Nuclear decay and the age of atoms.

[SW VandeCarr]

Nuclear decay and the "age" of atoms.

All atomic nuclei heavier than hydrogen were created in stars and would therefore seem to have different ages relative to some specific spacetime reference. Nuclear decay wrt a single atom is taken to be a temporally random event, but is it plausible to consider that every atomic nucleus has its own clock and if we knew how old it was, we could predict when it would decay? Even if we did not know how to read such a clock, its existence would frame nuclear decay in deterministic terms rather than as fundamentally random events.

Is there anything known or allowed for in the current state of nuclear physics that might allow individual nuclei to be distinguished by their age? I understand that the current paradigm is that all isotopes of a given element are exactly alike wrt to their nuclear structure/dynamics.

 

[humanino]

No it is not plausible, for many reasons. I guess the most basic is as follow. Nuclear decay rate follows an exponential distribution. That means precisely, no matter how old the sample, no matter how large the sample, there is a fixed fraction of the sample which will decay during the next period. This is a defining property of exponential decay : it does not "remember" in a certain sense.

Say your sample has a radio-active half-life of e.g. 1 minute. Every minute, half of your sample decays. When your sample becomes too small, of course, you end up having large statistical fluctuations. But if you have a ton of it, half the ton will decay during the next minute. If you have a kilogram, half the kilogram will decay during the next minute. Given reasonable weighting device accuracy, even if you have a gram you will not be able to tell whether more or less than half a gram decays during the next minute.

Beyond this simple argument, quantum field theory describes fundamental particles as excitations of fundamental unique fields. An electron for instance never remembers how it was created. All electrons are the same with the standard model. There was never a flaw in the standard model to describe physics at the scale of nuclei. If that changed, it would be big news.

 

[SW VandeCarr]

Beyond this simple argument, quantum field theory describes fundamental particles as excitations of fundamental unique fields. An electron for instance never remembers how it was created. All electrons are the same with the standard model. There was never a flaw in the standard model to describe physics at the scale of nuclei. If that changed, it would be big news.

Alright, but an atomic nucleus is not a fundamental particle. Heavy nuclei are being created all the time in stars. Is it unreasonable to consider that a terrestrial sample would be heterogeneous wrt the age of individual nuclei? The half-life is a statistical property of an ensemble. The mere fact that carbon 14 doesn't decay to carbon 12 (via C13) all at once suggests that individual C14 nuclei are distinguishable in some way.

 

[bcrowell]

Alright, but an atomic nucleus is not a fundamental particle.

True, but the laws of quantum mechanics don't work differently for fundamental and non-fundamental particles.

Heavy nuclei are being created all the time in stars. Is it unreasonable to consider that a terrestrial sample would be heterogeneous wrt the age of individual nuclei?

Sure, they're heterogeneous, but that doesn't have any effect on their expected future time until decay.

Although humanino is right, I will muddy the waters a little by saying that there are apparently good fundamantal reasons to believe that all radioactive decay processes are only approximately described by exponential probability distributions with future behavior independent of past behavior. There have been serious experiments done to test for this, but IIRC they came up negative -- presumably negative but not in conflict with theory. I wish I could remember an exact reference. I believe there was an experiment done at LBL ca. 1980's or 1990's.

 

[SW VandeCarr]

True, but the laws of quantum mechanics don't work differently for fundamental and non-fundamental particles.Sure, they're heterogeneous, but that doesn't have any effect on their expected future time until decay.

I agree it would not effect the expected time which is a statistical parameter applied to an individual (mean time to decay). The reason I'm asking is that I've been using nuclear decay as an example of true randomness in nature as opposed to Kolmogorov algorithmic pseudo-randomness. In thinking of counter-arguments, I wondered about this.