I Trying to understand how spontaneous emission works

[Groucho]

I'm reading Gerald Folland's "Quantum Field Theory: A Tourist Guide for Mathematicians" and I'm up to Section 6.2 which is called "A toy model for electrons in an atom". He has a nonrelativistic particle of mass M and a scalar field with quanta of mass m and the state space for the particle is L^2(T^3) for a 3-torus T^3 and the state space for the field is the Boson Fock space over L^2(T^3), and he describes the Hamiltonian for the particle, for the field, and for the interactions, and then starts calculating the expected time interval for the emission of a field quantum. So you start with the state corresponding to the particle in energy state n and no field quanta present, then apply the time evolution operator U(t) for some specific t>0, then apply the linear functional corresponding to the state where the particle is in state m and there is one field quantum present with momentum p, and the modulus squared of the result gives you the transition probability. I am trying to understand better how this actually links with actual experimental results.

Can we make sense of the idea of just staring constantly at a hydrogen atom and waiting to see if anything happens, is that an experiment that is actually feasible to do? I vaguely remember reading somewhere that if you do that then emission of a photon will not happen. Am I wrong about that?

 

[dextercioby]

You mean the Quantum Zeno Effect? It's been debunked already, as it's based on a misinterpretation of von Neumann's collapse postulate. https://en.wikipedia.org/wiki/Quantum_Zeno_effect

 

[Groucho]

Thanks, can you tell me more about the debunking? I can't find discussion of the debunking in the Wikipedia article.

 

[Groucho]

It seems as though to give an account of spontaneous emission of photons in a sample of excited hydrogen atoms you would have to give some kind of account of when collapse of the wavefunction takes place. Has work been done on this?

 

[Demystifier]

Can we make sense of the idea of just staring constantly at a hydrogen atom and waiting to see if anything happens, is that an experiment that is actually feasible to do? I vaguely remember reading somewhere that if you do that then emission of a photon will not happen. Am I wrong about that?

If you just stare, it will not influence the atom. But if you repeatedly probe the atom to check out if it has decayed, then you can really slow down the emission. Probing involves an active interaction with the atom, so it should not be surprising that it can influence the atom behavior. This is the real quantum Zeno effect, which has been verified experimentally.

 

[Demystifier]

You mean the Quantum Zeno Effect? It's been debunked already, as it's based on a misinterpretation of von Neumann's collapse postulate.

If you mean the Ballentine's debunking of the quantum Zeno effect, I have to tell that the Ballentine's debunking has been debunked, as he himself misinterpreted the collapse postulate. The quantum Zeno effect is a real effect observed in laboratories.

 

[dextercioby]

I didn't mean Ballentine's book, but some notes I found online from the famous Robert Geroch from the University of Chicago. I don't have them on my PC anymore and couldn't find them online :(

 

[Demystifier]

I didn't mean Ballentine's book, but some notes I found online from the famous Robert Geroch from the University of Chicago. I don't have them on my PC anymore and couldn't find them online :(

In the absence of those notes, I can only tell that Geroch is an expert for mathematical physics, but not an authority for conceptual questions such as wave function collapse.

 

[dextercioby]

And who could you define to be an authority in this domain?

 

[Demystifier]

And who could you define to be an authority in this domain?

Like in any other domain, by having a lot of published papers (in that domain), by receiving a lot of citations of those papers, by being frequently invited as an invited speaker at respectable conferences (in that domain), etc. (It is not required that everybody agrees with the ideas expressed in those papers.)