How many dimensions does the space of the world in which we live have?
What a question! Of course, three - an ordinary person will say and he will be right. But there is also a special breed of people who have the acquired property of doubting the obvious. These people are called "scientists" because they are specifically taught to do this. For them, our question is not so simple: the measurement of space is an elusive thing, they cannot be simply counted by pointing with your finger: one, two, three. You cannot measure their number with any device like a ruler or ammeter: space has 2.97 plus or minus 0.04 measurements. We have to think about this issue deeper and look for indirect ways. Such searches turned out to be a fruitful exercise: modern physics believes that the number of dimensions of the real world is closely related to the deepest properties of matter. But the path to these ideas began with a revision of our everyday experience.
It is usually said that the world, like any body, has three dimensions, which correspond to three different directions, say, "height", "width" and "depth". It seems clear that the "depth" depicted on the plane of the drawing is reduced to "height" and "width", is in a sense a combination of them. It is also clear that in real three-dimensional space, all conceivable directions are reduced to some three pre-selected ones. But what does "reduce", "are a combination" mean? Where will these "width" and "depth" be if we find ourselves not in a rectangular room, but in zero gravity somewhere between Venus and Mars? Finally, who can guarantee that the “height”, say, in Moscow and New York is one and the same “dimension”?
The trouble is that we already know the answer to the problem we are trying to solve, and this is not always useful. Now, if you could find yourself in a world, the number of dimensions of which is not known in advance, and look for them one at a time ... Or, at least, so abandon the available knowledge about reality in order to look at its initial properties in a completely new way.
Cobblestone - a tool of the mathematician
In 1915, the French mathematician Henri Lebesgue figured out how to determine the number of dimensions of space without using the concepts of height, width and depth. To understand his idea, it is enough to look closely at the cobbled pavement. On it you can easily find places where stones converge in three and four. You can pave the street with square tiles, which will adjoin each other in two or four; if you take identical triangular tiles, they will adjoin in two or six. But no master will be able to pave the street so that the cobblestones are everywhere adjacent to each other only two. It’s so obvious that it’s ridiculous to suggest otherwise.
Mathematicians are different from normal people precisely because they notice the possibility of such absurd assumptions and are able to draw conclusions from them. In our case, Lebesgue reasoned as follows: the pavement surface is undoubtedly two-dimensional. At the same time, there are inevitably points on it where at least three cobblestones converge. Let's try to generalize this observation: let's say that the dimension of some region is equal to N, if, when tiling it, it is impossible to avoid collisions of N + 1 or more "boulders". Now the three-dimensionality of space will be confirmed by any bricklayer: after all, when laying out a thick wall, in several layers, there will certainly be points where at least four bricks will touch!
However, at first glance it seems that one can find, as mathematicians say, a "counterexample" to Lebesgue's definition of dimension. It is a plank floor in which the floorboards touch exactly two. Isn't it tiling? Therefore, Lebesgue also demanded that the "cobblestones" used in the definition of dimensions be small. This is an important idea, and at the end we will come back to it again - from an unexpected angle. And now it is clear that the condition of the small size of the "cobblestones" saves Lebesgue's definition: for example, short parquet floors, unlike long floorboards, will necessarily touch three at some points. This means that the three dimensions of space are not just an opportunity to arbitrarily choose in it some three “different” directions. Three dimensions is a real limitation of our capabilities, which is easy to feel with a little playing with cubes or bricks.
Dimension of space through the eyes of Stirlitz
Another limitation associated with the three-dimensionality of space is well felt by a prisoner locked in a prison cell (for example, Stirlitz in Mueller's basement). What does this camera look like from his point of view? Rough concrete walls, a tightly locked steel door - in a word, one two-dimensional surface without cracks and holes, enclosing from all sides the enclosed space where he is. There is really nowhere to go from such a shell. Is it possible to lock a person inside a one-dimensional contour? Imagine how Mueller draws a circle on the floor around Stirlitz with chalk and goes home: this does not even make a joke.
From these considerations, another way is derived to determine the number of dimensions of our space. Let us formulate it as follows: it is possible to enclose a region of N-dimensional space on all sides only with an (N-1) -dimensional "surface". In two-dimensional space, the "surface" will be a one-dimensional contour, in one-dimensional space - two zero-dimensional points. This definition was invented in 1913 by the Dutch mathematician Brouwer, but it only became known eight years later, when it was independently rediscovered by our Pavel Uryson and the Austrian Karl Menger.
Here our paths diverge with Lebesgue, Brouwer and their colleagues. They needed a new definition of dimension in order to construct an abstract mathematical theory of spaces of any dimension up to infinite. This is a purely mathematical construction, a game of the human mind, which is strong enough even to cognize such strange objects as infinite-dimensional space. Mathematicians do not try to find out if there really are things with this structure: this is not their profession. On the contrary, our interest in the number of dimensions of the world in which we live is physical: we want to know how many there really are and how to feel their number “on our own skin”. We need phenomena, not pure ideas.
It is characteristic that all the examples given were borrowed more or less from architecture. It is this area of \u200b\u200bhuman activity that is most closely related to space, as it appears to us in ordinary life... To advance in the search for dimensions of the physical world further, you will need access to other levels of reality. They are accessible to humans thanks to modern technology, which means physics.
What does the speed of light have to do with it?
Let's briefly return to the Stirlitz left in the cell. To get out of the shell that reliably separated him from the rest of the three-dimensional world, he used the fourth dimension, which is not afraid of two-dimensional obstacles. Namely, he thought for a while and found himself a suitable alibi. In other words, a new mysterious dimension that Stirlitz took advantage of is time.
It is difficult to say who was the first to notice the analogy between time and the dimensions of space. They already knew about it two centuries ago. Joseph Lagrange, one of the creators classical mechanics, the science of body movements, compared it with the geometry of the four-dimensional world: his comparison sounds like a quote from modern books on the General theory of relativity.
Lagrange's line of thought, however, is easy to understand. In his time, graphs of the dependence of variables on time were already known, like the current cardiograms or graphs of the monthly course of temperature. Such graphs are drawn on a two-dimensional plane: along the ordinate, the path traversed variable, and along the abscissa - the elapsed time. In this case, time really becomes just “another” geometric dimension. In the same way, you can add it to the three-dimensional space of our world.
But is time really like spatial dimensions? There are two highlighted "meaningful" directions on the plotted plane. And directions that do not coincide with any of the axes do not make sense, they do not depict anything. On an ordinary geometric two-dimensional plane, all directions are equal, there are no selected axes.
At present, time can be considered the fourth coordinate only if it is not distinguished from other directions in the four-dimensional "space-time". It is necessary to find a way to "rotate" space-time so that time and spatial dimensions "mix" and can, in a certain sense, pass into each other.
