# B Proton decay probability (Bayesian or frequentist?)

1. Sep 6, 2016

### cube137

If an event has probability occurring say 1/100000000000000000000000000000000 times.. if you do the experiment 100000000000000000000000000000000 times.. you are supposed to get the hit at least once? This is the proton decay experiment.. it's more than the above probability figure.. but if you use bayesian analysis instead of frequentist, could you really get that probability and is it really a frequentist thing?

2. Sep 6, 2016

No, and no.

3. Sep 6, 2016

### cube137

No.. what I meant was if the experiment has 100000000000000000000000000000000 protons. At least one must decay if GUT is right.. but does this really happen..

4. Sep 6, 2016

No.

5. Sep 6, 2016

### cube137

The following is typical proton decay experiment i read "Much rests on the existence of proton decay, and yet we’ve never seen a proton die. The reason may simply be that protons rarely decay, a hypothesis borne out by both experiment and theory. Experiments say the proton lifetime has to be greater than about 10^34 years: That’s a 1 followed by 34 zeroes."....... "Because of quantum physics, the time any given proton decays is random, so a tiny fraction will decay long before that 10^34-year lifetime. So, “what you need to do is to get a whole bunch of protons together,” he says. Increasing the number of protons increases the chance that one of them will decay while you’re watching."...

But is the technique sound.. by having so many protons at experiment.. could one of them really decay now? What if one of them decays thousands of years from now.. and not really now in spite of having so many protons in the experiment sample..

6. Sep 6, 2016

### Staff: Mentor

When you flip a coin, it has probability 1/2 of coming up "heads." Does that mean that if you flip the coin 2 times, you will get "heads" at least once?

When you flip two coins, must at least one of them come up "heads"?

7. Sep 7, 2016

### dlgoff

Where's the Like Like button?

8. Sep 7, 2016

### cube137

This may work for small numbers.. but for something on the level of 10^34 years and proton decay. Maybe probability fails and that's why we don't see any decays. Hm.

9. Sep 7, 2016

Staff Emeritus
If anyone needs an example on why PF shouldn't allow personal theories, this is it. Do you really want to argue that math is wrong?

10. Sep 7, 2016

### Staff: Mentor

We can actually make the probabilities come out the same for proton decay as for coin-tossing if we state the question the right way.

You probably know about the "half life" of a particle, right? That's the time for which the probability of decay is 1/2. After one half-life, half of a collection of particles has decayed, on the average.

When physicists talk about the "lifetime" of a particle, they usually mean the "mean lifetime" ($\tau$) of an exponential-decay distribution, which is related to the half-life ($t_{1/2}$) by $t_{1/2} = \tau \ln 2 \approx 0.69 \tau$.

After one mean lifetime, the decay probability is about 36.8%. Or: after one mean lifetime, about 36.8% of a collection of particles has decayed.

So if by "lifetime" you mean "half-life", the probabilities are exactly the same as with coin-flipping. If you have two particles, after one half-life the probablility is 25% that neither of them has decayed; 50% that exactly one of them has decayed; and 25% that both of them have decayed. After one "mean lifetime" the probabilties are 13.5%, 46.6%, and 39.9% (if I did the arithmetic correctly).

11. Sep 7, 2016

### Staff: Mentor

Many threads would be more interesting if we did this. "Let me help you state your question the right way." Thank you @jtbell

12. Sep 7, 2016

### Staff: Mentor

The conversion to a half-life in years is a purely mathematical thing - obviously we cannot run the experiment for 1034 years. It does not matter, because both theory and experiment make statements about a different quantity: the probability that a proton decays within a year, or similar relevant timescales. If we observe 4*1034 protons for a year and see no decay, we know that the probability for a proton to decay within a year is smaller than 10-34 - otherwise we should have seen a decay (or probably more than one). This can be compared to GUT predictions.

13. Sep 7, 2016

### Jehannum

That sounded good in the voice of Master Po from Kung Fu.

Sorry for being flippant.

14. Sep 7, 2016

### Avodyne

Here is how to do the calculation.

Suppose the probability of a single proton decaying in one year is x, where x is a very small number. Suppose we have N protons, where N is a very large number. We watch the N protons for one year. The probability that none of them decay is (1-x)N. For large N and small x, this is well-approximated by exp(-Nx).

15. Sep 8, 2016

### cube137

Can anyone please share papers on the details of the experiment or the best reference or paper that shows beyond the shadows of a doubt
(with no possibility of error that protons don't decay). I need to make important decisions on donations and investments on GUT and Superstrings.

16. Sep 9, 2016

### davenn

you have to be kidding !!
now one here is likely to get involved in giving you info that may or may not help you with how to spend your money
when it fails for you are you going to come back here and rant about the bad info ???

Dave

17. Sep 9, 2016

Indeed.