perpendicular to each other marked out, and designated as co-ordinate
planes ( co-ordinate system ). A co-ordinate system _K_ then
corresponds to the embankment, and a co-ordinate system _K _ to the
train. An event, wherever it may have taken place, would be fixed in
space with respect to _K_ by the three perpendiculars _x, y, z_ on the
co-ordinate planes, and with regard to time by a time value _t_.
Relative to _K , the same event_ would be fixed in respect of space and
time by corresponding values _x , y , z , t _, which of course are not
identical with _x, y, z, t_. It has already been set forth in detail
how these magnitudes are to be regarded as results of physical
measurements.
image002
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
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