This method was found by Albert Einstein, who created the theory of relativity, and Hermann Minkowski, who gave it a rigorous mathematical form. They took advantage of the fact that nature has a universal speed - the speed of light.
Take two points in space, each at its own moment in time, or two "events" in the jargon of the theory of relativity. If you multiply the time interval between them, measured in seconds, by the speed of light, you get a certain distance in meters. We will assume that this imaginary segment is “perpendicular” to the spatial distance between events, and together they form “legs” of some right-angled triangle, the “hypotenuse” of which is a segment in space-time connecting the selected events. Minkowski suggested: to find the square of the length of the "hypotenuse" of this triangle, we will not add the square of the length of the "spatial" leg to the square of the length of the "temporary" leg, but subtract it. Of course, this may result in a negative result: then it is believed that the "hypotenuse" has an imaginary length! But what's the point in that?
When you rotate the plane, the length of any line drawn on it is preserved. Minkowski understood that it is necessary to consider such "rotations" of space-time, which preserve the "length" of the intervals between events proposed by him. This is how it is possible to achieve that the speed of light is universal in the constructed theory. If two events are connected by a light signal, then the "Minkowski distance" between them is equal to zero: the spatial distance coincides with the time interval multiplied by the speed of light. “Rotation”, proposed by Minkowski, keeps this “distance” zero, no matter how space and time mix during the “rotation”.
This is not the only reason why Minkowski's "distance" has real physical meaning, despite the definition, which is extremely strange for an unprepared person. Minkowski's "distance" provides a way to construct the "geometry" of space-time in such a way that both spatial and time intervals between events can be made equal. Perhaps this is precisely the main idea of \u200b\u200bthe theory of relativity.
So, the time and space of our world are so closely related to each other that it is difficult to understand where one ends and another begins. Together they form something like a stage on which the play "History of the Universe" is played out. The characters are particles of matter, atoms and molecules, from which galaxies, nebulae, stars, planets are assembled, and on some planets even living intelligent organisms (the reader should be aware of at least one such planet).
Based on the discoveries of his predecessors, Einstein created a new physical picture of the world, in which space and time were inseparable from each other, and reality became truly four-dimensional. And in this four-dimensional reality one of the two “fundamental interactions” known to the science of that time “dissolved”: the law of universal gravitation was reduced to the geometric structure of the four-dimensional world. But Einstein was unable to do anything with another fundamental interaction - electromagnetic.
Space-time takes on new dimensions
The general theory of relativity is so beautiful and convincing that immediately after it became known, other scientists tried to follow the same path further. Einstein reduced gravity to geometry? This means that it remains for his followers to geometrize electromagnetic forces!
Since Einstein exhausted the possibilities of the metric of four-dimensional space, his followers began to try to somehow expand the set of geometric objects from which such a theory could be constructed. Quite naturally, they wanted to increase the number of dimensions.
But while theorists were engaged in the geometrization of electromagnetic forces, two more fundamental interactions were discovered - the so-called strong and weak. Now it was necessary to combine four interactions. At the same time, a lot of unexpected difficulties arose, to overcome which new ideas were invented, leading scientists further and further from the visual physics of the last century. They began to consider models of worlds with tens and even hundreds of dimensions, and infinite-dimensional space was also useful. A whole book would have to be written to tell about this quest. Another question is important for us: where are all these new dimensions located? Is it possible to feel them in the same way as we feel time and three-dimensional space?
Imagine a long and very thin tube - for example, an empty fire hose inside, reduced a thousand times. It is a two-dimensional surface, but its two dimensions are unequal. One of them, length, is easy to notice - this is a "macroscopic" dimension. The perimeter, the "transverse" dimension, can only be seen under a microscope. Modern multidimensional models of the world are similar to this tube, although they have not one, but four macroscopic dimensions - three spatial and one temporal. The rest of the measurements in these models cannot be seen even under an electron microscope. To detect their manifestations, physicists use accelerators - very expensive but crude "microscopes" for the subatomic world.
While some scientists were perfecting this impressive picture, brilliantly overcoming one obstacle after another, others had a tricky question:
Can the dimension be fractional?
Why not? To do this, it is necessary to “simply” find a new dimension property that could connect it with non-integers, and geometric objects possessing this property that have fractional dimensions. If we want to find, for example, a geometric figure that has one and a half dimensions, then we have two ways. You can try to either subtract half a dimension from a two-dimensional surface, or add half a dimension to a one-dimensional line. To do this, we will first practice adding or subtracting an entire dimension.
There is a famous trick for children. The magician takes a triangular piece of paper, makes an incision on it with scissors, bends the sheet along the incision line in half, makes another incision, bends it again, cuts it one last time, and - ap! - in his hands there is a garland of eight triangles, each of which is completely similar to the original one, but eight times smaller in area (and eight times the square root in size). Perhaps this trick was shown in 1890 to the Italian mathematician Giuseppe Peano (or maybe he himself liked to show it), in any case, it was then that he noticed this. Take perfect paper, perfect scissors, and repeat the cutting and folding sequence an infinite number of times. Then the sizes of individual triangles obtained at each step of this process will tend to zero, and the triangles themselves will contract into points. Therefore, we will get a one-dimensional line from a two-dimensional triangle, without losing a piece of paper! If you do not stretch this line into a garland, but leave it as "crumpled" as we did when cutting, then it will fill the entire triangle. Moreover, no matter how strong a microscope we look at this triangle, magnifying its fragments any number of times, the resulting picture will look exactly the same as not magnified: scientifically speaking, the Peano curve has the same structure at all magnification scales, or is “scaled invariant ".
So, having bent countless times, the one-dimensional curve was able, as it were, to acquire dimension two. This means that there is hope that the less "crumpled" curve will have a "dimension" of, say, one and a half. But how do you find a way to measure fractional dimensions?
In the "cobblestone" definition of dimension, as the reader remembers, it was necessary to use rather small "cobblestones", otherwise the result could be wrong. But a lot of small "cobblestones" will be required: the more, the smaller their size. It turns out that to determine the dimension it is not necessary to study how the "cobblestones" are adjacent to each other, but it is enough just to find out how their number increases with decreasing value.
Take a straight line segment 1 decimeter long and two Peano curves that together fill a decimeter by decimeter square. We will cover them with small square "boulders" with a side length of 1 centimeter, 1 millimeter, 0.1 millimeter, and so on down to a micron. If we express the size of the "cobblestone" in decimetres, then the number of "cobblestones" equal to their size to the power of minus one is required per segment, and the size to the power of minus two for Peano curves. In this case, the segment definitely has one dimension, and the Peano curve, as we have seen, has two. This is not just a coincidence. The exponent in the ratio connecting the number of "cobblestones" with their size is really equal (with a minus sign) to the dimension of the figure covered by them. It is especially important that the exponent can be fractional number... For example, for a curve intermediate in its "crumpledness" between a regular line and sometimes densely filling the square of Peano curves, the value of the exponent will be more than 1 and less than 2. This opens the way we need to determine fractional dimensions.
