Relativity: The Special and General Theory

very exact grasp of this work in order to understand the fundamental
ideas of either the special or the general theory of relativity, I
shall leave it here at present, and revert to it only towards the end
of Part 2.


  Notes

*) Cf. the somewhat more detailed discussion in Appendix II.




PART II

THE GENERAL THEORY OF RELATIVITY


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
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.

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