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Relativity: The Special and General Theory
as possible. But in addition to K, all bodies of reference K¹ should be given preference in this
sense, and they should be exactly equivalent to K for the formulation of natural laws, provided that
they are in a state of uniform rectilinear and non?rotary motion with respect to K ; all these bodies
of reference are to be regarded as Galileian reference?bodies. The validity of the principle of
relativity was assumed only for these reference?bodies, but not for others (e.g. those possessing
motion of a different kind). In this sense we speak of the special principle of relativity, or special
theory of relativity.
In contrast to this we wish to understand by the "general principle of relativity" the following
statement : All bodies of reference K, K¹, etc., are equivalent for the description of natural
phenomena (formulation of the general laws of nature), whatever may be their state of motion. But
before proceeding farther, it ought to be pointed out that this formulation must be replaced later by
a more abstract one, for reasons which will become evident at a later stage.
Since the introduction of the special principle of relativity has been justified, every intellect which
strives after generalisation must feel the temptation to venture the step towards the general
principle of relativity. But a simple and apparently quite reliable consideration seems to suggest
that, for the present at any rate, there is little hope of success in such an attempt; Let us imagine
ourselves transferred to our old friend the railway carriage, which is travelling at a uniform rate. As
long as it is moving unifromly, the occupant of the carriage is not sensible of its motion, and it is for
this reason that he can without reluctance interpret the facts of the case as indicating that the
carriage is at rest, but the embankment in motion. Moreover, according to the special principle of
relativity, this interpretation is quite justified also from a physical point of view.
If the motion of the carriage is now changed into a non?uniform motion, as for instance by a
powerful application of the brakes, then the occupant of the carriage experiences a correspondingly
powerful jerk forwards. The retarded motion is manifested in the mechanical behaviour of bodies
relative to the person in the railway carriage. The mechanical behaviour is different from that of the
case previously considered, and for this reason it would appear to be impossible that the same
mechanical laws hold relatively to the non?uniformly moving carriage, as hold with reference to the
carriage when at rest or in uniform motion. At all events it is clear that the Galileian law does not
hold with respect to the non?uniformly moving carriage. Because of this, we feel compelled at the
present juncture to grant a kind of absolute physical reality to non?uniform motion, in opposition to
the general principle of relatvity. But in what follows we shall soon see that this conclusion cannot
be maintained.
Next: The Gravitational Field
Relativity: The Special and General Theory