It was in this way that, for example, the dimension of the coastline of Norway was determined - a country that has a very rugged (or “crumpled” - as you like) coast. Of course, the cobblestones of the coast of Norway did not take place on the ground, but on a map from a geographic atlas. The result (not absolutely accurate due to the impossibility in practice to reach infinitely small "boulders") was 1.52 plus or minus one hundredth. It is clear that the dimension could not have been less than one, since we are still talking about a "one-dimensional" line, and more than two, since the coastline of Norway is "drawn" on a two-dimensional surface of the globe.
Man as a measure of all things
Fractional dimensions are great, the reader might say here, but how do they relate to the question of the number of dimensions of the world in which we live? Could it happen that the dimension of the world is fractional and not exactly equal to three?
Examples of the Peano curve and the coast of Norway show that fractional dimension is obtained if the curved line is strongly "crumpled", laid in infinitesimal folds. The process of determining the fractional dimension also involves the use of infinitely decreasing "cobblestones" with which we cover the studied curve. Therefore, the fractional dimension, scientifically speaking, can manifest itself only "on a sufficiently small scale", that is, the exponent in the ratio connecting the number of "cobblestones" with their size can only go to its fractional value in the limit. On the contrary, one huge cobblestone can cover a fractal - an object of fractional dimension - of finite size is indistinguishable from a point.
For us, the world in which we live is, first of all, the scale on which it is available to us in everyday reality. Despite the amazing advances in technology, its characteristic dimensions are still determined by our visual acuity and the range of our walks, characteristic time intervals - by the speed of our reactions and the depth of our memory, characteristic values \u200b\u200bof energy - by the strength of those interactions that our body enters into with the surrounding things. We have not surpassed the ancients by much here, and is it worth striving for this? Natural and technological disasters somewhat expand the scale of "our" reality, but do not make them cosmic. The microcosm is all the more inaccessible in our everyday life... The world open before us is three-dimensional, "smooth" and "flat", it is perfectly described by the geometry of the ancient Greeks; the achievements of science should ultimately serve not so much to expand as to protect its borders.
So what is the answer to people waiting for the opening hidden dimensions our world? Alas, the only dimension available to us, which the world has beyond three spatial dimensions, is time. Is it little or much, old or new, wonderful or commonplace? Time is just the fourth degree of freedom, and you can use it in very different ways. Let us recall once again the same Stirlitz, by the way, a physicist by education: every moment has its own reason
Andrey Sobolevsky
Three-dimensional space - has three uniform dimensions: height, width and length. This is a geometric model of our material world.
To understand the nature of physical space, you first need to answer the question of the origin of its dimension. Therefore, the dimension value is, as you can see, the most significant characteristic of physical space.
Dimension of space
Dimension is the most general quantitatively expressed property of space-time. At present, the physical theory, which claims to be a spatio-temporal description of reality, takes the value of dimension as an initial postulate. The concept of the number of dimensions, or the dimension of space, is one of the most fundamental concepts of mathematics and physics.
Modern physics has come close to answering the metaphysical question that was posed back in the works of the Austrian physicist and philosopher Ernst Mach: "Why is space three-dimensional?" It is believed that the fact of three-dimensionality of space is associated with the fundamental properties of the material world.
The development of a process from a point generates space, i.e. the place where the implementation of the development program should take place. "The generated space" is for us the form of the Universe, or the form of matter in the Universe. "
So it was believed in ancient times ...
Even Ptolemy wrote about the dimension of space, where he argued that in nature there can be no more than three spatial dimensions. In his book On Heaven, another Greek thinker, Aristotle, wrote that only the presence of three dimensions ensures the perfection and completeness of the world. One dimension, Aristotle reasoned, forms a line. If we add another dimension to the line, we get a surface. Complementing the surface with another dimension forms a solid.
It turns out that “it is no longer possible to go beyond the bounds of a volumetric body to something else, since any change occurs due to some kind of deficiency, and there is no such thing here. The given train of thought of Aristotle suffers from one essential weakness: it remains unclear why it is the three-dimensional volumetric body that possesses completeness and perfection. At one time, Galileo justly ridiculed the opinion that "the number '3' is the number perfect and that it is endowed with the ability to communicate perfection to everything that has a Trinity."
What determines the dimensionality of space
Space is infinite in all directions. However, it can be measured only in three directions independent of each other: length, width and height; we call these directions the dimensions of space and say that our space has three dimensions, that it is three-dimensional. In this case, "an independent direction, we in this case call a line that lies at right angles to the other. Such lines, i.e. lying simultaneously at right angles to one another and not parallel to each other, our geometry knows only three. That is, the dimensionality of our space is determined by the number of possible lines in it, lying at right angles to one another. There can be no other line on the line - this is one-dimensional space. On the surface, 2 perpendiculars are possible - this is a two-dimensional space. In "space", three perpendiculars are three-dimensional space. "
Why is space three-dimensional?
Rare in earthly conditions, the experience of materialization of people often has a physical effect on eyewitnesses ...
But, in the concepts of space and time, there is still a lot that is unclear, giving rise to incessant discussions of scientists. Why does our space have three dimensions? Can multidimensional worlds exist? Is it possible for material objects to exist outside space and time?
The statement that physical space has three dimensions is just as objective as the statement, for example, that there are three physical condition substances: solid, liquid and gaseous; it describes a fundamental fact of the objective world. I. Kant stressed that the reason for the three-dimensionality of our space is still unknown. P. Ehrenfest and J. Whitrow showed that if the number of dimensions of space were more than three, then the existence of planetary systems would be impossible - only in a three-dimensional world can there be stable orbits of planets in planetary systems... That is, the three-dimensional order of matter is the only stable order.
But the three-dimensionality of space cannot be affirmed as an absolute necessity. It is a physical fact like any other and, as a consequence, it is subject to the same kind of explanation.
The question of why our space is three-dimensional can be solved either from the position of teleology, proceeding from the unscientific assertion that “the three-dimensional world is the most perfect of possible worlds”, or from a scientific-materialistic point of view, based on fundamental physical laws.
Contemporaries' opinion
Modern physics says that the characteristic of three-dimensionality is that it, and only it, makes it possible to formulate continuous causal laws for physical reality. But, " modern concepts do not reflect the true state of the physical picture of the world. Nowadays, scientists consider space as a kind of structure, consisting of many levels, which are also indefinite. And therefore, it is no coincidence that modern science cannot answer the question of why our space, in which we live and which we observe, is three-dimensional. "
Related space theory
In parallel worlds, events take place in their own way, they can ...
