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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
447Theory of Special Relativity
This quadratic expression is commonly known as an interval, and we denote it by s
2
; it is an invari-
ant, independent of the frame used to measure these coordinates. To see it, let us calculate the value
of x
2
c
2
t
2
(for simplicity) in S frame in terms of x and t in S frame:
xctxut ctux c
cu
2222 22222
222
−=
+
+
=−
γγ
γ
() ()
()
/
ttuxt ux txuc
xct
22
22
222
22+
′′
′′
+
{}
=
(
.
/1)
As an interval is an invariant quantity, we may use it to classify the possible events in space–time.
In particular, we may divide events into three types: those for which the invariant label is positive,
zero, or negative. Events for which the ...
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Publisher Resources

ISBN: 9781466569980