Uranium strings. Briefly about string theory

Key questions:

What are the fundamental components of the Universe - the "first bricks of matter"? Are there theories that can explain all the basic physical phenomena?

Question: is it real?

Today and in the foreseeable future, direct observation on such a small scale is not possible. Physics is in search, and ongoing experiments, for example, to detect supersymmetric particles or search for extra dimensions in accelerators, may indicate that string theory is on the right track.

Whether or not string theory is the theory of everything, it provides us with a unique set of tools to peer into the deep structures of reality.

String theory

Macro and micro

When describing the Universe, physics divides it into two seemingly incompatible halves - the quantum microcosm, and the macrocosm, within which gravity is described.

String theory is a controversial attempt to combine these halves into a "Theory of Everything".

Particles and interactions

The world is made of two types of elementary particles - fermions and bosons. Fermions are all observable matter, and bosons are carriers of the four known fundamental interactions: weak, electromagnetic, strong, and gravitational. Within a theory called the Standard Model, physicists have managed to elegantly describe and test the three fundamental forces, all but the weakest, gravitational. To date, the Standard Model is the most accurate and experimentally confirmed model of our world.

Why string theory is needed

The Standard Model does not include gravity, cannot describe the center of a black hole and the Big Bang, and does not explain the results of some experiments. String theory is an attempt to solve these problems and unify matter and interactions by replacing elementary particles with tiny vibrating strings.

String theory is based on the idea that all elementary particles can be represented as one elementary "first brick" - a string. Strings can vibrate, and different modes of such vibrations at a large distance will look to us like different elementary particles. One mode of vibration will make the string look like a photon, the other will make it look like an electron.

There is even a mod that describes the carrier of gravitational interaction - the graviton! Versions of string theory describe strings of two types: open (1) and closed (2). Open strings have two ends (3) located on membrane-like structures called D-branes, and their dynamics describe three of the four fundamental interactions - all except gravitational.

Closed strings resemble loops, they are not tied to D-branes - it is the vibrational modes of closed strings that are represented by a massless graviton. The ends of an open string can connect, forming a closed string, which, in turn, can break, turning into an open one, or come together and split into two closed strings (5) - thus, in string theory, the gravitational interaction is combined with all the others

Strings are the smallest of all objects that physics operates on. The size range V of the objects shown in the picture above extends over 34 orders of magnitude - if an atom were the size of the solar system, then the size of a string could be slightly larger than an atomic nucleus.

Additional measurements

Consistent string theories are only possible in higher-dimensional space, where in addition to the familiar 4 space-time dimensions, 6 additional dimensions are required. Theorists believe that these extra dimensions are folded into imperceptibly small forms - Calabi-Yau spaces. One of the problems of string theory is that there is an almost infinite number of versions of the Calabi-Yau convolution (compactification) that allows you to describe any world, and so far there is no way to find the version of qi compactification that would allow you to describe that what we see around.

supersymmetry

Most versions of string theory require the concept of supersymmetry, which is based on the idea that fermions (matter) and bosons (interactions) are manifestations of the same object, and can turn into each other.

Theory of everything?

Supersymmetry can be incorporated into string theory in 5 different ways, resulting in 5 different kinds of string theory, which means that string theory itself cannot claim to be a "theory of everything". All of these five kinds are interconnected by mathematical transformations called dualities, and this has led to the understanding that all these kinds are aspects of something more general. This more general theory is called M-Theory.

5 different formulations of string theory are known, but upon closer examination, it turns out that they are all manifestations of a more general theory

At school, we taught that matter consists of atoms, and atoms are made of nuclei around which electrons revolve. About the same way, the planets revolve around the sun, so it's easy for us to imagine. Then the atom was split into elementary particles, and it became more difficult to imagine the structure of the universe. On the particle scale, other laws apply, and it is not always possible to find an analogy from life. Physics has become abstract and confusing.

But the next step in theoretical physics brought back a sense of reality. String theory has described the world in terms that can be imagined again, and therefore easier to understand and remember.

The topic is still difficult, so let's go in order. First, we will analyze what the theory is, then we will try to understand why it was invented. And for dessert - a bit of history, string theory has a short history, but with two revolutions.

The universe is made up of vibrating strands of energy

Prior to string theory, elementary particles were considered points, dimensionless shapes with certain properties. String theory describes them as filaments of energy, which still have one size - length. These one-dimensional threads are called quantum strings.

