  This paper identifies specific angles of emission and reception of light for
which there exists a mass-energy counterpart to the well known transverse
Doppler shift. At these angles, the relationship of proper and relative
frequency is the same as that for proper and relative mass-energy of a source.
Paradoxically, the transverse Doppler shift is often used to demonstrate that
for specific angles of emission and reception the relationship of proper and
relative frequency of light is the same as that for proper and relative time.
But by carefully defining angles, this apparent paradox is resolved.
