I've always thought it odd that half-lives are calculated extrapolating average decay per second. Even if you observed a steady rate for 100 years, it seems a big assumption that it would remain constant for thousands, millions, or even billions of years.
Why is there such confidence in a constant rate? I've never heard it stated as anything but brute fact.
It is one of outcomes of the assumption that two identical particles will obey the same physical laws. If all atoms of a particular isotope have the same decay probability now, we assume that identical atoms had the same decay probability a long time ago, too.
The other consideration is Occam's Razor. Constant decay rates are simpler, so we stick with that idea until we are faced with an experiment that is difficult to explain without variable decay rates.
There is nothing preventing science from adopting the variable decay rate hypothesis. All it takes is one good experiment.
Great, simple explanation. Thanks!
I've always been skeptical of carbon dating. But I'm an English major, so what do I know.