Theoretical physics

Theoretical physics
describes the world through mathematics, as opposed to experimental physics. The first theoretical physicist was Isaac Newton (1642-1727)

The nucleus of an atom with electrons, elementary particles and quantum strings through the eyes of an artist. Fragment of the documentary film "Elegant Universe"

Quantum strings are very small, about 10 -33 cm long. This is a hundred million billion times smaller than the protons that are collided at the Large Hadron Collider. For such experiments with strings, one would have to build an accelerator the size of a galaxy. We haven't found a way to detect strings yet, but thanks to mathematics, we can guess some of their properties.

Quantum strings are open and closed. The open ends are free, the closed ends close to each other, forming loops. The strings are constantly "opening" and "closing", connecting with other strings and breaking up into smaller ones.

Quantum strings are taut. The tension in space occurs due to the difference in energy: for closed strings between closed ends, for open strings - between the ends of the strings and the void. Physicists call this void two-dimensional dimensional edges, or branes, from the word membrane.

centimeters is the smallest possible size of an object in the universe. It's called the Planck length.

We are made of quantum strings

Quantum strings vibrate. These are vibrations similar to vibrations of balalaika strings, with uniform waves and an integer number of minima and maxima. When vibrating, a quantum string does not emit sound; on the scale of elementary particles, there is nothing to transmit sound vibrations. It itself becomes a particle: it vibrates with one frequency - a quark, with another - a gluon, with a third - a photon. Therefore, a quantum string is a single building element, a "brick" of the universe.

It is customary to depict the universe as space and stars, but it is also our planet, and we are with you, and text on the screen, and berries in the forest.

Scheme of string vibrations. At any frequency, all waves are the same, their number is integer: one, two and three

Moscow region, 2016. There are a lot of strawberries - only mosquitoes are more. They are also made of strings.

Space is out there somewhere. Back to space

So, at the heart of the universe are quantum strings, one-dimensional strands of energy that vibrate, change size and shape, and exchange energy with other strings. But that's not all.

Quantum strings move in space. And string-scale space is the most curious part of the theory.

Quantum strings move in 11 dimensions

Theodor Kaluza
(1885-1954)

It all started with Albert Einstein. His discoveries showed that time is relative and united it with space into a single space-time continuum. Einstein's work explained gravity, the motion of planets, and the origin of black holes. In addition, they inspired contemporaries to new discoveries.

Einstein published the equations of the general theory of relativity in 1915-16, and already in 1919 the Polish mathematician Theodor Kaluza tried to apply his calculations to the theory of the electromagnetic field. But the question arose: if Einstein's gravity bends the four dimensions of space-time, what does the electromagnetic force bend? Faith in Einstein was strong, and Kaluza had no doubt that his equations would describe electromagnetism. Instead, he suggested that electromagnetic forces distort an additional, fifth dimension. Einstein liked the idea, but the theory did not pass the test of experiments and was forgotten until the 1960s.

Albert Einstein (1879-1955)

Theodor Kaluza
(1885-1954)

Theodor Kaluza
(1885-1954)

Albert Einstein
(1879-1955)

The first equations of string theory gave strange results. Tachyons appeared in them - particles with a negative mass that moved faster than the speed of light. This is where Kaluza's idea about the multidimensionality of the universe came in handy. True, five dimensions were not enough, just as six, seven or ten were not enough. The mathematics of the first string theory only made sense if our universe had 26 dimensions! Later theories were enough for ten, and in the modern one there are eleven of them - ten spatial and time.

But if so, why don't we see the extra seven dimensions? The answer is simple - they are too small. From a distance, a three-dimensional object will appear flat: a water pipe will appear as a ribbon, and a balloon will appear as a circle. Even if we could see objects in other dimensions, we would not consider their multidimensionality. Scientists call this effect compactification.

Extra dimensions are folded into imperceptibly small forms of space-time - they are called Calabi-Yau spaces. From a distance it looks flat.

We can represent seven additional dimensions only in the form of mathematical models. These are fantasies that are built on the properties of space and time known to us. When adding a third dimension, the world becomes three-dimensional, and we can get around the obstacle. Perhaps, according to the same principle, it is correct to add the remaining seven dimensions - and then you can go around space-time along them and get to any point of any universe at any time.

measurements in the universe according to the first version of string theory - bosonic. Now considered irrelevant

A line has only one dimension, its length.

A balloon is voluminous, it has a third dimension - height. But for a two-dimensional man, it looks like a line

Just as a two-dimensional man cannot represent multidimensionality, so we cannot represent all the dimensions of the universe.

