Chapter Seven: Einstein special theory of relativity

7.1 Pre- relativistic physics
The starting point for our work is Newton’s laws of motion. These can be
stated as follows:
· Free particles move with constant velocity.
· The vector force F is proportional to the rate of change of momentum i.e.
(mu )

· To every action there is an equal and opposite reaction.
The first of these laws singles out inertial frames as the non- accelerating ones.
Consider now a frame O [ i.e. a set of spatial coordinates (x, y, z) and a time
coordinate t ], and another frame O¢ with coordinates (x¢, y¢, z¢, t¢) which moves
in the x direction with uniform speed u relative to the frame O.
Common sense suggests that the two sets of coordinates are related by

7.2 The equations of electromagnetism
Maxwell s equations for the electromagnetic field [in units with
These equations show that one can have electromagnetic waves in a vacuum
which travel with a speed c = 3´108 m/s , thus light is a form of electromagnetic
radiation.
Figure
Ether was postulated as the medium which carries these waves [i.e. the speed c
is the speed with respect to the ether] and naturally this was identified with the
absolute space of Newton.
Attempts to measure the ether drift by Michelson and Morley in 1887 gave a
null result, so effects like stellar aberration could not be due to the earth
dragging the ether.

Another great problem was that Maxwell s equations did not appear to obey
the principle of Galilean Relativity i.e. they were not invariant under the
Galilean transformations. This means that in a moving space ship the electric
and optical phenomena should be different from those in a stationary ship!!!
Thus one could use for example optical phenomena to determine the speed of
the ship.
One of the consequences of Maxwell s equations is that if there is
a disturbance in the field such that light is generated, these electromagnetic
waves go out in all directions equally and at the same speed c. Another
consequence of the equations is that if the source of the disturbance is moving,
the light emitted goes through space at the same speed c. This is analogous to
the case of sound being likewise independent of the motion of the source. This
independence of the motion of the source in the case of light brings up an
interesting problem.