Einstein says in The Evolution of Physics:
We really have no choice. We tried to save the Galilean relativity principle by assuming that systems carry the ether along in their motion, but this led to a contradiction with experiment. The only way out is to abandon the Galilean relativity principle and try out the assumption that all bodies move through the calm ether-sea.
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Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 using the example of a ship traveling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary.
It is assumed that the medium should move with the motion of inertial frame along with the disturbance, as in the case of sound waves, for Galilean relativity to work. Thus, ether as the medium of light is expected to move with the inertial frame, but there is no experimental evidence found for that.
This can be explained by observing that the inertia associated with the medium of light is several orders of magnitude smaller than the inertia associated with the medium of sound. An object cannot move through a “medium” having the same order of inertia. But such restriction need not apply when the “medium” has a level of inertia several orders of magnitude smaller.
Galilean relativity applies only to objects and medium that has the same order of inertia. We simply have to be aware of this limitation. We need not abandon the Galilean relativity principle.
The error has been in viewing everything physical from the inertial frame of matter.
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Addition (September 27, 2019)
Lorentz transformation of relativity reduces to Galilean transformation when ‘c’ is infinite. That means that Galilean transformation applies to motion that is absolute. Newton looked the background of stars as the basis that was at absolute rest.
Therefore, Galilean transformation applies to absolute motion, which is the inverse of the density of substance (see The Universal Frame of Reference). Galilean transformation does not apply to relative motion except when density is constant.
Therefore, Galilean transformation applies in the material domain as long as the density of objects is comparable. This is not the case with Mercury, which 4 times as dense as the Earth and 12 times as dense as the Sun. That is why we get an error when we use Newton’s laws, that support Galilean transformation, to calculate the precession of the perihelion of Mercury’s orbit.
We get better results when we use Lorentz transformation because we are using light as the basis. This does not rectify the error completely because ‘c’ is very large but not infinite. We may be able to rectify the error completely if we can determine the absolute motions of all the bodies involved using their density and then use Galilean transformation.
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