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)
Distance, parallax and cubic parallax have the same kind of potential
existence even when the operations of measurement are not actually made---\emph{if}
you will move sideways you will be able to determine the angular shift, \emph{if}
you will lay measuring-rods in a line to the object you will be able to count
their number. Any one of the three is an indication to us of some existent
condition or relation in the world outside us---a condition not created by our
operations. But there seems no reason to conclude that this world-condition
\emph{resembles} distance any more closely than it resembles parallax or cubic
parallax. Indeed any notion of ``resemblance'' between physical quantities
and the world-conditions underlying them seems to be inappropriate. If the
length~$AB$ is double the length~$CD$, the parallax of~$B$ from~$A$ is half the parallax
of~$D$ from~$C$; there is undoubtedly some world-relation which is different
for $AB$ and~$CD$, but there is no reason to regard the world-relation of~$AB$ as
being better represented by double than by half the world-relation of~$CD$.
The connection of manufactured physical quantities with the existent
world-condition can be expressed by saying that the physical quantities are
\emph{measure-numbers} of the world-condition. Measure-numbers may be assigned
\index{Measure-code}%
according to any code, the only requirement being that the same measure-number
always indicates the same world-condition and that different world-conditions
receive different measure-numbers. Two or more physical quantities
may thus be measure-numbers of the same world-condition, \emph{but in different
codes}, e.g.\ parallax and distance; mass and energy; stellar magnitude and luminosity.
The constant formulae connecting these pairs of physical quantities
give the relation between the respective codes. But in admitting that physical
quantities can be used as measure-numbers of world-conditions existing
independently of our operations, we do not alter their status as manufactured
quantities. The same series of operations will naturally manufacture the
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same result when world-conditions are the same, and different results when
they are different. (Differences of world-conditions which do not influence
the results of experiment and observation are \Foreign{ipso facto} excluded from the
domain of physical knowledge.) The size to which a crystal grows may be a
measure-number of the temperature of the mother-liquor; but it is none the
less a manufactured size, and we do not conclude that the true nature of size
is caloric.
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