Why the Michelson experiment can only detect invariant light speed

In classical wave physics, the Doppler effect occurs when there is a relative motion between the source and observer. If there is no relative motion between source and observer, such as when they are at rest in the same inertial frame, there is no Doppler shift. In that case the observer measures the same frequency and wavelength as if he and the source were stationary in the aether.

In the Michelson experiment the light source is comoving with the observer (both being at rest in the Earth's inertial frame), so there is no Doppler shift:

f'=f, λ'=λ

Therefore the observer measures the speed of light as:

f'λ'=fλ=c

in all directions, just as if the Earth was stationary in aether.

Therefore he measures the same speed of light c as a stationary observer in the aether would. This is why it is not possible to detect any change in the speed of light caused by the motion of the Earth relative to the aether. Because it doesnt matter how fast the Earth moves, since the speed of light does not depend on the speed of the Earth.

I solved the mistery of the invariance with basic wave physics, which these geniuses could not do for 150 years because they were illogically applying galilean relativity/transformations to waves, and then made up non-sensical transformations and theories to explain why no variance could be detected by experiments like Michelson's. When all they had to do was apply classical wave physics correctly and use the wave equation to calculate the observed wave speed for a moving observer


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