Chapter 6
Special Theory of Relativity
6.1 Basic Concepts and Formulae ................................
Inertial frame
Laws of mechanics take the same form (invariant) in all inertial frames. An iner-
tial frame of reference is the one which moves with constant relative velocity in
which Newton’s laws of motion are valid. The principle that all inertial frames are
equivalent for the description of nature is called the principle of relativity.
Galilean Transformations
Reference frameS′moves alongx-axis with velocityνrelative toS. Spatial coor-
dinatesx,y,zare measured inSandx′,y′,z′inS′and timetandt′inSandS′
respectively. For simplicity,xandx′axes coincide. At the beginning (t=0),Sand
S′coincide. After timet,S′would have moved through a distanceνt. The Galilean
transformations are given by the set of relations.
x′=x−νt (6.1)
y′=y (6.2)
z′=z (6.3)
t′=t (6.4)In Galilean relativity time is absolute.
Fig. 6.1Reference framesS
andS′
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