According to this model, quantum strings travel always and everywhere, which means that the same strings encode the properties of all possible universes from their birth to the end of time. Unfortunately, our balloon is flat. Our world is only a four-dimensional projection of the eleven-dimensional universe onto the visible scales of space-time, and we cannot follow the strings.

Someday we'll see the Big Bang

Someday we will calculate the vibration frequency of strings and the organization of extra dimensions in our universe. Then we will learn absolutely everything about it and will be able to see the Big Bang or fly to Alpha Centauri. But so far this is impossible - there are no hints on what to rely on in the calculations, and you can only find the numbers you need by brute force. Mathematicians calculated that 10,500 options would have to be sorted out. The theory is deadlocked.

Yet string theory is still capable of explaining the nature of the universe. To do this, it must bind all other theories, become the theory of everything.

String theory will become the theory of everything. May be

In the second half of the 20th century, physicists confirmed a number of fundamental theories about the nature of the universe. It seemed a little more - and we will understand everything. However, the main problem has not yet been solved: theories work fine separately, but they do not give a general picture.

There are two main theories: the theory of relativity and quantum field theory.

options for organizing 11 dimensions in Calabi-Yau spaces - enough for all possible universes. For comparison, the number of atoms in the observable part of the universe is about 10 80

options for organizing Calabi-Yau spaces - enough for all possible universes. For comparison, the number of atoms in the observable universe is about 10 80

Theory of relativity
described the gravitational interaction between planets and stars and explained the phenomenon of black holes. This is the physics of a visual and logical world.

Model of the gravitational interaction of the Earth and the Moon in the Einsteinian space-time

quantum field theory
determined the types of elementary particles and described 3 types of interaction between them: strong, weak and electromagnetic. This is the physics of chaos.

The quantum world through the eyes of an artist. Video from MiShorts website

Quantum field theory with the addition of mass for neutrinos is called standard model. This is the basic theory of the structure of the universe at the quantum level. Most of the predictions of the theory are confirmed in experiments.

The Standard Model divides all particles into fermions and bosons. Fermions form matter - this group includes all observable particles, such as the quark and the electron. Bosons are forces that are responsible for the interaction of fermions, such as photon and gluon. Two dozen particles are already known, and scientists continue to discover new ones.

It is logical to assume that the gravitational interaction is also transmitted by its boson. It has not yet been found, however, they described the properties and came up with a name - graviton.

But unification of theories fails. According to the Standard Model, elementary particles are dimensionless points that interact at zero distances. If this rule is applied to the graviton, the equations give infinite results, which makes them meaningless. This is just one of the contradictions, but it well illustrates how far one physics is from another.

Therefore, scientists are looking for an alternative theory that can combine all theories into one. Such a theory is called a unified field theory, or theory of everything.

Fermions
form all types of matter except dark

Bosons
transfer energy between fermions

String theory can unite the scientific world

String theory in this role looks more attractive than others, since it immediately solves the main contradiction. Quantum strings vibrate, so the distance between them is greater than zero, and impossible calculations for the graviton are avoided. And the graviton itself fits well into the concept of strings.

But string theory is not proven by experiments, its achievements remain on paper. The more surprising is the fact that for 40 years it has not been abandoned - its potential is so great. To understand why this is so, let's look back and see how it has evolved.

String theory has experienced two revolutions

Gabriele Veneziano
(born 1942)

At first, string theory was not at all considered a contender for the unification of physics. It was discovered by accident. In 1968, a young theoretical physicist, Gabriele Veneziano, studied the strong interactions within the atomic nucleus. Suddenly, he found that they were well described by Euler's beta function, a set of equations that had been compiled 200 years earlier by the Swiss mathematician Leonhard Euler. It was strange: in those days, the atom was considered indivisible, and Euler's work solved only mathematical problems. Nobody understood why the equations worked, but they were actively used.

The physical meaning of Euler's beta function was clarified two years later. Three physicists, Yochiro Nambu, Holger Nielsen, and Leonard Susskind, suggested that elementary particles might not be points, but one-dimensional vibrating strings. The strong interaction for such objects was described by the Euler equations ideally. The first version of string theory was called bosonic, since it described the string nature of the bosons responsible for the interactions of matter, and did not touch on the fermions that matter.

The theory was crude. Tachyons appeared in it, and the main predictions contradicted the results of experiments. And although Kaluza's multidimensionality managed to get rid of tachyons, string theory did not take root.

