4 dimensional world. About the presence of the fourth, fifth and more dimensions

• Translation

You probably know that the planets move around the sun in elliptical orbits. But why? In fact, they move in circles in four-dimensional space. And if you project these circles onto three-dimensional space, they turn into ellipses.

In the figure, the plane represents 2 of the 3 dimensions of our space. The vertical direction is the fourth dimension. The planet moves in a circle in four-dimensional space, and its "shadow" in three-dimensional space moves in an ellipse.

What is this 4th dimension? It looks like time, but it's not exactly time. This is such a special time that flows at a speed inversely proportional to the distance between the planet and the sun. And relative to this time, the planet moves at a constant speed in a circle in 4 dimensions. And in normal time, its shadow in three dimensions moves faster when it is closer to the sun.

Sounds weird - but it's simple unusual way representations of ordinary Newtonian physics. This method has been known since at least 1980 thanks to the work of the mathematical physicist Jurgen Moser. And I found out about this when I received by email a paper by Jesper Goranson called "Symmetries in the Kepler problem" (March 8, 2015).

The most interesting thing about this work is that this approach explains one interesting fact. If we take any elliptical orbit, and rotate it in 4-dimensional space, then we get another valid orbit.

Of course, it is possible to rotate an elliptical orbit around the sun and in ordinary space, obtaining a valid orbit. The interesting thing is that this can be done in 4-dimensional space, for example, by narrowing or expanding the ellipse.

In general, any elliptical orbit can be turned into any other. All orbits with the same energy are circular orbits on the same sphere in 4-dimensional space.

Kepler's problem

Let's say we have a particle that moves according to the inverse square law. Its equation of motion will be

Where r- position as a function of time, r is the distance from the center, m is the mass, and k determines the force. From this we can derive the law of conservation of energy

For some constant E that depends on the orbit but does not change with time. If this force is an attraction, then k > 0, and on an elliptical orbit E< 0. Будем звать частицу планетой. Планета двигается вокруг солнца, которое настолько тяжело, что его колебаниями можно пренебречь.

We will study orbits with one energy E. Therefore, the units of mass, length and time can be taken as any. Let's put

M=1, k=1, E=-1/2

This will save us from unnecessary letters. Now the equation of motion looks like

And the conservation law says

Now, following Moser's idea, let's move on from ordinary time to new. Let's call it s and require that

Such time passes more slowly as you move away from the sun. Therefore, the speed of the planet with distance from the sun increases. This compensates for the planets' tendency to move more slowly as they move away from the sun in normal time.

Now let's rewrite the conservation law using the new time. Since I used a dot for derivatives with respect to ordinary time, let's use a prime for derivatives with respect to s. Then for example:

Using such a derivative, Goranson shows that the conservation of energy can be written as

And this is nothing but the equation of a four-dimensional sphere. The proof will come later. Now let's talk about what this means to us. To do this, we need to combine the usual time coordinate t and spatial coordinates (x, y, z). Dot

Moves in 4D space as the s parameter changes. That is, the speed of this point, namely

Moves in a 4D sphere. It is a sphere of radius 1 centered at a point

Additional calculations show other interesting facts:

T""" = -(t" - 1)

These are the usual harmonic oscillator equations, but with an additional derivative. The proof will be later, but for now let's think about what this means. In words, this can be described as follows: 4-dimensional speed v performs simple harmonic oscillations around the point (1,0,0,0).

But since v at the same time remains on the sphere centered at this point, then we can conclude that v moves with constant speed in a circle on this sphere. And this implies that the average value of the spatial components of the 4-dimensional velocity is 0, and the average t is 1.

The first part is clear: our planet, on average, does not fly away from the Sun, so its average speed is zero. The second part is more complicated: the usual time t moves forward with average speed 1 relative to the new time s, but the rate of its change fluctuates sinusoidally.

By integrating both parts

We'll get

a. The equation says that position r oscillates harmonically around a point a. Because the a does not change with time, it is a conserved quantity. This is called the Laplace-Runge-Lenz vector.

Often people start with the inverse square law, show that angular momentum and the Laplace-Runge-Lenz vector are conserved, and use these conserved quantities and Noether's theorem to show the existence of a 6-dimensional symmetry group. For negative energy solutions, this turns into a group of rotations in 4 dimensions, SO(4). With a little more work, you can see how the Kepler problem is paired with a harmonic oscillator in 4 dimensions. This is done through time reparametrization.

I liked Gorasnon's approach better because it starts with time reparametrization. This makes it possible to effectively show that the elliptical orbit of a planet is a projection of a circular orbit in four-dimensional space onto three-dimensional space. Thus, 4-dimensional rotational symmetry becomes apparent.

Goranson extends this approach to the inverse square law in n-dimensional space. It turns out that elliptical orbits in n dimensions are projections of circular orbits from n + 1 dimensions.

He also applies this approach to positive-energy orbits, which are hyperbolas, and to zero-energy orbits (parabolas). Hyperbolas get the symmetry of the Lorentz groups, and parabolas get the symmetry of the Euclidean groups. it known fact, but it's remarkable how easy it is to derive with the new approach.

