D O C . 3 1 I D E A S A N D M E T H O D S 1 3 7
If we know the laws of nature with respect to a (gravitation-free) system , then
we can by mere transformation learn the laws relative to , i.e., we learn about
the physical properties of a gravitational field by means of a purely speculative
method. At its basis here is the hypothesis that the principle of relativity also holds
in reference to coordinate systems that are mutually accelerated to each other, and
that the physical properties of space that rule relative to are completely equiv-
alent to a gravitational field (hypothesis of
equivalence).[38]
The generalization of the principle of relativity, therefore, points to a speculative
way of investigating the properties of the gravitational field.
Because all bodies in a gravitational field have the same fall, a stimulus arose
that pointed with irresistible force toward a generalization of the principle of rela-
tivity. 〈Consequently, it is necessary to point out that this result (of the equivalence
hypothesis) is supported with extraordinary precision, in particular by the tests
made by Eötvös. This is based upon the following consideration.〉 This experimen-
tal fact can also be phrased in a second especially remarkable form. According to
Newton’s law of motion, the fall of a body occurs according to the equation
On the other hand,
In these equations “inertial mass” means the mass that is responsible for the inertial
reaction of the body, “gravitational mass” is the constant responsible for the influ-
ence of the gravitational field on the same body—two constants which by defini-
tion are completely independent of each other. From both equations together fol-
lows
In order to keep the experimentally confirmed law
valid, it must also be true that
K
K′
K′
(inertial mass) (acceleration in fall)
(gravitational force of the earth). =
×
(gravitational force of the earth)
(intensity of the gravitational field) (gravitational mass). × =
(inertial mass) (acceleration in fall) ×
(gravitational mass) (intensity of the gravitational
field).
× =
(acceleration in fall) (intensity of the gravitational field) =