Theory of strings and superstrings. What is string theory - briefly and clearly for dummies

Have you ever thought that the Universe is like a cello? That's right - she didn't come. Because the Universe is not like a cello. But that doesn't mean it doesn't have strings. Let's talk about String Theory today.

Of course, the strings of the universe are hardly similar to those we imagine. In string theory, they are incredibly small vibrating threads of energy. These threads are more like tiny “rubber bands” that can wriggle, stretch and compress in all sorts of ways. All this, however, does not mean that it is impossible to “play” the symphony of the Universe on them, because, according to string theorists, everything that exists consists of these “threads.”

Physics contradiction

In the second half of the 19th century, it seemed to physicists that nothing serious could be discovered in their science anymore. Classical physics believed that there were no serious problems left in it, and the entire structure of the world looked like a perfectly regulated and predictable machine. The trouble, as usual, happened because of nonsense - one of the small “clouds” that still remained in the clear, understandable sky of science. Namely, when calculating the radiation energy of an absolutely black body (a hypothetical body that, at any temperature, completely absorbs the radiation incident on it, regardless of the wavelength - NS).

Calculations showed that the total radiation energy of any absolutely black body should be infinitely large. To get away from such obvious absurdity, the German scientist Max Planck in 1900 proposed that visible light, X-rays and other electromagnetic waves can only be emitted by certain discrete portions of energy, which he called quanta. With their help, it was possible to solve the particular problem of an absolutely black body. However, the consequences of the quantum hypothesis for determinism were not yet realized. Until, in 1926, another German scientist, Werner Heisenberg, formulated the famous uncertainty principle.

Its essence boils down to the fact that, contrary to all previously dominant statements, nature limits our ability to predict the future on the basis of physical laws. We are, of course, talking about the future and present of subatomic particles. It turned out that they behave completely differently from how any things do in the macrocosm around us. At the subatomic level, the fabric of space becomes uneven and chaotic. The world of tiny particles is so turbulent and incomprehensible that it defies common sense. Space and time are so twisted and intertwined in it that there are no ordinary concepts of left and right, up and down, or even before and after.

There is no way to say for sure at what point in space a particular particle is currently located, and what is its angular momentum. There is only a certain probability of finding a particle in many regions of space-time. Particles at the subatomic level seem to be “smeared” throughout space. Not only that, but the “status” of the particles itself is not defined: in some cases they behave like waves, in others they exhibit the properties of particles. This is what physicists call the wave-particle duality of quantum mechanics.

Levels of the structure of the world: 1. Macroscopic level - matter 2. Molecular level 3. Atomic level - protons, neutrons and electrons 4. Subatomic level - electron 5. Subatomic level - quarks 6. String level

In the General Theory of Relativity, as if in a state with opposite laws, the situation is fundamentally different. Space appears to be like a trampoline - a smooth fabric that can be bent and stretched by objects with mass. They create warps in space-time—what we experience as gravity. Needless to say, the harmonious, correct and predictable General Theory of Relativity is in an insoluble conflict with the “eccentric hooligan” – quantum mechanics, and, as a result, the macroworld cannot “make peace” with the microworld. This is where string theory comes to the rescue.

2D Universe. Polyhedron graph E8 Theory of Everything

String theory embodies the dream of all physicists to unify the two fundamentally contradictory general relativity and quantum mechanics, a dream that haunted the greatest “gypsy and tramp” Albert Einstein until the end of his days.

Many scientists believe that everything from the exquisite dance of galaxies to the crazy dance of subatomic particles can ultimately be explained by just one fundamental physical principle. Maybe even a single law that unites all types of energy, particles and interactions in some elegant formula.

General relativity describes one of the most famous forces of the Universe - gravity. Quantum mechanics describes three other forces: the strong nuclear force, which glues protons and neutrons together in atoms, electromagnetism, and the weak force, which is involved in radioactive decay. Any event in the universe, from the ionization of an atom to the birth of a star, is described by the interactions of matter through these four forces.

With the help of the most complex mathematics, it was possible to show that electromagnetic and weak interactions have a common nature, combining them into a single electroweak interaction. Subsequently, strong nuclear interaction was added to them - but gravity does not join them in any way. String theory is one of the most serious candidates for connecting all four forces, and, therefore, embracing all phenomena in the Universe - it is not for nothing that it is also called the “Theory of Everything”.

In the beginning there was a myth

Until now, not all physicists are delighted with string theory. And at the dawn of its appearance, it seemed infinitely far from reality. Her very birth is a legend.

Graph of Euler's beta function with real arguments

In the late 1960s, a young Italian theoretical physicist, Gabriele Veneziano, was searching for equations that could explain the strong nuclear force—the extremely powerful “glue” that holds the nuclei of atoms together, binding protons and neutrons together. According to legend, one day he accidentally stumbled upon a dusty book on the history of mathematics, in which he found a two-hundred-year-old function first written down by the Swiss mathematician Leonhard Euler. Imagine Veneziano's surprise when he discovered that the Euler function, long considered nothing more than a mathematical curiosity, described this strong interaction.

What was it really like? The formula was probably the result of Veneziano's many years of work, and chance only helped take the first step towards the discovery of string theory. Euler's function, which miraculously explained the strong force, has found new life.

Eventually, it caught the eye of the young American theoretical physicist Leonard Susskind, who saw that, first of all, the formula described particles that had no internal structure and could vibrate. These particles behaved in such a way that they could not be just point particles. Susskind understood - the formula describes a thread that is like an elastic band. She could not only stretch and contract, but also oscillate and squirm. After describing his discovery, Susskind introduced the revolutionary idea of ​​strings.

Unfortunately, the overwhelming majority of his colleagues greeted the theory very coolly.

Standard model

At the time, conventional science represented particles as points rather than as strings. For years, physicists have studied the behavior of subatomic particles by colliding them at high speeds and studying the consequences of these collisions. It turned out that the Universe is much richer than one could imagine. It was a real “population explosion” of elementary particles. Physics graduate students ran through the corridors shouting that they had discovered a new particle - there weren’t even enough letters to designate them. But, alas, in the “maternity hospital” of new particles, scientists were never able to find the answer to the question - why are there so many of them and where do they come from?

This prompted physicists to make an unusual and startling prediction - they realized that the forces at work in nature could also be explained in terms of particles. That is, there are particles of matter, and there are particles that carry interactions. For example, a photon is a particle of light. The more of these carrier particles - the same photons that matter particles exchange - the brighter the light. Scientists predicted that this particular exchange of carrier particles is nothing more than what we perceive as force. This was confirmed by experiments. This is how physicists managed to get closer to Einstein’s dream of uniting forces.

