Undergrad Radioactivity in quantum physics

[Kairos]

In a block of 1 kg of radioactive material that has reached its half-life, are the atoms in a superposed disintegrated/undecayed state (50-50), or are they all individually determined (50% disintegrated and 50% undecayed) before observation ?

 

[DrClaude]

This is Schrödinger's cat over again. In a 1 kg block, decoherence will be quite fast, and no individual atom left in a superposition for long.

 

[Kairos]

This is Schrödinger's cat over again. In a 1 kg block, decoherence will be quite fast, and no individual atom left in a superposition for long.

Thank you, so it's a question of the number of atoms. In this case, could a single atom be the superposition of an infinite number of decay states following the exponential decay curve? For example, in the case of slow beta- radioactivity, the emission of an electron would be spread out over billions of years? and it would never end, asymptotically.

 

[DrClaude]

Thank you, so it's a question of the number of atoms.

It is a question of an interaction with an environment. In this case, the other atoms act as the environment for a given atom, and it doesn't take long before those other atoms "observe" the decaying atom.

In this case, could a single atom be the superposition of an infinite number of decay states following the exponential decay curve? For example, in the case of slow beta- radioactivity, the emission of an electron would be spread out over billions of years? and it would never end, asymptotically.

Theoretically, an isolated atom will have a unitary time evolution and always be in a superposition. Of course, so such system is possible in reality.

 

[Kairos]

After the inevitable decoherence, there are two possibilities: either the atom is disintegrated and the story ends there, or it is not disintegrated. In the latter case, does it immediately re-enter a nondecayed/disintegrated superposition state?

This would mean that an unstable atom is constantly oscillating between coherence and decoherence?

 

[Lord Jestocost]

In a block of 1 kg of radioactive material that has reached its half-life, are the atoms in a superposed disintegrated/undecayed state (50-50), or are they all individually determined (50% disintegrated and 50% undecayed) before observation ?

After one half-life of a radioactive atom the probability is $1/2$ for the atom being non-decayed, and $1/2$ for being decayed. A probability $1/2$ for the two alternative possibilities (here: decayed/non-decayed) means that the two incompatible situations can now be considered equally possible at the instant of time meant by the prediction. These probabilities are valid for each radioactive atom in a bunch of $N$ radioactive isotopes of the same kind. In case of an observation on that bunch, half of the atoms are decayed and half of the atoms are non-decayed (if $N>>>1$). That’s all what physics has to say, nothing more or less.

 

[PeterDonis]

After the inevitable decoherence, there are two possibilities: either the atom is disintegrated and the story ends there, or it is not disintegrated.

You are assuming that the quantum wave function is the physical state of a single atom. That is interpretation dependent. Not all QM interpretations treat the wave function that way. If you want to discuss how a particular interpretation works, that discussion belongs in a separate thread in the interpretations subforum.

As far as basic QM is concerned, @Lord Jestocost is correct: it gives you the probability of decay as a function of time. That's all you can say. You can't say anything about what the atom is or is not "actually doing". QM, as a model independent of interpretation, says nothing about that. It only tells you the probabilities of different possible measurement outcomes.

 

[Kairos]

You are assuming that the quantum wave function is the physical state of a single atom.

Yes, that's it. I'm looking for an interpretation of single atom decay in the same way as the Malus polarization experiment with single photons.

The purely probabilistic 1/2,1/2 description is similar to that of classical physics.

 

[PeterDonis]

I'm looking for an interpretation of single atom decay

Due to this, I have moved this thread to the interpretations subforum.

 

[Vanadium 50]

Do we really need another Schroedinger's Cat variation?

 

[Kairos]

No, I just wanted to know how radioactivity is viewed theoretically in orthodox quantum physics. DrClaude's post #4 is very instructive for me: decayed/undecayed superposition very quickly destroyed by the environment under ordinary conditions. In my old (classical) physics classes, radioactivity was presented as insensitive to the physical conditions of the environment; it plays at least a small role in this decoherence..

My additional question in post #5 following this answer may be far-fetched. Sorry about that.

 

[Demystifier]

In my old (classical) physics classes, radioactivity was presented as insensitive to the physical conditions of the environment; it plays at least a small role in this decoherence..

See my https://www.arxiv.org/abs/2010.07575 Sec. 4.3 for an explanation why it looks as if the environment is irrelevant, despite the fact that there is no decay without environment.

 

[greypilgrim]

In a 1 kg block, decoherence will be quite fast, and no individual atom left in a superposition for long.

Shouldn't quantum Zeno effect slow down the decay considerably in this case, compared to decays of single isolated atomes?

 

[Nugatory]

Shouldn't quantum Zeno effect slow down the decay considerably in this case, compared to decays of single isolated atoms?

No, because the interaction with the environment isn't a preparation procedure for the original coherent superposition. "Continuously measured by the environment" is a sensible enough statement, but it relies on some fuzziness about what exactly is meant by "measurement", and it turns out that quantum zeno discussions are using the term in a different sense.

With QM.... At some point we always have to give up on natural language and turn to the math.