On the continuum origin of Heisenberg's indeterminacy relations

Abstract

If space is indistinguishable from the extension of a physical body, as is Descartes's conception, then transformations of space become transformations of physical bodies. Every point of space then has properties of physical bodies in some suitable non-singular sense of average over the space. Every point of space is then thinkable as a non-singular point particle possessing such (averaged) physical properties. Then, the location of such a point particle is, relative to another (similar) point particle, {\em indeterminate} over the extension of the physical body. Further, transformations of the space may ``move'' such a point particle in relation to another such point particle. These notions then provide a non-probabilistic explanation of Heisenberg's indeterminacy relations.