- Translation
When I talk with a person far from physics about possible additional dimensions of space, unknown to us, one of the most frequently asked questions is: “How do you imagine additional dimensions? I can only think of three, and I don't see how I can go further; It makes no sense to me.”
What we physicists don't do (at least no one I know claims to do) is imagine extra dimensions. My brain is limited in the same way as yours, and although this brain can easily create a three-dimensional image of a world in which I can move, I cannot force it to create an image of a four- or five-dimensional world, like you. My survival didn't depend on being able to imagine something like that, so perhaps it's not surprising that my brain isn't wired for it.
I instead (and judging by our exchange of ideas, most of my colleagues too) develop intuitions based on a combination of analogies, visualization tricks, and calculations. We will omit the calculations here, but many analogies and tricks are not so difficult to explain.
Thinking about extra dimensions can be learned in two steps.
- A simple step is to learn to imagine or describe the world with additional dimensions. You already know a few ways to do this, even if you don't realize it - and you can learn a little more.
- The more difficult stage is to learn how everything works in a world with additional dimensions. How to work with a needle in four dimensions, not three; whether the planets will orbit the Sun in six spatial dimensions; will protons and atoms form? Here you will need to learn unfamiliar tricks by imagining the differences between a world with only one or two dimensions and the three-dimensional world we know, and working by analogy.
- A world with zero dimensions is a point. Not much can be said about him now, but we will return to him.
- The one-dimensional world is already quite interesting.
- There's a lot more interesting stuff going on in 2D worlds.
- It is important to avoid confusion between spatial dimensions and the more general sense of the word "measurement" in ordinary language and in mathematics and statistics.
- Various examples of extra dimensions will follow, with an emphasis on what exactly “extra” means and how it is possible that there are dimensions in our world that we know nothing about.
- We'll also look at how exactly these subtle measurements can be detected.
One-dimensional worlds
A world with one spatial dimension is much simpler than a world with three, but there is something in it that can be speculated about. For example, there are several types of one-dimensional worlds. They not only have certain common properties, but also interesting differences.For the first example, let's look at measurement not as a physical concept, but as a more general concept. This will help you in many ways, such as distracting your intuition from natural misconceptions about what measurements are and how they work. Let's talk about annual earnings - how much money a person receives in a certain year. This is a dimension as suitable for study as any other.
Income dimension
Your income for the past year is a specific number in your local currency. It can be positive or negative, large or small; it can be represented as a point on a line, as in Fig. 1, which we will call the “income point”. Each point on the line represents a possible income.Rice. 1: a profit line of infinite length, the left side of which represents losses, the right side represents income.
What makes annual income a one-dimensional property is (very roughly speaking) the following:
Position in space is indicated by one unit of information: in our case, income.
Also note that it is continuous (or almost continuous) - if two people have different incomes A and B, we can find a third whose income is between A and B.
These two facts imply that income can change continuously along the income line, moving to the right or left - either to higher or lower income. There are no other options.
Of course, the income line has nothing to do with the physical space in which you and I can walk, but it is still a measurement. And (at least in principle) it has no end in either direction: there is (in principle) no limit to how much money a person can earn or lose in a year. This one-dimensional world isn't all that diverse, but we can still ask some meaningful questions about it:
- How is annual income distributed in the United States?
- What is the average annual income in Japan?
- How do the answers to these questions change over time?
Rainbow Dimension
And here is another, completely different world. A single dimension is formed by the colors of the rainbow, from red, through orange, to yellow, from there to green, [cyan], indigo and to violet [English-speaking people have six colors in the rainbow, they do not distinguish blue / approx. transl.]. From this point of view, colors form a one-dimensional world of finite size. Beyond red or violet there are invisible forms of flowers, but from the point of view of your eyes the dimension ends there. Now it is presented not as an endless line, but as a segment - the “rainbow line” in Fig. 2. Please do not confuse it with the color wheel - if it is closed, then our measurement begins with red and ends with purple. Again, position on the rainbow line is determined by one piece of information (color) and is continuous.
Rice. 2
This is obviously not a measurement of physical space either! You can throw a ball from your house to your neighbor's house, but you can't imagine throwing a ball from green to orange - it doesn't make sense. And still this will also be a measurement. There are many meaningful questions to ask here: How does the color of an apple move along the rainbow line as the apple turns from green to red? How many of each color are there in sunlight? If an orange star starts to turn red, will it turn yellow first?