“Attempts to find the answer to this question, remaining only within the limits of mathematics, are doomed to failure. The answer may lie in a new, underdeveloped area of \u200b\u200bphysics. " Let's try to find the answer to this question based on the provisions of the considered physics of connected spaces.
According to the theory of connected spaces, the development of an object proceeds in three stages, with each stage developing along its own selected direction, i.e. along its axis of development.
At the first stage, the development of the object proceeds along the initial selected direction, i.e. has one development axis. At the second stage, the system formed at the first stage rotates by 90 °, i.e. there is a change in the direction of the spatial axis, and the development of the system begins to go along the second selected direction, perpendicular to the original. At the third stage, the system's development rotates again by 90 °, and it begins to develop along the third selected direction, perpendicular to the first two. As a result, three nested spheres of space are formed, each of which corresponds to one of the axes of development. Moreover, all three indicated spaces are connected into a single stable formation by a physical process.
And because this process is implemented at all large-scale levels of our world, then all systems, including the coordinates themselves, are built according to the triad (three-coordinate) principle. Hence it follows that as a result of passing through three stages of the development of the process, a three-dimensional space is naturally formed, formed as a result of the physical process of development by three coordinate axes of three mutually perpendicular directions of development!
These intelligent entities appeared at the very dawn of the Universe ...
It is not for nothing that Pythagoras, who, as you can see, could have this knowledge, belongs to the expression: "All things consist of three." The same is said by N.K. Roerich: “The symbol of the Trinity is of great antiquity and is found throughout the world, therefore it cannot be limited by any sect, organization, religion or tradition, as well as personal or group interests, because it represents the evolution of consciousness in all its phases ... turned out to be scattered all over the world ... If you put together all the prints of the same sign, then perhaps it will turn out to be the most widespread and oldest among human symbols. No one can claim that this sign belongs to only one belief or is based on one folklore. "
It is not for nothing that even in ancient times our world was represented as a triune deity (three merged into one): something one, whole and indivisible, in its sacred significance far exceeding the original values.
We have traced the spatial specialization (distribution along the coordinate directions of space) within a single system, but we can see exactly the same distribution in any society from an atom to galaxies. These three types of space are nothing more than three coordinate states of geometric space.
I will describe it in mathematical language.
Consider the usual three-dimensional space in which we live. We perfectly understand what a point, a straight line and a plane are in this space. The intersection of two planes gives us a straight line, the intersection of two straight lines gives us a point. Each point in this space can be described by three coordinates: (x, y, z). The first coordinate usually means length, the second is width, third - the height a given point relative to the origin point. All this can be easily illustrated and imagined.
However, four-dimensional space is not that simple. Any point in this space can now be described by four coordinates: (x, y, z, t), where a new coordinate t is added, which in physics is often called time... This means that in addition to the length, width and height of a point, its position in time is also indicated, that is, where it is: in the past, in the present or in the future.
But let's move away from physics. It turns out that mathematically, a new axiomatic object is added in this space, called hyperplane... It can be conditionally represented as one whole "three-dimensional space". By analogy in three-dimensional space, the intersection of two hyperplanes gives us the plane... Various combinations of this thing with 4D shapes give us unexpected results. For example, in three-dimensional space, the intersection of a plane with a ball gives us a circle. By this analogy, in four-dimensional space the intersection of a four-dimensional ball with a hyperplane gives us a three-dimensional ball.It becomes obvious that it is practically impossible to mentally imagine and draw a four-dimensional space: biologically, our senses are adapted only to a three-dimensional case and below. Therefore, the four-dimensional space can be clearly described only in mathematical language, mainly with the help of actions with the coordinates of points.
However, it can be described in other language less accurately. Consider the concept of parallel worlds: in addition to our world, there are other worlds, in which some events went differently. Let's designate our world through the letter A, and some other world - through the letter B. From the point of view of four-dimensional space, we can say that world A and world B are different "three-dimensional spaces" that do not intersect. That's what it is parallel hyperplanes... And there are infinitely many of them. If it happens that if at a certain point in time in world A "grandfather died", and in world B "grandfather is still alive", then worlds A and B intersect in some four-dimensional figure, in which all events went the same way up to some point in time , and then the figure seemed to be "divided" into non-intersecting three-dimensional parts, each of which describes the state of the grandfather, whether he is alive or not. This could be described in two-dimensional format: there was one straight line, which then split into two non-intersecting lines.
Graphic representation of four-dimensional space
A.B. Fashchevsky , 2011Modern science represents the world around us in the form of three-dimensional space-time (four-dimensional space). It is rather difficult to define the concept of “time”, despite the obviousness of its existence. The term "arrow of time" characterizes it as an axis directed from the past to the future. Strictly speaking, it is impossible to consider time as the fourth dimension of space, because according to the rules of mathematics, it should be simultaneously perpendicular to all three available coordinate axes.
We owe the creation of three-dimensional space-time (four-dimensional space) to Heinrich Minkowski. In 1908, a German mathematician, developing the ideas of Einstein's theory of relativity, said: "From now on, space itself and time itself must turn into fiction, and only a certain kind of combination of both must still retain independence."
According to another version - “Minkowski and Einstein considered that three-dimensional space and time do not exist separately and that the real world is four-dimensional».
Thus, in order to substantiate (develop) their personal hypotheses, two citizens, in violation of the laws of mathematics, put three mutually perpendicular coordinate axes into a single whole and conditional comparative measure - time... (For more information about time - Wikipedia http://ru.wikipedia.org/wiki/Time). This folding can be compared to folding pineapple bricks or amperes liters. It is obvious that such an addition is contrary to common sense. However, physicists themselves do not deny that the main criterion modern physics it is not common sense, but the "beauty" of physical theory.
OUTPUT: The foundation of all modern physics is the private opinion of one citizen or the agreement of two citizens. The hypothesis of three-dimensional space-time, as a four-dimensional space, declared by them, contradicts the elementary foundations of mathematics and does not have any substantiation.
It is clear that theoretical physics at that time was at a dead end and further development paths were very vague. It was necessary to do something, and therefore they seized on the proposed hypothesis as an intermediate way out of the crisis. There is a well-known saying that there is nothing more permanent than temporary solutions. Unfortunately, nothing alternative was proposed, and physics went along the proposed path, as the only possible one. The recognition of this hypothesis by the scientific community caused the rapid development of physics - multidimensional spaces, wormholes, time travel, etc. The author of these lines considers the following scientific pearl to be the height of the wisdom of modern physics - "a seven-dimensional sphere in eleven-dimensional space" ... The question arises: what are the "achievements" of modern science with such a dubious foundation - the theory of relativity, quantum mechanics (which even its authors do not understand) , black holes, theories of the Big Bang and the expansion of the Universe, supergravity, string theory, dark matter and dark energy ..? The growing criticism of the current situation in the press testifies to the fact that the crisis in physics that arose more than a hundred years ago has not been overcome. There is only one reason - the uncontested hypothesis of three-dimensional space-time (four-dimensional space) still remains the foundation of the building of modern physics.
