anthropic
principle is probably true as far as it goes. It's probably necessary
to explain some aspects of what we observe of the Universe.