Measuring wind direction
But here is the third measurement option, and again different. If you listen to the weather forecast, they will tell you that the wind will soon start blowing from the north, or from the northwest, or from the southwest. Possible wind directions are also a measurement. Please note that this is not a spatial dimension! In this dimension, you cannot throw a ball the way you throw it up, to the left, or forward. This is a measurement of directions in space!
Rice. 3
How can we represent this dimension? There are at least two natural ways to do this, shown in Fig. 3. One uses a segment - the “aeolian line” (Aeolus is a demigod, the ruler of the air elements among the Ancient Greeks) - but the aeolian line differs from the rainbow line in its periodicity. The wind direction can change from north to east, then to south, then to west, and then again to north, continuously. And in our view, the line can be cut anywhere - compare the two lines at the top of Fig. 3, which equally well represent the aeolian line. The point is that the wind can go from the right end of the line straight to the left end, and vice versa, so it doesn't matter where you cut it. Or perhaps it is easiest to think of this periodic line as a circle. This is exactly what we do with a compass or weather vane!
Three different one-dimensional worlds
And here you have one-dimensional worlds. Look how rich in detail they are! Different sizes, different properties. On an income line, income can go up or down forever. On the rainbow line, your eyes can only move as far as purple, or the other way, only as far as red. And on the aeolian line, the wind can make a full circle as much as it wants - but at the same time it will always return to one of the directions.These varieties of one-dimensional worlds - infinite, finite, and finitely periodic, represented by an infinite line, segment and circle - are the basic ingredients for understanding the worlds of higher dimensions. I will contact them again and again. In Fig. 4 shows them, as well as the fourth type, which extends indefinitely in only one direction. An example of such a measurement would be temperature: it can be as large as you like, but there is a minimum possible temperature - absolute zero - so temperature forms a line starting at absolute zero and going up from there, but not down.
Rice. 4
How to depict dimensions, spatial and otherwise
I've mentioned or used a few different methods of presenting measurements in passing. Income can be represented as a number or an infinite line. A visible rainbow can be represented as a segment, or as a color, and also using a number - the wavelength of photons corresponding to a certain color. The direction of the wind can be represented by a circle, or a segment whose left end is connected to the right - or words like north, east, south, west - or a number defining the direction in degrees, going from 0 to 360 and back to 0. What we can representing one dimension in many different ways gives us enormous flexibility to train our intuitive work with additional dimensions.To illustrate these types of measurements, I have chosen concepts that have nothing to do with physical space—income, the color of the rainbow, wind direction—to show that spatial measurements are specific examples of a more general concept of measurement. Understanding this fact greatly facilitates attempts to imagine worlds with more than three dimensions. Remember how I mentioned the two parts of learning to think about extra dimensions? First, learn to imagine them; secondly, understand how everything is arranged and works in them. Spatial dimensions have features related to the way some things work in them, but not to their representation.
Spatial worlds with one effective dimension
Taking all this into account, let us consider the spatial worlds we regularly encounter with one effective dimension. Or, more precisely, situations in which a certain aspect of our world behaves as if space had only one dimension. We then say that the world for certain participants or objects becomes effectively one-dimensional.
Rice. 5
Imagine a tightrope walker balancing on a high rope. The tightrope walker's world is effectively one-dimensional (though it is, of course, actually still three-dimensional) since he is unable to move safely in any direction other than right to left or left to right. This world is like a rainbow world - it is finite in length, and when the tightrope walker reaches the end, he must turn around and walk back (or step off the rope, ending up in a situation in which the world becomes effectively one-dimensional). What more can be said? Position on the rope can be determined by one piece of information (for example, the distance from the left pole to the rope walker). Two tightrope walkers can meet on the same line, but not pass each other.
We can turn the world of the rope into an aeolian line by closing it into a circle (Fig. 6). In it, two tightrope walkers also could not pass each other - this is the main property of one-dimensional worlds. And it would still be a finite dimension. But a tightrope walker in such a situation could already walk in a circle continuously and endlessly without stopping.
Rice. 6
Other (effectively) one-dimensional worlds we know of are:
- Narrow road is a one-dimensional world for cars;
- A narrow path with a cliff - for a tourist climbing a mountain;
- Floors of a high-rise building - for an elevator.
