A game of aiming and evasion: General discussion and the by Rufus Isaacs

By Rufus Isaacs

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The prir,ciples and postulates discussed until now are incapablc of uniquely determining thc equations of gravitation. A stronger rcstriction and, moreover, a unique determination of thc equations of gravitation result if we assume the validity of thc large theoretical principles. 4. Theoretical Principles and Nonlinear Theory of Gravitation According to the remarks of the prevlOUS section, the weak (special-relativistic) equivalence principle and the special principle of relativity are comparatively weak restrietions.

17) Local Principles and the Theory of Gravitation Any choice for CI. other than the foregoing leads to the con- clusion that the active heavy mass of a static system differs from the inertial and passive heavy masses by an amount of the order (CI. - 2)M ce (CI. 18) In general, we obtain a deviation from Newton's action-reaction axiom rn A = rnl', and the conservation of the center-of-mass motion is no longer valid (see also below). The reason for this is that the active mass forms a static system only for the N ewtonian limit, the condition CI.

This Lorcntz covariance is valid io the special-relativistic tensor theory of gravitation, too. Hence there is no breakdown here that is compensated by gravitation al fields. 46) 51 Chapter 1 The equivalence principle reduces possible anisotropy effects to those that can conceivably be measured in laboratories that are not freely falling. 47) Vp. being the equatorial rotational speed of the Earth and M its mass. This kind of mass anisotropy, which should be measurable by the techniques of nuclear physics, does not seem to exist.

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