A Theorem on Space Quantization by Kronig R.

By Kronig R.

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Newton, 1726 [1999], p. 413) In other words, even if the Cartesian definition identifies a single motion proper to each body, that motion is disconnected from the fundamental concerns of physics, especially the understanding of dynamical phenomena. As Newton shows, however, the dynamical phenomena themselves provide a unique measure of the state of rotation of any body. What is more, Newton points out that the concept of rotation that he is defining is the very one that the Cartesians employ, implicitly, in their attempt at a dynamical understanding of the Solar System.

Is a merely fictitious cause, and not an observable thing. (Einstein, 1916, pp. 8–9) By this reasoning Einstein concluded that centrifugal and other inertial effects must be traced to some observable cause, such as the “distant masses,” in order to remove the “epistemological defect” of absolute rotation. While this was an important motivation for general relativity, however, it is hardly an apt criticism of Newton. The objection assumes that Newton has introduced a privileged frame of reference – any of the spaces that are defined by Corollary V – as a causal explanation of the phenomenon of centrifugal force.

Even more striking is that Newton derives the relativity principle explicitly as a corollary to the laws of motion: “When bodies are enclosed in a given space, their motions in relation to one another are the same whether the space is at rest or whether it is moving uniformly straight forward without circular motion” (Newton, 1726 [1999], p. 423). This is because those motions are determined by the forces of interaction among the bodies, and, by the second law of motion, these forces are entirely independent of the velocities of the bodies involved.

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