# On the Virtual Photons

1. Aug 21, 2010

### Anamitra

Virtual photons are not "observed" because they have a deficit of energy. When they are emitted from particles momentum is conserved but energy is not conserved. The deficit of energy is accommodated with the uncertainty relation:

delta_E * delta_t of the order of h_bar

Now if delta_t is large , $$\Delta$$E becomes very small and the uncertainty in energy disappears and we should have "true photons". The "infinite range" of electromagnetic interaction lends support to this assertion. But an electromagnetic interaction is never accompanied by the mediation of true photons even when we consider charges at macroscopic distances.

2. Aug 21, 2010

### muppet

I'm not sure it's really helpful to let a theorem from NRQM interfere with the definition of a concept from field theory. (After all, how much more relativistic could you get?)

To my mind, a virtual photon isn't virtual because of some uncertainty in the energy. Virtual photons are those that mediate interactions, and don't appear on the external legs of Feynman diagrams. What makes them 'virtual' is that as you have to consider zero-, one-, two-, ..., n- loop processes, it's not possible to say that some definite number of photons actually exist.

Also, I believe I'm right in saying that actually energy *is* conserved when a particle emits a virtual photon. The reason virtual particles are "off-shell" -i.e. don't satisfy $$p^{\mu}p_{\mu}=m^2c^4$$ is precisely so that they can carry whatever energy and momentum are necessary to ensure momentum and energy conservation at each vertex of a Feynman diagram, forcing their mass into a particular "non-standard" value.

3. Aug 23, 2010

### Anamitra

It is indeed true that both energy and momentum are conserved at the vertices of the Feynman-Diagrams. And the time interval of travel/propagation of the virtual photon is very small.If we apply the time-enery uncertainty relation there is no problem indeed.
Let us now consider a a pair of charges separated by a large macroscopic distance.

Is the process mediated by the exchange of the virtual electrons or the classical electromagnetic field?
In case the interaction is mediated by the virtual photons, it appears, there is some problem.

4. Aug 23, 2010

### haushofer

That's why I never really understood how the notion of "virtual" from nonrelativistic QM (energy-time uncertainty) is often mixed up with the notion of "virtual" in QFT (intermediate off-shell states which appear in perturbation theory).

5. Aug 24, 2010

### muppet

I really don't think there is. I don't understand why
1)You care about a supposed tension between different models of a process, one of which is obviously a better model than the other one. Like I said,
2)that even if we make allowances for a dodgy hand-waving semiclassical treatment within the framework of ordinary QM, you care about the fact that $$\Delta E$$ isn't huge. So what? These arguments are usually to justify the idea of pair production in the context of vacuum fluctuations without going into the full machinery of field theory. In that case, it's only the uncertainty in energy that allows the particles to exist, and the mass of the particle puts a lower bound on $$\Delta E$$. Here the it's the energy from the EM field that gives rise to their existence, and over macroscopic distance scales this approximation turns out to be better. Is that so disturbing? :tongue:

I think it's because students are introduced to the idea of photons long before they're introduced to field theory. For example, I don't know where you're from but the photoelectric effect is on A-level syllabuses in England, wheras I didn't do any field theory until my fourth year of university. The concepts of pair production etc. 'leak out' of their proper context (because they're interesting, and occasionally pedagogically useful), and the uncertainty principle + mass-energy relation trick is the easiest way of making the fix sound plausible. Even in an introductory QFT course (see e.g. Zee's text) it's a common way of introducing the idea that the union of QM and special relativity necessitates variable numbers of particles.