Scientists believe that if we fast forward to just after the Big Bang, when the Universe was trillions of degrees hotter, the particles that carry electromagnetism and the weak force will become indistinguishable and combine into a single force called the electroweak force. And if we go back even further in time, the electroweak interaction would combine with the strong one into one total “superforce.”

Even though all this is still waiting to be proven, quantum mechanics suddenly explained how three of the four forces interact at the subatomic level. And she explained it beautifully and consistently. This coherent picture of interactions ultimately became known as the Standard Model. But, alas, this perfect theory had one big problem - it did not include the most famous macro-level force - gravity.

Interactions between different particles in the Standard Model
Graviton

For string theory, which had not yet had time to “bloom,” “autumn” has come; it contained too many problems from its very birth. For example, the theory's calculations predicted the existence of particles, which, as was soon established, do not exist. This is the so-called tachyon - a particle that moves in a vacuum faster than light. Among other things, it turned out that the theory requires as many as 10 dimensions. It's not surprising that this has been very confusing to physicists, since it's obviously bigger than what we see.

By 1973, only a few young physicists were still grappling with the mysteries of string theory. One of them was the American theoretical physicist John Schwartz. For four years, Schwartz tried to tame the unruly equations, but to no avail. Among other problems, one of these equations persisted in describing a mysterious particle that had no mass and had not been observed in nature.

The scientist had already decided to abandon his disastrous business, and then it dawned on him - maybe the equations of string theory also describe gravity? However, this implied a revision of the dimensions of the main “heroes” of the theory – strings. By assuming that strings are billions and billions of times smaller than an atom, the “stringers” turned the theory’s disadvantage into its advantage. The mysterious particle that John Schwartz had so persistently tried to get rid of now acted as a graviton - a particle that had long been sought and that would allow gravity to be transferred to the quantum level. This is how string theory completed the puzzle with gravity, which was missing in the Standard Model. But, alas, even to this discovery the scientific community did not react in any way. String theory remained on the brink of survival. But that didn't stop Schwartz. Only one scientist wanted to join his search, ready to risk his career for the sake of mysterious strings - Michael Green.

Subatomic nesting dolls

Despite everything, in the early 1980s, string theory still had insoluble contradictions, called anomalies in science. Schwartz and Green set about eliminating them. And their efforts were not in vain: scientists were able to eliminate some of the contradictions in the theory. Imagine the amazement of these two, already accustomed to the fact that their theory was ignored, when the reaction of the scientific community blew up the scientific world. In less than a year, the number of string theorists has jumped to hundreds of people. It was then that string theory was awarded the title of Theory of Everything. The new theory seemed capable of describing all the components of the universe. And these are the components.

Each atom, as we know, consists of even smaller particles - electrons, which swirl around a nucleus consisting of protons and neutrons. Protons and neutrons, in turn, consist of even smaller particles - quarks. But string theory says it doesn't end with quarks. Quarks are made of tiny, wriggling strands of energy that resemble strings. Each of these strings is unimaginably small.

So small that if an atom were enlarged to the size of the solar system, the string would be the size of a tree. Just as different vibrations of a cello string create what we hear, how different musical notes, different modes (modes) of vibration of a string give particles their unique properties - mass, charge, etc. Do you know how, relatively speaking, the protons at the tip of your nail differ from the as yet undiscovered graviton? Only by the collection of tiny strings that make them up, and the way those strings vibrate.

Of course, all this is more than surprising. Since the times of Ancient Greece, physicists have become accustomed to the fact that everything in this world consists of something like balls, tiny particles. And so, not having had time to get used to the illogical behavior of these balls, which follows from quantum mechanics, they are asked to completely abandon the paradigm and operate with some kind of spaghetti scraps...

Fifth Dimension

Although many scientists call string theory a triumph of mathematics, some problems still remain with it - most notably, the lack of any possibility of testing it experimentally in the near future. Not a single instrument in the world, neither existing nor capable of appearing in the future, is capable of “seeing” the strings. Therefore, some scientists, by the way, even ask the question: is string theory a theory of physics or philosophy?.. True, seeing strings “with your own eyes” is not at all necessary. Proving string theory requires, rather, something else—what sounds like science fiction—confirmation of the existence of extra dimensions of space.

What is it about? We are all accustomed to three dimensions of space and one – time. But string theory predicts the presence of other—extra—dimensions. But let's start in order.

In fact, the idea of ​​the existence of other dimensions arose almost a hundred years ago. It came to the mind of the then unknown German mathematician Theodor Kaluza in 1919. He suggested the possibility of another dimension in our Universe that we do not see. Albert Einstein learned about this idea, and at first he really liked it. Later, however, he doubted its correctness, and delayed the publication of Kaluza for two whole years. Ultimately, however, the article was published, and the additional dimension became a kind of hobby for the genius of physics.

As you know, Einstein showed that gravity is nothing more than a deformation of space-time dimensions. Kaluza suggested that electromagnetism could also be ripples. Why don't we see it? Kaluza found the answer to this question - the ripples of electromagnetism may exist in an additional, hidden dimension. But where is it?

The answer to this question was given by Swedish physicist Oskar Klein, who suggested that Kaluza's fifth dimension is folded billions of times stronger than the size of a single atom, which is why we cannot see it. The idea of ​​this tiny dimension that is all around us is at the heart of string theory.

One of the proposed forms of additional twisted dimensions. Inside each of these forms, a string vibrates and moves - the main component of the Universe. Each form is six-dimensional - according to the number of six additional dimensions

Ten dimensions

But in fact, the equations of string theory require not even one, but six additional dimensions (in total, with the four we know, there are exactly 10 of them). They all have a very twisted and curved complex shape. And everything is unimaginably small.

How can these tiny measurements influence our big world? According to string theory, it's decisive: for it, shape determines everything. When you press different keys on a saxophone, you get different sounds. This happens because when you press a particular key or combination of keys, you change the shape of the space in the musical instrument where the air circulates. Thanks to this, different sounds are born.

String theory suggests that additional curved and twisted dimensions of space manifest themselves in a similar way. The shapes of these extra dimensions are complex and varied, and each causes the string located within such dimensions to vibrate differently precisely because of their shapes. After all, if we assume, for example, that one string vibrates inside a jug, and the other inside a curved post horn, these will be completely different vibrations. However, if you believe string theory, in reality the forms of additional dimensions look much more complex than a jug.