To understand the physical essence of four-dimensional space and the possibility of its graphic representation, we will have to return to the basics of scientific knowledge.
1. Zero space
(space with zero dimensions).
Zero space is a mathematical point.
Material from Wikipedia: “In geometry, topology and related branches of mathematics, a point is called an abstract object in space that has neither volume, nor area, nor length, nor any other measurable characteristics. Thus, a point is called a zero-dimensional object... The point is one of the fundamental concepts in mathematics; any geometric figure is considered to consist of points... Euclid defined a point as something that has no dimensions. In modern axiomatics of geometry, a point is a primary concept, given by a list of its properties. "
Let's conduct an experiment: in any convenient way we add (connect, combine, etc., for example, draw several lines through one point) several mathematical points until they completely coincide. The formula for this addition is as follows:
0 + 0 + 0 + ... + 0 = 0As a result of our actions, the original mathematical point, like the rest of the mathematical points used in this addition, did not change in size and, accordingly, did not acquire measurements. If you participate in this experiment with an infinite number of mathematical points, the result will also not change.
Zero Space Formula (math point)
0 + 0 + 0 + ... + 0 \u003d ZERO SPACE (math point)Let's denote the zero space (mathematical point) - 0PR, then:
0PR + 0PR + 0PR + ... + 0PR \u003d 0PRFINDINGS:
Any mathematical point is a folded infinity consisting of stacked (aligned) mathematical points. In turn, each of the mathematical points included in this infinity is a separate independent infinity, etc.
A mathematical point is an infinite set of coiled infinities - “infinity of infinities”.
ZERO SPACE CONSISTS OF "INFINITY OF INFINITY" Folded ZERO SPACES.
2. One-dimensional space.
One-dimensional space is a line.
A line, according to a geometry textbook, is made up of an infinite number of mathematical points. Within the framework of this work, this means that the line consists of an infinite number of null spaces... Obviously, the formula for adding (combining) mathematical points is 0 + 0 + 0 + ... + 0 = 0 - valid for zero space, cannot be used to form a one-dimensional space in the form of a line. All mathematical points forming a line must be disconnected (separated) from each other as a result of some action. Let's denote this unknown action, which separates adjacent mathematical points in a line, by the letter "and". It's obvious that an action that separates mathematical points in a line cannot be any of the known actions in mathematics such as "add", "multiply", "divide", etc.
One-dimensional space formula (1PR) will look like this:
0 and 0 and 0 and ... and 0 \u003d ONE-DIMENSIONAL SPACE (line) or - 0PR and 0PR and 0PR and ... and 0PR \u003d 1PR (line)The position of any arbitrary point on the line, relative to the point selected as the origin, is determined by one measurement - " x».
The line consists of an infinite number disconnected mathematical points.
ONE-DIMENSIONAL SPACE CONSISTS OF AN INFINITE QUANTITY DISCONNECTED ZERO SPACES.
3. Two-dimensional space.
Two-dimensional space is a plane.
Two-dimensional space is a plane consisting of an infinite number of lines or an infinite number of one-dimensional spaces. Obviously, for the formation of a plane, adjacent lines (one-dimensional spaces) must also be separated in order to avoid their addition (alignment).
Two-dimensional space formula (2PR) will look like this:
1PR and 1PR and 1PR and ... and 1PR \u003d 2PR (plane)The position of any arbitrary point on the plane relative to the point selected as the origin of coordinates is determined by two measurements - " x"And" y».
TWO-DIMENSIONAL SPACE CONSISTS OF INFINITE AMOUNT DISCONNECTED ONE-DIMENSIONAL SPACES.
4. Three-dimensional space.
Three-dimensional space is a filled volume.
Three-dimensional space is a volume consisting of an infinite number of planes or an infinite number of two-dimensional spaces. It is also obvious that in order to form a filled volume, adjacent planes (two-dimensional spaces) must be separated in order to avoid their addition (alignment).
Formula of three-dimensional space (3PR) will look like this:
2ПР and 2ПР and 2ПР and ... and 2ПР \u003d 3ПР (filled volume)The position of any arbitrary point in the filled volume, relative to the point selected as the origin, is determined by three dimensions - " x», « y"And" z».
THREE-DIMENSIONAL SPACE CONSISTS OF AN INFINITE QUANTITY DISCONNECTED TWO-DIMENSIONAL SPACES.
From the above, it is clear that spaces with higher dimensions consist of an infinite set of disconnected spaces of lower dimensions - one-dimensional from disconnected zeros, two-dimensional from disconnected one-dimensional, three-dimensional from disconnected two-dimensional.
In turn, the four-dimensional space should consist of an infinite set of disconnected three-dimensional spaces. However, this is impossible for an obvious reason - if there is one infinite three-dimensional space, each of the dimensions of which is equal to infinity (x \u003d y \u003d z \u003d ∞), then there is no room to accommodate any other three-dimensional space disconnected from this one. In the available three-dimensional space, you can select any larger or smaller filled volume, but it will be only a part of this three-dimensional space.
OUTPUT:
The creation of a four-dimensional space from an infinite set of disconnected three-dimensional spaces is impossible.
In order to understand what kind of space surrounds us, it is necessary to understand the addition and separation of spaces, having previously understood the difference between volume (geometric volume, three-dimensional volume) and three-dimensional space.
There is a strong opinion that three-dimensional figures in the form of a parallelepiped, sphere, cone, pyramid, etc. represent a three-dimensional space:
Upon closer examination, it can be seen that the parallelepiped is a set of six planes (six two-dimensional spaces), and the ball is one curved plane (one curved two-dimensional space) and both of these figures are not three-dimensional spaces. The thickness of the plane (wall) in any of these figures is equal to one mathematical point. There is a void inside each of the shapes.
As an analogy, we can give an example with a parallelepiped-shaped aquarium. If the aquarium is empty, then another aquarium of slightly smaller sizes can be inserted into it:
The difference between a three-dimensional volume and a three-dimensional space can be understood in the following example. If water is poured into a larger aquarium, it will be impossible to insert a smaller aquarium into it. its space is occupied by water. An aquarium filled with water is a three-dimensional space, and an empty aquarium is a three-dimensional space.
Three-dimensional space can be imagined in the form of a parallelepiped (x \u003d y \u003d z \u003d ∞), the entire volume of which is filled with two-dimensional spaces (parallel planes), each of which has a thickness of one mathematical point:
FINDINGS:
Volume (three-dimensional volume, geometric volume) is an abstract concept in the form of emptiness, limited by two-dimensional spaces.