• Gabriele Veneziano
• Yoichiro Nambu
• Holger Nielsen
• Leonard Susskind
• John Schwartz
• Michael Green
• Edward Witten

• Gabriele Veneziano
• Yoichiro Nambu
• Holger Nielsen
• Leonard Susskind
• John Schwartz
• Michael Green
• Edward Witten

But the true supporters of the theory remained. In 1971, Pierre Ramon added fermions to string theory, reducing the number of dimensions from 26 to ten. It started supersymmetry theory.

It said that each fermion has its own boson, which means that matter and energy are symmetrical. It doesn't matter that the observable universe is not symmetrical, Ramon said, there are conditions under which symmetry is still observed. And if, according to string theory, fermions and bosons are encoded by the same objects, then under these conditions, matter can turn into energy, and vice versa. This property of strings was called supersymmetry, and string theory itself was called superstring theory.

In 1974, John Schwartz and Joel Sherk discovered that some of the properties of strings matched remarkably well with those of the supposed carrier of gravity, the graviton. From that moment on, the theory began to seriously claim to be generalizing.

dimensions of space-time were in the first superstring theory

“The mathematical structure of string theory is so beautiful and has so many amazing properties that it must surely point to something deeper.”

First superstring revolution happened in 1984. John Schwartz and Michael Green presented a mathematical model that showed that many of the contradictions between string theory and the Standard Model could be resolved. The new equations also linked the theory to all kinds of matter and energy. The scientific world was in a fever - physicists abandoned their research and switched to the study of strings.

From 1984 to 1986, more than a thousand papers on string theory were written. They showed that many of the provisions of the Standard Model and the theory of gravity, which have been collected bit by bit for years, follow naturally from string physics. Research has convinced scientists that a unifying theory is just around the corner.

“The moment you are introduced to string theory and realize that almost all of the major advances in physics of the last century follow—and follow with such elegance—from such a simple starting point, clearly demonstrates to you the incredible power of this theory.”

But string theory was in no hurry to reveal its secrets. In place of the solved problems, new ones arose. Scientists have discovered that there are not one, but five superstring theories. In them, the strings had different types of supersymmetry, and there was no way to know which theory was correct.

Mathematical methods had their limits. Physicists are accustomed to complex equations that do not give exact results, but for string theory it was impossible to write even exact equations. And the approximate results of the approximate equations did not give answers. It became clear that a new mathematics was needed to study the theory, but no one knew which one. The ardor of scientists subsided.

Second superstring revolution thundered in 1995. The stagnation was ended by Edward Witten's report at a conference on string theory in Southern California. Witten showed that all five theories are special cases of one, more general superstring theory, in which not ten dimensions, but eleven. Witten called the unifying theory M-theory, or Mother of all theories, from the English word Mother.

But something else was more important. Witten's M-theory described the effect of gravity in superstring theory so well that it was called the supersymmetric theory of gravity, or supergravity theory. This inspired scientists, and scientific journals again filled with publications on string physics.

measurements of space-time in modern superstring theory

“String theory is a piece of 21st century physics that accidentally entered the 20th century. It may take decades, or even centuries, before it is fully developed and understood.

The echoes of this revolution are still heard today. But despite the best efforts of scientists, there are more questions in string theory than answers. Modern science is trying to build models of the multidimensional universe and is studying dimensions as membranes of space. They are called branes - remember the void, on which open strings are stretched? It is assumed that the strings themselves may turn out to be two- or three-dimensional. They even talk about a new 12-dimensional fundamental theory - F-theory, the Father of all theories, from the word Father. The history of string theory is far from over.

String theory hasn't been proven yet, but it hasn't been disproven either.

The main problem of the theory is the lack of direct evidence. Yes, other theories follow from it, scientists add 2 and 2, and it turns out 4. But this does not mean that the four consists of twos. Experiments at the Large Hadron Collider have not yet discovered supersymmetry, which would confirm the unified structural basis of the universe and would play into the hands of string physics supporters. But there are no rebuttals either. That is why the elegant mathematics of string theory continues to excite the minds of scientists, promising to unravel all the mysteries of the universe.