How the world works

Science today knows a set of numbers that are the fundamental constants of the Universe. They are the ones who determine the properties and characteristics of everything around us. Among such constants are, for example, the charge of an electron, the gravitational constant, the speed of light in a vacuum... And if we change these numbers even by an insignificant number of times, the consequences will be catastrophic. Suppose we increased the strength of the electromagnetic interaction. What happened? We may suddenly find that the ions begin to repel each other more strongly, and nuclear fusion, which makes stars shine and emit heat, suddenly fails. All the stars will go out.

But what does string theory with its extra dimensions have to do with it? The fact is that, according to it, it is the additional dimensions that determine the exact value of the fundamental constants. Some forms of measurement cause one string to vibrate in a certain way, and produce what we see as a photon. In other forms, the strings vibrate differently and produce an electron. Truly, God is in the “little things” - it is these tiny forms that determine all the fundamental constants of this world.

Superstring theory

In the mid-1980s, string theory took on a grand and orderly appearance, but inside the monument there was confusion. In just a few years, as many as five versions of string theory have emerged. And although each of them is built on strings and extra dimensions (all five versions are combined into the general theory of superstrings - NS), these versions diverged significantly in details.

So, in some versions the strings had open ends, in others they resembled rings. And in some versions, the theory even required not 10, but as many as 26 dimensions. The paradox is that all five versions today can be called equally true. But which one really describes our Universe? This is another mystery of string theory. That is why many physicists again gave up on the “crazy” theory.

But the main problem of strings, as already mentioned, is the impossibility (at least for now) of proving their presence experimentally.

Some scientists, however, still say that the next generation of accelerators has a very minimal, but still opportunity to test the hypothesis of additional dimensions. Although the majority, of course, are sure that if this is possible, then, alas, it will not happen very soon - at least in decades, at maximum - even in a hundred years.

Various versions of string theory are now considered to be the leading contenders for the title of a comprehensive, universal theory that explains the nature of everything. And this is a kind of Holy Grail of theoretical physicists involved in the theory of elementary particles and cosmology. The universal theory (also the theory of everything that exists) contains only a few equations that combine the entire body of human knowledge about the nature of interactions and the properties of the fundamental elements of matter from which the Universe is built.

Today, string theory has been combined with the concept of supersymmetry, resulting in the birth of superstring theory, and today this is the maximum that has been achieved in terms of unifying the theory of all four basic interactions (forces acting in nature). The theory of supersymmetry itself is already built on the basis of an a priori modern concept, according to which any remote (field) interaction is due to the exchange of interaction carrier particles of the corresponding kind between interacting particles (see Standard Model). For clarity, interacting particles can be considered the “bricks” of the universe, and carrier particles can be considered cement.

String theory is a branch of mathematical physics that studies the dynamics not of point particles, like most branches of physics, but of one-dimensional extended objects, i.e. strings
Within the standard model, quarks act as building blocks, and gauge bosons, which these quarks exchange with each other, act as interaction carriers. The theory of supersymmetry goes even further and states that quarks and leptons themselves are not fundamental: they all consist of even heavier and not experimentally discovered structures (building blocks) of matter, held together by an even stronger “cement” of super-energy particles-carriers of interactions than quarks composed of hadrons and bosons.

Naturally, none of the predictions of the theory of supersymmetry have yet been tested in laboratory conditions, however, the hypothetical hidden components of the material world already have names - for example, the electron (the supersymmetric partner of the electron), squark, etc. The existence of these particles, however, is theorized kind is predicted unambiguously.

The picture of the Universe offered by these theories, however, is quite easy to visualize. On a scale of about 10E–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 used to even at the level of elementary particles. At such small distances (and at such high energies of interactions that it is unimaginable) matter turns into a series of field standing waves, similar to those 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 can be excited. Each harmonic has its own energy state. According to the principle of relativity (see 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 it is quite easy to visualize a standing wave in a guitar string, the standing waves proposed by superstring theory are difficult to visualize - the fact is that the vibrations of superstrings occur in a space that has 11 dimensions. We are accustomed to four-dimensional space, which contains three spatial and one temporal dimensions (left-right, up-down, forward-backward, past-future). In superstring space, things are much more complicated (see box). 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 of the theory of multidimensional membranes - essentially, these are the same strings, but flat. As one of its authors casually joked, membranes differ from strings in about the same way that noodles differ from vermicelli.

This, perhaps, is all that can be briefly told about one of the theories that, not without reason, today claim 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 strict mathematical form due to the insufficiency of the mathematical apparatus to bring it into strict internal correspondence. 20 years have passed since this theory was born, and no one has been able to consistently harmonize some of its aspects and versions with others. What’s even more unpleasant is that none of the theorists proposing string theory (and especially superstrings) have yet proposed a single experiment in 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 exercises in comprehending esoteric knowledge outside the mainstream of natural science.

Studying the properties of black holes

In 1996, string theorists Andrew Strominger and Kumrun Vafa built on earlier results by Susskind and Sen to publish “The Microscopic Nature of Bekenstein and Hawking Entropy.” In this work, Strominger and Vafa were able to use string theory to find the microscopic components of a certain class of black holes, and to accurately calculate the entropy contributions of these components. The work was based on a new method that went partly beyond the perturbation theory used in the 1980s and early 1990s. The result of the work exactly coincided with the predictions of Bekenstein and Hawking, made more than twenty years earlier.

Strominger and Vafa opposed the real processes of black hole formation with a constructive approach. They changed the view of black hole formation, showing that they can be constructed by painstakingly assembling into one mechanism the exact set of branes discovered during the second superstring revolution.

With all the controls on a black hole's microscopic structure in hand, Strominger and Vafa were able to calculate the number of permutations of a black hole's microscopic components that would leave the overall observable characteristics, such as mass and charge, unchanged. They then compared the resulting number with the area of ​​the black hole's event horizon - the entropy predicted by Bekenstein and Hawking - and found perfect agreement. At least for the class of extreme black holes, Strominger and Vafa were able to find an application of string theory to analyze microscopic components and accurately calculate the corresponding entropy. The problem that had confronted physicists for a quarter of a century had been solved.

