The observer-dependence of cellular space-time structure

It is argued that space-time has a cellular structure, the exact structure being observer-dependent and consistent with the amount of energy he has available for refining his measuring apparatus. The usual concept of a single distance in continuous space is replaced by the concept of a distance set between cells, the elements of each set depending on the cellular structures of both the space and the measuring rod that is used in the measurement. The idea that there are many different ways of measuring the same observable is abandoned: instead, the definition of the original observable becomes split by the different measuring processes used, and the results of a measurement of each new observable defined by this splitting are predicted from the eigenvalues of a common operator by using an observer-dependent construction. Transformations between observers with different cellular structures are considered. The transformation is not as exact as in the continuous case, with at best a cell of one space being associated with a set of cells in the other. This transformation is determined by information being exchanged by the observers concerning the locations in their two spaces of a finite number of common events. The transformation becomes more exact as more information is exchanged.