Mathematical details

Because of the abundance of equations, I will put boxes around the important equations. The basic equations are conservation of energy, force, and change of variables, which give:

Let's start with conservation of energy:

Then we use

To obtain

A little algebra - and we get

This shows that the 4-dimensional speed

Remains on a sphere of unit radius centered at (1,0,0,0).

The next step is to take the equation of motion

And rewrite it using strokes (derivatives of s), not dots (derivatives of t). Starting with

And we differentiate to get

Now we use another equation for

And we get

Now it would be nice to get a formula for r"". Let's count first

And then we differentiate

Connecting the formula for r", something will be reduced, and we get

Recall that the conservation law says

And we know that t" = r. Therefore,

We get

Since t" = r, it turns out

As we need.

Now we get a similar formula for r""". Let's start with

And differentiate

Connect the formulas for r"" and r""". Something shrinks and remains

We integrate both parts and get

For some constant vector a. It means that r oscillates harmonically about a. Interestingly, the vector r and its norm r oscillate harmonically.

The quantum version of a planetary orbit is a hydrogen atom. Everything that we have calculated can be used in the quantum version. See Greg Egan for details.

Of all the types of parallel universes, the parallel universe boasts the longest history of scientific discussion. higher dimensions. Common sense and sense organs tell us that we live in three dimensions - length, width and height. No matter how we move an object in space, its position can always be described by these three coordinates. In general, with these three numbers, a person can determine the exact position of any object in the Universe, from the tip of his nose to the most distant galaxies.

At first glance, the fourth spatial dimension is contrary to common sense. For example, when smoke fills an entire room, we don't see it disappear into another dimension. Nowhere in our universe do we see objects that would suddenly disappear or float away to another universe. This means that higher dimensions, if they exist, must be smaller than an atom.

Three spatial dimensions form the foundation, the basis of Greek geometry. For example, Aristotle wrote in his treatise On Heaven:

"A quantity divisible in one dimension is a line, in two it is a plane, in three it is a body, and apart from these there is no other quantity, since three measurements the essence of everything measurements".

In 150 AD e. Ptolemy of Alexandria offered the first "proof" that higher dimensions are "impossible". In the treatise "On Distance" he argues as follows. Let's draw three mutually perpendicular straight lines (like the lines that form the corner of the room). Obviously, it is impossible to draw a fourth line perpendicular to the first three, therefore, the fourth dimension is impossible.

In fact, he managed to prove in this way only one thing: our brain is not able to visualize the fourth dimension. On the other hand, computers are constantly doing calculations in hyperspace.

For two millennia, any mathematician who dared to talk about the fourth dimension risked ridicule. In 1685, the mathematician John Wallis, in a polemic about the fourth dimension, called it "a monster in nature, no more possible than a chimera or a centaur." In the 19th century, the "king of mathematicians" Carl Gauss developed the mathematics of the fourth dimension to a large extent, but was afraid to publish the results for fear of a backlash. He himself, however, was experimenting and trying to determine whether purely three-dimensional Greek geometry really correctly describes the universe. In one experiment, he placed three assistants on tops of three neighboring hills. Each assistant had a lantern; the light of all three lanterns formed a gigantic triangle in space. Gauss himself carefully measured all the angles of this triangle and, to his own disappointment, found that the sum internal corners triangle is really 180°. From this, the scientist concluded that if deviations from standard Greek geometry exist, then they are so small that they cannot be detected by similar methods.

Painting: Rob Gonsalves, Canada, magical realism style

As a result, the honor of describing and publishing the foundations of higher-dimensional mathematics fell to Georg Bernhard Riemann, a student of Gauss. (After a few decades, this mathematics was wholly incorporated into Einstein's general theory of relativity.) In his famous lecture in 1854, Riemann overturned 2,000 years of Greek geometry in one fell swoop and established the foundations of the mathematics of higher, curvilinear dimensions; We still use this math today.

At the end of the XIX century. the remarkable discovery of Riemann thundered throughout Europe and aroused the widest interest of the public; the fourth dimension has created a real sensation among artists, musicians, writers, philosophers and artists. For example, art historian Linda Dalrymple Henderson believes that Picasso's Cubism was partly inspired by the fourth dimension. (Picasso's portraits of women, with the eyes facing forward and the nose on the side, are an attempt to present a four-dimensional perspective, because when viewed from the fourth dimension, you can see the face, nose and back of the head of a woman at the same time.) Henderson writes: “Like a black hole, the fourth the dimension had mysterious properties that could not be fully understood even by the scientists themselves. And yet the fourth dimension was much more understandable and conceivable than black holes or any other scientific hypothesis after 1919, with the exception of the theory of relativity.

But historically, physicists have viewed the fourth dimension as just a fun curiosity. There was no evidence of the existence of higher dimensions. The situation began to change in 1919, when the physicist Theodor Kaluza wrote a very controversial paper in which he hinted at the existence of higher dimensions. Starting with Einstein's general theory of relativity, he placed it in a five-dimensional space (four spatial dimensions and the fifth one is time; since time has already established itself as the fourth dimension of space-time, physicists now refer to the fourth spatial dimension as the fifth). If you make the universe smaller and smaller along the fifth dimension, the equations magically fall into two parts. One part describes Einstein's standard theory of relativity, but the other part turns into Maxwell's theory of light!