For many theorists, this discovery was an important and convincing argument in support of string theory. The development of string theory is still too crude for direct and precise comparison with experimental results, for example, with measurements of the mass of a quark or electron. String theory, however, provides the first fundamental explanation for a long-discovered property of black holes, the impossibility of explaining which has stalled the research of physicists working with traditional theories for many years. Even Sheldon Glashow, a Nobel laureate in physics and a staunch opponent of string theory in the 1980s, admitted in an interview in 1997 that “when string theorists talk about black holes, they are talking almost about observable phenomena, and that’s impressive.” "

String cosmology

There are three main ways in which string theory modifies the standard cosmological model. First, in the spirit of modern research, which is increasingly clarifying the situation, it follows from string theory that the Universe must have a minimum acceptable size. This conclusion changes the understanding of the structure of the Universe immediately at the moment of the Big Bang, for which the standard model yields a zero size of the Universe. Secondly, the concept of T-duality, that is, the duality of small and large radii (in its close connection with the existence of a minimum size) in string theory, is also important in cosmology. Thirdly, the number of space-time dimensions in string theory is more than four, so cosmology must describe the evolution of all these dimensions.

Brandenberg and Vafa model

At the end of the 1980s. Robert Brandenberger and Kumrun Vafa have taken the first important steps toward understanding how string theory will change the implications of the standard model of cosmology. They came to two important conclusions. First, as we move back to the Big Bang, the temperature continues to rise until the size of the Universe in all directions becomes equal to the Planck length. At this point the temperature will reach its maximum and begin to decrease. On an intuitive level, it is not difficult to understand the reason for this phenomenon. Let us assume for simplicity (following Brandenberger and Vafa) that all spatial dimensions of the Universe are cyclic. As we move backwards in time, the radius of each circle shrinks and the temperature of the universe increases. From string theory, we know that contracting the radii first to and then below the Planck length is physically equivalent to reducing the radii to the Planck length, followed by their subsequent increase. Since the temperature falls during the expansion of the Universe, unsuccessful attempts to compress the Universe to sizes smaller than the Planck length will lead to a cessation of temperature growth and its further decrease.

As a result, Brandenberger and Vafa arrived at the following cosmological picture: first, all spatial dimensions in string theory are tightly folded to a minimum size on the order of the Planck length. Temperature and energy are high, but not infinite: the paradoxes of the zero-size starting point in string theory are resolved. At the initial moment of the existence of the Universe, all spatial dimensions of string theory are completely equal and completely symmetrical: they are all curled up into a multidimensional lump of Planck dimensions. Further, according to Brandenberger and Vafa, the Universe goes through the first stage of symmetry reduction, when at the Planck moment of time three spatial dimensions are selected for subsequent expansion, and the rest retain their original Planck size. These three dimensions are then identified with the dimensions in the inflationary cosmology scenario and, through the process of evolution, take the form now observed.

Veneziano and Gasperini model

Since the work of Brandenberger and Vafa, physicists have been making continuous progress towards understanding string cosmology. Among those leading this research are Gabriele Veneziano and his colleague Maurizio Gasperini from the University of Turin. These scientists presented their own version of string cosmology, which in some places is similar to the scenario described above, but in other places is fundamentally different from it. Like Brandenberger and Vafa, to rule out the infinite temperature and energy density that arise in the standard and inflationary models, they relied on the existence of a minimum length in string theory. However, instead of concluding that, due to this property, the Universe is born from a lump of Planck dimensions, Gasperini and Veneziano suggested that there was a prehistoric universe that arose long before the moment called the zero point, and which gave birth to this cosmic “embryo” of Planck dimensions.

The initial state of the Universe in this scenario and in the Big Bang model are very different. According to Gasperini and Veneziano, the Universe was not a hot and tightly twisted ball of dimensions, but was cold and had an infinite extent. Then, as follows from the equations of string theory, instability invaded the Universe, and all its points began, as in the era of inflation according to Guth, to rapidly scatter to the sides.

Gasperini and Veneziano showed that because of this, space became increasingly curved and as a result there was a sharp jump in temperature and energy density. A little time passed, and the three-dimensional region of millimeter dimensions inside these endless expanses was transformed into a hot and dense spot, identical to the spot that is formed during inflationary expansion according to Guth. Then everything went according to the standard scenario of Big Bang cosmology, and the expanding spot turned into the observable Universe.

Since the pre-Big Bang era was undergoing its own inflationary expansion, Guth's solution to the horizon paradox is automatically built into this cosmological scenario. As Veneziano put it (in a 1998 interview), “string theory hands us a version of inflationary cosmology on a silver platter.”

The study of string cosmology is quickly becoming an area of ​​active and productive research. For example, the scenario of evolution before the Big Bang has been the subject of heated debate more than once, and its place in the future cosmological formulation is far from obvious. However, there is no doubt that this cosmological formulation will be firmly based on physicists' understanding of the results discovered during the second superstring revolution. For example, the cosmological consequences of the existence of multidimensional membranes are still unclear. In other words, how will the idea of ​​the first moments of the existence of the Universe change as a result of the analysis of the completed M-theory? This issue is being intensively researched.

This is already the fourth topic. Volunteers are also asked not to forget what topics they expressed a desire to cover, or maybe someone has just now chosen a topic from the list. I am responsible for reposting and promoting on social networks. And now our topic: “string theory”

You've probably heard that the most popular scientific theory of our time, string theory, implies the existence of many more dimensions than common sense tells us.

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 claims to be the Theory of Everything.

But it turned out that the most convenient number of dimensions required 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 this is 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 not called theoretical for nothing. All her achievements exist so far only on paper. So, to explain why we can only move in three-dimensional space, scientists started talking about how the unfortunate remaining dimensions had to shrink into compact spheres at the quantum level. To be precise, not into spheres, but into Calabi-Yau spaces. These are three-dimensional figures, inside of which there is their own world with its own dimension. A two-dimensional projection of such a manifold looks something like this:

Yes, this seems a little far-fetched. But maybe this is precisely what explains why the quantum world is so different from the one we perceive.

Let's go back a little into history

In 1968, a young theoretical physicist, Gabriele Veneziano, was poring over the many experimentally observed characteristics of the strong nuclear force. Veneziano, who was then working at CERN, the European Accelerator Laboratory in Geneva, Switzerland, worked on this problem for several years until one day he had a brilliant insight. Much to his surprise, he realized that an exotic mathematical formula, invented about two hundred years earlier by the famous Swiss mathematician Leonhard Euler for purely mathematical purposes - the so-called Euler beta function - seemed capable of describing in one fell swoop all the numerous properties of the particles involved in strong nuclear interaction. The property noticed by Veneziano provided a powerful mathematical description of many features of the strong interaction; it sparked a flurry of work in which the beta function and its various generalizations were used to describe the vast amounts of data accumulated from the study of particle collisions around the world. However, in a sense, Veneziano's observation was incomplete. Like a rote formula used by a student who does not understand its meaning or meaning, Euler's beta function worked, but no one understood why. It was a formula that required explanation.

