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It was recently pointed out to me that the finite electron mass puts a lower bound on the Mandelstam variable t describing the square of the transferred momentum in the centre-of-mass frame, [itex]t_{min}=m_{e}^{2}[/itex].

This solved a problem I was worrying about (the finiteness of the tree-level approximation to elastic scattering), but gave me a new one to worry about.

I've often heard it said that whenever a photon leaves a radio-transmitter to be received by my radio, it must be slightly off-shell, simply by virtue of the fact that it's emitted and absorbed. But apparently the minimal virtuality of the photon is set by the electron mass, which corresponds to an energy in thegamma ray spectrum, right?

So if all of this is true, then why does classical electrodynamics describe radio waves well when the virtuality of a photon is vastly larger than its 3-momentum?

Thanks in advance.

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# Virtuality of a nearly on-shell photon

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