Really, the question is does Compton scattering violate conventional theories of QM, QED, or whatever other flavour of quantum theory you're having?
I keep turning it over in my head. And I keep coming up with funny problems.
The description for single photon and single electron.
Fine..........But in terms of more than one atom, something like path integrals do not make sense. Considering an EM wave. Events would have to happen, at different times and locations, then magically unhappen. If each interaction with an atom is with a full photon, it would require infinite energy. Or only one atom could be disturbed(or peturbed if you like).
What it's saying to me, is the momentum of the entire light wave is evenly distributed across its' entire wave front. And in a scattering collision. The loss of momentum is transmitted to the entire wave, without a wave collapse - the momentum can be lost to more than one atom . And single photon on it's shortest path just wouldn't explain what's happening. Or if it does the explanation just has to be wrong.
It does not violate quantum theory. And what it demonstrates is that light isn't a wave. It is something other than a wave.
I keep toying it over. And looking up stuff. And every idea I come up with seems to fall down somewhere. It's deeply confusing. The photon, within the constraints of the speed of light, seems to be everywhere and simultaneously nowhere. Or that it has infinite energy everywhere at once - which doesn't make sense. Or that the energy is ,evenly or unevenly, distributed - which doesn't make sense for other reasons.
I keep thinking up experiments. A double slits experiment, with a few planets in the way, and maybe a gas cloud somewhere. My interference patterns are telling me my photon is everywhere between the slits and the detector. Sometimes it collides with the planets - but sometimes it doesn't and has seemed to pass through them. Other times it might collide with an atom and go through a Compton scatter. But it's not going to collide with every atom in its' path.
I'm confused. I've been looking over a lot of equations. Some I understand - others not so well, and there's nothing jumping out at me.
The problem is you are trying to understand a quantum system in terms of classical ideas. The photon isn't a wave, but nor is it a particle. You have to strip away all these ideas. The state of a quantum system has a description that is not the same as the state of a classical system.
Yes....But. Certain classical ideas work incredibly well up to a point. Something like Compton's E= pc, Planck's E = hf, and a few more. They work incredibly well up to a point. Something like the observations in how radio waves behave when they're broadcast. But then holes begin to appear.
But, if you're building radio transmitters. For the sake of getting on with it, and building something that will work. You can treat your transmissions, as a wave propagating through a medium - or even a flux of light particles that can bounce around. Either approach will give you results that are in agreement with observation. You can even approximate how many light particles you're getting from your antenna, by how much power you're pumping into it. It's a good example of a how a theory can be in agreement with observation and still be wrong - all you need is one observable snag in the idea, and it's completely wrong.
But any description of the quantum system should naturally emerge to explain the classical. Classical rules can't just be explained as broken down at a critical level.
I'm trying to hack my way through it, it'll take me a while, but I'll get there. But when someone says something like "Oh, there is no classical reality. It's all just a hologram, made of vibrating bits of string in hidden dimensions", they probably just given themselves just a little too much liberty.
But some of the things I've read, seem to me at the moment, just seem to be convoluted descriptions and not explanations of what is already observable. A guy with an radio transmitter could probably work out the probability of a photon scattering, reflecting, etc. He could work out constants and equation and if his name was Bob, he could call it Bob's Law.
I'd like to see equations where factors from QT slot neatly into classic equations. Maybe they're all there, I just haven't seen them yet.
I've just seen the Wigner function. Damn....it's going to take me a really long time to work through all this.
Damn damn damn damn.
I'm still bothered.
"Questions about what decides whether the photon is to go through or not and how it changes its direction of polarization when it does go through cannot be investigated by experiment, and should be regarded outside the domain of science." Dirac - Principles of Quantum Mechanics.
I don't like Dirac's statement for a number of reasons. There are good explanations of polarisation, that do not require any magic. And the nature of how light is transmitted through a polarizer is important to know.
It's an annoying statement. Who the hell does Paul Dirac think he is, to go setting the boundaries of science.
He also goes on to say, electrons ejected (I assume it's photo electric effect) by polarised light have specific direction (I assume the direction is related to probability of the incident light's polarisation angle).
I do not know. Would some experiments on hyper-fine crystal at near zero reveal a level of determinacy that's just not there at higher scales. Something like X-ray crystallography, but at a higher grain.
I remember going over a question much like yours. One issue comes down to knowing the `size' of a photon; this is best understood as its coherence volume. Thus if you think of a fully coherent laser pulse, each photon is the the size of the pulse and they all occupy the same volume.
The strange part is that all interactions happen at a point. Even though a photon can occupy in principle an enormous volume, if it interacts its energy and momentum are delivered to a single point instantly (not at the speed of light). I think pretty much everything is known about how this occurs, but not why.
Classical wavemechanics (and a little trust) gets you a long way in quantum mechanics, which is essentially why Schroedinger got a Nobel prize.
I think your over thinking it. And over thinking it in a classical way.
A lot of people have tried for a long time to punch holes in Quantum Theory and I dont know of anyone who has been successful.
Basically Quantum Mechanics works like this
1. You ask a question about how a system behaves
2. You use the known mathematical Quantum rules to do calculation
3. Quantum mechanics spits out an answer
4. Test answer against experimental results
5. Step 3 and Step 4 should give the same number
Quantum Mechanics doesnt really care whats going in the system except at the point the measurement is made. And when the measurement is made it agrees with what the theory predicts the measurement will be (so far anyway).
This is the "Shut up and just measure" approach which Heisenberg and his Gottingen team developed.