Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/10

 a gravitational field is no longer present. Freely moving bodies move according to the inertia law, clocks and measuring rods behave according to the laws of the special theory of relativity. The local inertial systems have a relative acceleration with respect to each other, and it is in general not possible for a finite region to make a transformation of the gravitational field. The author now deals with a homogeneous gravitational field which he regards as one whose field effect disappears throughout its whole extent when considered from a suitable rigid system. According to classical mechanics all things would have independent accelerations, which is impossible in the inertial system where the special theory of relativity holds good. The first part of the present paper discusses this homogeneous gravitational field but is restricted to processes in a plane. The second problem dealt with is the determination of the time surface for an observer in the gravitational field, for which the special theory of relativity supplies the necessary basis. The last section of the paper makes a comparison with the general theory. The paper is mathematical throughout." Sci. Abs. 25A:2216, 1922.

In German.

Translated title: Space and time in relativity theory.

"The author follows Kant in assuming that space and time are not derived from experience, but exist a priori in the mind, and also in the view that the inductive investigation of natural science is justified by the conformity to law of the relations between natural objects. Also in his conclusion that the minimum of congruence and uniformity that is necessarily conjoined with the concept of this conformity, therefore represents the a priori foundation of natural science. In order to make definite the concept of the physical continuum discussed at length in the paper, coordinates have to be introduced. Such a continuum can be constructed from a finite number of observations, provided that the distance between two adjacent points is represented by a definite quadratic differential form of the relative coordinates dx: in this case any infinitesimal rigid point system can move freely throughout the continuum. The only continuum throughout which rigid point system can move freely is the Euclidean continuum. In the case of a four-fold world representation, not resolvable into space and time, it will always be possible to order the representation in accordance with the requisite functional conditions, since the sum total of the a priori foundations is equivalent to the two conditions: (1) that it is possible by observation to determine the space-time