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Principia Physica

Nature volume 162, pages 4445 (10 July 1948) | Download Citation



IN this book the author presents a new conception of the general principles of physics by trying to construct an axiomatic system in which no descriptions of facts are used which are not "logically definable". Maintaining that the notion of the continuum does not fulfil this condition, he demands that metric geometry be excluded from physics altogether, and that the space-time system be put on a purely arithmetical basis. In other words, the universe is considered to be a discontinuous manifold or point lattice. Quaternion algebra is found to provide the most adequate mathematical description for such a system and to account automatically for the four-dimensionality of space-time and its splitting up into three space-like and one time-like dimensions. In contrast to the usual concept of a dynamic universe to be described by events, the new concept is that of a static universe to be described by its structure, which reflects itself in the group properties of the algebra used for this description. Accordingly, the fundamental laws of physics cannot have the form of differential equations but have to be expressed in the form of integral equations, that is, free of metric, the integrals used being essentially Stieltjes integrals, the definition of which also holds for a discrete set of variables.

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