After Einstein basically completed his experience of the relativistic theory of gravitation, he repeatedly tried to build, based on it, his model of the universe, which many regard as perhaps the most important part of his work.
However, the Einstein's equation of gravitation, under the same assumption about the uniform distribution of "matter" ("homogeneity and isotropy of space"), did not give an escape from cosmological paradoxes: the "universe" turned out to be unstable, and in order to prevent its contraction by gravity, Einstein did not find anything better. how, like Zeliger, insert into your equation one more term - the same universal so-called cosmological constant. This constant expresses the hypothetical force of repulsion of stars. Therefore, even in the absence of masses in the relativistic de Sitter model, a constant negative curvature of space-time is obtained.
Under such conditions, the solution of gravitational equations gave Einstein a finite world, closed in itself due to the "curvature of space", like a sphere of finite radius, - a mathematical model in the form of a cylinder, where a curved three-dimensional space forms its surface, and time is an undistorted dimension running along generatrix of the cylinder.
The universe has become "boundless": moving along a spherical surface, it is understandable, it is impossible to bump into any border - but nevertheless it is not infinite, but finite, so that light, like Magellan, can go around it and return from the other side. Thus, it turns out that the observatory, observing two different stars on opposite sides of the sky through a fantastically strong telescope, may turn out to see the same star from its opposite sides, and their identity can be established by some features of the spectrum. So it turns out that the isolation of the world is accessible to experimental observation.
Based on such a model, it turns out that the volume of the world, as well as the mass of its matter, turns out to be equal to a completely definite final value. The radius of curvature depends on the amount of "matter" (mass) and its rarefaction (density) in the universe.
Cosmologists are busy with the great calculations of the "radius of the world." According to Einstein, it is equal to 2 billion light years! For this radius, due to the general "curvature of space", no rays and bodies; can't get out.
This "modern idea" to replace infinity with limitless isolation, where reproaches for finiteness, say, "misunderstanding" because there are no "finite straight lines", arose at least in the middle of the century before last, when it was carried out by Riemann 3.
And now, for a century and a half, it has been explained by the parable of the instructive limitation of creatures flat, like a shadow, crawling on a two-dimensional ball: knowing neither height nor depth, wise "flat people" are amazed to discover that their world has neither beginning nor end and still finite.
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On this basis, the question itself: what is beyond the boundaries of a closed universe? - according to the positivist custom, they only respond with condescending irony - as if they were “meaningless,” because the sphere has no boundaries.
As for Olbers' photometric paradox, Einstein's static model did not even give a semblance of its resolution, since light must always spin in it.
The opposition of attraction and repulsion meant the instability of the universe: the slightest push - and the model will either begin to expand - and then our island of stars and light scatters into the endless ocean, the world is empty. Or shrink - whichever outweighs what is the density of matter in the world.
In 1922, the Leningrad mathematician A. A. Fridman solved the Einstein equations without a cosmological term and found that the universe should expand if the density of matter in space is more than 2 x 10 to minus 29 degrees g / cm3. Einstein did not immediately agree with Friedman's conclusions, but in 1931-1932 he noted their great fundamental importance. And when, in the 1920s, de Sitter found in Slipher's works indications of a "redshift" in the spectra of spiral nebulae, confirmed by Hubble's studies, and the Belgian astronomer Abbot Lemaitre suggested, according to Doppler, the reason for their divergence, some physicists, including Einstein, saw this as an unexpected experimental confirmation of the "expanding universe" theory.
Replacing infinity with "unlimited" isolation is sophism. The expression "curvature of space-time" physically means a change in space ("curvature") of the gravitational field; this is directly or indirectly acknowledged by the greatest experts in Einstein's theory. The components of the metric tensor or other measurements of "curvature" play the role of Newtonian potentials in it. Thus, “space” is simply a type of matter - the gravitational field.
This is the usual confusion of concepts among positivists, which goes back to Plato, Hume, Maupertiuis, Clifford and Poincaré, and leads to absurdities. First, to the separation of space from matter: if gravity is not matter, but only the form of its existence - "space", then it turns out that the "form of matter" extends far from "matter" (as the positivists call only mass) and there it is bent and closes. Secondly, this leads to the representation of "space" as a special substance - in addition to matter: "space" carries energy and interacts causally with matter. Thirdly, this leads to the absurdity of "space in space" - the usual ambiguity of the positivists in the use of this word: the geometry of "space" is determined by the distribution of matter in space, - in such and such a place in space ("near the masses") "space" was curved …
Meanwhile, Einstein's "closedness of the universe" in reality can mean the closure of only its individual formation, which is nothing extraordinary: closed and stellar systems, and planets, and organisms, and molecules, and atoms, and elementary particles. Nuclear forces do not spread beyond an area of 3 x 10 to minus 13 cm, but this space is open to electromagnetic and gravitational forces.
Astronomers suggest the existence of "black holes" - collapsed stars with such a strong gravitational field that it does not "release" light. It can be assumed that there is somewhere a limit to the propagation of gravitational forces, open to some other forces. In a similar way, the black and sparkling blizzard of galaxies accessible to our telescopes can be relatively closed - some part of the world that includes the world we know.
If cosmologists were clearly aware that we are talking about the relative isolation of some part of the universe, then the calculations of the radius of this part would not enjoy such excited attention of the mystics.
By postulating various additional conditions in Newtonian, Einstein's, and other theories of gravitation, many possible cosmological models are obtained. But each of them, apparently, describes only some limited area of the universe. No matter how much the successes of cognition inspire us, it is oversimplified and erroneous to represent the whole world according to the model of the cognized - a monotonous heap of the same, making absolute the properties and laws of its separate part.
Infinity is fundamentally unknowable by finite means. Neither cosmology, nor any other of the special sciences can be the science of the whole infinite world. And in addition, such extrapolation also provides food for various mystical speculations.