This was an amazing revelation. Perhaps the secret of light is hidden in the fifth dimension! This decision shocked even Einstein; it seemed to provide an elegant unification of light and gravity. (Einstein was so shocked by Kaluza's suggestion that he hesitated for two years before agreeing to publish his paper.) Einstein wrote to Kaluza: I liked your idea extremely... The formal unity of your theory is amazing.”

For many years, physicists have wondered: if light is a wave, then what, in fact, oscillates? Light can travel billions of light-years of empty space, but empty space is a vacuum, there is no substance in it. So what oscillates in a vacuum? Kaluza's theory made it possible to put forward a specific assumption about this: light is real waves in the fifth dimension. Maxwell's equations, which accurately describe all the properties of light, are obtained in it simply as equations for waves that move in the fifth dimension.

Imagine fish swimming in a shallow pond. Perhaps they are not even aware of the existence of the third dimension, because their eyes look to the sides, and they can only swim forward or backward, right or left. Perhaps the third dimension even seems impossible to them. But now imagine rain on the surface of a pond. Fish cannot see the third dimension, but they can see shadows and ripples on the surface of the pond. Similarly, Kaluza's theory explains light as ripples that move through the fifth dimension.

Kaluza also gave an answer to the question of where the fifth dimension is. Since we do not see any signs of its existence around, it must be "rolled up" to such a small extent that it is impossible to notice it. (Take a two-dimensional sheet of paper and roll it tightly into a cylinder. From afar, the cylinder will appear as a one-dimensional line. It turns out that you have rolled up a two-dimensional object and made it one-dimensional.)

For several decades, Einstein began to work on this theory from time to time. But after his death in 1955, the theory was quickly forgotten and turned into a funny footnote in the history of physics.

Fragment from the book of Peter D. Uspensky " New model universe":

The idea of ​​the existence of hidden knowledge, superior to the knowledge that a person can achieve by one's own efforts, grows and strengthens in the minds of people when they understand the insolubility of many issues and problems facing them.

A person can deceive himself, he can think that his knowledge is growing and increasing, that he knows and understands more than he knew and understood before; however, sometimes he becomes sincere with himself and sees that in relation to the basic problems of existence he is as helpless as a savage or a child, although he has invented many clever machines and tools that have complicated his life, but have not made it clearer.
Speaking even more frankly with himself, a person may recognize that all his scientific and philosophical systems and theories are similar to these machines and tools, because they only complicate problems without explaining anything.

Among the insoluble problems surrounding man, two occupy a special position - the problem of the invisible world and the problem of death.

Without exception, all religious systems, from such theologically developed to the smallest details like Christianity, Buddhism, Judaism, to the completely degenerate religions of the "savages", which seem "primitive" to modern knowledge - they all invariably divide the world into visible and invisible. In Christianity: God, angels, devils, demons, souls of the living and the dead, heaven and hell. In paganism: deities personifying the forces of nature - thunder, sun, fire, spirits of mountains, forests, lakes, spirits of water, spirits of houses - all this belongs to the invisible world.
Philosophy recognizes the world of phenomena and the world of causes, the world of things and the world of ideas, the world of phenomena and the world of noumenons. In Indian philosophy (especially in some of its schools) the visible or phenomenal world, Maya, is an illusion, which means a false concept of not visible world, is generally considered non-existent.

In science, the invisible world is the world of very small quantities, and also, oddly enough, of very large quantities. The visibility of the world is determined by its scale. The invisible world is, on the one hand, the world of microorganisms, cells, the microscopic and ultramicroscopic world; it is followed by the world of molecules, atoms, electrons, "vibrations"; on the other hand, it is a world of invisible stars, distant solar systems, unknown universes.

The microscope expands the boundaries of our vision in one direction, the telescope in another, but both are very small compared to what remains invisible.

Physics and chemistry give us the opportunity to investigate phenomena in such small particles and in such distant worlds that will never be available to our vision. But this only reinforces the idea that there is a huge invisible world around a small visible one.
Mathematics goes even further. As has already been pointed out, it calculates such ratios between quantities and such ratios between these ratios that have no analogies in the visible world surrounding us. And we are forced to admit that the invisible world differs from the visible one not only in size, but also in some other qualities that we are unable to determine or understand and which show us that the laws found in physical world, cannot refer to the invisible world.
Thus, the invisible worlds of religious, philosophical and scientific systems are, after all, more closely connected with each other than it seems at first glance. And such invisible worlds of different categories have the same properties common to all. These properties are. First, they are incomprehensible to us; incomprehensible from the ordinary point of view or for ordinary means of knowledge; secondly, they contain the causes of the phenomena of the visible world.

The idea of ​​causes is always connected with the invisible world. In the invisible world of religious systems, invisible forces control people and visible phenomena. In the invisible world of science, the causes of visible phenomena stem from the invisible world of small quantities and "fluctuations".
In philosophical systems, the phenomenon is only our concept of the noumenon, i.e. an illusion, the true cause of which remains hidden and inaccessible to us.

Thus, at all levels of his development, man understood that the causes of visible and observable phenomena are beyond the scope of his observations. He found that among the phenomena available to observation, some facts can be considered as the causes of other facts; but these conclusions were not sufficient for understanding everything that happens to him and around him. To explain the causes, an invisible world is needed, consisting of "spirits", "ideas" or "vibrations".

