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Obviously our problem can be exactly formulated in the following

manner. What are the values x′, y′, z′, t′, of an event with

respect to K′, when the magnitudes x, y, z, t, of the same event

with respect to K are given? The relations must be so chosen that

the law of the transmission of light in vacuo is satisfied for

one and the same ray of light (and of course for every ray) with

respect to K and K′. For the relative orientation in space of the

co-ordinate systems indicated in the diagram (Fig. 2), this

problem is solved by means of the equations:

image003

y′ = y

z′ = z

image004

This system of equations is known as the "Lorentz

transformation."[9]

[9] A simple derivation of the Lorentz transformation is given in

Appendix I.

If in place of the law of transmission of light we had taken as

our basis the tacit assumptions of the older mechanics as to the

absolute character of times and lengths, then instead of the

above we should have obtained the following equations:

x′ = x - vt

y′ = y

z′ = z