P O P U L A R P R I N C E T O N L E C T U R E S 6 0 3
follow from the principles of Galileo and Newton, we know perfectly well that we can
speak of all systems if they are moving with respect to each other in uniform and rectilinear
motion as equivalent systems. In other words, the laws of mechanics are just the same if we
refer them to a system which is moving with uniform and rectilinear velocity with respect
to another system. If, however, we refer to another system which is moving with a rotational
motion with respect to another system, then it is well known that the laws of mechanics are
not the same as they are when referred to a system at rest.
What we mean by an inertial system, then, in the special theory of relativity is a system
which moves with respect to another system with a uniform velocity in a straight line.
The principle of relativity states that all inertial systems—that is, all systems which
move with uniform and rectilinear velocity with respect to each other—the equivalent in
expressing the laws of natural phenomena.
The second law that we state is the law of constancy of the velocity of light. Now these
two laws are experimental laws; the experiments which prove these are indirect, but they
are hypotheses which we make, and then we try to find out how nearly all natural phenom-
ena fall in with them.
Now there are first of all certain very—there are to be—very striking contradictions be-
tween these two principles and the principles derived from the assumption that there is one
system which has the unique properties of being absolutely at rest. The simplest way to
think of it is to suppose that you start a ray of light referred to a system which we can say
is absolutely at rest. Say that it goes a distance C in one second. Now, if it is referred to a
system which is moving with the velocity V then, referred to the second system it would
travel with a velocity of C plus or minus V, depending upon whether the ray is moving in
the direction of V or opposite.
That, however, which is a consequence of assuming that there is a system which has the
unique properties of being at rest, is directly in contradiction to the principle we stated of
the constancy of the velocity of light.
Now, this is capable of experimental verification, and it was tested by the famous exper-
iments of Michelson, who measured accurately the velocity of light when travelling in the
direction of the earth’s motion and also traveling at right angles to the direction of the
earth’s motion. According to our ordinary ideas, we would expect to find a difference in
velocity of light in the two cases. Michelson found absolutely no difference. And therefore
there is a contradiction between the two principles that we stated, the principle of relativity
and the principle of the constancy of the velocity of light, with the assumption that there is
one unique system which we can speak of as a system at rest.
The only thing that we are left with, then, is to assume that the assumptions that we have
made in formulating our ideas of motion are fundamentally wrong. And the particular fea-
tures of our fundamental ideas which we have got to change are first of all, the definition
of what we mean by two simultaneous events. If we have two events which take place at
different places, what exactly do we mean when we say that these two events are simulta-
neous? In order to test whether they are simultaneous or not we have to make use of the
principle of the propagation of light.