Reference: Einstein’s 1920 Book
Section XI (Part 1)
The Lorentz Transformation
Please see Section XI at the link above.
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Summary
Classical mechanics holds that space and time intervals between two events are independent of the condition of motion of the body of reference.
It is possible to derive a mathematical relationship for the distance and time characteristics of coordinate systems, such that, the velocity of light always has the same value despite their different motions.
Every event can be represented uniquely in each coordinate system. That coordinate system has a unique motion relative to other coordinate systems. The mathematical relationships among the coordinates of different systems is thus generated by the fact that the speed of light remains constant for all coordinate systems despite their different motions. This gives us the Lorentz transformations.
If we substitute an infinitely large value for the velocity of light c in the Lorentz transformation, we obtain the Galilean transformation.
We can readily see that, in accordance with the Lorentz transformation, the law of the transmission of light in vacuo is satisfied for coordinate systems moving with different velocities.
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Comments
The mathematical derivation of Lorentz transformation is based on the considerations expressed in Appendix I.
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