In article <firstname.lastname@example.org>, Wally W. <email@example.com> writes: >On Mon, 17 Dec 2012 18:43:41 +0000, Dr J R Stockton wrote: >>In sci.math message <rubrum-0653B8.firstname.lastname@example.org>, Sun, 16 Dec 2012 15:43:20, Michael Press <email@example.com> posted:
>>>> The main assumption in this is that the probability that an >>>> atom which has not decayed by time T will still have a probability >>>> of decay between T and U which is independent of anything which has >>>> happened before time T, and only depends on U-T. >> >>>I am asking for the basis of the unpredictability >>>in physical theory. Assuming it is random is to >>>beg the question. >>> >>>I hold that the wave theory of matter does not >>>predict random occurrences. >> >>Little can be done about ignorance of such profundity. You reject the >>mainstream physics of the last 85 years or thereabouts. > >It seems like a reasonable question to me. > >The completeness with which we understand small-scale physics doesn't >affect whether something deterministic is happening under the hood. > >If radioactive decay is random, why should an isotope have a knowable >half-life? Why wouldn't the half-life also be random, or more variable >than it seems to be?
Let's try a few analogies.
First, a real simple case. Take a handful of coins. Shake them around a little, and toss them onto a flat surface. Do you agree that the face each one will show is a roughly random event, and that it's not correlated with the face that any other coin will show? Do you also agree that roughly half of the coins will show one face and half the other?
What about the motions and positions of air molecules? Even though each molecule's position is (from a macro point of view) random an uncorrelated with others' positions, do you still believe that roughly half the air molecules in a room are going to be one each side of the room's center?
Assuming that you made it through those, let's get a little more complicated. Get several thousand six-sided dice. Throw them all up in the air. Do you agree that the face each die shows is more or less random, and not correlated with the face that any other die shows? Do you also agree that roughly one-sixth of them will show a 3?
Now, throw out all of the dice that show a 3. You've got an hour to do that. An hour after the first throw, throw the remaining dice, and again remove the ones showing a 3. Now, you should have about 70% as many dice left as you started with.
An hour later, do it a third time. After cleanup, you should have about 58% as many dice as you started with. And after your fourth throw and cleanup, the number of dice left should be down to about 48% of the original number.
If you do this another four times, you'll be down to about 23% of the original count.
So, every four hours, the number of remaining dice gets cut by roughly one-half. That means this process has a half-life of about four hours. This is true even though "half-life" is a macro-level property of a collection of uncorrelated events.