Speaking of string theory, one cannot fail to mention Brian Greene, a professor at Columbia University and a tireless popularizer of the theory. Green lectures and appears on television. In 2000, his book The Elegant Universe. Superstrings, Hidden Dimensions, and the Search for the Ultimate Theory" became a finalist for the Pulitzer Prize. In 2011, he played himself in episode 83 of The Big Bang Theory. In 2013, he visited the Moscow Polytechnic Institute and gave an interview to Lenta-ru

If you do not want to become an expert in string theory, but want to understand what world you live in, remember the cheat sheet:

1. The universe is made up of strands of energy—quantum strings—that vibrate like the strings of musical instruments. Different frequency of vibration turns the strings into different particles.
2. The ends of the strings can be free, or they can be closed to each other, forming loops. The strings are constantly closing, opening and exchanging energy with other strings.
3. Quantum strings exist in an 11-dimensional universe. The extra 7 dimensions are folded into imperceptibly small forms of space-time so we can't see them. This is called dimension compactification.
4. If we knew exactly how the dimensions in our universe are folded, then perhaps we could travel through time to other stars. But while this is not possible - too many options need to be sorted out. They would be enough for all possible universes.
5. String theory can unite all physical theories and reveal the secrets of the universe to us - there are all prerequisites for this. But there is no evidence yet.
6. Other discoveries of modern science follow logically from string theory. Unfortunately, this doesn't prove anything.
7. String theory has survived two superstring revolutions and many years of neglect. Some scientists consider it science fiction, others believe that new technologies will help prove it.
8. Most importantly, if you plan to tell your friends about string theory, make sure that there is no physicist among them - you will save time and nerves. And you'll look like Brian Green at the Polytechnic Institute:

Ultimately, all elementary particles can be represented as microscopic multidimensional strings in which vibrations of various harmonics are excited.

Attention, fasten your seat belts tighter - and I will try to describe to you one of the strangest theories from among the scientific circles seriously discussed today, which can finally give the final clue to the structure of the Universe. This theory looks so wild that, quite possibly, it is correct!

Various versions of string theory are today considered as the main contenders for the title of a comprehensive universal theory that explains the nature of everything that exists. And this is a kind of Holy Grail of theoretical physicists involved in the theory of elementary particles and cosmology. Universal Theory (aka. theory of everything) contains only a few equations that combine the entire set of human knowledge about the nature of interactions and properties of the fundamental elements of matter from which the Universe is built. Today, string theory has been combined with the concept supersymmetry, resulting in the birth superstring theory, and today this is the maximum that has been achieved in terms of unifying the theory of all four main interactions (forces acting in nature). The theory of supersymmetry itself has already been built on the basis of an a priori modern concept, according to which any remote (field) interaction is due to the exchange of particles-carriers of an interaction of the corresponding kind between the interacting particles ( cm. standard model). For clarity, the interacting particles can be considered the "bricks" of the universe, and the particles-carriers - cement.

Within the framework of the standard model, quarks act as building blocks, and interaction carriers are gauge bosons, which these quarks exchange with each other. The theory of supersymmetry goes even further and states that the quarks and leptons themselves are not fundamental: they all consist of even heavier and experimentally undiscovered structures (bricks) of matter, held together by an even stronger “cement” of super-energetic particles-carriers of interactions than quarks. in hadrons and bosons. Naturally, in laboratory conditions, none of the predictions of the theory of supersymmetry has yet been verified, however, the hypothetical hidden components of the material world already have names - for example, seelectron(supersymmetric partner of an electron), squark etc. The existence of these particles, however, is unambiguously predicted by theories of this kind.

The picture of the universe offered by these theories, however, is quite easy to visualize. On scales of the order of 10 -35 m, that is, 20 orders of magnitude smaller than the diameter of the same proton, which includes three bound quarks, the structure of matter differs from what we are accustomed to even at the level of elementary particles. At such small distances (and at such high interaction energies that it is unthinkable), matter turns into a series of field standing waves, similar to those that are excited in the strings of musical instruments. Like a guitar string, in such a string, in addition to the fundamental tone, many overtones or harmonics. Each harmonic has its own energy state. According to principle of relativity (cm. The theory of relativity), energy and mass are equivalent, which means that the higher the frequency of the harmonic wave vibration of the string, the higher its energy, and the higher the mass of the observed particle.

However, if a standing wave in a guitar string is visualized quite simply, the standing waves proposed by superstring theory are difficult to visualize - the fact is that superstrings vibrate in a space that has 11 dimensions. We are accustomed to a four-dimensional space, which contains three spatial and one temporal dimensions (left-right, up-down, forward-backward, past-future). In the space of superstrings, things are much more complicated (see inset). Theoretical physicists get around the slippery problem of "extra" spatial dimensions by arguing that they are "hidden" (or, in scientific terms, "compactified") and therefore are not observed at ordinary energies.

More recently, string theory has been further developed in the form theory of multidimensional membranes- in fact, these are the same strings, but flat. As one of its authors casually joked, membranes differ from strings in much the same way that noodles differ from vermicelli.

