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%%% Primary Title: Special and General Principle of Relativity
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%%% Filename: SpecialAndGeneralPrincipleOfRelativity.tex
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\begin{document}
\subsection{Special and General Principle of Relativity}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}
The basal principle, which was the pivot of all our previous
considerations, was the special principle of relativity, \emph{{\it i.e.}} the
principle of the physical relativity of all \emph{uniform} \htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html}. 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 \htmladdnormallink{relative motion}{http://planetphysics.us/encyclopedia/CoriolisEffect.html}. 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:
\begin{enumerate}
\item The carriage is in motion relative to the embankment,
\item The embankment is in motion relative to the carriage.
\end{enumerate}
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
\begin{enumerate}
\item the embankment as reference-body,
\item the railway carriage as reference-body,
\end{enumerate}
\noindent then these general laws of nature ({\it 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 $K$, $K'$ 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 \htmladdnormallink{particle}{http://planetphysics.us/encyclopedia/Particle.html} 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 $K'$ 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 ({\it 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 $K$, $K'$,
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.
\subsection{References}
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.
\end{document}
