Reference: Einstein’s 1920 Book
Section V (Part 1)
The Principle of Relativity (In the Restricted Sense)
Please see Section V at the link above.
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Summary
Uniform translation means constant velocity and direction with no rotation. If that is the case with different coordinate systems then they are all Galilean in nature, and the mechanical laws of Galilei-Newton hold good with respect to all of them.
The principle of relativity (in the restricted sense) states that the natural phenomena run their course with respect to all Galilean coordinate systems according to exactly the same general laws.
Classical mechanics affords an insufficient foundation for the physical description of natural phenomena, such as, the phenomena of electrodynamics and optics. So the validity of the principle of relativity needs to be looked at more closely.
The principle of relativity applies with great accuracy in the domain of mechanics. It is possible that Galilean system we have chosen in this domain is “absolutely at rest,” while the systems that describe the phenomena of electrodynamics and optics are “in motion.”
The Galileian co-ordinate system of the earth is in motion relative to the Galileian co-ordinate system of the sun. One would expect anisotropic properties due to change in directions of the earth but none have been found so far. Therefore, the principle of relativity applies at least over the range of motion for the matter.
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Comments
The changes in the state of motion of various Galilean co-ordinate systems, in the material domain, do not appreciably affect the validity of the principle of relativity. In other words, the law of inertia is pretty much constant for matter in spite of differences in motion.
It is possible that there are imperceptible changes in inertia responsible for the changes in motion.
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