# How does a photon carry force?

Can you explain why virtual photons do not obey this law? I'm not challenging that you are correct, but I hadn't seen before that virtual photons fail this equation. Or am I misreading you?
You are not misreading me, that's a fact.
About the reasons for which they don't obey the law, instead, I have less knowledge.
Let's try with an example, if the conclusions are wrong I hope someone helps correcting me.
Two electrons collide head-on along the x axis with equal and opposite speeds. The virtual photon image describes this process with the exchange of a virtual photon between the two electrons. If every electrons, because of the velocity change in the process, acquires a momentum p, then the virtual photon carries a momentum p. Now let's see the energy. Every electron, after the collision, has exactly the same energy as before, so if energy conservation still have to hold, the virtual photon should have zero energy. How's possible that a real particle has momentum but no energy?

tiny-tim
Homework Helper
Hi FireBones!
But which is (I am just asking) the physical meaning of a particle (I'm talking of virtual particles of course) which energy E and momentum p don't obey E2 = (cp)2 + (mc2)2 ?
How much or to which extent can we believe in the physical existence of a matematical tool which is very useful in physics but cannot be directly measured? (Difficult question, I know)
Can you explain why virtual photons do not obey this law? I'm not challenging that you are correct, but I hadn't seen before that virtual photons fail this equation. Or am I misreading you?
"not obeying this law" is usually called "off mass-shell" … see http://en.wikipedia.org/wiki/On_shell_and_off_shell" [Broken]
But this means that all photons have to be force carriers, not just these virtual ones. While I alluded to virtual ones in the Feynman book, it seems that this is unnecessary. If "the carrier of the EM force" is a suitable definition for "photon," than any photon should be transmitting EM force...not just the virtual ones.
Neither real nor virtual photons "carry" force … the force comes from the field, and the virtual photons are mathematically connected with the field.
About the reasons for which they don't obey the law, instead, I have less knowledge.
Let's try with an example, if the conclusions are wrong I hope someone helps correcting me.
Two electrons collide head-on along the x axis with equal and opposite speeds. The virtual photon image describes this process with the exchange of a virtual photon between the two electrons. If every electrons, because of the velocity change in the process, acquires a momentum p, then the virtual photon carries a momentum p. Now let's see the energy. Every electron, after the collision, has exactly the same energy as before, so if energy conservation still have to hold, the virtual photon should have zero energy. How's possible that a real particle has momentum but no energy?
That's a valid proof of why, if a single virtual photon was exchanged, it would have to be off mass-shell.

But the correct mathematical description of a collision between two electrons is that an infinite number of virtual photons (and virtual electrons! ) are involved, of all possible momentums (moreover, if they are on mass-shell, they also appear at all possible locations in space-time, but if they are off mass-shell, they have no location, and exist in an imaginary "momentum-space").

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Hi FireBones!

"not obeying this law" is usually called "off mass-shell" … see http://en.wikipedia.org/wiki/On_shell_and_off_shell" [Broken]

Neither real nor virtual photons "carry" force … the force comes from the field, and the virtual photons are mathematically connected with the field.

That's a valid proof of why, if a single virtual photon was exchanged, it would have to be off mass-shell.

But the correct mathematical description of a collision between two electrons is that an infinite number of virtual photons (and virtual electrons! ) are involved, of all possible momentums (moreover, if they are on mass-shell, they also appear at all possible locations in space-time, but if they are off mass-shell, they have no location, and exist in an imaginary "momentum-space").
Wow, I understood that completely... which probably explains the sudden nose-bleed... and blindness... and incontinence... and headache. Ahh... virtual particles... *gulps aspirin*

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Force = change in momentum

Photon carries momentum !

Force = change in momentum

Photon carries momentum !
:uhh:

The photon provides kinetic energy, the direction does not matter. The reason why is because there is no physical state that exists where the electron crashes into the nucleus. This means that if an electron is given kinetic energy it will always be beneficial to keeping the electron in orbit.
Hmm...what about the neutron star? i think electrons and protons collide with neutrons and release neutrinos by the effect of the weak force.

Hmm...what about the neutron star? i think electrons and protons collide with neutrons and release neutrinos by the effect of the weak force.
That is a matter of degeneracy... a unique case.

Just a detail …

that's not "the" Physics FAQ, it's John Baez's Physics FAQ.
The first sentence is "This is the web version of the Usenet Physics FAQ." The Title is "Usenet Physics FAQ". The Copyright statement doesn't mention him. The main text mentions some history of original creation and maintenance, but his name is absent. The "Thanks" at the bottom does mention him, along with many others. The individual page cited is by Matt McIrvin.

Am I missing somewhere where proper citation format is given?

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The first sentence is "This is the web version of the Usenet Physics FAQ." The Title is "Usenet Physics FAQ". The Copyright statement doesn't mention him. The main text mentions some history of original creation and maintenance, but his name is absent. The "Thanks" at the bottom does mention him, along with many others. The individual page cited is by Matt McIrvin.

Am I missing somewhere where proper citation format is given?
He meant to clarify that it was the physics FAQ of a different site, not this one. I think.

tiny-tim
Homework Helper
Usenet Physics FAQ

He meant to clarify that it was the physics FAQ of a different site, not this one. I think.
Thanks, Frame Dragger!

Yes, PF has its own FAQs on various topics, which are normally referred to first.
The first sentence is "This is the web version of the Usenet Physics FAQ." The Title is "Usenet Physics FAQ". The Copyright statement doesn't mention him. The main text mentions some history of original creation and maintenance, but his name is absent. The "Thanks" at the bottom does mention him, along with many others. The individual page cited is by Matt McIrvin.
Yes, I assumed that since it was on the well-known John Baez website that it was organised by him.

I now realise that he's just one of eleven hosts in seven different countries …

From http://math.ucr.edu/home/baez/physics/index.html" [Broken] …
This is the web version of the Usenet Physics FAQ (Frequently Asked Questions). Its purpose is to provide good answers to questions that have been discussed often in sci.physics and related usenet newsgroups. The articles in this FAQ are based on those discussions and on information from good reference sources. That does not mean that they are always perfect and complete.​

Thanks go to John Baez, Ronen Ben-Hai, Jay Brown, Jon Butterworth, Alan Cairns, Dave Edsall, Harald Falkenberg, Philip Gibbs, Amarendra Godbole, Chris Hillman, Chung-rui Kao, Matt McIrvin, Joe Mirando, Matthew Parry, Han-Tzong Su, Nathan Urban, Johan Wevers, Sam Wormley, and the various organisations for hosting us! If any other non-commercial sites would like to mirror this FAQ, please contact the editor.​

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:uhh:
Yes, that is the whole point, with QED picture there is no "action at a distance" since I said that force is change in momentum, anything that carries momentum can exert a force by passing on the momentum.
Every photon can only be specified by its momentum and its polarization

abrogard