Last-modified 29-July-2000 . . . . . . . . . . . . . . . . . . . . . Save the images: plosk2en.gif , sphere1en.dif

Ni”k Kronov


I assert: the universe is expanding because in ours four-dimensions world three dimensions of space also one dimension - time are connected geometrically so that the expanding of space inevitably follows from the flowing of time. In particular, it means that the expansion of the universe could have stopped just if the flowing of time will stopped. So the statement of the generally accepted theory is incorrect that it depends on amount of matter in the universe - whether the expansion of the universe will stop sometime replaced with compression, or the expansion will be continuing always.

I. A. Klimishin in his book "The Relativist Astronomy" (Moscow: Science, 1981, p.247) writes: "The theory of "Big Bang" that is to say the theory of the Hot Universe cannot give the answer to a question "why are the universe expanding". As an academician J. B. Zeldovich has noted: "Into this theory the expansion had been incorporated initially. As theorists say, it had been incorporated "by hands", by the unfounded setting of the initial conditions. On the questions, why does the universe expand, why are the galaxies scattering nowadays, the answer is, that per the first second (but can be earlier) there was an initial speeds distribution corresponding to the scattering"".

But I think, it should be clear that any distribution of speeds of material objects cannot result the scattering because "speed" physically means a movement in space, therefore sheerly there is no place where the matter can be scattered.

It is impossible visual to imagine the space of universe - three-dimensional also having no borders, and at the same time final, closed with itself like a ring. But if we shall discard one of three space dimensions and, as a model of the universe, we can imagine two-dimensional space with the same characteristics - for example, surface of a toy balloon. Let's draw many points allocated more or less in regular intervals on all surface of the toy balloon. The points represent particles of substance per the first seconds of existence of the homogeneous universe. Let's ask the supporters of the generally accepted theory, who also compare the space of universe with a surface of a toy balloon: what kind of the "initial distribution of speeds" should be, in order the points can be scattered? Which way should the speeds of a movement of these points be directed in space of the model, that is to say on a surface of a ball? The answer from the theorists is not audible. But the answer is clear: there is not such a direction. Thus the other statement of the generally accepted theory is unsound also: that the scattering continuing - ostensibly, by inertia - already not of particles but galaxies formed from them - is being braked by force of gravitation. But you see, the braking follows from the equations expressing the law of preservation of energy: the increase of potential energy of gravitation, because of removal of the galaxies from each other, should be compensated by reduction of kinetic energy of their movement. But itís impossible: itís visual evidently that in two-dimensional space, that is to say on a surface of a ball, there is not any an especial point, whence particles originally have flown away and where the braking force would attract back the todayís galaxies formed from this particles. The absence in present space of such "the center of Big Bang" follows also from "the Cosmology Principle" that lays down the axiom about large-scale homogeneity and isotropy of the universe. As Albert Einstein has neglected by universality of the Newton's law of addition of speeds for the sake of a constancy of speed of light - as it is necessary to neglect by universality of the law of preservation of energy for the sake of a constancy of speed of expansion of the universe, that, as I shall show below, is connected to a constancy of speed of light and flowing of time.

A psychologist Max Vertheimer in the book "Productive thinking" wrote: "Physicists of the past were trying to construct a perpetual mobile. After many unsuccessful attempts, suddenly a question had arisen: how will physics look, if the fundamental laws of nature would made impossible existence of the perpetual mobile? Having become central, this question has resulted in huge changes. Also Einstein had a question: how will physics look, if on a nature of things under all conditions the speed of light will be constant?".

And here I offer a question too: how will physics and the universe look if the truth is that a "radius" of universe grows with constant speed and this speed is equal to speed of light?

