The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
Science
The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
It is evident from experience that a four-fold mesh-system must be used;
and accordingly an event is located by four coordinates, generally taken as
\index{Coordinates}%
$x$,~$y$, $z$,~$t$. To understand the significance of this location, we first consider
the simple case of two dimensions. If we describe the points of a plane figure
by their rectangular coordinates $x$,~$y$, the description of the figure is complete
and would enable anyone to construct it; but it is also more than complete,
because it specifies an arbitrary element, the orientation, which is irrelevant
to the intrinsic properties of the figure and ought to be cast aside from
a description of those properties. Alternatively we can describe the figure by
stating the distances between the various pairs of points in it; this description
is also complete, and it has the merit that it does not prescribe the
orientation or contain anything else irrelevant to the intrinsic properties of
the figure. The drawback is that it is usually too cumbersome to use in
practice for any but the simplest figures.
Similarly our four coordinates $x$,~$y$, $z$,~$t$ may be expected to contain an
arbitrary element, analogous to an orientation, which has nothing to do with
the properties of the configuration of events. A different set of values of
$x$,~$y$, $z$,~$t$ may be chosen in which this arbitrary element of the description is
altered, but the configuration of events remains unchanged. It is this
arbitrariness in coordinate specification which appears as the indeterminateness
of the space-time frame. The other method of description, by giving the
distances between every pair of events (or rather certain relations between
pairs of events which are analogous to distance), contains all that is relevant
to the configuration of events and nothing that is irrelevant. By adopting
this latter method we can strip away the arbitrary part of the description,
leaving only that which has an exact counterpart in the configuration of the
external world.
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