  The relativistic Doppler effect comes from the fact that observers in
different inertial reference frames experience space and time differently,
while the speed of light remains always the same. Consequently, a wave packet
of light exhibits different frequencies, wavelengths, and amplitudes. In this
paper, we present a local approach to the relativistic Doppler effect based on
relativity, spatial and time translational symmetries, and energy conservation.
Afterwards we investigate the implications of the relativistic Doppler effect
for the quantum state transformations of wave packets of light and show that a
local photon is a local photon at the same point in the spacetime diagram in
all inertial frames.
