Saturday, October 22, 2011

The Semi-Classical School of Jaynes and Scully

When I was in grad school back in the 90's and first started piecing together the picture of quantum atoms as tiny oscillating charge distributions, my professor told me that a fair amount of work had been done on that picture in the 1960's by someone named Jaynes. It seems that despite the simplifications prevelant in the popularizations, real physicists knew that things like the photo-electric effect could be explained on a phenomenological (descriptive) level just as well by the wave theory as by the particle theory of light. It seems that the Jaynes school set out to see just how far this could be carried through on a mathematical level as well.
So I understood that the basic ideas of my approach were already well-known in the physics community. It was only about two years ago that I learned how wrong I was.
It is pretty easy to set up a calculation in quantum mechanics using the wave theory of light. You have the same atoms, the same potential, the same Schroedinger equation; all you do add a new potential V=kz in the vicinity of the atom and allow the potential V to oscillate sinusoidally in time. If you can write the equation then in principle, the equation can be solved.
So far this is the same as my approach. What I would then go on to do is track the motion of the atomic charge in the presence of this oscillating field, see how the charge distribution also begins to oscillate, calculate the new field due to these oscillating charges according to Maxwell's equations, and add these new fields to the original "driving" field to get the resultant.
I learned only recently that this was not the method of the Jaynes school! What they did was simply to apply their oscillating field to an atom in the ground state, and then using the standard calculational techniques, determine the transition probabilites from the ground state to the excited state. They were still looking for the same old quantum leaps instead of following through on the actual time evolution of the process.
This was a pretty big disappointment. I had thought that the so-called "semi-classical approach" was what I and the Jaynes school had both been practising. It turns out that either they were really doing the "hemi-semi-classical approach", or I was actually doing the "75%-classical approach". Either way, we were not on the same page.
I learned this in the course of some very nasty arguments in I was originally trying to defend my picture of atomic antennas on its own merits, by logic. Finally I did what I hate to do and invoked authority to defend my ideas: "I'm only making the same argument that Jaynes made in the 1960's". I was shot down right away. There are no oscillating charge distributions in the Jaynes picture, only pure eigenstates. The jump from one pure eigenstate to another may be stimulated by an oscillating field instead of a "photon", but it still works on the basis of quantum leaps.
Was the Jaynes school then merely doing mathematical acrobatics, or did they have a physical picture like I did? My road to quantum mechanics began with the crystal radio. I had discovered a physical picture which showed me that energy is exchanged between two systems over a huge volume of space that has nothing to do with the physical dimension of the systems, but rather is based on the wave-on-wave interaction extending over dimensions measured in wavelengths. That is why a tiny crystal radio antenna can absorb quantities of power that are equivalent to an area of hundreds of square meters, even though the physical cross-section of the antenna may be measured only in square centimeters. Did the Jaynes school share these kinds of pictures with me? They did not!
I found this out conclusively about five years ago after reading the Wikipedia article on "photons". At the bottom of the article they linked to a video of the Nobel Prize lecture by Roy Glauber and several research papers on the "history of the photon", which I actually sent away for. The Glauber lecture was horrible, but that's another story. One of the articles in the package was by Scully, a leading member and perhaps the recognized heir to the Jaynes school, and I was shocked to read what he said about the photoelectric effect (and I'm paraphrasing here): that most of the phenomena associated with the effect can be equally well explained by the wave theory, but there is a problem with the absorption cross section! He then explicitly writes out the cross-sectional area of a typical atom and observes that the amount of radiant energy passing through this cross section is much too small to account for the rate of prompt emmision measured in typical experiments.
How does he not know that he is using the wrong cross section!? He obviously doesn't understand the crystal radio, or he would be using the wavelength of the light for his relevant cross-section, and he would get an area a million or so times greater. And this is just if he is talking about the photo-electric effect on a single atom, more precisely the photo-ionization effect. If he is talking about light striking a metal plate, he needs to use the whole area of the plate, because that is the size of the wave function of a single electron. It's appalling to me that people at the very top of the game in physics are working on such a sophisticated mathematical level without having the physical pictures to back it up.
Finally, I ought to mention that I don't like Scully. When my professor told me about the Jaynes school he said I might want to contact them about doing PhD research. I wrote a four-page handwritten letter to Scully outlining some of my ideas and waited eagerly for a response. Finally, after a few months I phoned him. He had no idea who I was. "Yes, I get a lot of letters but I don't really have time to read them". No apology. Maybe he doesn't have time, or maybe he read mine and thought I was a quack, but that's no excuse. Don't people like that have assistants to at least send out standard form rejection letters?


Peter Bourne said...

Are you discarding the notion of "Excited States" altogether or just "Quantum Leaps"
The way I was picturing this is that the atom acting as an antenna will have certain 'Resonance' frequencies . When EMR interacts with an atom will cause it to resonate depending on the frequency of the EMR.
These 'Resonate states' would be equivalent to the excited states but without the quantum leap.
Am I way off base here ?

Marty Green said...

I don't think you're on track here. Quantum mechanics is funny. When you solve the equation for an atom, you get eigenfunctions which look like resonant states. But they don't act like resonant states. The things we recognize as resonances, or natural oscillations which die away gradually...turn out to be the mathematical superposition of two of the eigenfunctions.

So yes, I still recognize the excited states (like everyone else)...those are just the eigenfunctions. I just don't accept that the atom jumps from one excited state to another with nothing in between.