# Relativistic Doppler effect and Quantum Mechanics

Consider the situation below. I’m at a point in space along with a bunch of detector away from any gravitational field. I see a star moving away from me at a relative speed of $$v$$by measuring the velocity I can know the frequency shift of the light. That is the redshift. $$f=F*\sqrt{\frac{1-(v/c)}{1+(v/c)}}$$

Here f is the observed frequency and F is the source frequency.

Now consider this. For a photon of light which is near to the source, the energy can be given by $$E=h*F$$ But the same photon near me or my detector( which is close to me) will have the energy $$E’=h*f$$ Since $$F>f$$ Therefore $$E>E’$$ *from the above Doppler shift equation

Since this energy is lost where exactly is it lost ?

Does it get absorbed by the ‘fabric of space time’?

But if energy is conserved and $$E=E’$$ Then what am I missing from the above equations?

• Energy is not invariant under Lorentz transformations. I.e. different observer disagree. For each observer energy is conserved though (if you forget about an expanding universe) – lalala Mar 18 '18 at 20:11
• @lalala: That should be an answer. – user4552 Mar 18 '18 at 20:16

• Thanks for the answer . But what if the universe is expanding? Does that mean that$$E=E’$$ or does it mean that energy is lost? – physics2000 Mar 19 '18 at 4:41