Gabriele Veneziano

This changed in 1970, when Yoichiro Nambu of the University of Chicago, Holger Nielsen of the Niels Bohr Institute, and Leonard Susskind of Stanford University were able to discover the physical meaning behind Euler's formula. These physicists showed that when elementary particles are represented by small, vibrating one-dimensional strings, the strong interaction of these particles is exactly described by the Euler function. If the string segments were small enough, these researchers reasoned, they would still appear like point particles, and therefore would not contradict experimental observations. Although this theory was simple and intuitively attractive, the string description of the strong force was soon shown to be flawed. In the early 1970s. High-energy physicists have been able to peer deeper into the subatomic world and have shown that a number of string-based model predictions are in direct conflict with observational results. At the same time, there was a parallel development of quantum field theory—quantum chromodynamics—which used a point model of particles. The success of this theory in describing the strong interaction led to the abandonment of string theory.
Most particle physicists believed that string theory had been consigned to the trash bin forever, but a number of researchers remained faithful to it. Schwartz, for example, felt that “the mathematical structure of string theory is so beautiful and has so many amazing properties that it must surely point to something deeper” 2 ). One of the problems physicists had with string theory was that it seemed to provide too much choice, which was confusing. Some configurations of vibrating strings in this theory had properties that resembled the properties of gluons, which gave reason to truly consider it a theory of the strong interaction. However, in addition to this, it contained additional interaction carrier particles that had nothing to do with the experimental manifestations of the strong interaction. In 1974, Schwartz and Joel Scherk of France's École Technique Supérieure made a bold proposal that turned this apparent disadvantage into an advantage. After studying the strange vibration modes of the strings, reminiscent of carrier particles, they realized that these properties coincide surprisingly closely with the supposed properties of the hypothetical particle carrier of gravitational interaction - the graviton. Although these "minuscule particles" of gravitational interaction have yet to be detected, theorists can confidently predict some of the fundamental properties that these particles should have. Sherk and Schwartz found that these characteristics are exactly realized for some vibration modes. Based on this, they suggested that the first advent of string theory failed because physicists overly narrowed its scope. Sherk and Schwartz announced that string theory is not just a theory of the strong force, it is a quantum theory, which, among other things, includes gravity).

The physics community reacted to this suggestion with great reserve. In fact, according to Schwartz's memoirs, “our work was ignored by everyone” 4). The paths of progress were already thoroughly cluttered with numerous failed attempts to combine gravity and quantum mechanics. String theory had failed in its initial attempt to describe the strong force, and it seemed pointless to many to try to use it to achieve even greater goals. Subsequent, more detailed studies in the late 1970s and early 1980s. showed that string theory and quantum mechanics have their own, albeit smaller, contradictions. It seemed that the gravitational force was again able to resist the attempt to integrate it into a description of the universe at the microscopic level.
That was until 1984. In a landmark paper that summarized more than a decade of intensive research that had been largely ignored or rejected by most physicists, Green and Schwartz established that the minor inconsistency with quantum theory that plagued string theory could be allowed. Moreover, they showed that the resulting theory was broad enough to cover all four types of forces and all types of matter. Word of this result spread throughout the physics community, with hundreds of particle physicists stopping work on their projects to take part in an assault that seemed to be the final theoretical battle in a centuries-long assault on the deepest foundations of the universe.
Word of Green and Schwartz's success eventually reached even the first-year graduate students, and the previous gloom was replaced by an exciting sense of participation in a turning point in the history of physics. Many of us stayed up late into the night, poring over the hefty tomes of theoretical physics and abstract mathematics that are essential to understanding string theory.

If you believe scientists, then we ourselves and everything around us consists of an infinite number of such mysterious folded micro-objects.
Period from 1984 to 1986 now known as "the first revolution in superstring theory". During this period, more than a thousand papers on string theory were written by physicists around the world. These works conclusively demonstrated that the many properties of the standard model, discovered through decades of painstaking research, flow naturally from the magnificent system of string theory. As Michael Green noted, “The moment you are introduced to string theory and realize that almost all the major advances in physics of the last century have flowed—and flowed with such elegance—from such a simple starting point, clearly demonstrates the incredible power of this theory.”5 Moreover, for many of these properties, as we will see below, string theory provides a much more complete and satisfactory description than the standard model. These achievements convinced many physicists that string theory could deliver on its promises and become the ultimate unifying theory.

Two-dimensional projection of a three-dimensional Calabi-Yau manifold. This projection gives an idea of ​​how complex the extra dimensions are.

However, along this path, physicists working on string theory again and again ran into serious obstacles. In theoretical physics, we often have to deal with equations that are either too complex to understand or difficult to solve. Usually in such a situation, physicists do not give up and try to obtain an approximate solution to these equations. The situation in string theory is much more complicated. Even the derivation of the equations itself turned out to be so complex that so far only an approximate form of them has been obtained. Thus, physicists working in string theory find themselves in a situation where they have to look for approximate solutions to approximate equations. After several years of amazing progress made during the first superstring revolution, physicists were faced with the fact that the approximate equations used were unable to correctly answer a number of important questions, thereby hindering further development of research. Without concrete ideas for moving beyond these approximate methods, many physicists working in the field of string theory experienced a growing sense of frustration and returned to their previous research. For those who remained, the late 1980s and early 1990s. were a testing period.

The beauty and potential power of string theory beckoned to researchers like a golden treasure locked securely in a safe, visible only through a tiny peephole, but no one had the key that would unleash these dormant forces. The long period of “dryness” was interrupted from time to time by important discoveries, but it was clear to everyone that new methods were required that would go beyond the already known approximate solutions.

The stalemate ended with a breathtaking talk given by Edward Witten in 1995 at a string theory conference at the University of Southern California—a talk that stunned a room filled to capacity with the world's leading physicists. In it, he unveiled a plan for the next stage of research, thereby ushering in the “second revolution in superstring theory.” String theorists are now working energetically on new methods that promise to overcome the obstacles they encounter.

For the widespread popularization of TS, humanity should erect a monument to Columbia University professor Brian Greene. His 1999 book “The Elegant Universe. Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory” became a bestseller and won a Pulitzer Prize. The scientist’s work formed the basis of a popular science mini-series with the author himself as the host - a fragment of it can be seen at the end of the material (photo Amy Sussman/Columbia University).

clickable 1700 px

Now let's try to understand the essence of this theory at least a little.

