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Comment by kevinventullo | Hacker News Reader

If the half-life is 10^22 years, doesn’t that mean after one year you’d expect a proportion of (0.5)^(10^-22) of the atoms to be the same? This is very close to 1-A^-1 where A is Avogadro’s number. I think this means that with a mol of this stuff, you’d expect about one atom to decay after a year.

If I have that right, it does seem mind blowing that they were able to detect it.

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Half-lives that long really begs the question to me - does every heavy nucleus (i.e. heavier than Iron-56) have a half-life? Does Gold-197 which is 'stable' actually just have a half-life of 10^50, or 10^100 years?

There are nuclides heavier than 56Fe, for which no decay mode is energetically allowed. 197Au is not one of them, because it could in principle do alpha decay. Wikipedia has a long list of theoretically stable nuclides (no decay mode possible), and observationally stable nuclides (at least one decay mode possible, but not observed): https://en.wikipedia.org/wiki/List_of_nuclides

Also, proton decay is a thing. At a certain point, if the proton is unstable, the half life of the nucleus is longer than the proton itself.

No, it isn't. According to the Standard Model, the proton is stable at every time scale. And no proton decay has ever been observed.

The Standard Model that is known to be, at best, incomplete?

Only in that it doesn't incorporate gravity. And given the extremely low energy scale of gravity, it's unlikely to make a difference here.

There are extensions to the Standard Model being used to search for dark matter, but until one of those is actually found experimentally, you can't say that it makes the Standard Model incomplete. It's sound within its domain -- aggravatingly so, since that makes it really hard to figure out what's next.

Proton decay may be a thing but it's not predicted by current models.

But similar to your example, neutron decay is a thing (a free neutron has a halflife of about 10 minutes), and yet many nuclei are stable for much longer.

Proton decay is predicted by many models -- it's the reason the first huge water-Cherenkov detectors were built. The surprising thing is that, for some reason, they've never been observed to decay.

If they can’t decay then time can’t stop.

The theory is that everything, even subatomic particles has a half life. But these are so long that we are not able to perceive them with present day technology. Eventually the whole universe will fall apart into degenerate matter and then much later even the remnants will decay. But such decay is happening all the time, just not fast enough to result in measurable effects (fortunately!).

Not true. neutrons decay within minutes, protons and electrons dont decay within SM

Also to nitpick - “half life” is not applicable to subatomic particles

Free neutrons do, but bound ones do not afaik, and electrons and protons do decay but we do not know how long it takes, but there is some lower bound. And yes, you're correct, I should not have used the term 'half life' because that implies a different kind of event. Lifetime would have been a better term to use.

Protons and electrons do not decay according to the Standard Model.

I'm familiar with the theory but: it's technically an open problem, isn't it? Whether it lives forever or has some average life-span or not. At least, that's what I got from reading about this. It is very well possible that I'm wildly out of date but from memory: there are some subtle problems with the present day theory that could be fixed but they would require for proton and electron decay to be possible. But all that has happened so far is that we've established a (very high) lower bound to how long these particles live, but there is no hard rule that says they can't decay, it's just that if they do (as in: we find experimental proof that they do) then the Standard Model will be ripe for an upgrade.

And that in turn might get us one step closer to a UFT.

In the standard model the (proton, electron) is the lightest particle charged under the global (baryon number, lepton number) conservation respectively. So they are truly stable according to the SM.

However, there are many good reasons to expect that physics beyond the standard model do not conserve B or L (or B-L, which is what's actually conserved in the SM). In those models one expects proton decays for sure.

However, even in those models, electric charge is conserved. Unless there are gauge-variant dynamics at very high energy electric charge will always be conserved and electrons (and positrons), being the lightest electrically charged particles, will be absolutely stable.

This is like a decay of the gaps argument :)

That's apt :)

At 10^22 years, where do we draw the line between what we consider stable and what is "radioactive" or "decays"? If the heat death theory of the universe is true, then isn't everything above iron eventually going to "decay"?

If proton decay is real, all atoms will eventually cease to exist, but it is still an open question. More than one experiments are still waiting for an event.

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