Spring-mass analog for quantum field theory?

Question

Has anybody attempted a pedagogical introduction to the interaction between an atom and the electromagnetic field using this one-dimensional system? Both the atom and the quantum field are represented by spring(s) and mass(es), and weak coupling is achieved by a spring with small spring constant, k. This spring exerts a small attractive force by Hooke's law, F=-k(Xatom-Xmass), between the atom and the central black mass that represents the field at one point. The system can be solved by finding the normal modes of the classical Hamiltonian and reducing it to a system of independent SHOs. Many years ago, I did something like this for the Mossbauer Effect, where I showed how the gamma ray can deliver its momentum to a phonon.

Have you read Zee's QFT in a nutshell, I would swear he has something like that, except as a 2 d mattress, in the very early stages of his book. — , Aug 28 '16 at 18:15

score 3 · Accepted Answer · answered Aug 28 '16 at 18:34

3

Second page in, on Zee's QFT in a Nutshell, he has:

He then starts to construct a colossal Langrangian (but not suprisingly gives up quickly) based around the p.e. and k.e. of every point in the "mattress" . He also bemoans the fact that "we have not been able to get away from this idea of harmonic oscillators and wavepackets" as the bedrock of theoretical physics for 75 plus years.

answered Aug 28 '16 at 18:34

Thanks @count_to_10 . There is no way a person like me could ever "get away" from the SHO. I'm not trying to invent new physics but explain the old, and my current interest is explaining Bell's theorem at the simplest possible level. Except for the fact that the photon is such an odd critter, the simplest understanding would use photon polarization . What I really need is a Schroedinger equation for photons, or perhaps Bell's theorem using a 2 or 3 dimensional harmonic oscillator connected to a streched string with quantized transverse waves. I could solve that problem, I think. – Guy Vandegrift Aug 28 '16 at 18:48
I'm sure you have heard Sydney Coleman' s remark that "learning QFT was basically higher and higher levels of abstraction of the S.H.O." and a recent textbook I have optimisically starts with "Some of the material in this book is wrong, but if we are really, really lucky, MOST of it is wrong", as we seemed (to the author) to have reached an experimental limit to discover new "stuff" & kickstart new theories. – Aug 28 '16 at 19:05
One way to avoid QFT in a photon Bell's theorem experiment is to have a wave function for photons. But, alas, according to What equation describes the wavefunction of a single photon? this seems to be a can of worms. – Guy Vandegrift Aug 28 '16 at 19:41
Please accept that although I know the basic principles of Bell's theorem, how it's checked and what it implies, that's about it. Personally, I am surprised that it does not feature more prominently in more theories. But that is only one post, and I from what I read on this site, unproven assertions are like buses, there will be a different one along in a minute. QFT has manage to incorporate all aspects of QM that I have come across so far, so..... – Aug 28 '16 at 19:53
My understanding of Bell's theorem can be reduced to this diagram. Nobody can seem to understand it unless I explain it, but once understood, the diagram says it all...except for the 100% correlation of measurements when the two filters are aligned. I have a plausibility argument based on symmetry and a Schrodinger-like wave equation for photons, but referees of a journal might not like that. – Guy Vandegrift Aug 28 '16 at 20:11

Spring-mass analog for quantum field theory?

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