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

Let's put a dot next to the segment. To fit both of these objects, we will need a two-dimensional space with 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, residents 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, these two men:

Each of them will see their comrade like this:

And in this situation:

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.

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

But for an 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 disappearing unpredictably. Attempts to calculate the length and place of origin of such objects using the laws of physics of two-dimensional space are doomed to failure.

We, inhabitants of the three-dimensional world, see everything as two-dimensional. Only moving 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 amazing ways depending on our relationship with it or time.

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

They usually depict how gravity bends space-time. It bends... 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, and behind an obstacle through which in our realities it could not penetrate without making a hole in it? What about black holes? 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 used to perceiving it?

The clock is ticking

Time adds another coordinate to our Universe. In order for a 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 movement is carried out only in one direction - from the past to the future. Moreover, only the present is real. Neither the past nor the future exists, just as breakfasts and dinners do not exist from the point of view of an office clerk during his lunch break.

But the theory of relativity does not agree with this. From her point of view, time is a full-fledged dimension. All events that have existed, exist and will exist are equally real, just like the sea beach is real, regardless of where exactly the dreams of the sound of the surf took us by surprise. Our perception is just something like a spotlight that illuminates a certain segment on a straight line of time. Humanity in its fourth dimension looks something like this:

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

Until now, all theories worked with a large number of spatial dimensions, and the temporal one was always 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. And physicists, too, so what? For example, American astrophysicist Itzhak Bars sees the root of all troubles with the Theory of Everything as the overlooked second time dimension. 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 may remain unchanged. So, if you move along one time axis that intersects another at a right angle, then at the intersection point the 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 mere trifle, you will agree. In reality, everything is much more complicated.

Exact time in a universe with two time dimensions will be determined by two values. Is it difficult 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 specialists in mapping time, just as cartographers map the two-dimensional surface of the globe.

What else distinguishes two-dimensional space from one-dimensional space? The ability to bypass an obstacle, for example. This is completely beyond the boundaries of our minds. A resident of a one-dimensional world cannot imagine what it is like 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 what it's like to pass through time diagonally. Not to mention 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 (time) 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 period of time from the Big Bang to the End of the World.

Those of you who have read about time travel know what an important role the curvature of the space-time continuum plays in it. This is the fifth dimension - it is in it that four-dimensional space-time “bends” in order to bring two points on this line closer together. Without this, travel 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 into a “two-dimensional” plane with all that it implies in the form of the ability to turn a corner.

A little earlier, our particularly 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 this way: probabilities. The future is not a stick, but a whole broom of possible scenarios. We will find out which one will come true when we get there.

Each of the probabilities exists in the form of 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 should I bend it? And again correctly - in the sixth dimension, which gives this entire 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 under other conditions, and operating 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. This is the totality of all the histories of all universes with all the laws of physics and all the initial conditions. Period again.

Here we hit the limit. To imagine the tenth dimension, we need a straight line. And what other point could there be on this line if the ninth dimension already covers everything that can be imagined, and even that which is impossible to imagine? It turns out that the ninth dimension is not just another starting point, but the final one - for our imagination, at least.

String theory states that it is in the tenth dimension that strings vibrate—the basic particles that make up everything. If the tenth dimension contains all universes and all possibilities, then strings exist everywhere and all the time. I mean, every string exists both in our universe and in any other. At any time. Straightaway. Cool, huh?

Physicist, string theory specialist. He is known for his work on mirror symmetry, related to the topology of the corresponding Calabi-Yau manifolds. Known to a wide audience as the author of popular science books. His Elegant Universe was nominated for a Pulitzer Prize.

In September 2013, Brian Greene came to Moscow at the invitation of the Polytechnic Museum. A famous physicist, string theorist, and professor at Columbia University, he is known to the general public primarily as a popularizer of science and the author of the book “The Elegant Universe.” Lenta.ru spoke with Brian Greene about string theory and the recent difficulties that the theory has faced, as well as quantum gravity, the amplituhedron and social control.

Literature in Russian: Kaku M., Thompson J.T. “Beyond Einstein: Superstrings and the quest for the final theory” and what it was The original article is on the website InfoGlaz.rf Link to the article from which this copy was made -

At school we learned that matter is made up of atoms, and atoms are made up of nuclei around which electrons revolve. The planets revolve around the sun in much the same way, 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. At the particle scale, different laws apply, and it is not always possible to find an analogy from life. Physics has become abstract and confusing.

But the next step of theoretical physics returned a sense of reality. String theory described the world in terms that are again imaginable and therefore easier to understand and remember.

The topic is still not easy, so let's go in order. First, let's figure out what the theory is, then let's try to understand why it was invented. And for dessert, a little history; string theory has a short history, but with two revolutions.

The universe is made up of vibrating threads of energy

Before string theory, elementary particles were considered points - dimensionless shapes with certain properties. String theory describes them as threads of energy that do have one dimension - length. These one-dimensional threads are called quantum strings.

Theoretical physics

Theoretical physics
describes the world using 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 "Elegant Universe"

Quantum strings are very small, their length is about 10 -33 cm. This is a hundred million billion times smaller than the protons that collide at the Large Hadron Collider. Such experiments with strings would require building 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, while the closed ends close on each other, forming loops. Strings are constantly “opening” and “closing”, connecting with other strings and breaking up into smaller ones.

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

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

We are made of quantum strings

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

The universe is usually depicted as space and stars, but it is also our planet, and you and me, and the text on the screen, and berries in the forest.

Diagram 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 more mosquitoes. They are also made of strings.

And space is out there somewhere. Let's go back to space

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

Quantum strings move through space. And space on the scale of strings is the most interesting part of the theory.

Quantum strings move in 11 dimensions

Theodore 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 movement of planets, and the formation of black holes. In addition, they inspired their contemporaries to make 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 Einsteinian gravity bends the four dimensions of spacetime, what do electromagnetic forces bend? Faith in Einstein was strong, and Kaluza had no doubt that his equations would describe electromagnetism. Instead, he proposed that electromagnetic forces were bending an additional, fifth dimension. Einstein liked the idea, but the theory was not tested by experiments and was forgotten until the 1960s.

Albert Einstein (1879-1955)

Theodore Kaluza
(1885-1954)

Theodore Kaluza
(1885-1954)

Albert Einstein
(1879-1955)

The first string theory equations produced strange results. Tachyons appeared in them - particles with negative mass that moved faster than the speed of light. This is where Kaluza’s idea of ​​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 had enough of ten, but 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.

The 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. By adding a third dimension, the world becomes three-dimensional and we can bypass the obstacle. Perhaps, using the same principle, it is correct to add the remaining seven dimensions - and then using them you can go around space-time and get to any point in any universe at any time.

