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In radio communication each accelerated electron in the transmitter antenna interacts with an electron in the receiver antenna by exchanging a photon.

Is that photon always a virtual photon as described in the diagram below rather than a "real" photon?

enter image description here

As I understand it, Feynman's definition of a virtual photon in his book QED is any exchanged photon that does not appear in the initial or final conditions. Therefore by his definition radio works by using virtual photons.

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This is a perceptive question. Consider the following from the Wikipedia article "Virtual Particle":

As a consequence of quantum mechanical uncertainty, any object or process that exists for a limited time or in a limited volume cannot have a precisely defined energy or momentum. This is the reason that virtual particles — which exist only temporarily as they are exchanged between ordinary particles — do not necessarily obey the mass-shell relation. However, the longer a virtual particle exists, the more closely it adheres to the mass-shell relation. A "virtual" particle that exists for an arbitrarily long time is simply an ordinary particle.

However, all particles have a finite lifetime, as they are created and eventually destroyed by some processes. As such, there is no absolute distinction between "real" and "virtual" particles. In practice, the lifetime of "ordinary" particles is far longer than the lifetime of the virtual particles that contribute to processes in particle physics, and as such the distinction is useful to make.

Also, consider this from the Wikipedia article "Near and far field":

In the quantum view of electromagnetic interactions, far-field effects are manifestations of real photons, whereas near-field effects are due to a mixture of real and virtual photons. Virtual photons composing near-field fluctuations and signals, have effects that are of far shorter range than those of real photons.

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  • $\begingroup$ So in practice all photons are virtual since they have a finite lifetime. A "real" photon is an unachievable ideal which represents the limit where the lifetime goes to infinity. However, it becomes useful to approximate photons as real. This is in the same spirit as, say, approximating a piece of iron as a rigid body. $\endgroup$ – Brian Moths Dec 19 '13 at 15:39
  • $\begingroup$ @NowIGetToLearnWhatAHeadIs, see this question: physics.stackexchange.com/questions/17087/slightly-off-shell and Ron's answer: "The reason people say this is because all particles you see are absorbed after a finite time, and the notion of on-shell is asymptotic. The finite time means that they are really internal lines in a diagram, and so ever-so-slightly off shell. The exactly on-shell S-matrix is an asymptotic quantity, relevant only in the holographic limit." $\endgroup$ – Alfred Centauri Dec 19 '13 at 15:47
  • $\begingroup$ @AlfredCentauri : "However, the longer a virtual particle exists, the more closely it adheres to the mass-shell relation.". The problem, with this formulation, is that we are mixing position space and momentum space. If we look at a propagator in position space, we get (very roughly) $D(x) \sim \frac{1}{x^2}$. So, the main contribution to the amplitudes are around $x^2=0$. But there is no special constraint on differences of time, here $x^o$. It just indicates that the main contribution corresponds to $\vec x^2- (x^o)^2 \sim 0$ $\endgroup$ – Trimok Dec 19 '13 at 15:59
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The question here really is: "When are photons not virtual?". As explained in this article:

A virtual particle is one that has borrowed energy from the vacuum, briefly shimmering into existence literally from nothing. Virtual particles must pay back the borrowed energy quickly, popping out of existence on a time scale set by Werner Heisenberg's uncertainty principle.

So to answer your question- a photon exchanged over long ranges is outside of the scale of the uncertainty principle so the photon exchanged between the two electrons is real. Also see: http://en.wikipedia.org/wiki/Virtual_particle#Actual_and_virtual_particles_compared

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Radio and the like are best described quantum mechanically in terms of coherent states of the electromagnetic field. These states don't have a definite "number of photons", but are rather like an infinite mush of harmonic oscillator states that behave the most like classical electromagnetism.

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