Arguing by analogy with existing dimensions, it should be assumed that if the fourth dimension existed, it would mean that right here, next to us, there is some other space that we do not know, do not see and cannot go into. Into this "region of the fourth dimension" from any point of our space it would be possible to draw a line in a direction unknown to us, which we cannot determine or comprehend. If we could imagine the direction of this line coming from our space, then we would see the "area of ​​the fourth dimension."

Geometrically, this means the following. One can imagine three mutually perpendicular lines to each other. With these three lines we measure our space, which is therefore called three-dimensional. If there is an "area of ​​the fourth dimension" lying outside our space, then, in addition to the three perpendiculars known to us, which determine the length, width and height of objects, there must be a fourth perpendicular, which determines some kind of incomprehensible to us, new extension. The space measured by these four perpendiculars will be four-dimensional.

It is impossible to define geometrically or imagine this fourth perpendicular, and the fourth dimension remains extremely mysterious to us. There is an opinion that mathematicians know about the fourth dimension something inaccessible to mere mortals. It is sometimes said, and this can be found even in the press, that Lobachevsky "discovered" the fourth dimension. In the past twenty years, the discovery of the "fourth" dimension has often been attributed to Einstein or Minkowski.

In fact, mathematics has very little to say about the fourth dimension. There is nothing in the fourth dimension hypothesis that makes it mathematically unacceptable. It does not contradict any of the accepted axioms and therefore does not meet with special opposition from mathematics. Mathematics fully admits the possibility of establishing the relations that must exist between four-dimensional and three-dimensional space, i.e. some properties of the fourth dimension. But she does all this in the most general and indefinite form. Precise definition There is no fourth dimension in mathematics.

The fourth dimension can be considered geometrically proven only in the case when the direction of the unknown line going from any point of our space to the area of ​​the fourth dimension is determined, i.e. found a way to construct the fourth perpendicular.

It is difficult even approximately to outline what significance the discovery of the fourth perpendicular in the universe would have for our entire life. The conquest of the air, the ability to see and hear at a distance, the establishment of relations with other planets and star systems - all this would be nothing compared to the discovery of a new dimension. But so far it hasn't. We must admit that we are powerless before the mystery of the fourth dimension - and try to consider the issue within the limits that are available to us.

Upon a closer and more precise study of the problem, we come to the conclusion that for existing conditions it is impossible to solve it. Purely geometric at first glance, the problem of the fourth dimension is not solved geometrically. Our geometry of three dimensions is not enough to investigate the question of the fourth dimension, just as planimetry alone is not enough to investigate questions of stereometry. We must discover the fourth dimension, if it exists, purely empirically, – and also to find a way of its perspective image in three-dimensional space. Only then can we create a geometry of four dimensions.

The most superficial acquaintance with the problem of the fourth dimension shows that it must be studied from the side of psychology and physics.

The fourth dimension is incomprehensible. If it exists, and if, nevertheless, we are not able to cognize it, then, obviously, something is missing in our psyche, in our perceiving apparatus, in other words, the phenomena of the fourth dimension are not reflected in our sense organs. We must figure out why this is so, what defects cause our immunity, and find the conditions (at least theoretically) under which the fourth dimension becomes understandable and accessible. All these questions belong to psychology, or perhaps to the theory of knowledge.

We know that the area of ​​the fourth dimension (again, if it exists) is not only unknowable for our mental apparatus, but is inaccessible purely physically. It no longer depends on our defects, but on special properties and conditions of the area of ​​the fourth dimension. We need to figure out what conditions make the area of ​​the fourth dimension inaccessible to us, find the relationship of the physical conditions of the area of ​​the fourth dimension of our world and, having established this, see if there is anything similar to these conditions in the world around us, if there are any relations similar to relations between 3D and 4D regions.

Generally speaking, before constructing the geometry of four dimensions, it is necessary to create the physics of four dimensions, i.e. find and determine the physical laws and conditions that exist in the space of four dimensions.

"We can't solve problems using the same mindsets that we used to create problems." (Albert Einstein)

via quantum-tech. ru and blogs.mail.ru/chudatrella.

» we will touch on the well-known problem of the number of dimensions in general and the transition to them in particular. We will try to consider this issue not from a traditionally mystical point of view, but from a practical point of view (with the help of practical exercises and educational videos).

The transition to the fourth dimension interested people for a very, very long time. However, there are still two groups of views that have different attitudes towards the fourth dimension. One of the groups is the spatial fourth dimension, and the second is the temporal about It's the fourth dimension.

The spatial fourth dimension is very well illustrated in one of the issues of Tramway magazine, where an article about a four-dimensional mouse was published (if anything, it is called “THE-YOU-ROH-DIMENSIONAL MOUSE” and you can read it here http://tramwaj.narod .ru/Archive/LJ_archive_2.htm). There, such an analogy was drawn: for the inhabitants of one dimension (line), any two-dimensional beings will be perceived only as components of one dimension. Everything that goes beyond this dimension will not be noticed (because there is nothing to look at).

