Owing to the principle of relativity, the present state of knowledge
explicitly allows Maxwell's equations to be solved not only in the rest
frame of an electromagnetic transmitter but also directly in the rest
frame of the receiver without use of the Lorentz transformation and the
Lorentz force. Recently, such a calculation was first performed for the
Hertzian dipole. The analysis of the resulting formula breaks new
scientific ground and indicates that Maxwell's equations predict that
electromagnetic waves in vacuum propagate at the speed of light, notably
for each receiver, even when these receivers have relative velocities
with respect to each other. Although this paradoxical phenomenon was
expected, the finding that Maxwell's equations nevertheless predict a
classical Doppler effect was unexpected and indicates inconsistent or
not yet fully understood aspects of canonical Lorentz-Einstein
electrodynamics consisting of Maxwell's equations, Lorentz force and
Lorentz transformation.