Three-dimensional space consists of an infinite set of disconnected two-dimensional spaces, each of which consists of an infinite set of disconnected one-dimensional spaces, each of which, in turn, consists of an infinite set of disconnected zero spaces.
THREE-DIMENSIONAL SPACE REPRESENTS A REAL PHYSICAL OBJECT IN THE FORM OF A THREE-DIMENSIONAL GEOMETRIC VOLUME, EACH DIMENSIONS OF WHICH IS EQUAL INFINITY, FILLED IN EACH INFINITY MEASUREMENT OF INFINITY.
THREE-DIMENSIONAL SPACE CANNOT CONTAIN EMPTY IN THE FORM OF EMPTY SPACE, EMPTY VACUUM, ETC.
A contradiction arises - either the foundations of scientific knowledge are correct and the space around us consists of something (matter, ether, elements of a physical vacuum, dark matter or something else), or A. Einstein's theory with its absolute emptiness of three-dimensional space-time is correct.
The addition of spaces can be represented as follows. Take zero space (mathematical point) in the form of a box (parallelepiped) without a lid, all dimensions of which are zero, and the wall thickness is also zero:
It is obvious that an infinite number of such boxes can be inserted inside this box, because it and their dimensions and wall thickness are zero:
This action can be compared to nesting disposable cups or nesting dolls into each other, but the number of cups or nesting dolls to be inserted is infinite. Such nesting can be imagined in the following form (all sizes of boxes are equal to zero):
Output: Addition of zero spaces is an action of combining (overlaying) an infinite set of zero spaces without changing their original dimensions.
Adding a zero space with many zero spaces does not require any ordering or sequence of actions.
Obviously, abstract zero, one, two and three-dimensional spaces can add up to each other in any combination. they are all basically made up of mathematical points (zero spaces). These spaces are called abstract because mutual arrangement the points from which they consist is taken as the initial condition. Zero space can be added to three-dimensional or one-dimensional to be added to two-dimensional or three-dimensional to be added to three-dimensional (sequentially, a point with a point of each of the spaces). The folding of spaces means the folding of a space with a greater dimension into a space with a lower dimension. When two or more spaces with the same dimension are added together, only one space with the original dimension remains. The addition of abstract spaces does not require any effort or energy expenditure. The ideal state (ideal space) is the addition of all abstract zero, one, two and three-dimensional spaces into one zero space (one mathematical point).
The creation (formation) of real one, two and three-dimensional spaces requires the obligatory occurrence of some kind of action that allows you to keep neighboring mathematical points (zero spaces) from adding up. This action is indicated in this work by the sign “ and"And is called, unlike other mathematical operations" Disconnection».
The existence of "separation" of mathematical points is confirmed by the very fact of the existence of the world around us. If this action did not take place, the world around us would instantly collapse into one mathematical point (into one zero space) and would cease to exist. Separating mathematical points and spaces is a fundamentally new action, in which there is an obstacle to the addition of spaces (addition of mathematical points).
Any mathematical point (zero space) consists, as shown earlier, of an infinite number of stacked mathematical points (zero spaces). Consider, as an example, a null space consisting of two null spaces:
The only way (according to the author) to separate adjacent mathematical points - zero spaces (i.e. create a space more high level) is giving them opposite directions of rotation:
This can be more clearly illustrated by the example of counter rotation of zero spaces in the form of a ball with a diameter equal to zero:
Let's consider the essence of rotation in more detail:
and) Rotating math point around one axis coordinates will be flat figure - circle.
b) around two axes coordinates will represent a volumetric figure - ball(sphere).
in) Rotate math point at the same time around three axes coordinates will be - rotating ball.
Simultaneous rotation of a point around three coordinate axes is equivalent to the rotation of this point around one additional axis "F" passing through the origin.
The rotation of a point around one additional axis is more visual. F"Passing through the origin of coordinates, as its simultaneous rotation around three coordinate axes, can be represented in the following form:
The planes of revolution V x, V y and V z are perpendicular to the surface of the rotating ball formed by V x, y, z.
Additional axis "F" of rotation V x, y, z passes through the origin "0", but in general it does not coincide with any of the coordinate axes. The position of the "F" axis relative to the coordinate axes is determined by the value of V x, V y and V z.
Output:
Any rotation is perpendicular to all three coordinate axes simultaneously.
Rotation depending on direction (clockwise or counterclockwise) can vary from 0 to –N and from 0 to + N, where N is the number of revolutions of rotation or the speed of rotation (the direction of rotation is clockwise denoted by a plus sign, and counterclockwise by a minus sign).
Output:
Rotation is the fourth dimension of space.
The kinetic energy of rotation of a material body (for example, a flywheel) is determined by the formula:
Consequently, rotation represents energy... From here we can conclude:
FOUR-DIMENSIONAL SPACE IS "ENERGY SPACE".
Graphically, the four-dimensional "space-energy" can be represented as follows:
It is obvious that the existence of this four-dimensional space upsets the energy balance. Accordingly, the real physical four-dimensional space should consist only of an even number of energies with opposite directions of rotation, the sum of which is equal to zero:
Let's consider the essence of rotation. To rotate a metal ball, an axis of rotation is required - a hole in the ball, an axle, bearings, supports, or a shaft, bearings, supports, etc. are required, depending on the technical solution. For a four-dimensional space, the problem of ensuring the very possibility of rotation of opposite energies around an axis can be solved only if these energies are represented in the form of oppositely directed rotating vortex tori:
Graphically, a real physical four-dimensional "space - energy" can be represented as a volume formed by two energies with opposite directions of rotation:
Four-dimensional space is a volume (V \u003d π · D2 · L / 4) filled with energy (counter axial and circular rotation of the right and left vortex tori).
The emergence of a four-dimensional "space-energy" ( severing two adjacent math points inside one math point) can be represented as follows:
THE WORLD SURROUNDING US IS AN ENDLESS THREE-DIMENSIONAL VOLUME FILLED WITH AN ENDLESS NUMBER OF SINGLE FOUR-DIMENSIONAL SPACES FORMED BY RIGHT AND LEFT VORTEX VORTEX CONSISTING.
The world around us is a four-dimensional "space-energy" consisting of an infinite set of disconnected single four-dimensional spaces:
The world around us is a four-dimensional "space-energy" and has four dimensions.
Any point of the four-dimensional "space-energy" is characterized by its location and the amount of energy relative to the point selected as the origin:
The location of any point is determined by three dimensions in the form of linear coordinates "X", "Y", "Z".
The amount of energy "E" at any point is determined by one measurement - comparison with the amount of energy at the point taken as the origin.