In the same way, the inhabitants of the two-dimensional space (plane) can see the inhabitants of the three-dimensional space only as their two-dimensional imprints-projections. They simply have nothing to see the third dimension. That is, if a person got into this two-dimensional space, then in best case the local inhabitants of the plane got acquainted with the prints of his soles. And at worst - a transverse cut 🙂

Similarly, residents of the third dimension (that is, you and me) can only see four-dimensional beings as their three-dimensional projections. That is, ordinary bodies having length, width and height.

The higher dimension has one major advantage over the lower dimension: higher dimensional beings can break the laws of lower dimensional physics. So, if in a two-dimensional universe, on a plane, a resident is put in a prison, then he will not be able to get out of it, surrounded on all two sides (since there are only two dimensions) by walls. But if you put a three-dimensional being (or rather, only its projection) in such a prison, then it easily leaves two dimensions, say, upwards - and finds itself outside the two-dimensional prison.

Exactly the same goodies are available to four-dimensional beings in our three-dimensional universe. Agree, all this sounds very tempting, mystical, and when mastering the fourth dimension, it promises to bring a lot of bonuses such as peeping in the women's locker rooms 🙂 Perhaps that is why high ethics are among the requirements for those moving into this dimension.

But let's not delve into the mystical wilds - after all, we promised practice, not mysticism. To do this, let's generalize. Yes, one normal measurement perpendicular to the other and the third, forming the familiar coordinate axes:

Whereas, according to this logic, the fourth spatial dimension should be perpendicular to these three.

The transition to the fourth spatial dimension is carried out with the help of the development of a special organ of perception of this dimension. This organ is commonly referred to as the third eye. Since under this phrase that only is not understood, we will not use it. Moreover, the fourth spatial dimension is perceived by no means with the eyes. As a tip for developing the organ of perception of the fourth spatial dimension, we will give an exercise from the book of P.D. Ouspensky (a student of Gurdjieff, if anything) "TERTIUM ORGANUM" (third organ, if translated):

Train to see (for a start - in the imagination) three-dimensional figures (cubes, pyramids, spheres, etc.) from all sides at once.

Here is such a simple description of a complex exercise. We hope everything is clear: usually we can see a maximum of 3 sides of the cube. And we must imagine the cube as if we saw it from all six sides at once. Puzzle, huh? 🙂

In order to get more mass about the fourth spatial dimension, you can take advantage of these videos:

The first part of the video about the fourth dimension:

The second part of the video about the fourth dimension

Having considered the practical training for the transition to the spatial fourth dimension, let's consider one more point. Oddly enough, the fourth (as well as the fifth, sixth ... eleventh) spatial dimensions is by no means an empty phrase. At least in light of recent advances in superstring theory.

So, in order for the laws of physics to work equally at both micro and macro levels (from a level thousands of times smaller than the size of a molecule to intergalactic distances), the formulas must contain eleven spatial dimensions. Three of these dimensions are expanded, and the rest are collapsed, which is why we do not perceive them. Although the vibrations of the constituent subatomic particles are very dependent on these curled dimensions.

Unfortunately, the ancient magicians did not even suspect about these folded dimensions, so the transition to these folded dimensions remains completely occult, that is, secret. For if anyone figured out how to do it, he did not say how.

Now is the time to move on to the fourth dimension in terms of time. This approach has been widely developed by physicists, so there is not much to say here. The only apparent difference in time about of the first dimension is that it is impossible to move backward along it, as along three spatial ones. Only forward. However, this is not entirely true - and it is this nuance that gives the key to the transition to the fourth time. about e measurement.

Moreover, if in order to perceive the fourth spatial dimension, you need to train a special organ, to work with the fourth temporal s m dimension organ is already there. And moreover, with the help of this body, people can move along this dimension both back, into the past, and forward, into the future.

Have you already guessed what this thing is that allows you to travel in time?

That's right, it's the human mind.

Therefore, the transition to the fourth time about e measurement is only a figurative expression. We are all already in this fourth time about m dimension. However, not everything is the same. There are people who remember only yesterday and do not look beyond tomorrow. Their fourth dimension is scanty, and life is hard (although from the outside it may seem cheerful and carefree).

And, conversely, there are people who are able to look far, far into the past, compare the data obtained with observations from the present and make practical implications about both the near and the distant future. As you can see, these people have mastered the fourth dimension to a very large extent. As a result, the life of such people is much more stable, calm and happy.

Therefore, the question is not in the transition in time about not the fourth dimension, but in the deepening of this dimension. Well, for this you need to train your mind. How to do it? Yes, very simple. The main thing is to work out the main activity of the mind: to compare data from the past with data from the present and draw the right conclusions. Well, there are just a huge number of methods.

Another nuance is the data that the mind uses to work. After all, if the data received for processing is erroneous (from the past or from the present), then the conclusions will be erroneous. And then you get not the fourth dimension, but some kind of garbage.

Why are the received data from the past and present erroneous? It's very simple: because it is misjudged data due to painful experience. Example: a person was bitten by a dog, and now whenever he sees dogs, he receives data not about their real intentions or appearance, but a glitch from the past associated with pain. Therefore, conclusions for the future (for example, "all dogs are dangerous") will be false. And the fourth dimension is with a wormhole.

How to avoid such mistakes? Naturally, correctly assessing the data obtained in the presence of pain, collision or loss. How to do it? These ways are much less than ways to improve thinking. But they are, and you can find them if you wish 🙂

Thus, the transition to the fourth dimension depends on where you want to go.

