A Euclidean-Like Discrete Spacetime from the Unification of a Multitude of Hypercubic Lattices

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.

Particle-Wave Duality Resulting from the Granulation of Fields in a Hypercubic Lattice

“…The likelihood of a granulated field also arises from the transformation of the usual units into the two units Δx and S of a hypercubic lattice with multiple directions [5], where Δx is the smallest distance of a lattice and S stands for the number of lattices in which a phenomenon is present. The conversion results in an expression of the field strength in one lattice or subspace:…”

“…In a hypercubic lattice, the movement of the particle field can only take place along one of the three spatial axis, which is very unrealistic. In a more realistic multidirectional discrete space, the entire space is split up into n directions subspaces each with their own set of spatial directions [5]. The number of spatial directions n directions comprises at least 10 22 subspaces.…”

“…The space-point of a multidirectional lattice is a time series of vertices connected in time, the vertices being part of subspaces with different spatial directions ref. [5].…”

Physical Constants as Result of the Many Hypercubic Lattices of a Multidirectional Discrete Space

“…A set of loosely connected hypercubic lattices (as given in [3]) is used here as an example of a multidirectional discrete space. Such a space is discrete at the level of the lattice and in the number of hypercubic lattices it consists of.…”

“…The correspondence of physical properties with space characteristics is possible in a multidirectional discrete space, a discrete space with many spatial directions within an overarching four-dimensional space. Reference [3] gives an example of such a space where the space consists of very many hypercubic lattices, the subspaces.…”