In the future, remember: we live in an apparent three-dimensional world, and everything we encounter seems three-dimensional to us. But sometimes our three-dimensional world (or rather, part of it) can behave as effectively one-dimensional, or two-dimensional (can you think of examples?) or even zero-dimensional! (Anyone who has ever been unlucky enough to be stuck in a traffic jam that goes nowhere knows what this zero-dimensional world is like!) This intuition will be very useful to us later.
It is really difficult to imagine other dimensions besides the three in which we live. But it is possible. I suggest you try this.
For a better understanding, let's imagine ourselves in a one-dimensional world. This is easy for us residents of three-dimensional space to do. In a one-dimensional world, there is only one dimension. Let's call it "length". Let's try to feel how difficult it will be for a representative of the one-dimensional world to imagine, understand and describe the simplest example from our three-dimensional world.
So the task: a representative of a one-dimensional world, (one-dimensional) tries to describe and imagine a room - in the simplest case: Four walls, a door through which he enters (crawls in, since he has no legs, this is another dimension of “height”), floor and ceiling.
So, our one-dimensional person enters the door and marks for himself the beginning (border) of a new world. Having reached the wall, he notes the distance traveled. And he gets some idea of the room in which he finds himself. Do you understand(?) that this idea is far from true? (This is just the length!). To get a complete picture of the room, he must, like an electron beam drawing a “picture” on a TV screen, line by line, measure the length of the room from wall to wall. And then, and this will be the most difficult thing for him (!), to imagine, to combine into a single “flat picture” (this is already a two-dimensional space!) the results of length measurements. Do not forget that the concept of “width” is unknown to him! And in order to get a three-dimensional view, he must similarly examine the walls, that is, the “height”. And then try again to bring together all the measurement results! Do you understand(?!) that this is an almost impossible task for him!
For a “flat man,” an imaginary inhabitant of a two-dimensional world, “living” in a “world” of length and width, but who does not know the concept of “height,” this is much easier to do. He has "visual perception", an understanding of length and width! But, unlike us, there is no understanding of heights! He himself, and the entire world he perceives, is “FLAT”!
Apparently you have observed a funny picture when an ant, once on the surface of a leaf, panics when it reaches its edge. Shock! Edge of the plane! End! He turns around and runs back.
It is difficult for “One-dimensional” and “Ploskatyk” to imagine a three-dimensional world, and even a curved surface. Analogy: Place an ant (a representative of the “Ploskatik”) on a sheet of paper folded into a ring. Gradually turn the ring so that the ant is always at the top. He will run circle after circle around the ring, believing that he is running straight. But, we are three-dimensional, we clearly see that he is running around the ring (circle)!
Now imagine that “Ploskatik” (an inhabitant of a two-dimensional world) is standing in front of a closed door to another room. He can’t see who’s there or what’s there! And he won’t know this until he opens the door! But, to us three-dimensional, “from above” (!), all this is perfectly visible! (See the picture below of the house plan. “Top View”).
Hence the 1st conclusion: “THE WORLD OF THE LOWER LEVEL” is visible, as they say, “at a glance.”
Now let’s try to imagine the next, 4th level of multidimensionality.
For example, let's take a quadrangular pyramid and look at it from the base. What will we see? Right! Square, quadrilateral! (The top is not visible to us!). That is, in volume, looking only from this one point, we will not be able to see it and evaluate it correctly! For a three-dimensional representation, we need to look at it from other points of view, to see it from a different angle! Looking only from the side of the base, a truncated pyramid, a cube and a parallelepiped will look like the same square or quadrangle. But in order to immediately “see the whole figure”, we need a “third eye”! An eye that would see this figure from the third side!
But for a full-fledged presentation, even this is not enough (suddenly, there are depressions, holes, notches, flaws on the edges!). And accordingly, our brain should have brought all this together (!), and “see” the pictures visible with the eyes as a single whole! It is no coincidence that we “twist and twirl” an unfamiliar thing, examining it from all sides. It is interesting to note that experts who study the human brain note that it is used by much less than half. Maybe it is designed for a HUGE PERCEPTION OF THE WORLD?
There is an expression, alas, I don’t know who it belongs to:
The mind knows how to look at the world,
Because mortal eye
It misleads us.
Now let's try to move to the fourth dimension. Look at your palm. And now on the other hand...