Happy transitions!

If so, write in the comments!

If we compare a flat sheet of paper and a box, we will see that a sheet of paper has length and width, but no depth. The box has length, width and depth.

The world familiar to us consists of three dimensions, but let's imagine existence in two-dimensional space. In this case, everything will look like drawings on a sheet of paper. Objects will be able to move in any direction on the surface of this paper, but it will be impossible to rise or fall on the surface of this very paper.

Let's imagine a square drawn in two-dimensional space - no object can get out of the square, unless there is a hole in it, or a hole. Moving under and over the square will be impossible.

What is the fourth dimension

Another thing is in the three-dimensional world - having drawn a square around any object, it costs nothing then for this very object to step over it or crawl up. Now let's imagine that the object is placed inside a cube or, for example, in a room with a ceiling, a floor and four solid walls. No object will be able to get out of the room, provided that there are no holes in it.

Of course, all this is quite clear and understandable. It is also clear that almost all phenomena can be explained from the position of the three-dimensional world. For example, it is simple and clear why liquid can be placed in a jug or why a dog can live in a kennel.

Now it is worth considering the paranormal phenomena - materialization and dematerialization. Famous psychic, Charles Bailey could materialize hundreds of objects in an iron cage in the presence of numerous, skeptical witnesses. It is quite possible that the objects passed between the bars of the iron cage, and this is absolutely inexplicable from the point of view of the three-dimensional world.

To explain such phenomena, a hypothesis was put forward that there is a fourth dimension of space, inaccessible under normal circumstances. However, from time to time, objects have the ability to enter and exit the fourth dimension.

transcendental physics

Exists special work titled "Transcendental Physics", dedicated to the study of the concept of the fourth dimension and written by Johann Karl Friedrich Zellner. In his work, the author took as an example the phenomena created by the psychic Henry Slade. Tom was able to make an object disappear entirely, and then make that very object appear somewhere else. In addition, he could materialize two solid rings around a table leg.

Some time later, Slade was imprisoned for fraud, and this caused irreparable damage to Dr. Zellner's reputation. However, this seems irrelevant today, since Zellner was able to offer the world a carefully crafted theory. In addition, Slade's fraud remains in question.

Excerpt from "Transcendental Physics":

“Among the evidence, there is nothing more convincing and significant than the transfer of material bodies from closed space. Although our 3D intuition cannot allow a non-material exit to open in a closed space, 4D space provides such an opportunity. Thus, the transfer of the body in this direction can be carried out without affecting the three-dimensional material walls. Since we, three-dimensional beings, lack the so-called intuition four-dimensional space, we can only formulate its concept by analogy from the lower region of space. Imagine a two-dimensional figure on the surface: a line is drawn on each side, and an object fits inside. By moving only on the surface, the object will not be able to get out of this two-dimensional enclosed space, unless there is a break in the line.

The current stage of the evolution of mankind is characterized by the absence of the overwhelming majority of people of the ability to perceive the four-dimensional world - the "second sight", as well as the underdevelopment of an aspect of consciousness that is more perfect than the intellect - intuition.

The disclosure and subsequent development of a new (sixth) sense organ is the future of a person of a new (sixth) race. In the meantime, humanity is going through a transitional period on the way to new opportunities, which is confirmed by the emergence of so-called psychics.

In this regard, only a small part of the planet's population has experience of interaction with the world of higher dimensions. The majority modern people living in really multidimensional world, still perceives and realizes only its most primitive part - the three-dimensional physical world.

This circumstance favors the invention of various fantastic images attributed to worlds of higher dimensions. This, in turn, is reflected not only in the works of science fiction writers, but also in science.

Examples of such scientific fantasies are the 4D continuum, dark matter, wormholes, tesseracts, simplices, superstrings, branes... complete unsuitability three-dimensional mathematical apparatus for understanding and describing multidimensional spaces.

COMMENT. What is called "multidimensional" spaces in mathematics has nothing to do with reality, since they do not take into account such properties of truly multidimensional spaces as materiality and permeability; space is endowed with non-spatial properties, and the property of extension, contrary to common sense, extends beyond the limits of three dimensions.

3D illusions about multidimensionality

The main trouble with mathematics is that it tends more towards orthodox beliefs than towards science, since it is built not on updated knowledge about the world, but on Inviolable Sacred Dogmas which neither absurdity, nor paradoxes, nor scientific discoveries, nor a series of crises, nor millennia of struggle against dogmatism are able to shake.

Below we list only a part of the most odious Dogmas (and their consequences), which makes the knowledge of the multidimensional structure of the world around us with the help of SUCH mathematics fundamentally impossible.