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

A line has only one dimension - length

A balloon is three-dimensional and has a third dimension—height. But to a two-dimensional man it looks like a line

Just as a two-dimensional man cannot imagine multidimensionality, so we cannot imagine 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 an eleven-dimensional universe onto the visible scales of space-time, and we cannot follow the strings.

Someday we will see the Big Bang

Someday we will calculate the frequency of string vibrations and the organization of additional 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 for now this is impossible - there are no hints on what to rely on in the calculations, and you can only find the necessary numbers by brute force. Mathematicians have calculated that there will be 10,500 options to sort through. The theory has reached a dead end.

Yet string theory is still capable of explaining the nature of the universe. To do this, it must connect 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 that a little more and we would understand everything. However, the main problem has not yet been solved: the theories work great individually, but do not provide an overall picture.

There are two main theories: relativity theory 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

There are enough options for organizing Calabi-Yau spaces 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 gravitational interaction of the Earth and the Moon in 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 added 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 theory's predictions 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 electron. Bosons are the forces that are responsible for the interaction of fermions, such as the photon and the 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. They haven’t found it yet, but they described its properties and came up with a name - graviton.

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

Therefore, scientists are looking for an alternative theory that can combine all theories into one. This theory was called the unified field theory, or theory of everything.

Fermions
form all types of matter except dark matter

Bosons
transfer energy between fermions

String theory could 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 that the distance between them is greater than zero, and impossible calculation results for the graviton are avoided. And the graviton itself fits well into the concept of strings.

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

String theory has gone through 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, young theoretical physicist Gabriele Veneziano studied the strong interactions inside the atomic nucleus. Unexpectedly, he discovered that they were described well by Euler’s beta function, a set of equations that the Swiss mathematician Leonhard Euler had compiled 200 years earlier. This was strange: in those days the atom was considered indivisible, and Euler’s work solved exclusively 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, Yoichiro 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 ideally by the Euler equations. The first version of string theory was called bosonic, since it described the string nature of bosons responsible for the interactions of matter, and did not concern the fermions that matter consists of.

The theory was crude. It involved tachyons, and the main predictions contradicted the experimental results. And although it was possible to get rid of tachyons using Kaluza multidimensionality, 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 theory still has loyal supporters. In 1971, Pierre Ramon added fermions to string theory, reducing the number of dimensions from 26 to ten. This marked the beginning 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 asymmetrical, 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 be converted 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 the properties of the supposed carrier of gravity, the graviton, remarkably closely. 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.”

The 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 related the theory to all types of matter and energy. The scientific world was gripped by fever - physicists abandoned their research and switched to studying 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 had been pieced together over the years, follow naturally from string physics. The 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 the major advances in physics of the last century have flowed—and flowed with such elegance—from such a simple starting point clearly demonstrates the incredible power of this theory.”

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

Mathematical methods had their limits. Physicists are accustomed to complex equations that do not give accurate results, but for string theory it was not possible to write even accurate equations. And approximate results of approximate equations did not provide answers. It became clear that new mathematics was needed to study the theory, but no one knew what kind of mathematics it would be. The ardor of scientists has subsided.

Second superstring revolution thundered in 1995. The stalemate was brought to an end by Edward Witten's talk at the String Theory Conference in Southern California. Witten showed that all five theories are special cases of one, more general theory of superstrings, in which there are not ten dimensions, but eleven. Witten called the unifying theory M-theory, or the 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 encouraged scientists, and scientific journals again filled with publications on string physics.

space-time measurements in modern superstring theory

“String theory is a part of twenty-first century physics that accidentally ended up in the twentieth century. It may take decades, or even centuries, before it is fully developed and understood."

The echoes of this revolution can still be heard today. But despite all the efforts of scientists, string theory has more questions than answers. Modern science is trying to build models of a multidimensional universe and studies dimensions as membranes of space. They're called branes—remember the void with open strings stretched across them? 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 has not yet been proven, but it has not been disproved either.

The main problem with 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 supporters of string physics. But there are no denials either. Therefore, the elegant mathematics of string theory continues to excite the minds of scientists, promising solutions to all the mysteries of the universe.

When talking about string theory, one cannot fail to mention Brian Greene, a professor at Columbia University and a tireless popularizer of the theory. Green gives lectures and appears on television. In 2000, his book “Elegant Universe. Superstrings, Hidden Dimensions, and the Search for the Ultimate Theory" was 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 don’t want to become an expert in string theory, but want to understand what kind of world you live in, remember this cheat sheet:

1. The universe is made up of threads of energy—quantum strings—that vibrate like the strings of a musical instrument. Different vibration frequencies turn strings into different particles.
2. The ends of the strings can be free, or they can close on each other, forming loops. The strings are constantly closing, opening and exchanging energy with other strings.
3. Quantum strings exist in the 11-dimensional universe. The extra 7 dimensions are folded into elusively small forms of space-time, so we don't see them. This is called dimension compactification.
4. If we knew exactly how the dimensions in our universe are folded, we might be able to travel through time and to other stars. But this is not possible yet - there are too many options to go through. There would be enough of them for all possible universes.
5. String theory can unite all physical theories and reveal to us the secrets of the universe - there are all the prerequisites for this. But there is no evidence yet.
6. Other discoveries of modern science logically follow from string theory. Unfortunately, this doesn't prove anything.
7. String theory has survived two superstring revolutions and many years of oblivion. Some scientists consider it science fiction, others believe that new technologies will help prove it.
8. The most important thing: 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 Greene at the Polytechnic:

Superstring theory, in popular parlance, envisions the universe as a collection of vibrating strands of energy—strings. They are the basis of nature. The hypothesis also describes other elements - branes. All matter in our world consists of vibrations of strings and branes. A natural consequence of the theory is the description of gravity. That's why scientists believe it holds the key to unifying gravity with other forces.

The concept is evolving

The unified field theory, the theory of superstrings, is purely mathematical. Like all physics concepts, it is based on equations that can be interpreted in certain ways.

Today no one knows exactly what the final version of this theory will be. Scientists have a rather vague idea of ​​​​its general elements, but no one has yet come up with a final equation that would cover all superstring theories, and it has not yet been possible to confirm it experimentally (although it has also been disproved). Physicists have created simplified versions of the equation, but so far it does not fully describe our universe.

Superstring theory for beginners

The hypothesis is based on five key ideas.

