# Virtual photons, what makes them virtual?

The electromagnetic force can be described by the exchange of virtual photons.

The virtual photon thing baffles me a little. I get that virtual particles are supposed to be short lived, but as photons live for zero units of proper time I can't see how their lifetime can be used to distinguish between virtual and non-virtual.

Another idea I had was that virtual photons are only those associated with the electromagnetic field, non-virtual ones are not. But in this case, I could not see what was wrong with this: If I have a photon detecting instrument it is just detecting the force carrying particles of the electromagnetic interactions between it and the thing I am using it to observe? (even if that thing is a long way away)

Are virtual photons just photons that you don't observe? Or, is there some kind of photon that is not connected with the electromagnetic field? Or something else? Or perhaps there is no concrete distinction to be made?

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If I remember correctly, virtual photons are one of the concepts that are introduced by theoretical calculations of QFT/QED. Basically you can introduce them, because you do not violate Heisenberg's uncertainty principle. They come in handy in certain calculations to do some trickery. –  sebastian Jun 23 at 16:13
A virtual photon need not be what we call 'on the mass shell'. This means it doesn't have to follow the usual dispersion relation. For virtual photons e.g., this means $\omega = ck$ needn't be satisfied. In fact, virtual photons shouldn't even be thought of as particles. We associate the name with mathematical expressions that are reminiscent of the actual particles when doing calculations in interacting QFT. –  Wouter Jun 23 at 16:16
In other words, virtual photons don't "exist." They're just tricks of math that work, and give some surprisingly accurate predictions of reality that are so good, we have to accept them as "real." –  markovchain Jun 23 at 16:38
–  Qmechanic Jun 23 at 16:41
@Qmechanic Thanks. The end of Arnold Neumaiers answer addresses my question directly, though his opinion seems to be rather controversial. –  Lucas Jun 23 at 17:08

Virtual particles appear when one wants to calculate cross sections and branching ratios for elementary particle interactions. This is done with the prescription of Feynman diagrams

Feynman Diagram of Electron-Positron Annihilation

In the above diagram the external "legs" are real particles with the quantum numbers given in the standard model table, including the mass.

The red line between the dots (interaction vertices) can be considered either a virtual electron going to the right and at the interaction point becomes a positron, since a backwards in time electron is a positrong. Or a positron going to the left and becoming an electron ( since a backwards int time positron is an electron). You may not believe it, but this translates into a mathematical formula which gives the value for the cross section for e+ e- annihilation into two gamma.

The virtual exchanged particle has the quantum numbers of the real particle, that is why the name carries, but it can be off mass shell: its four momentum does not dot into the mass squared.

Here are different Feynman diagrams which enter into calculating scattering crossections.

The exchanged particles between the vertices are virtual. They have all the quantum numbers of their name, except the mass which is off mass shell. The photon is characterized by spin=1 and charge=0. The m=0 is not an attribute of a virtual photon.

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