第46页 / 共212页

t′ = t

This system of equations is often termed the "Galilei

transformation." The Galilei transformation can be obtained from

the Lorentz transformation by substituting an infinitely large

value for the velocity of light c in the latter transformation.

Aided by the following illustration, we can readily see that, in

accordance with the Lorentz transformation, the law of the

transmission of light in vacuo is satisfied both for the

reference-body K and for the reference-body K′. A light-signal is

sent along the positive x-axis, and this light-stimulus advances

in accordance with the equation

x = ct,

i.e. with the velocity c. According to the equations of the

Lorentz transformation, this simple relation between x and t

involves a relation between x′ and t′. In point of fact, if we

substitute for x the value ct in the first and fourth equations

of the Lorentz transformation, we obtain:

image005

from which, by division, the expression

x′ = ct′