You see either one side or the other... Now place your palm vertically between the gas, closing your eyes one by one, you can see both sides! That is, you see the palm - AT THE SAME TIME! THOSE. VOLUME!
Now imagine that you have playing cards glued to your palm (on the back and outside). And that you have a third eye, between the existing two! You could also see the drawing of the “card covers”!
Multidimensional vision implies this. Isn't that where the expression "see through" comes from? This is the same as a “one-dimensional” who walks along the corridor, but does not notice the “side” doors! There are none for him!!! In his one-dimensional space!!! He has no concept of right-left, there is only one dimension - straight!!!
Usually the fourth dimension is understood as time. Let's try to consider this analogy: You downloaded a movie, it is stored as a file. File name (you probably know comments and reviews about it). But! But you don’t know the details of the film! This is similar to the quadrilateral pyramid analogy. It seems that there is some kind of idea, but there is no complete three-dimensional “picture”! Remember the example with the one-dimensional person studying the room! How much time and effort and mental stress he needs to put into building a single picture!
But, having watched the film, you now know it in detail, and can easily find the desired “scene” and frame if desired. And although the film, like our life, consists of separate “frames”, over time, this allows us to accumulate “LIFE EXPERIENCE”, which IS A COMPREHENSIVE VISION OF THE MEANING OF LIFE, EACH OF US. Here is the answer: “WHY DO WE COME INTO THIS WORLD.”
Let me return to the above quote, quatrain:
Through the eye, not with the eye
The mind knows how to look at the world,
Because mortal eye
It misleads us.
How unusual our World would look if we had the opportunity to see it not only in the light we see. But, also in the range of radio waves, infrared and ultraviolet light, alpha, beta, x-ray and gamma radiation! And you never know what others are unknown to us!
The Vedas mention Legs and Arlegs, inhabitants of worlds endowed with the ability to perceive many dimensions. It seems to me that in the religious sense these are Guardian Angels. They see the essence of things, on a level inaccessible to us. They are able to see our world “from the inside”, and even in the future. Similar to the example with cards and film. In exactly the same way, as we can see from our three-dimensional world, there is the imaginary world of “flat people”, considered using the example of the house plan shown in the figure.
Now the expression becomes clear: God is not a crumb, HE SEES EVERYTHING! ...
The second conclusion: multidimensional vision is the vision of an object simultaneously from different sides, at different levels. Vision of an object “from the inside and in time”, in various ranges of physical perception. Down to the elementary understanding at the atomic level, and all known and unknown ranges of electromagnetic radiation.
Bottom line: I don’t expect everyone to understand everything. But, I hope, I added a drop of interest to this issue.
PS: there are many videos on YouTube explaining the understanding of multidimensionality. It's fascinatingly interesting.
Sincerely,
On the path to devotion
Cosmology
Ontology and cosmology
"Ontology", according to generally accepted terminology, is a branch of philosophy that studies the nature of being. The origin of the universe and its cosmology is a question that concerns not only science, but also philosophy and especially its metaphysical branch called ontology. Thus, ontology as a whole deals with the study of being.
Cosmology, on the other hand, studies the origin, evolution and fate of the universe. Because cosmology focuses on the origins of the universe, difficult questions inevitably arise. Physics as such deals with that part of existence that is accessible to direct observation, measurement and mathematical interpretation. But the origin of the universe can hardly be observed directly.
Stephen Hawking writes about it this way: “Since events before the Big Bang have no observable consequences, we can say that time begins from the moment of the Big Bang. The events before the Big Bang are simply uncertain because there is no way to measure these events."
Therefore, scientists usually avoid metaphysical aspects of cosmology that are not directly observable. Since the events before the Big Bang are not defined and cannot be measured, then there is no point in discussing them.
Despite Hawking and company's attempts to develop a "Theory of Everything", there is no mathematical model that captures cosmic phenomena in their entirety. In addition to directly observable phenomena, ontology and cosmology include metaphysical as well as philosophical aspects.
Physicists study the relationships between space and time. Space is believed to have three dimensions: length, height and width. If a point is “stretched” in space, it becomes a one-dimensional line. A line “with width” is a two-dimensional plane. And a two-dimensional plane “with height” becomes a three-dimensional cube. The existence of the cube is stable relative to the fourth dimension, time.
