The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
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The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
It has been explained in the early chapters of \Title{Space, Time and Gravitation}
that observers with different motions use different reckonings of space and
time, and that no one of these reckonings is more fundamental than another.
Our problem is to construct a method of description of the world in which
this indeterminateness of the space-time frame of reference is formally
recognised.
Prior to Einstein's researches no doubt was entertained that there existed
a ``true even-flowing time'' which was unique and universal. The moving
observer, who adopts a time-reckoning different from the unique true time,
must have been deluded into accepting a fictitious time with a fictitious
space-reckoning modified to correspond. The compensating behaviour of
electromagnetic forces and of matter is so perfect that, so far as present
knowledge extends, there is no test which will distinguish the true time from
the fictitious. But since there are many fictitious times and, according to
this view, only one true time, some kind of distinction is implied although its
nature is not indicated.
Those who still insist on the existence of a unique ``true time'' generally
rely on the possibility that the resources of experiment are not yet exhausted
and that some day a discriminating test may be found. But the off-chance
that a future generation may discover a significance in our utterances is
scarcely an excuse for making meaningless noises.
Thus in the phrase \emph{true time}, ``true'' is an epithet whose meaning has yet
to be discovered. It is a blank label. We do not know what is to be written
on the label, nor to which of the apparently indistinguishable time-reckonings
it ought to be attached. There is no way of progress here. We return to
firmer ground, and note that in the mass of experimental knowledge which
has accumulated, the words \emph{time} and \emph{space} refer to one of the ``fictitious''
times and spaces---primarily that adopted by an observer travelling with the
earth, or with the sun---and our theory will deal directly with these space-time
frames of reference, which are admittedly fictitious or, in the more usual
phrase, \emph{relative to an observer with particular motion}.
The observers are studying the same external events, notwithstanding
their different space-time frames. The space-time frame is therefore something
overlaid by the observer on the external world; the partitions representing
his space and time reckonings are imaginary surfaces drawn in the
world like the lines of latitude and longitude drawn on the earth. They do
\PageSep{9}
not follow the natural lines of structure of the world, any more than the
meridians follow the lines of geological structure of the earth. Such a mesh-system
\index{Mesh-system}%
is of great utility and convenience in describing phenomena, and we
shall continue to employ it; but we must endeavour not to lose sight of its
fictitious and arbitrary nature.
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