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Regarding:
Thus an e/m wave doesn't "carry" mass thus no momentum -- there is a charge
at the "originating" site which does impose a force on the distant site
thus it may cause some momentum at that site. We just imagine a wave
momentum which we hope will make calculations easier -- just as we talk
about E/M "fields" which are not "real" either but are sometimes helpful
to imagine.
This is simply incorrect. [...] Any attempt
(even at the purely classical, nonquantum level) to "integrate out" the
field degrees of freedom from the (charged matter + EM field + their
mutual interactions) Lagrangian results in a very nonlocal particle-only
theory which can only be solved perturbatively in inverse powers of c^2.
[...]