Physicists are trying to solve the problems of existence by studying the nature of three-dimensional space moving in the fourth dimension - time. Therefore, they are interested in questions related to the materials that make up three-dimensional objects, as well as how these objects move in the space-time continuum. As a result, we have mathematical formulas that describe such phenomena as the speed of a falling body. Formulas like these help us create useful technologies for life. Since the times of early civilizations, humanity has made significant progress in the application of various mathematical formulas to the processes of movement of objects.
In Egypt, India, and Ancient Greece, people observed the movement of stars and planets and studied geometric shapes. Pythagoras considered mathematics a mystical science capable of revealing the secrets of the universe. Ancient pyramids were built based on astronomical observations. As humanity progressed, these mathematical formulas began to be used to create military weapons. Both Leonardo da Vinci and Galileo Galilei devoted many hours to thinking about the design of projectile trajectories. In this way they contributed to the development of ballistics.
Newton's laws made it possible to make significant progress in understanding the nature of various phenomena. However, in the 20th century it became clear that Newtonian mechanics was not able to explain the movement of subatomic particles, as well as the movement of distant planets. Einstein, Niels Bohr, Heisenberg developed a model of non-Newtonian reality. Quantum physics and the theory of relativity appeared.
But none of these theories provides an explanation of the nature of reality beyond the world of objects that obey the laws of physics. Einstein insisted that reality is not three-dimensional. He believed that when studying reality it is necessary to include the fourth dimension - time.
Mind: 5th dimension?
But physical science deliberately ignores phenomena that cannot be described mathematically. On the other hand, the universal philosophy of all ancient traditions has long recognized the existence of more than four dimensions.
What can be said about the mind?
Does the world exist in our mind or, on the contrary, is the mind a creation of the material world? Physicists reject the very posing of such a question. If the world exists in the mind, then reality is subjective. The meaning of the words “subjective” and “objective” is quite complex and not always clear to ordinary people. It is the language of philosophy, intended for members of the learned elite living in ivory castles. But look: if you are a subject, then the world is an object, the object of your perception through sight, hearing, touch, smell, taste. All these types of perception are carried out in the mind. Cognitive scientists will say that it all happens in the brain. But is the mind in the brain or is the brain in our mind? We are advised not to ask such questions. Questions about the existence of the mind are taboo for university science.
According to the teachings of the philosophical school of logical positivism, we should accept only what can be proven. But the reality of the mind is unprovable: its mathematical model does not exist. Millions of computer scientists have worked intensively since the 1980s to create a working artificial intelligence model using powerful supercomputers. Raymond Kurzweil, the inventor of optical text recognition and speech recognition systems, believes that an era of singularity is coming, in which computers will be much more efficient than humans. However, the functioning of the mind still defies mathematical interpretation. At the same time, brilliant intellectuals deny the very existence of the mind.
It is believed that Berkeley's idealism was refuted long ago by a man who kicked a chair and said, "Thus I refute Berkeley." But where is that man? And where is that chair? The debunker and his chair are long gone, but Berkeley's ideas continue to spark debate. Bishop Berkeley asked an intriguing question: if the world is not perceptible, how can it exist? The world exists only insofar as it is accessible to sensations. If there is no perception, then there is no being. This is considered extreme. However, quantum physicists, studying the behavior of subatomic particles, have discovered that the presence of an observer affects reality. Perhaps it's time to pay attention to the mental universe. Is the mind another dimension? From an ontological point of view, it is impossible to exclude the mind as a dimension of reality.
Are there other dimensions of reality?
So length, width and height give us three dimensions. By adding time, we get another dimension. Mental reality constitutes the fifth dimension. And cognitive science, or intelligence, can be considered the sixth dimension. Finally, mental reality and cognitive reality are actually aspects of a higher dimension: consciousness. Thus, a true ontology must consider more than just space and time. Ontology must also consider the nature of mind, intelligence and consciousness.
Unfortunately, academic science deliberately avoids any experiments “with a flavor” of metaphysics. There is no mathematical model of consciousness. The various forces and energies operating at the level of subatomic particles are difficult to study. Why take on problems that have no explanation?
Physicists study the relationships between matter and energy, the nature of various forces, and the speeds of moving objects.
