_{1}

^{*}

The low-dimensional model of the space-time is considered where time is a real coordinate with dimensionality of length. The inertia law appears within this model as a consequence of the geometrical structure of the space.

The time is considered in Mechanics as one of the four coordinates (

The formal geometrical interpretation of time is known where time is considered as an imaginary fourth coordinate with the dimensionality of length in the four dimensional pseudo Euclidean space (Minkowski space) [

This work is a соntinuation of author’s investigations of possibility to explain physical phenomena by geometrical properties of the space-time [

One of the simplest examples of topological products of spaces is shown at

Topological products of spaces are a particular case of fiber spaces, and the theory of fiber spaces are now in the course of development [

Let us consider motions of free bodies in empty space that is motions without external fields of force. As in general relativity, we suggest that motions of such bodies take place along geodesic lines of the empty space-time, that is along shortest pathes between points of this space. Shortest pathes on the cylinder’s surface are segments of the screw lines on this surface. Recall known relations for a screw line [

where

Consider the motion of a free body along the screw line with a small pitch of screw, when

Then the displacement

And the corresponding path

It follows from (3) and (4) that

Replace here

where

where

We show now that above variable

This displacement looks as a sequence of periodical appearances and disappearances of this body in Euclidean space. But for sufficiently small

Let us suggest that

Discontinuous displacements with such high frequencies will be detected as continuous ones by any of modern devices.

And here is the main point. If displacements of free bodies, described by (7), can be considered as continuous ones then (7) should be considered as the law of motion of free bodies in the Euclidean space, that is as the Galilei’s inertia law. And this will be the case only if we identify variable

It is shown that within the framework of the suggested model of the space-time there is no fundamental difference between notions “space” and “time”: both of them are represented by coordinates of the one space with specific geometry. It was shown also that there is a one-to-one correspondence between time coordinate (length of the body’s displacement along the screw geodesic line) and the same body’s displacement in the Euclidean space. This means that any kind of motion in Euclidean space can be chosen as a standard for measuring of time. Periodical movements (clocks) happened to be the most convenient in operation.

Notice in conclusion that suggested low-dimensional model of the space-time has mainly a methodical value. This work indicates at possible geometrical structure of the real space of events, namely, a topological product of our three-dimensional Euclidean space and the space with a topology of some closed manifold.

Olkhov, O.A. (2017) On Possibility of Geometrical Interpretation of Time. Journal of High Energy Physics, Gravitation and Cosmology, 3, 173-177. https://doi.org/10.4236/jhepgc.2017.32018