(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 Iines.  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 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.