That, perhaps, is all that can be briefly told about one of the theories, not without reason claiming today to be the universal theory of the Great Unification of all force interactions. Alas, this theory is not without sin. First of all, it has not yet been brought to a rigorous mathematical form due to the insufficiency of the mathematical apparatus for bringing it into strict internal correspondence. It has been 20 years since this theory came into being, and no one has been able to consistently harmonize some of its aspects and versions with others. Even more unpleasant is the fact that none of the theorists who propose the theory of strings (and, especially, superstrings) has not yet proposed a single experiment on which these theories could be tested in the laboratory. Alas, I am afraid that until they do this, all their work will remain a bizarre game of fantasy and an exercise in comprehending esoteric knowledge outside the mainstream of natural science.

See also:

How many dimensions are there?

We, ordinary people, have always had enough of three dimensions. Since time immemorial, we have been accustomed to describing the physical world in such modest terms (a saber-toothed tiger 40 meters in front, 11 meters to the right and 4 meters above me - a cobblestone for battle!). The theory of relativity has taught most of us that time is the essence of the fourth dimension (the saber-toothed tiger is not just here - it threatens us here and now!). And so, starting from the middle of the 20th century, theorists began to talk that in fact there are even more dimensions - either 10, or 11, or even 26. Of course, without explaining why we, normal people, do not observe them, here could not manage. And then the concept of "compactification" arose - the adhesion or collapse of dimensions.

Imagine a garden watering hose. Up close, it is perceived as a normal three-dimensional object. It is necessary, however, to move away from the hose at a sufficient distance - and it will appear to us as a one-dimensional linear object: we simply cease to perceive its thickness. It is this effect that is commonly referred to as the compactification of measurement: in this case, the thickness of the hose turned out to be “compactified” - the scale of the measurement scale is too small.

This is exactly how, according to the theorists, the really existing additional dimensions disappear from the field of our experimental perception, which are necessary for an adequate explanation of the properties of matter at the subatomic level: they are compactified, starting from a scale of about 10 -35 m, and modern observation methods and measuring instruments simply do not able to detect structures on such a small scale. Perhaps this is exactly how it is, or perhaps things are completely different. While there are no such devices and methods of observation, all the above arguments and counter-arguments will remain at the level of idle speculation.

Ecology of knowledge: The biggest problem for theoretical physicists is how to combine all the fundamental interactions (gravitational, electromagnetic, weak and strong) into a single theory. Superstring theory just claims to be the Theory of Everything

Counting from three to ten

The biggest problem for theoretical physicists is how to combine all fundamental interactions (gravitational, electromagnetic, weak and strong) into a single theory. Superstring theory just claims to be the Theory of Everything.

But it turned out that the most convenient number of dimensions needed for this theory to work is as many as ten (nine of which are spatial, and one is temporal)! If there are more or less dimensions, mathematical equations give irrational results that go to infinity - a singularity.

The next stage in the development of superstring theory - M-theory - has already counted eleven dimensions. And another version of it - F-theory - all twelve. And it's not a complication at all. F-theory describes 12-dimensional space with simpler equations than M-theory describes 11-dimensional space.

Of course, theoretical physics is called theoretical for a reason. All her achievements so far exist only on paper. So, to explain why we can only move in three-dimensional space, scientists started talking about how the unfortunate other dimensions had to shrink into compact spheres at the quantum level. To be precise, not into spheres, but into Calabi-Yau spaces. These are such three-dimensional figures, inside of which there is its own world with its own dimension. A two-dimensional projection of similar manifolds looks something like this:

More than 470 million such figurines are known. Which of them corresponds to our reality is currently being calculated. It is not easy to be a theoretical physicist.

Yes, it does seem a bit far-fetched. But perhaps this explains why the quantum world is so different from what we perceive.

Period, period, comma

Start over. Zero dimension is a point. She has no size. There is nowhere to move, no coordinates are needed to indicate the location in such a dimension.

Let's put a second point next to the first one and draw a line through them. Here is the first dimension. A one-dimensional object has a size - length, but no width or depth. Movement within the framework of one-dimensional space is very limited, because the obstacle that has arisen on the way cannot be bypassed. To determine the location on this segment, you need only one coordinate.

Let's put a point next to the segment. To fit both of these objects, we need already a two-dimensional space that has length and width, that is, area, but without depth, that is, volume. The location of any point on this field is determined by two coordinates.

The third dimension arises when we add a third coordinate axis to this system. It is very easy for us, the inhabitants of the three-dimensional universe, to imagine this.

