Abstract
An autonomous discrete space is proposed consisting of a huge number of four dimensional hypercubic lattices, unified along one of the four axes. The unification is such that the properties of the individual lattice are preserved. All the unifying axes are parallel, and the other axes have indeterminate mutual relations. The two kinds of axes are non-interchangeable resembling time and space of reality. The unification constitutes a framework without spatial properties. In case the axes with indeterminate relations are present at regular intervals in the time and the space, a Euclidean-like metric and goniometry can be obtained. In thus defined space-like structure, differences in speed and relativistic relations are only possible within regions of space enclosed by aberrations of the structure.
Highlights
Because of the discrete features of matter such as the same mass for the same elementary particles and the overall validity in space of the physical constants, it seems obvious to assume that space has a discrete structure
What can be seen as an indication is the prediction of Smolin and others [1] that spacetime is made of discrete pieces by combining of quantum physics and special relativity
A discrete alternative for the continuous space is offered in form of a merging of a huge number of hypercubic lattices
Summary
Because of the discrete features of matter such as the same mass for the same elementary particles and the overall validity in space of the physical constants, it seems obvious to assume that space has a discrete structure. T. de Groot 1176 philosophy, lattice-like discrete spaces are suggested which have no reference to another space. To be a discrete alternative to continuous space, more results are required from wellchosen regularities or deviations of the space structure
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