Is the decay of a radioactive isotope predictable (causally determined) or not?

At this point it seems to be a result of quantum indeterminacy. In other words, since the Heisenberg uncertainty principle is in effect at that level, all we can determine is probability (hence a predictable half-life), and not specifics of events. So, it really comes down to whether or not you believe quantum mechanics. I do, and so I say no, we will not be able to determine it fully. However, many say that QM is incorrect, and so if they’re right, then yes, it is deterministic and we will (hopefully) one day be able to understand it as such.

To calculate it down to the nanosecond we would have to be able to measure the radiactive decay to an even greater precision than that, both in time and particle count, and we would have to be able to obtain the exact number of atoms in a sample. And by exact I mean every single one of them, with a margin of error of zero. Not to mention that there might be minor fluctuations in the decay rate that would make nanosecond accuracy impossible.

I would imagine that these details are determined at the quantum level, where Heisenberg’s observations on observation would seem to apply, so I’m not a physicist, but I would say that logic suggests it is indeterminate.

Great, question. @ETpro.

At the end of the first paragraph in your link I think there’s a pretty significant clue. It says: “This is a stochastic process on the atomic level, in that it is impossible to predict when a given atom will decay,[1] but given a large number of similar atoms the decay rate, on average, is predictable.”

If on average atoms of the same type decay at approximately the same time, a law governing the decay of radioactive isotopes is implied. This is to say, they are decaying not truly randomly, but according to some unknown principal or system which they can’t defy.

Side question: Is it even possible for a radioactive isotope NOT to decay? Or must they decay by, again, some unknown law?

The point is, there’s a cause for the decay. We don’t know what it is, and hence we can’t yet investigate that cause to determine nanosecond precision of the event. But with certainty, these radioactive isotopes are obeying some rules and doing their thing on a punch clock.
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As an example, imagine a crazy ass hurricane flowing through a village that destroys every house. Every house will succumb to the winds on their own time. But all approximately around the same time as the hurricane existed. There are so many factors involved in why a house might last a little longer under pressure or give in quickly that it would be difficult to predict which one would go first, seventeenth or last. It would also be difficult to predict the nanosecond that any single house might collapse or get blown away by the pressure they are experiencing. Our not being able to predict these things with accuracy doesn’t imply that the the materials of the houses have an uncausal link to reality. It simply implies that we don’t know exactly when it will happen.

There are many things that are causally determined but not predictable. The idea of chaotic systems come to mind. The appearance of a tornado in a certain location at a certain time is not predictable; however, it is causally determined. Chaotic systems are systems that are sufficiently complicated that the accuracy of the measurement of initial conditions required to make an accurate prediction of the end results is too precise for our instruments to measure. Even if we knew the physical laws that the system abides by we could only make statistical predictions of results. The jury’s still out on whether quantum mechanics is causal. It is non-local, but that still leaves room for a chaotic causal function. We can’t test whether or not decay is truly stochastic or just chaotic because we have no accurate control over the atom’s initial conditions. The only way to determine the difference between stochastic and chaotic behavior is by testing the same initial conditions.

Reality is inherently probabilistic.

What we call “causality” is, on a quantum scale, really just an average of random events over time.

That average is causal—a system will always have the same average of radioactive decay over time. But when it comes to the individual particles, they simply don’t work that way, mechanically.

@BhacSsylan So I am gathering in looking up info from these answers. Thanks.

@ragingloli I do not believe you could calculate it down to the year, much less the nanosecond, given what we currently know about radioactive decay. Let’s say we have create one atom of a radioactive isotope having a half-life of 1 second. We will not have half an atom in 1 second. We will either still have a radioactive atom, or it will have released energy and decayed. The 1-second half-life means that if we tested enough individual atoms, 50% would decay within 1 second. With a very large number of atoms, the large numbers principle means we can simply measure how long till the radioactivity falls to half its previous level and derive a half-life.

@dpworkin That is what I expected when posting this question, but in following up on answers so far, I am becoming convinced that @BhacSsylan has it exactly right.

@ninjacolin Atoms of the same isotope don’t decay at anything close to the same time. Carbon 14 has a half-life of about 5730 years. An individual atom of it might decay 1 second after being produced. But after 5730 years, half of a large sample will have emitted energy and become nitrogen 14 atoms. Another half will decay in the next 5730 years—and so on. It is an exponential rate of decay.

@Shuttle128 Apparently there is work underway to try to sort out just this question. It is testable, but not easy to test. See http://en.wikipedia.org/wiki/Quantum_chaos

@Qingu Actually, there are measurable differences between causally based chaotic dynamical systems and truly stochastic systems when measured over time.

Thankls to everyone for the thoughts. Looking up your suggested answers has helped me understand how little I understand. :-)

It’s not entirely predictable. If you got a thousand C-14 atoms and wait 20,000 years it’s possible that none of them have decayed. But that is very unlikely.

It’s even possible that nuclear fusion inside the Sun stops for an entire second. But that is even more unlikely.