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For other waves like water or sound, it is easy to understand Doppler effect, because for those waves, the speed of wave in different inertia reference frames changes.

But for light wave, the speed is a constant regardless which inertia frame the observer is in.

Think about the following experiment. There are two inertia refernece frames:

X: Stationary

Y: Moving away from X at a constant speed (zero acceleration)

A laser receiver is fixed to the stationary reference frame X, which can only be triggered by blue laser.

A laser emitter is fixed to the moving reference frame Y, which only emits blue laser.

For an observer in Y, he sees blue laser shining on the receiver, so he sees that the receiver is triggered.

But for another observer in X, he sees red laser (due to Doppler redshift) shining on the receiver, so he see that the receiver is not triggered.

How do you explain this paradox? What is wrong? If there is no redshift, everything reconciles.

enter image description here

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Your "paradox" is solved by noting that although the observer in frame Y believes he is shining a blue laser towards the switch, nothing happens. Your sentence "so he sees that the receiver is triggered" is incorrect. That is because, as you say, the light received in X is redshifted.

According to an observer in frame Y, the switch would need ultraviolet light to trigger it. i.e. Observers in different frames of reference would disagree on the required frequency to trigger the switch, though they could easily do the calculation to show that they did agree on the frequency as seen in the stationary frame of the switch.

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  • $\begingroup$ But shouldn't all laws of physics are the same in different inertia reference frames? If an electron is agitated by blue laser in X, shouldn't it also in Y? $\endgroup$
    – ayuanx
    Jan 1, 2016 at 10:22
  • $\begingroup$ I guess that means all kinds of abstract "values" are relative to reference frames, except SPEED OF LIGHT? $\endgroup$
    – ayuanx
    Jan 1, 2016 at 10:42
  • $\begingroup$ The "laws of physics" are invariant. In frame Y the switch is receding from the laser with some speed. The two situations are not the same. Yes, may things in relativity are frame-dependent: lengths, time intervals, frequencies, energies. Along with the speed of light, rest mass is invariant, but there are also other more abstract quantities. $\endgroup$
    – ProfRob
    Jan 1, 2016 at 10:52

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