# Q & A: age of universe

Most recent answer: 10/22/2007
Q:
we were taught that only 90 half lives of anything, a gram, a ton, a planet, would be reduce to an atom. In other words, cutting something down a half at a time, only 90 cuts would be necessary to arrive at the atom level. If this is true, and if the half life of a proton is about 10^30 power years, then would’nt IT be true that multiplying 10^30 years times 90 half-lives would be the possible life span of the universe, assuming matter doesn’t regenerate itself. Thanks ..DON
- DON (age 51)
NUCLEAR POWER PLANT, SOUTH NEW JERSEY
A:
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)