Page 303 -

FIGURE 9.2
Scrambled image of Pb. 9.16.

9.4 Lorentz Transformation*

9.4.1 Space-Time Coordinates
Einstein’s theory of special relativity studies the relationship of the dynamics
of a system, if described in two coordinate systems moving with constant
speed one from the other. The theory of special relativity does not assume, as
classical mechanics does, that there exists an absolute time common to all
coordinate systems. It associates with each coordinate system a four-dimen-
sional space (three space coordinates and one time coordinate). The theory of
special relativity associates a space-time transformation to go between two
coordinate systems moving uniformily with respect to each other. Each real
point event (e.g., the arrival of a light flash on a screen) will be measured in
both systems. If we distinguish by primes the data of the second observer
from those of the first, then the first observer will ascribe to the event the
coordinates (x, y, z, t), while the second observer will ascribe to it the coordi-
nates (x′, y′, z′, t′); that is, there is no absolute time. The Lorentz transforma-
tion gives the rules for going from one coordinate system to the other.
Assuming that the velocity v between the two systems has the same direc-
tion as the positive x-axis and where the x-axis direction continuously coin-

© 2001 by CRC Press LLC