Four-dimensional "space-energy" has no beginning or end, all points of this space are absolutely equal and, accordingly, there cannot be a dedicated (privileged) coordinate system in this space.
The world around us will look like this:
A GRAPHIC IMAGE OF THE FORMATION OF THE FOUR-DIMENSIONAL WORLD SURROUNDING US, CONSISING OF MANY FOUR-DIMENSIONAL SPACES INSIDE ONE MATHEMATICAL POINT (ZERO SPACE), as an analogue of the BIG EXPLOSION looks like this:
Taking into account that the unfolded infinity inside the mathematical point represents two infinite sets of right and left vortex tori in the form of energy, it can be argued that folded infinity turned into two opposite infinities - right and left.
The separation of just two mathematical points immediately leads to the formation of a single four-dimensional space. Volume consists of area times length. The filled volume consists of energy, which is the fourth dimension. The area and length are formed with the oncoming movement of energies. Consequently, it is impossible to have one, two and three-dimensional spaces in our world, which is perfectly confirmed in practice. Also, it is impossible for spaces with a dimension of more than four to arise in our world by earlier this reason - lack of a place to find them.
It is obvious that vortex tori forming a four-dimensional space, and having the same components of the direction of rotation, can form more complex structures - right and left vortex tubes. Vortex tubes can be closed in right and left vortex rings, which leads to the formation of various vortex chains from right and left vortex rings:
The presence of vortex chains allows (by self-assembly) to create from them relatively stable vortex structures in the form of a ball (sphere), torus, etc. Further complication of the structure of space at one of the stages leads to the formation of structures that we call electrons, protons and further to the formation of matter, planets, stars, galaxies, etc.
Some definitions:
DISCONNECTION - THIS IS A DIVISION INTO LEFT AND RIGHT.
ROTATION ≡ ENERGY
ENERGY IS DIVIDED INTO TWO TYPES:
- right-handed energy (energy of rotation of the right vortex torus)
- left-handed energy (rotational energy of the left vortex torus)
SPACE - THIS IS AN INFINITE THREE-DIMENSIONAL VOLUME FORMED BY THE ENERGIES OF AN INFINITE NUMBER OF RIGHT AND LEFT VORTEX TORES.
MATTER - THIS IS AN ELEMENTARY UNIT OF SPACE FORMED BY DISCONNECTING TWO NEIGHBORING MATHEMATICAL POINTS (TWO ZERO SPACES) AND CONSISTS OF RIGHT AND LEFT ENERGIES.
SPACE IS FORMED BY MATTER.
MATTER DIMENSIONS AIM TO ZERO.
- TWO KINDS OF ENERGY FORM SPACE.
- SPACE IS FORMED BY TWO TYPES OF ENERGY.
THE WORLD AROUND US IS BINARY IN ITS BASIS.
IN THE WORLD AROUND US, THERE IS NOTHING BUT ENERGY.
In this work, the introduction of the fourth dimension of space in the form of energy "E" obliges to revise the dimensionality of traditional spaces in the form of a line, a plane and a filled volume:
- Line is an abstract two-dimensional space ... The coordinates of any point on the line, relative to the point selected as the origin, are determined by two dimensions: " x"- lengths and" e"- energy.
- The plane is an abstract three-dimensional space. The coordinates of any point on the plane, relative to the point selected as the origin, are determined by three dimensions - " x"- lengths," y"- width and" e"- energy.
- The filled volume is a real four-dimensional space. The coordinates of any point of the filled volume, relative to the point selected as the origin of coordinates, are determined by four dimensions - " x"- lengths," y"- width," z"- heights and" e"- energy.
One-dimensional space does not exist, because any comparison of a selected point with a point of origin requires two measurements at once - energy and relative position.
It was stated above in the text that it is impossible to create a four-dimensional space. There seems to be a contradiction, but it is not. In abstract spaces - one-dimensional (line), two-dimensional (plane) and three-dimensional (volume) - the relative position of points is set as an initial condition. In any real physical space, adjacent points in space must be separated (disconnected) from each other. Otherwise, all points (spaces) will merge into one mathematical point. As a mechanism for their separation, the "DISCONNECTION" is proposed in the form of endowing neighboring mathematical points with opposite (right and left) energies. As shown, energy is the fourth dimension of space. Thus, there is no contradiction - a mechanism for separating adjacent mathematical points is simply added to the existing traditional dimensions of spaces in the form of an additional dimension. Abstract one, two and three-dimensional spaces are translated into real spaces by adding to any of them a mechanism for separating adjacent mathematical points in the form of the fourth dimension. In the process of translation, it turned out that the separation of two adjacent mathematical points in any of these spaces leads to one result - the emergence of a four-dimensional space-energy. Accordingly, only four-dimensional space-energy can be real physical space. All other spaces can only be abstract, which is perfectly confirmed in practice in the form of the four-dimensional world around us.
Earlier it was shown that without "Disconnection" all spaces and all mathematical points will add up to one common point. Let's call this point - "Mathematical START point". The “mathematical point of the BEGINNING” is an object around which there is nothing - no matter, no space, no energy, no emptiness, no dimensions, or anything else, ie absolute NOTHING or ZERO. Inside the "Mathematical point of the BEGINNING" is a convolved "infinity of infinities" of mathematical points (zero spaces), also equal to ZERO. Thus, the equilibrium state: zero equals zero. " The mathematical point of the BEGINNING "is, in principle, the only possible object. We can say that this is the "ONLY BEGINNING OF ALL" or that it is the "BEGINNING BEGINNING".
The emergence of four-dimensional space from the "Mathematical point of the BEGINNING" (Initial zero space) should be understood as a qualitative change in state - the transition of one rolled "infinity of infinities" into two unfolded opposite infinities with the instant formation of an infinite four-dimensional space, and not as a gradual filling with energy of some earlier existing empty volume. An infinite number of mathematical points were already inside one "Mathematical STARTING point" by definition, as a curled up infinity. The unfolding of two opposite infinities occurs as a phase transition within the "Mathematical point of the BEGINNING" - the instant emergence of an infinite four-dimensional space from an infinite number of zero spaces, consisting of two types of energy. In this case, the equilibrium state is not violated - the sum of two opposite (opposite) infinities remains equal to zero.
The unfolding of two opposite infinities in the form of two opposite energies - right and left, should be understood as their interconnection and close interweaving. Any sufficiently small part of four-dimensional space, vacuum, interstellar space, any elementary particle, and further protons, electrons, atoms, molecules, matter, planets, stars and galaxies are simultaneously composed of two types of energy - right and left.
It is rather difficult to deny the objective presence of energy, time and three dimensions of space in the world around us.
Time is a characteristic of energy, showing the sequence of changes in its value at a given point in four-dimensional space with respect to the point selected as the origin.
