Why all classical physicists expected light speed to vary...and why they were wrong.
The ONLY reason why classical physicists were expecting to see a variance in the speed of light for moving observers was because they were illogically applying Galileean relativity to waves, and added the speed of the observer to the speed of the wave, thus getting c+v or c-v as the speed of the wave in the observer's frame. If they didn’t all do that foolish thing, they would have NOT expected the speed of light to vary for moving observers ! Which means that, if they correctly understood and applied classical physics, they should have expected it to NOT vary, aka INVARIANCE instead of VARIANCE !
The latter is clearly wrong from a classical physics framework because the speed of the wave only depends on the properties of the medium, and because the wave has a PREFFERED FRAME which is the rest frame of the MEDIUM. Therefore it is illogical to use the rest frame of the Observer as the preffered frame of the wave, and then use Galileean additions to calculate the speed of the wave. Doing that only returns the CLOSING SPEED between observer and wave crests, which is NOT the speed of the wave. The logical and correct way to calculate the speed of the wave in the frame of the observer is by using the WAVE EQUATION, v=flambda, and using the (Doppler shifted) observed frequency and wavelength, as shown below:
Galileean relativity treats all frames as equal, so any rest frame can be used as a preffered frame. But they’re obviously NOT equal in the case of waves, since their preffered frame is always the rest frame of their medium, and that cannot be changed with the rest frame of a moving observer. It is illogical and wrong to do that, and ALL physicists did that fundamental error ! That’s why they were expecting the speed of light to vary for moving observers. Because they were foolishly and illogically applying Galileean relativity to waves.
Galileean relativity only applies to particles/objects, and not to waves. Because particles/objects inherit the speed of the frame they are in, for example if you throw a ball in moving train the ball’s speed adds to that of the train. Waves dont do that. If you move a speaker in air the speed of the sound emmited by the speaker does not add to the speed of the speaker, because the speed of the wave only depends on the properties of its medium. So galilean relativity/velocity addition clearly does NOT apply to any waves, including sound and light waves.


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