1. In mathematics, there supposedly really exist spaces with dimensions less than three; while 0D-"space" is a point, 1D-"space" is a line, 2D-"space" is a surface;
2. Math point size zero, but it allegedly exists;
3. Allegedly, there really exists an empty space - the "space" of a dimensionless point;
4. The sizes of bodies are inexplicably determined by the sum of the sizes of dimensionless points;
5. From the zero size of a point, its non-materiality also follows;
6. From the non-materiality of a point (0D-"space"), the non-materiality of any space follows;
7. It follows from the non-materiality of space that space is not recognized as an attribute (an integral property) of matter;
8. From the misunderstanding of the inseparable connection between space and matter, the most ridiculous delusion follows, allowing the “transfer” of 3D entities to higher-dimensional spaces:
   firstly, because 3D objects already contain the matter of all higher dimensions, that is, they are already available to all higher spatial entities;
   secondly, complete belonging to a higher-dimensional space requires the complete elimination of the lower 3D material shell, which is tantamount to death in a 3D world.
9. The consequence of the previous delusions is the absence in mathematics of the concept of "spatial environment";
10. From the misunderstanding of the incomparability of the properties of matter of different dimensions, the absurdity of the requirement of orthogonality of spatial "axes", the operation of adding vectors and finding scalar sums for a set of different-sized spaces follows.
11. The last delusion manifests itself, in particular, in an attempt to sum the velocity vector of 4D light with the velocity vector of its 3D source moving in another space;
12. A striking evidence of the complete misunderstanding of the essence of multidimensionality by mathematicians is the widespread identification of multicomponent 3D vectors (x 1 , x 2 , x 3 , ... x n) with supposedly multidimensional mathematical constructions.

    Let's show it on the example of a vector of properties of a 3D-piece of sugar with the following vector components: length x 1 ; width x 2; height x 3; weight x 4; color x 5; flavor x 6; production time x 7 . In terms of mathematics, we get a 7-dimensional (!) Vector. However, there will be only three spatial dimensions in this 7-component construction.

    This example also makes it easy to understand that the usual three-dimensional space, given out in relativism as Minkowski's 4D space-time, has nothing to do with the fourth spatial dimension.

For the above and other reasons, practically all currently known attempts to model 4D space by means of three-dimensional mathematics are nothing more than 3D fantasies on the topic of multidimensionality that is inaccessible to dogmatic thinking.

Where to look for the fourth dimension

So, if all the above attempts at scientific understanding of multidimensional spaces are nothing more than science fiction, then several reasonable questions arise:

• Where, then, is hidden at least the closest real 4D space to us?
• And does it exist at all?
• And if it exists, why don't we see it?

First of all, it should be said that the four-dimensional space is the same reality as the three-dimensional space we observe.

To the question "Then why don't we see him?" the easiest way to answer is with another question: “Why doesn’t anyone bother that we don’t see the contents of computer disks, electricity, radio waves, radiation, our own aura, other people’s thoughts”? Even ghosts can only be seen in photographs.

It will be more difficult to understand the answer to the question: "Where is the four-dimensional space"?

However, the correct answer is: “We are all inside 4D space; it not only surrounds us, it surrounds and fills us and the entire 3D Universe, including outer space and the space inside atoms; in this case, nucleons are formed by particles of 4D matter.”

The matter of four-dimensional space is called physical ether, in modern physics, most often - the physical vacuum.

According to one of the hypotheses, an ether particle (amer) is an electron-positron pair. Thus, in the unexcited state, an amer, like an atom, is electrically neutral, but unlike an atom, it does not contain a nucleus.

Nuclear-free 4D ethereal matter plays the role of an intermediary (layer) between the atomic 3D physical and 5D astral worlds:

• an ether particle is approximately 8 orders of magnitude thinner physical atom;
• the astral atom is approximately 8 orders of magnitude thinner than the ethereal particle;
• relative to the physical atom, the astral atom is thinner by 16 orders of magnitude.

At the atomic level of matter structuring, a difference of 8 orders means a transition to a new dimension:

• 3D physical atom ≈ 10 -8 cm;
• 4D particle of ether ≈ 10 -16 cm;
• 5D-astral atom ≈ 10 -24 cm.

In the real world, a quantitative change in the size of matter within one dimension (for atoms of the same dimension) is periodically accompanied by dialectical abrupt transitions to new ones. quality levels, for example:

• physical atom → physical body→ physical celestial body...;
• astral atom → astral body→ astral planet and so on.

Mathematics, ignoring the law of transition quantitative changes into qualitative and other fundamental laws of the Universe, produces only illusory-mystical conjectures about multidimensionality, based solely on the quantitative, a continuous and linear increase in the size of matter from a non-existent zero to an imaginary infinity.

This mathematical lawlessness contains another reason for scientific fantasies about multidimensional worlds and spaces.

The hypothesis of the multidimensional organization of the Universe mentioned above is in good agreement with observations and everyday experience, psychic data and experimental results, as well as with information from Eastern spiritual practices, occult, theosophical and esoteric sources.

Properties of the fourth dimension

Trying to represent the properties of a hypothetical 4D space, one cannot replace common sense with three-dimensional mathematical dogmas. Otherwise, unpleasant surprises await us.

Is a 4th orthogonal axis possible?

For most of us, three-dimensional space is associated with the three axes of the Cartesian coordinate system. Therefore, many readily (without bothering with doubts and reflections) agree with the unsubstantiated dogma of the orthogonality of N coordinate axes for a space of N dimensions.

At the same time, for some reason, the simplest thought is completely forgotten: “After all, if we cannot even imagine “something”, that is, mentally create an appropriate image, then this “something” does not exist in principle!

Mathematicians explain the fact that we do not understand the flight of their multidimensional fantasies by the limitations of our mental abilities, since, they say, the world around us is three-dimensional. However, in fact, all the talk about the limitations of our imagination is a deliberate lie, since a person can easily construct at least 6-dimensional images from the 7-dimensional matter of thought.

