Kinematics, dynamics, and the scale of time

Abstract

1—In two previous papers the laws of dynamics and the Newtonian approximation to the law of gravitation have been derived on a purely kinematic basis. That is, they have been deduced rationally, starting from the individual observer’s awareness of a temporal sequence for events at himself, and from his assigning of measures of distance and epoch by means of light-signals and appropriately rated and synchronized clocks; explicit procedure for this rating and synchronization having been stated in terms of the observer’s own experiences. No appeal was made in the derivations to any empirical laws of dynamics or gravitation, or even to the principle of relativity or to the principle of the constancy of the velocity of light. Recourse to these last two was avoided by careful statement of exactly what is meant by “uniform velocity” ,by intro­duction of the notion of kinematic equivalence . Laws of dynamics and gravitation emerged by embodying in analysis the programme out­lined by Mach, according to which all the matter in the universe is relevant to the description of dynamical laws of nature and must necessarily be taken into account in describing the motion even of a free particle; this programme was carried out by introducing the notion of statistical equivalence , which amounts to a definition of the systems of moving particles proposed for consideration (as affording a representation of the universe) as those whose motion and distribution satisfy what has been called the cosmological principle . It is particularly to be noticed that the cosmological principle is not a concealed law of nature but is simply a definition defining the subject of study, just as in any gravitational problem we must define what we are discussing— one-body problem, three-body problem, etc. The reason that, in systems defined by means of the cosmological principle, not only no recourse to empirical laws of nature is needed but regularities playing the part of laws of nature can be derived, is that essentially the cosmological principle is a mode of specifying an extrapolation of certain kinds of phenomena . If laws of nature are supposed to be derived as inductive generalizations from observed phenomena, then it is preferable to extrapolate phenomena and derive the correspond­ing laws rather than to extrapolate laws and predict phenomena. We have no more warrant for extrapolating laws than for extrapolating the phenomena from which they have been learned. We have no justification for believing in world-wide principles as a sort of super-authority.