Abstract

One considers the discrete space-time geometry \(\mathcal {G}_{\mathrm {d}}\), which is given on the set of points (events), where the geometry of Minkowski is given. This discrete geometry is not a geometry on lattice. Motion of a free particle is considered in \(\mathcal {G}_{\mathrm {d}}\). Free motion in \(\mathcal {G}_{\mathrm {d}}\) can be reduced to a motion in geometry of Minkowski \(\mathcal {G}_{\mathrm {M}}\) in some force field. Primordial free motion in \(\mathcal {G}_{\mathrm {d}}\) appears to be stochastic. In \(\mathcal {G }_{\mathrm {M}}\) it is difficult to describe the force field responsible for stochastic motion of a particle. The nature of this force field appears to be geometrical.

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