But is it really that easy to describe a physical object? Let's take baseball for example. If you know where the pitcher is standing and how fast he is throwing the ball, you can tell exactly when the ball will reach the catcher's glove. Right? My physics teacher in high school explained all this to me. Of course, it is not enough to know that the pitcher is throwing the ball at 90 miles per hour and that he is 90 feet away from the catcher. You also need to take into account the height of the hill on which the pitcher stands. Next, there is also gravity. Gravity influences the direction of velocity as the ball fired by Sandy Koufax travels. Air has mass. The ball will experience friction as it moves through the air. We need a mathematical formula. But even if we carefully take into account all the variables that go into the equation of ball motion, there is another problem. The earth moves through space and time. And, as we know from Einstein's theory, space and time are relative. If you can perfectly calculate the speed of a baseball, you can predict the outcome. But where is the Earth? What is the catcher's position in absolute measurements?
Another problem is time. Does time exist? Or is it just a relative abstract entity constructed by humans to explain various aspects of their physical reality? The problem is that even if you can separate physical reality from consciousness, it is difficult to provide absolute proof of even something as purely objective as throwing a baseball. This uncertainty makes life extremely difficult for scientists.
The application of reality research at the physical level is usually one or another technology. But think about it: does technology always really work? In fact, the consequences of technological progress are often harmful to both people and the planet. Therefore, although metaphysical reasoning can unnerve us or, on the contrary, calm us down, it still makes sense to reflect on ontology.
The author completely agrees with V. Aleksandrov’s remark and believes that he very correctly drew attention to some aspect of one of the fundamental issues of modern theoretical physics. However, the laws of scientific popularization do not always allow us to accurately and strictly describe modern theories of space-time. This confirms the work of such outstanding scientists as Hawking, Kaku, Green, Wilskin.
Therefore, if we do not simply assume that multidimensional physical space is obtained by increasing the number of school Cartesian coordinates, as is often found in the literature, then we will need a whole story about “where the additional dimensions came from” and how they are used in modern physics.
The mystery of Einstein's will
There is a legend that, shortly before leaving for another world with the words: “well, now I’ll find out how it all works,” the great physicist Albert Einstein managed to combine all known physical fields in one formula. The genius wrote down his calculations in a simple school notebook, which he entitled “Unified Field Theory.” The brilliant creator of new physics thought a lot about the further fate of his epoch-making discovery and, in the end, decided that humanity was not yet ready to control space-time and travel through other dimensions...
Rumors about “Einstein's Testament” spread immediately after his death, and their sources are still unclear. Perhaps this is due to the unfinished works of the scientist, in which there are strange gaps and innuendoes. At the same time, most of his biographers are confident that if “Einstein’s Testament” existed, then, most likely, it was burned and scattered along with his ashes over the vastness of the Atlantic according to the last will of the genius.
Einstein's amazing world is based on his theory of relativity, which links gravity to the geometry of space-time itself. This can be thought of as an elastic surface in which all bodies form funnels of different shapes. For example, all the bodies of the solar system will roll into the spatial depression of our star, and the earth’s funnel will contain the Moon, artificial satellites, all objects on the surface and, of course, you and me.
A great success for Einstein's theory came after the astronomical discoveries of the deflection of light rays from distant stars near the Sun. Much later, astronomers recorded amazing cosmic gravitational lenses. This is how the intriguing mystery of multiple images of very distant quasi-stellar objects - quasars - was solved. Nearer galaxies distort their image with their “ripples in space-time,” causing the appearance of such bizarre shapes as the famous “Einstein cross.”
But the wonders of Einstein’s world do not end there. The theory of relativity explains how to get to other dimensions!
To do this, you will have to dive into the bottomless pits of space near the famous black holes. And, although scientists are still arguing about what is inside such “gravitational collapsars,” where matter seems to fall “inside itself,” Einstein himself, along with his colleague Nathan Rosen, confidently predicted that it is there that the real path to other dimensions is hidden . They managed to construct unique mathematical transitions between “puncture” points in space-time. “Einstein Rosen bridges” can connect very distant parts of the visible universe of the Metagalaxy, although many of the details are unclear.
Today, physicists will no longer be surprised by new models of “wormholes” and “wormholes” leading, according to Einstein’s theory of gravity, into the unknown from the core of black holes. On the other hand, the theory of relativity itself is constantly evolving. Maybe soon theorists will be able to combine electromagnetism with gravity, realizing the main dream of the great scientist. Along this path, many hopes are associated with the further development of Einstein's theory of supergravity, which unites the incomparable micro- and macro-worlds.