The obvious conclusion: There has never been a big bang, expansion or contraction of the Universe and there never will be. The theory of relativity, black holes, dark matter and dark energy, multidimensionality of space and other "achievements" of modern science are a beautiful shell of emptiness on which they are built.
Disconnection of an infinite number of neighboring mathematical points inside one "Mathematical STARTING point" creates a four-dimensional space filled with energies inside it. The sum of the right and left energies that form the four-dimensional space of our world is equal to zero. This can be shown as follows:
"Mathematical START point" (collapsed infinity) \u003d 0 Four-dimensional space - two expanded infinities + E + (–E) \u003d 0Or 0 = 0
Thus, the world around us can be considered either as a fluctuation of ZERO, or as a fluctuation of folded infinity equal to zero, which unfolds in two opposite infinities, in total equal to zero, which is essentially the same fluctuation of zero. If the world around us exists, then this means that the probability of unfolding the collapsed infinity in the form of a "Mathematical Start Point" in two opposite infinities is greater than zero.
Formally, the world around us or the UNIVERSE is both infinite and equal to zero - for an observer inside our world it is eternal, infinite and has no boundaries, and for an outside observer (if he could be outside our world) it is equal to zero.
It should be noted that the "Mathematical STARTING point" is an ideal space and can exist only in a single copy. Thus, when the adjacent mathematical points are separated inside the “Mathematical point of the BEGINNING”, the unfolding of two opposite infinities occurs and only one UNIVERSE is formed, eternal and infinite.
Graphically, the four-dimensional "Space - energy" can be depicted in the following form (point "M", chosen as the origin, has an energy greater than zero):
No point in the four-dimensional space-energy can have energy equal to zero or less than zero. This explains the reason that the lowest possible temperature on the Celsius scale is –273 degrees, and the maximum temperature is not limited.
A few words about the air
The world around us is a structured four-dimensional space-energy - from quarks, protons and electrons to stars and star clusters. The infinity of the observed world, both in the direction of increasing the size of objects, and in the direction of decreasing them, allows us to assume the general structuredness of the four-dimensional space, as its inherent property. In accordance with this, the ether can be called the energy structure of the four-dimensional space-energy, located below the observed (or below the recorded) at a given time, the maximum size of objects. For example, from quarks to elementary units of matter.
The copyright for this work belongs to
Fashchevsky Alexander Boleslavovich
[email protected] , http://afk-intech.ru/
We live in a three-dimensional world: length, width and depth. Some may argue: "What about the fourth dimension - time?" Indeed, time is also a dimension. But the question of why space is measured in three dimensions is a mystery to scientists. New research explains why we live in a 3D world.
The question of why space is three-dimensional has tormented scientists and philosophers since ancient times. Indeed, why exactly three dimensions, and not ten or, say, 45?
In general, space-time is four-dimensional (or 3 + 1-dimensional): three dimensions form space, the fourth dimension is time. There are also philosophical and scientific theories about the multidimensionality of time, which suggest that there are actually more measurements of time than it seems: the usual arrow of time, directed from the past to the future through the present, is just one of the possible axes. This makes possible various sci-fi projects, such as time travel, and also creates a new, multivariate cosmology that allows for the existence of parallel universes. However, the existence of additional time dimensions has not yet been scientifically proven.
Let's go back to our 3 + 1-dimensional dimension. We know very well that the measurement of time is associated with the second law of thermodynamics, which states that in a closed system - such as our Universe - entropy (a measure of chaos) always increases. The universal disorder cannot decrease. Therefore, time is always directed forward - and nothing else.
In a new article published in the EPL, the researchers suggested that the second law of thermodynamics may also explain why space is three-dimensional.
"A number of researchers in the field of science and philosophy addressed the problem of the (3 + 1) -dimensional nature of space-time, justifying the choice of this particular number by its stability and the possibility of maintaining life," - said study co-author Julian Gonzalez-Ayala from the National Polytechnic Institute in Mexico and the University of Salamanca in Spain, Phys.org. “The value of our work lies in the fact that we present reasoning based on a physical model of the dimension of the Universe with a suitable and reasonable scenario of space-time. We are the first to declare that the number “three” in the dimension of space arises as an optimization of a physical quantity ”.
Previously, scientists drew attention to the dimension of the Universe in connection with the so-called atropic principle: "We see the Universe like this, because only in such a Universe could an observer, a person, arise." The three-dimensionality of space was explained by the possibility of maintaining the Universe in the form in which we observe it. If there were many dimensions in the Universe, according to Newton's law of gravitation, stable orbits of planets and even the atomic structure of matter would not be possible: electrons would fall on nuclei.
In this study, the scientists took a different path. They assumed that space is three-dimensional due to a thermodynamic quantity - the Helmholtz free energy density. In a universe filled with radiation, this density can be thought of as pressure in space. Pressure depends on the temperature of the universe and on the number of spatial dimensions.
Researchers have shown what could have happened in the first fraction of a second after the Big Bang, called the Planck era. The moment the universe began to cool, the Helmholtz density reached its first maximum. Then the age of the Universe was a fraction of a second, and there were exactly three spatial dimensions. The key idea of \u200b\u200bthe study is that the three-dimensional space was "frozen" as soon as the Helmholtz density reached its maximum value, which prohibits the transition to other dimensions.
The figure below shows how this happened. Left - free energy densityHelmholtz (e) reaches its maximum value at a temperature of T \u003d 0.93, which occurs when the space was three-dimensional (n \u003d 3). S and U represent entropy densities and internal energy densities, respectively. It is shown on the right that the transition to multidimensionality does not occur at temperatures below 0.93, which corresponds to three dimensions.
This was due to the second law of thermodynamics, which allows transitions to higher dimensions only when the temperature is above the critical value - not a degree lower. The universe is continuously expanding and elementary particles, photons, lose energy - that's why our world is gradually cooling: Now the temperature of the Universe is much lower than the level that suggests a transition from the 3D world to multidimensional space.
The researchers explain that spatial dimensions are similar to states of matter, and the transition from one dimension to another resembles a phase transition - such as melting ice, which is possible only at very high temperatures.
“During the cooling of the early Universe and after reaching the first critical temperature, the principle of entropy increment for closed systems could prohibit certain changes in dimensionality,” the researchers comment.
This assumption still leaves room for the higher dimensions that existed in the Planck era, when the universe was even hotter than it was at the critical temperature.
Additional dimensions are present in many cosmological models - primarily in string theory. This study may help explain why in some of these models the extra dimensions have disappeared or remained as tiny as they were in the first fractions of a second after the Big Bang, while 3D space continues to grow throughout the observable universe.
In the future, the researchers plan to improve their model to include additional quantum effects that could occur in the first split second after the Big Bang. In addition, the results of the augmented model can also serve as a reference for researchers working on other cosmological models, such as quantum gravity.