This means only one thing: mathematicians could well explain their “multidimensional visions” to us, of course, if there was at least a drop of reality in them. In the meantime, we are all doomed to worship the dogma of the "fourth orthogonal axis", without even the slightest explanation about its construction.

Thus, another false dogma of "four perpendiculars" to one point turns into another stumbling block on the way to understanding the real multidimensional world.

What do measurements measure?

Why exactly three spatial dimensions, no more and no less? Obviously, because the atom, and with it all the rest of matter, has strictly three spatial characteristics: length, width and height.

What characterize these three characteristics of space? Of course, length material objects in three possible directions: forward↔back, left↔right, up↔down.

Is it possible to specify some other additional characteristics of the length? Not! Common sense categorically rejects such fantasies. Only three extension characteristics can be represented for matter of any dimension.

Does matter have other properties besides extension? Of course, there is: color, viscosity, temperature... But three-dimensional matter has only one spatial property - extension.

Perhaps 4D matter has an additional spatial property? Exactly! The 4D amer, due to its “thinness”, has an additional spatial property in relation to the 3D atom – permeability. In the work, the fourth dimension of space is called " depth».

According to the author, both terms cannot be considered successful. The term "permeability" can be erroneously attributed to 3D matter, since it is permeable to matter of all higher dimensions. The term "depth" coincides with the terminology of Euclid to characterize a completely different property (length) of the body.

In this regard, the term " nesting”, more precisely conveying the essence of the immersion of higher spaces real world to the lower ones. Let's demonstrate a combination of spatial characteristics of extent and nesting using the example of a 5D space:

• three length characteristics (forward↔back, left↔right, up↔down);
• two nesting characteristics (in↔out of 3D space, in↔out of 4D space).

It is clear that the 7D space will have the same three length characteristics, and there will be two more nesting characteristics, that is, four, and in general - 3 + 4 - seven.

It is easy to see that the given interpretation of the multidimensionality of the real world excludes the orthogonality of the directions of extension with the directions of nesting, and the latter also among themselves. This allows us to stop conjectures on the topic of multiple orthogonality for high-dimensional spaces.

What is invested in what?

A huge number of publications tell us that a speculative two-dimensional "space" is embedded in a three-dimensional one. The most common example of a 2D "space" is a sheet of a book. Well, then a “brilliant” conclusion is made about the nesting of the already real 3D space in the space of four dimensions and then in a similar way. As a result, fantastic pseudo-multidimensional constructions appear in the form of tesseracts, simplices, and other pseudo-hyper-polyhedra.

It is completely useless to appeal to common sense here, because the entire queen of sciences is built on an unshakable faith in the reality of “spaces” with dimensions less than three. Therefore, in order to expose such manipulations with false spaces, let's take note of two fundamentally important points that took place:

• The lower space in the example with the book was mentally “embedded” in the higher, that is, in a space with a larger number of dimensions;
• All the spaces appearing in the example are filled one type of matter, that is, the three-dimensional substance of paper.

If we now move from the religious dogmas of mathematics to examples from real life, then we will see that a 4D electron is embedded in a 3D atom, a 4D radio wave is embedded in a 3D radio receiver. In this case, everything happens exactly the opposite, previously taken note of the points:

• In real life, the higher space is embedded in the lower;
• Matter real spaces different dimension is different.

If we acted in accordance with the rules of mathematics from the first example, then it would turn out that an atom can be embedded in an electron, and a radio receiver in a radio wave, which, of course, is absurd, as well as mathematical "spaces" with dimensions less than three.

conclusions

1. Understanding multidimensional spaces within the framework of modern (three-dimensional) mathematics is fundamentally impossible.
2. For the study of multidimensional spaces, it is necessary to develop a new section of "Multidimensional Mathematics".
3. The exit of mathematics from the crisis is impossible without the rejection of thousands of years of dogmatism in favor of a revised scientific paradigm.

Literature

1. Mikisha A. M., Orlov V. B. Explanatory Mathematical Dictionary: Basic Terms. – M.: Rus. yaz., 1989. - 244 p.
2. Minkowski space: From Wikipedia. – http://ru.wikipedia.org/wiki/Minkowski_Space
3. Alexander Kotlin. How to understand four-dimensional space? -
4. Alexander Kotlin. Cosmic octaves are the key to a new understanding of the World. -
5. Alexander Kotlin. Fundamentals of mathematics - lawlessness cubed. – 02/27/2014. -
6. Blavatsky H. P. The Secret Doctrine: Synthesis of Science, Religion and Philosophy. Volume 1: Cosmogenesis. - L .: Ecopolis and culture, 1991. - 361 p.
7. Nikolay Uranov. Bring joy. Fragments of letters. 1965-1981. - Riga: World of Fire, 1998. - 477 p.
8. The beginning of Euclid. Books XI-XV. Translation from Greek and comments by D. D. Mordukhai-Boltovsky with the participation of M. Ya. Vygodsky and I. N. Veselovsky. - Mrs. Publishing house of technical-theoretical. literature, M.-L.: 1950. - 335 p.
9. Alexander Kotlin. How to understand 10-dimensional space? -