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Relativity: The Special and General Theory

Special and General Principle of Relativity
The basal principle, which was the pivot of all our previous considerations, was the
special principle of relativity, i.e. the principle of the physical relativity of all uniform
motion. Let as once more analyse its meaning carefully.
It was at all times clear that, from the point of view of the idea it conveys to us, every
motion must be considered only as a relative motion. Returning to the illustration we
have frequently used of the embankment and the railway carriage, we can express the fact
of the motion here taking place in the following two forms, both of which are equally
justifiable :
(a) The carriage is in motion relative to the embankment,
(b) The embankment is in motion relative to the carriage.
In (a) the embankment, in (b) the carriage, serves as the body of reference in our
statement of the motion taking place. If it is simply a question of detecting or of
describing the motion involved, it is in principle immaterial to what reference-body we
refer the motion. As already mentioned, this is self-evident, but it must not be confused
with the much more comprehensive statement called "the principle of relativity," which
we have taken as the basis of our investigations.
The principle we have made use of not only maintains that we may equally well choose
the carriage or the embankment as our reference-body for the description of any event
(for this, too, is self-evident). Our principle rather asserts what follows : If we formulate
the general laws of nature as they are obtained from experience, by making use of
(a) the embankment as reference-body,
(b) the railway carriage as reference-body,
then these general laws of nature (e.g. the laws of mechanics or the law of the
propagation of light in vacuo) have exactly the same form in both cases. This can also be
expressed as follows : For the physical description of natural processes, neither of the
reference bodies K, K1 is unique (lit. " specially marked out ") as compared with the other.
Unlike the first, this latter statement need not of necessity hold a priori; it is not
contained in the conceptions of " motion" and " reference-body " and derivable from
them; only experience can decide as to its correctness or incorrectness.
Up to the present, however, we have by no means maintained the equivalence of all
bodies of reference K in connection with the formulation of natural laws. Our course was
more on the following lines. In the first place, we started out from the assumption that
there exists a reference-body K, whose condition of motion is such that the Galileian law
holds with respect to it : A particle left to itself and sufficiently far removed from all
other particles moves uniformly in a straight line. With reference to K (Galileian
reference-body) the laws of nature were to be as simple 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
 
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