"Neil" wrote in message
...
This is a curious problem. It looks basic enough to have been considered
before,
but I find nothing related anywhere.

Background: The gravitational Doppler shift formula is straightforward when
the
energy change is proportionately small. Tracking energy E, we take
E_received = E0 (1 - g dot h/c^2).
Following the equivalence principle, we expect this to apply in general to
relative gravity fields, whether "real" or caused by relative motion, or even
the *combination of both*.
snip
Just so there isn't any confusion about proper versus measured length, here's
the corrected portion referencing proper elevator height L0:

E_received = E0 [1 - gamma*g L0 (1 + v/c)/c^2]


Since the g' felt in K' is multiplied by gamma (check with transformations), the
actual discrepancy versus relative g' is
E_received = E0 [1 - g' L0 (1 + v/c)/c^2]. This seems like it would violate
energy conservation, since the photon's energy change does not correspond to the
work doing moving the mass-energy in the local g', but remember that when we
move the elevator, the impulse from photon emission and reception must be
accounted for.