set of coordinates ( ,). It is also possible to synchronize these two coordinate
systems. When the train passes the mark on the platform, then x = 0 and the
station clock is at t = 0. If Jim sets = 0 at this point, and puts = 0 on his
wristwatch, there is now a connection between these coordinates.
As the train passes through the station Jim sets off for the cafeteria car. We
can calculate how far he is from the station after five minutes. We know that the
train is travelling at 1 mile per minute, so in that time it has travelled 5 miles and
Jim has walked of a mile (from his speed of 2 mph multiplied by time
5/60). So in total Jim is a distance (x) which is 510/60 miles from the station.
The relation between x and is therefore given by x = + v × t (here v = 60).
Turning the equation around to give the distance Jim has travelled relative to the
reference frame on the train, we get
The concept of time in the classical Newtonian theory is a one-dimensional
flow from the past to the future. It is universal for all and it is independent of
space. Since it is an absolute quantity, Jim’s time on board the train is the same
for the station master on the platform t, so
These two formulae for and , first derived by Galileo, are types of
equations called transformations, as they transform quantities from one reference
frame to another. According to Newton’s classical theory, the speed of light
should be expected to obey these two Galilean transformations for and.
By the 17th century people recognized that light had speed, and its
approximate value was measured in 1676 by the Danish astronomer Ole Römer.
When Albert Michelson measured the speed of light more accurately in 1881, he
found it was 186,300 miles per second. More than this, he became aware that
the transmission of light was very different from the transmission of sound.
Michelson found that, unlike the speed of our observer on the moving train, the
direction of the light beam had no bearing on the speed of light at all. This
paradoxical result had to be explained.