The supporters of the generally accepted theory diligently reveal all the consequences, that appear from its algebraic formulas but for some reason they do not wish to see the consequences, that appear from their own geometrical model - of the toy balloon model. You see, they could ask themselves some questions: what is this radius of the balloon is, that is to say this additional dimension, the perpendicular to the dimensions of space? May it be time? What is the speed with which the radius of the balloon grows and why it grows, that is to say why space of the universe is expanding? Where on the ball there is the horizon of a visible part of the universe and what is located behind the horizon? What is the speed of the galaxies, that are stationed behind horizon and are moving away from us? Is its speed greater than speed of light?

Unfortunately, the supporters of the generally accepted theory prefer to criticize my model instead of to answer at first in essence the criticism stated here to them. To escape from the answer, they even are ready to refuse from their own model of a toy balloon and from visual presentation in general, by hinting that the absence of a visual model is attribute of depth and complexity of their theory.

My model of the universe has not the described contradictions of the generally accepted theory. In my model the "scattering" of particles and galaxies is seeming. Therefore the scattering cannot be braked by force of gravitation. The seeming scattering appears because space of the universe is expanding like a toy balloon surface is stretching when you inflate the balloon. Space can be expanded only because our world, except of three dimensions of space, has the fourth dimension - time, that flows constantly and evenly. It is visual visible on the model of the universe - on a toy balloon. Besides two dimensions of the balloon surface, that is to say of two dimensions of space, the balloon has the third dimension - a line passing through each point of the surface and the center of the ball from which the expanding had begun. In the theory of relativity this line is known as "an axis of time" ("an arrow of time") or "a world line" of the given point of space. Each point of a surface of the ball, that is each point of two-dimensional space, is moving along its "world line" with speed of light when the ball is swelling. Because, according to the theory of relativity, factor of proportionality between change of coordinate of a point on its "world line" and time it is speed of light. In the theory of a relativity it is supposed that the world lines of all points of space are parallel but according to my model they all go out from one center that now is (on model) very far - according to my calculations, on distance of 14 billions of light years. But this is a radius of the model of the universe - a radius of our toy balloon. It corresponds to age of the universe that equal 14 billions years.

Thus: 1. From the special theory of relativity (STR) we know the principle (the model) of a "world line" that simultaneously represents a stationary model of the plane world (plane space-time).

plosk2en.gif 3 Kb

- Here the point "A", where we are, is moving with the speed of light from the past to the future along its world line (the vertical line). Also all other points of the plane represented by a horizontal line, are moving together with all planets, stars and galaxies - on model two-dimensional - that are taking place in this plane representing our three-dimensional space and stretching unboundedly in all directions. Two horizontal broken lines on the figure are the same space of the universe at any moments of the past and the future. Time at the Newton's model also has no beginning in the past and no ending in the future as it is visible on the figure.

2. This known model of a "world line" (the above-placed figure is taken from the part "The Theory of Relativity" of the textbook "General Physics") is connected by me with also known - from the general theory of a relativity (GŰR) - the principle of bending and closeness of space of the universe. As though I am bending a horizontal line on the figure, am closing its ends and thus I receive a model of an universe that isnon-stationary and constantly being expanded. The next figure is not present in the textbooks and here is my discovery with the important consequences.

sphere1e.gif 3 Kb

- Here the point "A" (where we are) is moving again with speed of light from the past to the future along its world line that is to say all sphere is swelling - its radius grows with speed of light. At present time the radius ÔŠ of the model is equal, according to my calculations, 14 billions of light years.

I remind: space of the universe "at the given moment", that is to say all of its points, is (on the model) a surface of a ball - a sphere. The points are named "the events" because they are not only points of space but also of space-time. The points of volume inside the ball are "all events of the past". And unlimited volume outside of the ball are "events of the future". Light reaches us only from the galaxies, the distance up to which (along a surface of the ball) is no more than 14 billions of light years. Inasmuch as the ball is swelling, this "horizon", seen by us, is leaving from us with speed of light. But also the galaxies, located on this horizon, leave with speed of light. Therefore we always can see only the same limited area of the universe. Besides we see the distant objects with delay that is equal to the time of passage of light from them up to us. The rest of approximately 5 time large part of the universe always remain for us unobservable. But according to the Cosmological Principle - the principle of large-scale uniformity and isotropy of the universe - in the 5/6 part of the universe, inaccessible to our supervision, all are, in general, the same that it is in a part visible by us.