Roughly speaking, the essence of supergravity is the presence of additional dimensions in 11-dimensional space-time. Here, boundless scope opens up for physical and mathematical fantasies. After all, as has already been said, theoretically one can find both particle worlds and entire universes “packed” into other dimensions.
The author can fully imagine the indignation of many of his colleagues who read the last lines. To our deepest regret, it is in no way possible to talk more or less strictly about new theories of space-time in one article. After all, the mathematical apparatus of group theory is extremely difficult to popularize.
However, one should not lose hope: the theory of relativity was also once considered the most difficult mathematical construction, and today it is successfully studied in school.
The Mystery of the Hidden Dimensions
While building modern theories of other spaces and dimensions, theoretical physicists once encountered a very strange result, published back in the early 20s. last century by Professor Theodor Kaluza of the University of Königsberg.
This Polish-German physicist from the very beginning appreciated the deep potential inherent in the theory of relativity, and on its basis created a number of original geometric structures for various physical fields. At the next stage, he boldly decided to combine the geometry of gravity and electromagnetism. Ultimately, Kaluza was able to unexpectedly obtain an unusually curved five-dimensional space-time, including both gravity and Maxwell's electromagnetic field.
For a long time, contemporaries viewed Kaluza’s constructions as just a mathematical puzzle that had no analogue in the physical world. In 1926, the Swedish physicist and mathematician Oskar Klein took up the development of the Kaluza theory, after which it became known as the Kaluza-Klein theory.
This half-forgotten work at one time greatly interested Einstein, pushing him to the task of his entire subsequent life - the search for a Unified Field Theory. Unfortunately, he was never able to advance along this path, because he could not fit the existence of elementary particles into his constructions. Half a century passed until Kaluza’s ideas attracted the attention of the modern creators of the Theory of Everything (as physicists call the unified theory of all known particles and forces). This is where the idea of a real multidimensional space arose, in which geometry connects all existing physical fields.
Naturally, an obvious question immediately arises: how do additional spatial dimensions appear in the surrounding World? The answer is one term: compactification. This means that every “extra” dimension beyond the three known ones is curled up like a spring on a supermicroscopic scale. Here a striking “landscape” of the jet theory arises, where the smallest material objects have the appearance not of familiar points, but of extended structures. Vibrating like the most ordinary strings, they generate the spectrum of all known elementary particles.
This is how the most “ordinary” multidimensional dimensions, so beloved not only by theoretical physicists, but also by science fiction writers, enter our world. Is it possible to see them somehow? Or at least indirectly feel the presence of these depths of the microcosm?
Calculations show that this requires absolutely unimaginable energies, and a particle accelerator to study this problem will occupy the entire solar system. However, scientists do not lose heart and are looking for new ways into multidimensional space. These could be some still unknown cosmic phenomena, or new effects on the next generation of the LHC...
Branches of metaverses
Theoretical constructions of multidimensional worlds became familiar among mathematicians back in the 20s. of the past century, but physicists from the very beginning treated them with great prejudice. After all, it is enough to add one extra dimension, and the planets will begin to break away from their orbits, and matter will become unstable, crumbling into individual atoms. All this is wonderfully described in the book of the prominent scientific historian and popularizer G.E. Gorelik, which is called “Why is space three-dimensional?” Many brilliant artistic and popular illustrations from the world of many dimensions can also be found in the mathematician M. Gardner. These books not only deeply scientifically analyze the dimension of our World, but also consider alternative options in which there would be no place not only for man, but for protein life in general.
However, much more often there are works in which multidimensional worlds are practically no different from our four-dimensional Universe, they only contain a larger number of coordinates. On this occasion, the outstanding American physicist, Nobel laureate Steven Weinberg once remarked that this is reminiscent of the position of ufologists, who are overwhelmingly confident that in contact with aliens we will definitely encounter, if not little green men from flying saucers, then certainly something something like beetles or octopuses.
Another long-standing problem, considered since ancient times, is also connected with the dimension of our Universe: what minimal particles do space and time consist of? The smallest cells of space-time can be found in theories of quantum supergravity and superstring models. All of them are located in a space of other dimensions, somewhat reminiscent of a sheet of fabric woven from string fibers. At the same time, theorists wisely stipulate in advance that these extremely small objects are fundamentally unobservable and can only somehow manifest themselves at ultra-high energies.
