It's not quite true that exactly 90 half-lives is enough to eliminate
anything. The exact number depends on how much you start with. Still we
can follow out your question, which makes good sense. If you wait some
100 proton half-lives, then there won't be any protons left in the
galaxy. That's not the end of the universe but it certainly would be
the end of matter as we know it. I believe that half-lives as short as
10^30 years for the proton have been ruled out experimentally, but even
if the real number turns out to be say 10^35 years, the idea still
holds. Not to worry- things around here would be pretty messed up by
then anyway.
Mike W.
You'd not have to wait even that long! Imagine only having half the
protons around -- that'd only be one lifetime. The current experimental
limits from the Particle Data Group put the lifetime of a proton at
longer than 2.1x10^29 years for the most difficult decay mode to detect
(a proton just "disappears experimentally -- well, its charge has to go
somewhere, and this is arranged by a charge-exchange interaction inside
a nucleus -- a neutron turns into a proton and some neutral objects are
emitted."). Most plausible decay modes, which involve the emission of
charged objects which have some kinetic energy are easier to detect and
limits are of the order 10^33 years for some of these. We believe that
"baryon number", that is, the number of particles composed of three
quarks, minus the number of corresponding antiparticles, is constant,
in nearly all interactions. Of course this cannot be true forever, as
all the protons and neutrons in the universe had to come from
somewhere, and the Big Bang is hypothesized to be initially balanced
between matter and antimatter -- tiny difference between matter and
antimatter reactions are necessary for the asymmetry between protons
and antiprotons we see now. But these reactions, you can imagine, might
run in reverse. But you need very high energies to do that, and in the
available energies around, baryon number seems to be conserved and
protons do not decay.
Some "grand unified theories" which unify the strong and
electroweak forces, do in fact predict finite proton lifetimes, which
is why people try so hard to detect proton decay. So far there's no
evidence for proton decay, but it could be lurking there at such a low
rate we cannot yet detect it.
I'm not an expert on this (the field has advanced in even the last
few years), but black holes don't seem to respect baryon number
conservation -- they "forget" how many protons you threw into them, and
know only about total charge, energy, and angular momentum. Black holes
subsequently evaporate by Hawking radiation, creating all kinds of
particles, but mostly photons (I suppose there would be some baryons in
there too). Some models exist where black holes can be responsible for
baryon creation, but I don't find them hugely plausible. This would be
one way the universe could "regenerate" the decayed protons. On a grand
scale, if the universe were to recollapse (endure a "Big Crunch") and
explode again in another Big Bang, we'd get to play the whole game over
again, but experimental evidence seems to be pointing away from this
possibility and towards an accelerating expansion. In any event, it
looks as if the universe is going to be a cold place with big distances
between clumps of matter long before the protons give out (if ever).
Tom
(published on 10/22/2007)