Let's try to imagine how the inhabitants of two-dimensional space see the world. For example, here are these two people:

Each of them will see his friend like this:

And with this layout:

Our heroes will see each other like this:

It is the change of point of view that allows our heroes to judge each other as two-dimensional objects, and not one-dimensional segments.

And now let's imagine that a certain three-dimensional object moves in the third dimension, which crosses this two-dimensional world. For an outside observer, this movement will be expressed in a change in two-dimensional projections of the object on a plane, like broccoli in an MRI machine:

But for the inhabitant of our Flatland, such a picture is incomprehensible! He can't even imagine her. For him, each of the two-dimensional projections will be seen as a one-dimensional segment with a mysteriously variable length, appearing in an unpredictable place and also unpredictably disappearing. Attempts to calculate the length and place of occurrence of such objects using the laws of physics of two-dimensional space are doomed to failure.

We, the inhabitants of the three-dimensional world, see everything in two dimensions. Only the movement of an object in space allows us to feel its volume. We will also see any multidimensional object as two-dimensional, but it will change in an amazing way depending on our relative position or time with it.

From this point of view, it is interesting to think, for example, about gravity. Everyone has probably seen pictures like this:

It is customary to depict how gravity bends space-time. Curves... where? Exactly not in any of the dimensions familiar to us. And what about quantum tunneling, that is, the ability of a particle to disappear in one place and appear in a completely different one, moreover, behind an obstacle through which, in our realities, it could not penetrate without making a hole in it? What about black holes? But what if all these and other mysteries of modern science are explained by the fact that the geometry of space is not at all the same as we are accustomed to perceive it?

The clock is ticking

Time adds one more coordinate to our Universe. In order for the party to take place, you need to know not only in which bar it will take place, but also the exact time of this event.

Based on our perception, time is not so much a straight line as a ray. That is, it has a starting point, and the movement is carried out only in one direction - from the past to the future. And only the present is real. Neither the past nor the future exist, just as breakfasts and dinners do not exist from the point of view of an office clerk at lunchtime.

But the theory of relativity does not agree with this. From her point of view, time is a valuable dimension. All the events that have existed, exist and will continue to exist are equally real, as real as the sea beach is, no matter where exactly the dreams of the sound of the surf took us by surprise. Our perception is just something like a searchlight that illuminates a certain segment on the time line. Humanity in its fourth dimension looks something like this:

But we see only a projection, a slice of this dimension at each individual moment of time. Yes, yes, like broccoli in an MRI machine.

Until now, all theories have worked with a large number of spatial dimensions, and time has always been the only one. But why does space allow multiple dimensions for space, but only one time? Until scientists can answer this question, the hypothesis of two or more time spaces will seem very attractive to all philosophers and science fiction writers. Yes, and physicists, what is already there. For example, the American astrophysicist Itzhak Bars sees the root of all troubles with the Theory of Everything as the second time dimension, which has been overlooked. As a mental exercise, let's try to imagine a world with two times.

Each dimension exists separately. This is expressed in the fact that if we change the coordinates of an object in one dimension, the coordinates in others can remain unchanged. So, if you move along one time axis that intersects another at a right angle, then at the point of intersection, time around will stop. In practice, it will look something like this:

All Neo had to do was place his one-dimensional time axis perpendicular to the bullets' time axis. A real trifle, agree. In fact, everything is much more complicated.

The exact time in a universe with two time dimensions will be determined by two values. Is it hard to imagine a two-dimensional event? That is, one that is extended simultaneously along two time axes? It is likely that such a world would require time-mapping specialists, just as cartographers map the two-dimensional surface of the globe.

What else distinguishes a two-dimensional space from a one-dimensional one? The ability to bypass an obstacle, for example. This is completely beyond the boundaries of our mind. An inhabitant of a one-dimensional world cannot imagine how it is to turn a corner. And what is this - an angle in time? In addition, in two-dimensional space, you can travel forward, backward, or even diagonally. I have no idea how it is to go diagonally through time. I'm not talking about the fact that time underlies many physical laws, and it is impossible to imagine how the physics of the Universe will change with the advent of another time dimension. But it's so exciting to think about it!

Very large encyclopedia

Other dimensions have not yet been discovered, and exist only in mathematical models. But you can try to imagine them like this.

As we found out earlier, we see a three-dimensional projection of the fourth (temporal) dimension of the Universe. In other words, every moment of the existence of our world is a point (similar to the zero dimension) in the time interval from the Big Bang to the End of the World.