Thus the circumference of the "toy balloon", that is to say circumference of the universe is equal to 2pR=88 billions of light years. Interestingly - and it is not present in the textbooks, it follows from my model, the galaxies that are in the part of the universe inaccessible to our supervision, that is to say on distance from 14 up to 44 billions of light years from us, are leaving from us with speeds large than speed of light. It is possible, as these speeds of scattering are seeming but are not speeds of movement of matter in space. Actually all galaxies remain approximately on the same places, and its "scattering" takes place because the space of universe is being expanded, is swelling like the two-dimensional membrane of a toy balloon is stretching. The distances between all material objects gravitating one to another in the universe now increase for one year just on 1/14,000,000,000. Hence, amount of energy of gravitation in the universe increase at the same proportion. But any "braking of speed" of seeming scattering of galaxies and reduction of its kinetic energy cannot be. Hence the energy is arising continually! At an initial period of existence of the universe the energy and matter were arising in huge quantities. But also now the energy arising inside the Sun thus amounts, according to my calculations, not less than 1/1200 of its radiation. Thus, according to my model, fundamental the Law of Conservation of energy is not absolute: the expansion of space increases quantity of energy in the universe.

My model shows visually how and why space is being bent under action of gravitation forces: the membrane of the "toy balloon" is weighed down to its center in points representing stars or galaxies, as the smaller distance up to the center corresponds to the slowed down flowing of time in a gravitation field of the concentrated mass of substance. So-called "black holes" are submitted also visually. Let's assume that 7 billions years ago, when the radius of our toy balloon was twice less, in some point on its surface such large mass had been concentrated that in a field of its gravitation time has stopped at all, that is to say the distance between this point and the center of the ball has ceased to grow. But all the rest of the surface of the balloon was continuing to be swelling with speed of light. And now the "black hole" is a funnel with depth of 7 billions of light years from a surface of the ball up to this point. But even the light cannot reach a bottom of the funnel so the bottom as if is leaving from us with speed of light, because the surface of the balloon, where we are, continues to be swelling with speed of light. This visual picture of black holes wouldnít turn out, if a radius of the "toy balloon" is being increased with the speed that is not equal speed of light as the supporters of the generally accepted theory imagines.

Physicist D. I. Kazakov wrote: "Due to power of mathematics the physicists can look there, where the imagination does not penetrate, but after this on a place of mathematical abstraction the human thought generates an visual image again". But the supporters of the generally accepted theory of "Big Bang" who were fascinated by the algebraic equations1 (FOOTNOTE-1: About so-called "Piphagorís syndrome" see an article by R. A. Aronov "Theater of absurdity: is it necessary to the modern physics" at the "Questions of philosophy monthly", No 12, 1997), have ignored more visual geometry and even have been distracted from a physical reality. You see, the Minkovsky's four-dimensional world, with which they operate, is a mathematical design, its four dimensions are equal in rights but it is incorrect physically. In the real physical world the fourth dimension - time - has a nature that is different from a nature of three dimensions of space. By stretching a point it is possible to speak about "moving" of particles and galaxies in the four-dimensional space-time but the vectors of their speeds and accelerations also the forces, that are braking or accelerating the movement, can be located just in three-dimensional space. The unequal rights of dimensions of space and of time are displayed as well in large-scale geometry of the physical four-dimensional world: each of three dimensions of space is closed on itself as a ring, and the ring is expanding from zero with flowing of time but the dimension of time is not closed and has a point of a beginning - so-called the point of "Big Bang", that is to say the point of a beginning of existence not only of space but also of time and of matter.

9 Jan. 1996

Ni”k Kronov

The most complete version of this text in English:

Welcome to my Guest Book. My E-mail:

Back to my homepage: