Randomness of Radioactive Decay?

Question

Im curious to know(from a quantum mechanical standpoint)just exactly WHY radioactivity is truly random. What prevents such a process from having any kind of (statistical)pattern?I once read an anecdote that radioactive nuclei cannot exchange information, is that true? If so , then why.

Answer 1

Oh it certainly has a statistical pattern.  Suppose you flip a coin.  The probability distribution function is half heads, half tails.  Suppose you flip 2.  The PDF is 1/4 hh, 1/4 tt, and 1/2 ht.  Suppose you flip 100, the PDF is almost a Gaussian centered on 50 heads/50 tails.

Suppose you flip 1000000.  Now the PDF is a Gaussian centered on 500k heads 500k tails and the coefficient of variation that is extremely low.  We can state with near certainty that the fraction of heads will be 50% with very little margin of error.

It's the same with radioactivity.  The PDF of the lifetime of any given one is an exponential decay function.  It could decay quickly or it may take a long time.  But if you have a few gajillion decaying items, their lifetimes will follow the PDF almost perfectly.  So you can state with extreme certainty that almost exactly half of them will decay in the half-life time.

------------

Now the question of WHY the individual decays are truly, honest to god, random, is more interesting.  Quantum mechanics lets us calculate the PDF for the lifetime, but gives us no way of telling when exactly the decay will happen.  But maybe there is some underlying hudden variables that we don't understand that drive the nucleus to decay at one time or another.  Well it turns out that you can do experiments to look for such underlying causes (not in nuclei but using other systems).  And there are none.  Or if there are, they must talk to each other at faster than light speed, which is philosophically unattractive.  So as best we can tell, quantum events are truly, honest-to-god random.  God just rolls dice.

Answer 2

2nd Law of Thermodynamics. It only appears random when you look at it very very closely, but when you zoom out, all radioactive decay and rate of decay have definable measureable functions.

Answer 3

That's a very good question.  Don't expect an answer that makes intuitive sense.  Almost none of quantum mechanics does that.  Here's one way it's described.  A quantum-scale event with many possible outcomes has a wavefunction that's a statistically weighted sum of all the possible outcomes.  When the event is measured in a way that can distinguish among the choices, the wavefunction collapses to the single outcome.  For some really strange ways that particles look like they are communicating, look into quantum entanglement.