How Do Virtual Photons Create Attractive Forces Between Particles?

[Vorde]

How does the exchange of virtual photons result in an attractive force (for example between a proton and electron)?

 

[mathman]

"QED" by Richard Feynman gives a complete and readable explanation.

 

[tiny-tim]

How does the exchange of virtual photons result in an attractive force (for example between a proton and electron)?

virtual photons and virtual electrons (or other massive particles) are both involved

https://www.physicsforums.com/library.php?do=view_item&itemid=287" are what Professor Susskind calls a "mathematical abstraction" …

they appear in mathematical calculations, but not in the physics …

they don't require a physical explanation ​

try a tag search (or an ordinary forum search) for "virtual particles" for some interesting discussions on exactly this topic

 

[EWH]

One closely related attractive force due to "virtual particles", the Casimir effect, has a direct and intuitive classical counterpart. In the Casimir effect, when say, two plates are brought very close together, there is an attractive force due to the fact that there are fewer wavelengths of vacuum fluctuations (therefore a reduced range of energies of virtual particles) between the plates than outside that region. Longer waves won't fit between the plates. There are more waves outside the plates than between tham so the plates are pushed together. The same thing happens when two ships come alongside each other in a choppy sea. The calm water between the ships pushes less on the inner side of the hulls than the higher waves on the outer side and the ships are driven together.

(This can be dangerous, and a range of schemes have been used to cope with the effect ranging from fenders made from old tires to complicated systems to allow naval resupply at sea.)

(Also note that this doesn't answer the question you actually asked.)

 

[Bill_K]

Vorde, You're probably visualizing the photons as little bullets that get batted back and forth between the two particles, and every time a photon hits its target, that particle will recoil a little bit, getting pushed back. Not the way it works, of course!

We draw a Feynman diagram, in which particle A emits a photon and particle B later absorbs it. What you need to remember is that this picture is not a literal snapshot of what's happening - it's more abstract. You can draw a Feynman diagram either in position space (x) or in momentum space (p). In classical mechanics you can specify both x and p at the same time, but in quantum mechanics you have to choose one or the other.

Specifically if you draw particle A to the left of particle B, that does not say anything about the momentum of the photon that's exchanged. It can push to the left or to the right, either one. So our classical instinct that A must be pushing B away leads us astray.

 

[Vorde]

Vorde, You're probably visualizing the photons as little bullets that get batted back and forth between the two particles, and every time a photon hits its target, that particle will recoil a little bit, getting pushed back. Not the way it works, of course!

We draw a Feynman diagram, in which particle A emits a photon and particle B later absorbs it. What you need to remember is that this picture is not a literal snapshot of what's happening - it's more abstract. You can draw a Feynman diagram either in position space (x) or in momentum space (p). In classical mechanics you can specify both x and p at the same time, but in quantum mechanics you have to choose one or the other.

Specifically if you draw particle A to the left of particle B, that does not say anything about the momentum of the photon that's exchanged. It can push to the left or to the right, either one. So our classical instinct that A must be pushing B away leads us astray.

Thats not what I was thinking, I'm aware of all the quantum intricacies. I was under the impression that the transfer of photons from any electromagnetic system (like a electron orbiting a proton) caused the attraction (or replusion), I was wondering how that exchange produces attraction.

In response to mathman, I have read QED, but I read it in quite a rush (I was on a plane) so I'm re-reading it right now, i'll probably be done in the next several days which may answer my queries.

Thank you all by the way.

 

[Bill_K]

i'm aware of all the quantum intricacies.

Ok fine. That's more than I can say! If you'd asked for example, "How does the exchange of virtual photons result in an attractive (or repulsive) force" I'd have known that you weren't thinking in terms of billiard balls. Coulomb repulsion is just as hard to explain as attraction.

I'm sure that Feynman has a better explanation of this, but let me add a few comments anyway. The Lagrangian has three parts: matter, electromagnetic and interaction

L = L_m + L_int + L_em where L_int = j^μ A_μ and L_em = ½ F^μνF_μν

j^μ is the current vector associated with the matter, and A_μ = (A, φ) is the electromagnetic 4-potential.

If this was a classical Lagrangian the answer to your question would be simple: vary L with respect to A_μ and get a field equation that looks like ◻A^μ = j^μ. For a particle sitting at the origin the solution of this is like A⁰ ~ 1/r. Put this result into the expression for the energy density (which turns out to be ½(E² + B²)) and you'll find that particles with different charges like (lower energy) to be together (attraction) while particles with similar charges like to be apart (repulsion).

If that all sounds familiar to you, we can go ahead and discuss the quantum version! The trick is to find a way of incorporating quantum effects (like photon emission) and classical effects (like Coulomb repulsion) side by side. In the first attempt by Dirac, A₀ was left as a classical field and not quantized at all. But his theory was unsatisfactory because it didn't preserve Lorentz invariance. The current approach is to quantize all four components of A_μ and then try to show how the exchange of an infinite number of timelike (A₀) photons leads to a Coulomb potential. In fact, that part of the Lagrangian pertaining to timelike photons is never expanded into Feynman diagrams at all, it is split off and treated separately.

I'd better stop at this point and see if you are still with me on this!

 

[Shaw1950]

One way of looking at it is to look at Coulomb scattering of two negatively (or positively) charged particles.

In the Classical (non-Quantum) picture the two particles slow down before rebounding; simultaneously, the energy in the electric field rises and then falls again (as does the field itself) over a short time period. To me that short-lived field is the classical equivalent of the "virtual photon".

With QM the short-lived energy in the field gains uncertainties that were absent in the Classical field description - so called fluctuations. If you to measure the field multiple times, you would get slightly different results, all clustering around a mean. It's as if the electric field is flickering in the QM picture.

I'd be grateful to some of you experts commenting on this interpretation.

 

[Shaw1950]

Dear Bill, I am with you, please tell me more about the method(s) of solving the timelike (A0) component. I gather pertubation methods are out, so what alternatives are available? I also understand that the path integral solution was only published in 1979 by Duru and Kleinert, so what preceded that?

Also Feynman in his QED lectures illustrates the hydrogen atom as a series of virtual photon exchanges, but I thought that perturbation was inapplicable to this static bound state?