According to Doppler redshift, the frequency of the EM radiation decreases if the emitting object is receding from the observer - this produces the problem in the quantisation of energy - the observed photon energy should be less than the energy emitted, so is conservation of energy violated?
Unable to find an explanation here, I asked this question one day and my physics teacher produced a proof of that the total energy is conserved between the emission and the effect of redshift. He has given the permission to post the proof here in case anyone is interested to have a look.
Here's the proof:
When a photon is received from a galaxy receding from us with a recession velocity v, its observed frequency is reduced by an amount Δf where: Δf/f ≈ v/c
so: Δf ≈ vf/c
This means its energy appears reduced by an amount:
hΔf ≈ hvf/c (1)
However, the photon has momentum, so the object in the receding galaxy that emitted the photon will experience an equal and opposite change in momentum:
mΔv = h/λ (2)
This will increase its kinetic energy in our frame of reference by an amount ΔKE, where:
ΔKE = ½ m(v+Δv)^2 - ½ mv^2 = ½ mv^2+ ½ x 2mvΔv + ½mΔv^2 - ½ mv^2
≈ mvΔv (3)
(since the ½mΔv2 term is negligible in comparison)
Substituting equation (2) into (3), we have:
ΔKE ≈ hv/λ ≈ hvf/c
We can see that the loss of energy of the redshifted photon in our frame of reference is exactly equal to the gain in kinetic energy of the object that emitted the photon as observed in our frame of reference, thus there is no violation of energy conservation.
We'd appreciate it very much if anyone could kindly criticise this proof =)