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 inertial 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 frame S
moves along x-axis with velocity ν relative to S. Spatial coordinates x, y, z are measured in S and x
, y
, z
in S
and time t and t
in S and S
respectively. For simplicity, x and x
axes coincide. At the beginning (t = 0), S and
S
coincide. After time t, S
would have moved through a distance νt. 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. 6.1 Reference frames S
and S
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