A laboratory for light
The fractional stretch of a photon’s wavelength. Doppler, gravitational, and cosmological shift are three faces of the same 4-vector ratio. Only the last of those has no global energy ledger.
1 + z = λo / λe = (kμ uμ)e / (kμ uμ)o
Frequency is −k · u. Doppler and gravity have conserved charges. Cosmology does not — that is the energy disconnect.