Leading superstring theorist Juan Maldaseia recently aphoristically noted that modern physicists live in anticipation of a miracle when some unexpected experiment or even cosmic observation will confirm that the skeleton of the Universe contains additional bones of invisible dimensions.
In this case, we just have to be patient...
Mysteries of space-time
It should be noted that journalists and writers have long noticed the confusion reigning in the theories of physicists. Thus, a common opinion in the pseudo-scientific literary community is that any conceivable miracles and transformations are the work of aliens from other dimensions. Modern magicians and psychics go even further. Those who seriously believe that their paranormal tricks are explained by the space of another reality. It is quite natural that the most “fashionable” theoretical concept of a multiple Universe - the Multiverse - is closely connected with multidimensional variants of generalization of superstrings, etc. "M-theories".
The idea of the existence of other dimensions and parallel worlds is far from new. There is a lot of different information on this topic, where the authors in their articles try to answer, perhaps, a number of basic questions: do other dimensions exist? who lives there? and is it possible to get there? It is clear that today no one doubts their existence. Even prominent scientists do not rule out the possibility that other dimensions are real. However, no matter how much is written and explained, we must admit the fact that in reality we really don’t know anything about them. There is still debate among scientists about how many dimensions there really are. Different numbers are given: 8, 16 and even 32. They cannot come to a consensus on the issue of our closest “neighbor” - the 4-dimensional dimension. Some argue that already starting from him, one of the determinants of this dimension is time. Others, comparing it with the analogue of our 3-dimensional world, believe that in addition to length, width and height, in the 4-dimensional world there is a determining quantity not time, but simply some component unknown to us.
Of course, more information has been obtained about parallel worlds, mainly because they are all located in our native 3-dimensional dimension. In addition, the people who visited these worlds (there are many stories and evidence on this matter) also made a certain contribution.
The situation is different with other dimensions (multidimensional worlds), which are extremely difficult for us to understand. There is not a single witness who was there (although, perhaps, there are, but more on that later) to convey to us at least some information. It is clear that no matter who lives there, they are far superior to us in mental development. And if we consider that starting from the 4th dimension (?) and above there is a time component, this means that they are subject to time.
This is the same as comparing people with creatures living in the second dimension, or as they are also called - “planars” (from the word plane). They don’t even suspect the existence of such a thing as height and, as a result, cannot describe our space. For us, flatness is a common phenomenon. We constantly encounter it in everyday life. Calculating the perimeter, area, finding the coordinates of a point, and so on is not difficult even for an ordinary schoolchild, while we are not yet able to understand multidimensional worlds.
Is there a connection between all these worlds? Perhaps it exists. Let's look at one elementary example. As already noted, creatures living in the 2nd dimension cannot understand our three-dimensional world. Imagine that you pierced their 2-dimensional world (sheet of paper) with an ordinary pencil. What will a resident of the flat world see in this case? And he will see a hole appear out of nowhere in his 2-dimensional space, while the pencil will remain invisible to them.
There are also plenty of similar mysteries in our space. For example, take ball lightning, which also appears out of nowhere and disappears into nowhere. Another example is a black hole, which, like a vacuum cleaner, sucks into itself everything that is within its reach. Isn't it true that this example is similar to the example with a pencil? Therefore, we can assume that this and a number of other mysterious phenomena may actually be somehow connected with other dimensions.
So will people be able to visit these worlds? It is theoretically possible to get into any existing dimension different from ours, with the exception of two-dimensional. Logic dictates that in a world of greater “space” there will always be room for less. This idea can be expressed in other words: the larger the door, the easier it is to enter and exit, and this has already happened. We are talking about the sensational Philadelphia experiment, in which the names of brilliant scientists Albert Einstein and Nikola Tesla appear. Then, with the participation of the destroyer Eldridge, it was decided to conduct an extremely unusual experiment, which consisted of creating an “invisible ship” by enveloping the ship in an electromagnetic “cocoon”. But something went wrong and “Eldridge,” instead of simply hiding from the all-seeing radar beams, as researchers suggest, during his disappearance he visited another dimension.
The consequences of the experiment were terrible: the destroyer was missing parts of its hull, and a real tragedy happened to its crew. Many of them suffered burns of unknown origin. The rest either died or went crazy.
But today the burns received can be explained by powerful microwave radiation, but here is the reason why