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So, the speed of an observer affects its perceived energy of light. How does "conservation of energy" apply? (I don't know what is contributing to the energy of this system.)

If you imagine an idealized light source, where photons come into existence out of nowhere, then there is no conservation of energy (energy is being created). But in a more realistic model where photons are emitted as a result of electron excitation, say, energy is conserved because the electron recoils when firing off the photon, so the extra observed energy of a blueshifted photon can be found in the extra kinetic energy of the electron as observed in that same frame of reference.

Different observers will perceive different values for the photons' energy, but they will all observe that the total energy does not change.

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