Virtual Photon Lifetime: Proton in Atom Nucleus

[Jonny_trigonometry]

QFT states that all forces are due to the exchange of virtual particles, I'm interested in photons and their role in the EM force.

I was wondering what the maximum time allowed for existence of an exchange photon is when it's emmitted from a proton in the nucleus of an atom. I'm thinkin' that the number of protons in the nucleus (possibly neutrons too), and number of electrons in the cloud enveloping the nucleus has a relation to this also. My question is, what is the average time of existence of a virtual photon in these conditions, be it a function of Z and or #e or not?

Do I have to give more constraints like the atom is at rest, in zero gravity (flat spacetime), not in the vicinity of any other atoms? Can someone direct me towards a website that has some tables of virtual photon lifetimes for various situations like the above mentioned ones? Does the energy of the emmitting particle have anything to do with the energy of the photon emmitted?

 

[Jonny_trigonometry]

Do I have an incorrect understanding of how things like this work? anybody?

ok, here's my answer:

in order for a photon to be virtual, it must be undetectable by any means of measuring, so it's on "the other side" of the energy-time unceratinty relation. It must be less than h bar/2.

so, deltaE*deltaT must be less than hbar/2. since the photon is created out of nothing, deltaE is hf, so deltaT<1/(f*4Pi). what is f? I'll guess and say that it's the frequency of the proton's matter wave: f = mpc^2/h. This is such a sorry excuse for real physics I know: delta T max is about 1.0512*10^-24 seconds, which means it can only travel about 10^-16 meters... Yeah, I have no idea how to answer the question, that's why I ask.

 

[masudr]

A higher energy particle can be created out of the vacuum for shorter periods of time. So if you want a very high-energy photon (which corresponds to a higher frequency photon - say a photon in the X-ray region of the EM spectrum) it will only last in the vacuum for a short period of time.

But this is a very simple way to look at things; the full machinery of QFT is fairly complicated and involved mathematically.

 

[Jonny_trigonometry]

hmm, yes. What is the average photon frequency that mediates the coloumb force in a helium atom in ground state? Is it such a frequency that it can only travel out to about 5*10^-11 meters?

 

[masudr]

Coulomb force is a (good) approximation that breaks down in atomic scales. I don't know enough QED to give you your answer.

 

[snooper007]

From Feynman diagram, you can see that
virtual photon doesnot obey mass-energy relationship.
we can consider it as a massive photon, which acn only exist
in a very short time.