Einstein 1920: Simple Derivation of the Lorentz Transformation

Reference: Einstein’s 1920 Book

This paper presents Appendix 1 from the book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original publication of this book by Henry Holt and Company, New York (1920).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

The heading below is linked to the original materials.


Simple Derivation of the Lorentz Transformation

Please see Appendix 1 at the link above.



The math of Lorentz transformation is based on the consideration that the velocity of light is constant regardless of the velocity of the observer. This means that the space-time characteristics of the observer must change depending on his velocity, such that, from the viewpoint of light the velocity of the observer is zero. This produces the following equations.

When the velocity of the observer is negligible compared to the velocity of light, we have the familiar Galilean transformation. But when the velocity becomes a sizable fraction of the velocity of light the denominator in the above equations becomes less than 1, and the space-time characteristics expand.

When the velocity of the observer is very close to the velocity of light, the space time characteristics have expanded to near infinite. We may relate this to the electromagnetic spectrum. At the frequencies of light, the space-time characteristics are really magnified. At the frequency of electron inside the atom, the space-time characteristics have shrunk. When one reaches the frequency of the nucleus of atom, we have solidity due to extreme shrinkage of space-time characteristics. This is the frequency we are most familiar with. It is the frequency of the material universe.

The frequency spectrum extends from light to matter. It is a spectrum of substance that is manifested in the dimension of inertia. Inertia is how substantive the substance is. It is measured as the “duration” of substance. This is the fourth dimension and not some abstract notion of time.

The Lorentz transformation was not interpreted this way. The special theory of relativity hinted at it but did not relate it to the electromagnetic spectrum. But now we can say that the greatest contribution of the special theory of relativity is to bring this dimension of inertia to our awareness.


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