In QED, how do two particles attract each other by exchanging photons?

Answer 1

Hi eric j

Interesting question. The most appropriate answer will depend on how much maths and physics you've studied - I'll try a rough analogy answer andthen point you at some more detailed discussion if you're a physics student.

Exchange bosons (like the virtual photons exchanged between two charged particles) exchange momentum and energy. It's easy to imagine how this happens in a repulsion scenario:

Suppose two charged particles are represented by two people on ice skates on a frozen lake. Person A throws a heavy ball (representing the photon) to person B. As person A throws the ball he begins to move backwards with the recoil from the throw. When person B catches the ball they also move backwards with the momentum of the ball. If you can't see the ball then the two people appear to have moved away from each other by some "force".

To model attraction we have to include quantum features of the exchange. the key feature we'll include is Heisenberg Uncertainty. Recall that position and momentum are non-commuting operators - the more tightly we define momentum the more position is uncertain, and vice versa. If the momentum of the exchange photon is tightly defined then its position is smeared out, the probability density extends beyond the two particles involved. Back to our people on the lake, you might imagine that this time A and B start out facing back to back, A throws the ball away from B, which means A gets pushed by the recoil towards B. The ball gets "delocalised" and ends up curving around and coming at B from the front. B catches it, and moves towards A with the ball's momentum.

This might sound a little contrived - what you have to remember is that quantum interactions don't often translate well into everyday classical scenarios. If you've read anything of Feynman's on introductory QED (eg the strange theory of light and matter) then you'd be familiar with Feynman diagrams, and the notion of "probable paths" rather than actual paths. The path taken by the ball in the analogy above is possible, but it's unrealistic to suggest that looped paths are a feature of attractive exchanges. At the end of the day quantum theories are interaction based, what happens in between interactions is storytelling (and actually irrelevent). For this particular interaction the calculated scattering matrix for two like charged particles looks different from that calculated for two unlike charged particles (they differ by a minus sign). When compared to unscattered states you get a divergent result for low energies which tells you whether the particles will repel or attract.


Hope this helps!
The Chicken

Answer 2

The Coulomb force is the exchange of (virtual) photons. That's one reason why QED is so cool--the same propagator which describes the photon, when used in a source/sink framework, results in the Coulomb force. I recommend A. Zee's "Introduction to Quantum Field Theory." It really cleared that up for me, and it's very readable.

Answer 3

Photons are Cartesian junction polarized node particles.

Answer 4

Here's a really good explanation.

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html