# I Differences in photons from protons vs photons from e-?

1. May 22, 2017

### Idunno

In an effort to understand how an electron and proton attract each other in the QFT picture, I am wondering if there any differences at all between photons (virtual or whatever) emitted by electrons and photons emitted by protons?

For instance, do photons from protons have a different spin or polarization than those emitted by electrons? Are they out of phase or something? Do photons from protons tend to make electrons emit photons, whereas photons from electrons that hit other electrons tend to make those electrons absorb the photons?

Anything like this?

2. May 22, 2017

### Staff: Mentor

No.
Try this link for a start: http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

3. May 22, 2017

### Idunno

Thank you for replying. I was looking at that very article for a time today and yesterday.

The article you link states the following:

"When I include all of these possibilities, it turns out that I can approximate the photon's momentum-space wave function usably well by the following: the wave function is a function proportional to the electric charge of the emitting particle (in a sense this defines what electric charge is), and it has a few big, narrow spikes in it. One spike is proportional to -i times the charge, and is to the left of the origin; the other spike is minus that and is to the right of the origin. (There is also a third spike at zero momentum that has a real amplitude, but it turns out not to do anything important at the end of the day—it provides a constant potential energy—so I'll ignore it.) The imaginary component of the photon wave function looks like this, if the emitting particle was a negatively charged electron:

|
+i | zero momentum p -->
| |
| v
0 __________|________________________________________
|
|
|
-i |
|

If the emitting particle was positively charged, this picture is upside down."

So, it seems to me that, according to the article, there is a difference between a photon emitted by a proton and a photon emitted by an electron, at least in the imaginary part of their respective wavefunctions. Any other wavefunction differences between them?

If you or anyone else could be kind enough to help me understand this difference in any way that might be helpful, I would be grateful.

4. May 23, 2017

### vanhees71

The Coulomb field of a charge is not described by single photons but by a resummation of infinitely many Feynman diagrams. See, e.g., the chapter on the soft-photon approximation in Weinberg, Quantum Theory of Fields, vol. 1.

5. May 23, 2017

### Staff: Mentor

At the level of approximation being used, no. But it is an approximation, and a rather crude one. You should read very carefully all the disclaimers in that article; they are important. The key point for your question is a bit later in the article than the diagram you posted--the second diagram after that and the accompanying text. Note carefully how the sign change affects the result, as described in the text accompanying that diagram.

6. May 23, 2017

### Idunno

You put a proton by itself in a box, moving very slowly, you put an electron in same box, and the electron shoots a single photon at the proton. What happens?

If the proton moves towards the electron, either

The photon has some sort of information about what charge produced it (contained in its various features), either in its spin or polarization or way its wave carries its momentum or *something*.

OR

It was lucky, because it's a cumulative effect from many photons and is related to the emission rates (or some similar concept) of both proton and electron emitting photons.

I can't envision any other possibilities. Which is it?

7. May 23, 2017

### Staff: Mentor

How do you get the electron to "shoot" a single photon at the proton? If you are thinking that we have some experimental apparatus that lets us control this, you are quite mistaken. If you think we can somehow observe single photons being "shot" between the proton and electron in the box, even if we can't control their emission, you are also quite mistaken. Finally, if you are thinking that the photons are little billiard balls, each carrying a definite quantity of momentum, even if we can't directly observe them, you are once more quite mistaken.

Then you need to spend some time learning quantum field theory.

Neither.