The Mathematical Theory of Relativity — John Shaqi
The Mathematical Theory of RelativityEddington, Arthur Stanley, Sir
Science
The Mathematical Theory of Relativity
Eddington, Arthur Stanley, Sir
Relativity (Physics)
Having regard to this distinction between physical quantities and world-conditions,
we shall not define a physical quantity as though it were a feature
in the world-picture which had to be sought out. \emph{A physical quantity is
defined by the series of operations and calculations of which it is the result.}
The tendency to this kind of definition had progressed far even in pre-relativity
physics. Force had become ``$\text{mass} × \text{acceleration}$,'' and was no longer an invisible
agent in the world-picture, at least so far as its definition was concerned.
Mass is defined by experiments on inertial properties, no longer as ``quantity
of matter.'' But for some terms the older kind of definition (or lack of
definition) has been obstinately adhered to; and for these the relativity
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theory must find new definitions. In most cases there is no great difficulty
in framing them. We do not need to ask the physicist what conception
he attaches to ``length''; we watch him measuring length, and frame our
definition according to the operations he performs. There may sometimes be
cases in which theory outruns experiment and requires us to decide between
two definitions, either of which would be consistent with present experimental
practice; but usually we can foresee which of them corresponds to the ideal
which the experimentalist has set before himself. For example, until recently
the practical man was never confronted with problems of non-Euclidean space,
and it might be suggested that he would be uncertain how to construct a
straight line when so confronted; but as a matter of fact he showed no
hesitation, and the eclipse observers measured without ambiguity the bending
of light from the ``straight line.'' The appropriate practical definition was so
obvious that there was never any danger of different people meaning different
loci by this term. Our guiding rule will be that a physical quantity must be
defined by prescribing operations and calculations which will lead to an
unambiguous result, and that due heed must be paid to existing practice;
the last clause should secure that everyone uses the term to denote the same
\emph{quantity}, however much disagreement there may be as to the \emph{conception}
attached to it.
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