How is energy conserved during redshift?
Redshift is not produced by DISTANT objects, but by RECEDING objects. There is no decrease in energy, it just reaches us a little less at a time, sort of on the installment plan – because its source is moving away from us! Redshift is the same phenomenon as the Doppler effect, where the frequency (pitch) of an approaching sound increases, but the pitch of a receding sound decreases. There is no change in the energy of the sound, but its different pitch is an artifact of the movement of the source relative to the recipient. Frequency of sound waves produce pitch, frequency of light waves is color. Moving away, pitch is lower or light is redder; moving toward you makes the pitch higher or the light bluer.
Yes, this is one of the good questions in special relativity. The relationship E=hf applies in an observer’s frame of reference, to a photon emitted or absorbed by a stationary particle. But the distant emitting object is not stationary in our frame, therefore the energy of the emitted photon [in our frame] must be calculated by a more complicated formula involving both the emitted frequency f1 and v/c, where v is the velocity of the receding object. When you apply this, the energy of the emitted photon in our frame turns out to be less than its energy hf1 in the frame of the receding object, and is in fact (surprise!) equal to hf2 where f2 is the received (Doppler-shifted) frequency. Phew!
It comes from Conservation of Energy. Gravity warps space ====> Space near a mass is at a lower energy potential than space farther from the mass (General Relativity). Even photons leaving a star must lose energy to climb out of the gravitational well. They cannot slow down since c is constant so they must lose energy some other way. The way energy is lost is by increasing wave length, red shift. In the case of a Black Hole the photons lose all their energy and disappear. Also, stars are moving away from us in an expanding universe, so the Doppler Effect also occurs.
