[vlasta2]

With sound waves, your speed is added to the speed of sound and you hear a different note. With light, the speed remains at c, but perceived energy of the photons is still affected (energy must be preserved after all). And energy ~ wavelength ~ color.

You can also think about it being one of these "zero (weight of a photon at rest) multiplied by infinity (energy of objects moving at c) gives a finite number (actual energy of a photon)". The last number still behaves nicely.

[undershirt]

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.)

[psykotic]

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.

[elwin]

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