Reference: Einstein’s 1920 Book
Section VI (Part 1)
The Theorem of the Addition of Velocities Employed in Classical Mechanics
Please see Section VI at the link above.
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Summary
In classical mechanics, we have the theorem of addition of velocities when there is a system of reference that itself is moving relative to another system of reference. But this theorem does not always hold in reality.
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Comments
When a body of reference is moving, its internal inertia also plays a part. That is why different bodies have different uniform velocities inherently. But, in material domain, the difference in inertia is so small that it is practically imperceptible.
Therefore, in most cases in the material domain the inertia can assumed to be constant. This allows velocities of the same order of magnitude to be simply added. But when the two velocities are not of the same order of magnitude, the theorem of addition cannot be applied.
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