Those of you who have read about time travel know how important the curvature of the space-time continuum is. This is the fifth dimension - it is in it that the four-dimensional space-time "bends" in order to bring two points on this straight line closer together. Without this, the journey between these points would be too long, or even impossible. Roughly speaking, the fifth dimension is similar to the second - it moves the "one-dimensional" line of space-time to the "two-dimensional" plane with all the consequences in the form of the possibility to turn the corner.

A little earlier, our especially philosophically minded readers probably thought about the possibility of free will in conditions where the future already exists, but is not yet known. Science answers this question like this: probabilities. The future is not a stick, but a whole broom of possible scenarios. Which of them will come true - we'll find out when we get there.

Each of the probabilities exists as a "one-dimensional" segment on the "plane" of the fifth dimension. What is the fastest way to jump from one segment to another? That's right - bend this plane like a sheet of paper. Where to bend? And again, correctly - in the sixth dimension, which gives the whole complex structure "volume". And, thus, makes it, like three-dimensional space, "finished", a new point.

The seventh dimension is a new straight line, which consists of six-dimensional "points". What is any other point on this line? The whole infinite set of options for the development of events in another universe, formed not as a result of the Big Bang, but in other conditions, and acting according to other laws. That is, the seventh dimension is beads from parallel worlds. The eighth dimension collects these "straight lines" into one "plane". And the ninth can be compared to a book that contains all the "sheets" of the eighth dimension. It is the totality of all histories of all universes with all laws of physics and all initial conditions. Point again.

Here we hit the limit. To imagine the tenth dimension, we need a straight line. And what could be another point on this straight line, if the ninth dimension already covers everything that can be imagined, and even what cannot be imagined? It turns out that the ninth dimension is not another starting point, but the final one - for our imagination, in any case.

String theory claims that it is in the tenth dimension that strings, the basic particles that make up everything, make their vibrations. If the tenth dimension contains all universes and all possibilities, then strings exist everywhere and all the time. I mean, every string exists in our universe, and every other. At any point in time. Straightaway. Cool, yeah? published

Physicists are accustomed to working with particles: the theory has been worked out, experiments converge. Nuclear reactors and atomic bombs are calculated using particles. With one caveat - gravity is not taken into account in all calculations.

Gravity is the attraction of bodies. When we talk about gravity, we represent the earth's attraction. The phone falls from the hands onto the asphalt under the influence of gravity. In space, the Moon is attracted to the Earth, the Earth to the Sun. Everything in the world is attracted to each other, but to feel it, you need very heavy objects. We feel the attraction of the Earth, which is 7.5 × 10 22 times heavier than a person, and we do not notice the attraction of a skyscraper, which is 4 × 10 6 times heavier.

7.5×10 22 = 75,000,000,000,000,000,000,000

4×10 6 = 4,000,000

Gravity is described by Einstein's general theory of relativity. In theory, massive objects bend space. To understand, go to the children's park and put a heavy stone on the trampoline. A funnel will appear on the rubber of the trampoline. If you put a small ball on a trampoline, it will roll down the funnel to the stone. Something like this, the planets form a funnel in space, and we, like balls, fall on them.

Planets so massive they warp space

In order to describe everything at the level of elementary particles, gravity is not needed. Compared to other forces, gravity is so small that it was simply thrown out of quantum calculations. The force of the earth's gravity is less than the force that holds the particles of the atomic nucleus, 10 38 times. This is true for almost the entire universe.

10 38 = 100 000 000 000 000 000 000 000 000 000 000 000 000

The only place where gravity is as strong as other forces is inside a black hole. This is a giant funnel in which gravity collapses space itself and draws in everything that is nearby. Even light enters a black hole and never comes back.

To work with gravity as with other particles, physicists came up with a quantum of gravity - the graviton. We did some calculations, but they didn't match. Calculations showed that the energy of the graviton grows to infinity. And this should not be.

Physicists first invent, then search. The Higgs boson was invented 50 years before the discovery.

Problems with divergences in the calculations disappeared when the graviton was considered not as a particle, but as a string. Strings have a finite length and energy, so the energy of a graviton can only grow up to a certain limit. So scientists have a working tool with which they study black holes.

Advances in the study of black holes help to understand how the universe came into existence. According to the Big Bang theory, the world grew from a microscopic point. In the first moments of life, the universe was very dense - all modern stars and planets gathered in a small volume. Gravity was as strong as other forces, so knowing the effects of gravity is important to understanding the early universe.

Advances in the description of quantum gravity are a step towards the creation of a theory that will describe everything in the world. Such a theory will explain how the universe was born, what is happening in it now, and how its end will be.