D O C . 3 1 I D E A S A N D M E T H O D S 1 1 9
to the law of light propagation. Experience shows at least that also with respect
to , all directions are optically equivalent.
There is a contradiction between conclusion (b) and experimental finding (c).
The special theory of relativity resolves this contradiction in the following manner.
It retains the statements (a) and (c) and demonstrates the falsity of conclusion (b).
Before we resolve the contradiction, we generalize statement (c)—based on the
fact that terrestrial experiments alone can in no way demonstrate the progressive
movement of the earth—by stating the theorem that is also valid in Newtonian me-
chanics: If one starts out with an “admissible” coordinate system (an inertial sys-
tem of classical mechanics), then every system that is moving uniformly and is
non-rotating relative to is equivalent to , and the laws of nature are exactly the
same in both and (principle of special relativity).
6. Epistemological Note
A theory has physical content only if the quantities tied together in equations make
physical sense, i.e., it has to be stipulated precisely how these quantities 〈in nature〉
can be determined 〈or calculated〉 from results of direct measurements. A theory
says nothing about nature if the stipulations of relations between mathematical
quantities of the theory and the results of measurements are
missing.[16]
If I talk, for example, about the length of a rod, then I want to say that the basic
unit of measurement can be laid out times next to it. When I say the Cartesian
coordinates of a point are , then I claim, first, that from rods of equal lengths,
when their ends are suitably joined, a cubic lattice can be constructed, such that
(rigid) rods behave like distances of Euclidean geometry. Further, I take such a lat-
tice 〈system〉 in a certain state of motion as given, define a point as the origin and
the Cartesian coordinates in a certain way as countings obtainable through this lat-
tice.
When I speak of the temporal duration of a process, I mean, as a physicist, the
number of periods that have elapsed on the clock that is used as a basis, counting
from the beginning to the end of the process. (Preliminary, imprecise definition.)
It is true that a physical theory can have mathematical quantities that do not sat-
isfy these conditions; they then are auxiliary parameters which 〈per se〉 have no
other meaning than to simplify the expression of laws in certain cases or to unify
the theoretical framework. We shall talk later about important cases of this kind.
K′
[p. 6]
K
K′
K K
K K′
l
l
x y z , ,
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