Meaning of Halflife
What do you mean?
Suppose there's an alien species with a halflife of, say, 70 years. You randomly pick out
16 baby aliens and track them to see how long they live. After 70 years, of course, 8 of
them will still be alive.
That doesn't sound so weird. If you tracked a group of human babies, you might
get the same results.
True...but remember that the halflife is always the same, regardless of how old the aliens are.
After another 70 years, 4 of those 8 will still be living, now 140 years old. And half of
those--2 aliens--will survive to the age of 210. Another 70 years go by, and there's
one alien left, age 280.
That is kind of strange.
It gets stranger. Let's say that your great-great-great-great-grandchildren, who have been
faithfully continuing your study, now decide they want to examine the lives of some aliens of
the younger generation. In addition to our 280-year-old friend--let's call him Methuselah--they
also begin tracking 15 new babies. Now there are 16 aliens in the study again, and, as before,
8 of them will be alive after 70 years.
Methuselah isn't going to make it, though.
Methuselah has just as much chance of surviving the next 70 years as any one
of the 15 babies. In fact, he has just as good a chance as any one of them
of living another 280 years. The probability of decay has nothing to
do with the history of any individual atom, or alien; otherwise the halflife
wouldn't be constant. Radioactive atoms just don't grow old the way we do.