Relativity - The Special and General Theory | Page 5

identical construction ; the man at the
railway-carriage window is holding one of them, and the man on the footpath the other.
Each of the observers determines the position on his own reference-body occupied by the
stone at each tick of the clock he is holding in his hand. In this connection we have not
taken account of the inaccuracy involved by the finiteness of the velocity of propagation
of light. With this and with a second difficulty prevailing here we shall have to deal in
detail later.
Notes
*) That is, a curve along which the body moves.

THE GALILEIAN SYSTEM OF CO-ORDINATES
As is well known, the fundamental law of the mechanics of Galilei-Newton, which is
known as the law of inertia, can be stated thus: A body removed sufficiently far from
other bodies continues in a state of rest or of uniform motion in a straight line. This law
not only says something about the motion of the bodies, but it also indicates the
reference-bodies or systems of coordinates, permissible in mechanics, which can be used
in mechanical description. The visible fixed stars are bodies for which the law of inertia
certainly holds to a high degree of approximation. Now if we use a system of
co-ordinates which is rigidly attached to the earth, then, relative to this system, every
fixed star describes a circle of immense radius in the course of an astronomical day, a
result which is opposed to the statement of the law of inertia. So that if we adhere to this
law we must refer these motions only to systems of coordinates relative to which the
fixed stars do not move in a circle. A system of co-ordinates of which the state of motion
is such that the law of inertia holds relative to it is called a " Galileian system of

co-ordinates." The laws of the mechanics of Galflei-Newton can be regarded as valid
only for a Galileian system of co-ordinates.

THE PRINCIPLE OF RELATIVITY (IN THE RESTRICTED SENSE)
In order to attain the greatest possible clearness, let us return to our example of the
railway carriage supposed to be travelling uniformly. We call its motion a uniform
translation ("uniform" because it is of constant velocity and direction, " translation "
because although the carriage changes its position relative to the embankment yet it does
not rotate in so doing). Let us imagine a raven flying through the air in such a manner
that its motion, as observed from the embankment, is uniform and in a straight line. If we
were to observe the flying raven from the moving railway carriage. we should find that
the motion of the raven would be one of different velocity and direction, but that it would
still be uniform and in a straight line. Expressed in an abstract manner we may say : If a
mass m is moving uniformly in a straight line with respect to a co-ordinate system K,
then it will also be moving uniformly and in a straight line relative to a second
co-ordinate system K1 provided that the latter is executing a uniform translatory motion
with respect to K. In accordance with the discussion contained in the preceding section, it
follows that:
If K is a Galileian co-ordinate system. then every other co-ordinate system K' is a
Galileian one, when, in relation to K, it is in a condition of uniform motion of translation.
Relative to K1 the mechanical laws of Galilei-Newton hold good exactly as they do with
respect to K.
We advance a step farther in our generalisation when we express the tenet thus: If,
relative to K, K1 is a uniformly moving co-ordinate system devoid of rotation, then
natural phenomena run their course with respect to K1 according to exactly the same
general laws as with respect to K. This statement is called the principle of relativity (in
the restricted sense).
As long as one was convinced that all natural phenomena were capable of representation
with the help of classical mechanics, there was no need to doubt the validity of this
principle of relativity. But in view of the more recent development of electrodynamics
and optics it became more and more evident that classical mechanics affords an
insufficient foundation for the physical description of all natural phenomena. At this
juncture the question of the validity of the principle of relativity became ripe for
discussion, and it did not appear impossible that the answer to this question might be in
the negative.
Nevertheless, there are two general facts which at the outset speak very much in favour of
the validity of the principle of relativity. Even though classical mechanics does not
supply us with a sufficiently broad basis for the theoretical presentation of all physical
phenomena, still we