D O C . 3 3 2 O N T H E E T H E R 3 3 3

geometry.) The configuration laws governing rigid bodies, excluding relative mo-

tions, temperature, and deformation influences as are ideally laid down in Euclid’s

geometry, employ the concept of the rigid body; Euclidean geometry does not con-

ceive of any surrounding influences as existing independently of the bodies or act-

ing on the bodies and influencing their configuration laws. The same is true of non-

Euclidean geometries of constant curvature, when these influences are interpreted

as (permissible) laws of nature about the stacking of bodies. This would be differ-

ent were we to be forced to assume a geometry of variable curvature; that would

mean that the possible contact configurations of practically rigid bodies were de-

termined differently for different cases by environmental influences. In this in-

stance one would have to say, in the light of our consideration, that such a theory

would be making use of an ether hypothesis. Its ether would be something physi-

cally real, as good as matter. If the configuration laws did not depend on physical

factors, such as the clustering and state of motion of

bodies[1]

in their vicinity, etc.,

then one would denote this

ether[2]

as “absolute” (i.e., independent of influences by

some other objects).

A (physically interpreted) Euclidean geometry needs an ether no more than does

the kinematics or phoronomics of classical mechanics; its theorems make clear,

physical sense if one only assumes that the influences of motion on measuring rods

and clocks assumed in the special theory of relativity do not

exist.[3]

It is different in Galilean and Newtonian

dynamics.[4]

The law of motion “mass

× acceleration = force” does not just make a statement about material systems, not

even when, as in Newton’s astronomical fundamental law, force is expressed by in-

tervals, hence by dimensions, whose real definition can be based on measurements

with rigid measuring bodies. This is so because the real definition of acceleration

cannot be based wholly on observations of rigid bodies and clocks. It cannot be at-

tributed to measurable intervals between the points constituting the mechanical

system. For its definition, a coordinate system is also needed, that is, a reference

body in a suitable state of motion. If the state of motion of the coordinate

system[5]

is chosen differently, then the Newtonian equations do not apply with reference to

it. In those equations, the environment in which the bodies are moving also figures

implicitly as a real factor in the laws of motion alongside the real bodies and their

mutual distances definable by measuring bodies. In Newton’s theory of motion,

“space” has physical reality—in contrast to the case of geometry and kinematics.

Let us denote this physical reality, which is incorporated within the observable pon-

derable bodies in Newton’s law of motion, as the “ether of mechanics.” The occur-

rence of centrifugal effects in a (rotating) body, whose material points do not alter

their distances from one another, shows that this ether should not merely be under-

stood as an imaginary form in Newtonian theory; rather, something real in nature

corresponds to it.

[p. 87]