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Roger W. Norman wrote:
> Actually you're getting into probability, which suggests that one can't
> predict WHICH atom will decide to decay. The fact is that at least ONE atom
> will decay at a predicted time.
I am not a nuclear scientist, but as I understand it, it is the exact
opposite of that. The probability that any atom will decay during a
particular time interval is independent of the probabilities of all
the other atoms decaying. In fact, if my understanding is correct,
the theory is that the probability of decay is independent of everything,
i.e. it's truly random.
To me, it's pretty clear that if the above assumptions are true
(independent probability for each atom), then the time at which
all atoms will have decayed is totally unpredictable. To see
this, pick any time interval you want. You might typically see
lots of decay events during this time interval. But it's clear
that as you decrease the time interval, the chances of having no
events during that time interval increase. (Imagine you pick
1 nanosecond as your interval for a tiny chunk of some substance
with a long half-life.) So there has to be, for any chunk of
some substance, a finite time interval for which it's very likely
that no decay events occur. Since decay events are random (i.e.
follow an exponential probability distribution), they have no
"memory", which means that after that time interval, you have
not moved any closer to a decay event than you were. So, if
there's a finite chance that a time interval can elapse and you
can have no progress toward the end state, then the time it takes
for the process to complete can never be predicted.
> In an entirely unstable isotope, the
> probability becomes a universe where ALL the atoms can decide to decay at
> the exact same time, which means boom.
Well, if by "entirely unstable isotope", you mean a substance where
the probability that an atom will decay instantaneously is 100%, then
yeah. But in practice, as far as I know the probability of decay
over a finite time interval is always finite. Even when they make
a tiny sample of Element 106 in the lab and it only exists for 0.1
milliseconds or whatever before it decays, it still doesn't decay
*instantly*.
On the other hand, what is the probability that in the one-second
interval after I hit th "send" button on this post, that all the
atoms in some object (like my mechanical pencil) would decay?
Well, based on the theory I've heard, I'd have to conclude that
the probability isn't zero. However, because decay is pretty
unlikely for each atom, and since the probability is pretty much
independent, you basically just multiply all the probabilities
together. Even if you had 100 atoms that each had a 50% chance
of decaying in the next 1 second, you'd still only have a
1 in 1,267,650,600,228,229,401,496,703,205,376 chance of them all
decaying in one second. So, scaling that up to a mechanical pencil
reduces the probability even further, and the probability that all
of the atoms in the entire universe would all go at once is just so
vanishingly small (although still theoretically non-zero), that this
particular form of universe destruction is not a big worry.
🙂
Now, what did all this have to do with audio? Oh yeah, all that
pesky background radiation creates noise. Darn that stuff!
- Logan
/www.thepowerhour.com/articles/du_effects.htm
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