1. Superstring theory predicts that all objects in our world are composed of vibrating threads and membranes of energy.
2. It tries to combine general relativity (gravity) with quantum physics.
3. Superstring theory will allow us to unify all the fundamental forces of the universe.
4. This hypothesis predicts a new connection, supersymmetry, between two fundamentally different types of particles, bosons and fermions.
5. The concept describes a number of additional, usually unobservable dimensions of the Universe.

Strings and Branes

When the theory emerged in the 1970s, the threads of energy in it were considered 1-dimensional objects - strings. The word "one-dimensional" means that the string has only 1 dimension, length, unlike, for example, a square, which has length and height.

The theory divides these superstrings into two types - closed and open. An open string has ends that do not touch each other, while a closed string is a loop with no open ends. As a result, it was found that these strings, called type 1 strings, are subject to 5 main types of interactions.

The interactions are based on the ability of the string to connect and separate its ends. Since the ends of open strings can combine to form closed strings, it is impossible to construct a superstring theory that does not include looped strings.

This turned out to be important because closed strings have properties physicists believe that could describe gravity. In other words, scientists realized that instead of explaining particles of matter, superstring theory could describe their behavior and gravity.

Over the years, it was discovered that, in addition to strings, the theory also needed other elements. They can be thought of as sheets, or branes. Strings can be attached to one or both sides.

Quantum gravity

Modern physics has two basic scientific laws: general relativity (GTR) and quantum. They represent completely different fields of science. Quantum physics studies the smallest natural particles, and general relativity, as a rule, describes nature on the scale of planets, galaxies and the universe as a whole. Hypotheses that attempt to unify them are called theories of quantum gravity. The most promising of them today is the string instrument.

The closed threads correspond to the behavior of gravity. In particular, they have the properties of a graviton, a particle that transfers gravity between objects.

Joining forces

String theory attempts to combine the four forces - electromagnetic force, strong and weak nuclear forces, and gravity - into one. In our world they manifest themselves as four different phenomena, but string theorists believe that in the early Universe, when there were incredibly high energy levels, all these forces are described by strings interacting with each other.

Supersymmetry

All particles in the universe can be divided into two types: bosons and fermions. String theory predicts that there is a relationship between them called supersymmetry. Under supersymmetry, for every boson there must be a fermion and for every fermion a boson. Unfortunately, the existence of such particles has not been experimentally confirmed.

Supersymmetry is a mathematical relationship between elements of physical equations. It was discovered in another branch of physics, and its application led to its renaming as supersymmetric string theory (or superstring theory, in popular parlance) in the mid-1970s.

One of the benefits of supersymmetry is that it greatly simplifies equations by eliminating some variables. Without supersymmetry, equations lead to physical contradictions such as infinite values ​​and imaginary

Since scientists have not observed the particles predicted by supersymmetry, it is still a hypothesis. Many physicists believe that the reason for this is the need for a significant amount of energy, which is related to mass by the famous Einstein equation E = mc 2. These particles may have existed in the early universe, but as it cooled and energy spread out after the Big Bang, these particles moved to lower energy levels.

In other words, the strings, which were vibrating as high-energy particles, lost energy, turning them into lower-vibrating elements.

Scientists hope that astronomical observations or particle accelerator experiments will confirm the theory by identifying some of the higher-energy supersymmetric elements.

Additional dimensions

Another mathematical implication of string theory is that it makes sense in a world with more than three dimensions. There are currently two explanations for this:

1. The extra dimensions (six of them) have collapsed, or, in the terminology of string theory, compacted into incredibly small sizes that will never be perceived.
2. We are stuck in a 3-dimensional brane, and other dimensions extend beyond it and are inaccessible to us.

An important area of ​​research among theorists is mathematical modeling of how these extra coordinates might relate to ours. The latest results predict that scientists will soon be able to detect these extra dimensions (if they exist) in upcoming experiments, as they may be larger than previously expected.

Understanding the goal

The goal that scientists strive for when studying superstrings is a “theory of everything,” i.e., a unified physical hypothesis that describes all physical reality at a fundamental level. If successful, it could clarify many questions about the structure of our universe.

Explaining Matter and Mass

One of the main tasks of modern research is to find solutions for real particles.

String theory began as a concept describing particles such as hadrons by various higher vibrational states of a string. In most modern formulations, the matter observed in our universe is the result of the lowest energy vibrations of strings and branes. Higher vibrations generate high-energy particles that currently do not exist in our world.

The mass of these is a manifestation of how strings and branes are wrapped up in compactified extra dimensions. For example, in the simplified case of being folded into a donut shape, called a torus by mathematicians and physicists, the string can wrap around this shape in two ways:

• short loop through the middle of the torus;
• a long loop around the entire outer circumference of the torus.

A short loop will be a light particle, and a long loop will be a heavy one. When strings are wrapped around torus-shaped compactified dimensions, new elements with different masses are formed.

Superstring theory briefly and clearly, simply and elegantly explains the transition of length to mass. The folded dimensions here are much more complex than a torus, but in principle they work the same way.

It is even possible, although it is difficult to imagine, that the string wraps around the torus in two directions at the same time, resulting in a different particle with a different mass. Branes can also wrap around extra dimensions, creating even more possibilities.

Definition of space and time

In many versions of superstring theory, measurements collapse, making them unobservable at the current level of technology.

It is currently unclear whether string theory can explain the fundamental nature of space and time any further than Einstein did. In it, measurements are a background for the interaction of strings and have no independent real meaning.

Explanations were proposed, not fully developed, concerning the representation of space-time as a derivative of the total sum of all string interactions.

This approach does not correspond to the ideas of some physicists, which led to criticism of the hypothesis. Competitive theory uses the quantization of space and time as its starting point. Some believe that in the end it will turn out to be just a different approach to the same basic hypothesis.

Gravity quantization

The main achievement of this hypothesis, if confirmed, will be the quantum theory of gravity. The current description in General Relativity does not agree with quantum physics. The latter, by imposing restrictions on the behavior of small particles, leads to contradictions when trying to explore the Universe on extremely small scales.

Unification of forces

Currently, physicists know four fundamental forces: gravity, electromagnetic, weak and strong nuclear interactions. From string theory it follows that they were all once manifestations of one.

According to this hypothesis, as the early universe cooled after the big bang, this single interaction began to break up into different ones that operate today.

High-energy experiments will someday allow us to discover the unification of these forces, although such experiments are far beyond the current development of technology.

Five options

Since the superstring revolution of 1984, development has proceeded at a feverish pace. As a result, instead of one concept, there were five, called type I, IIA, IIB, HO, HE, each of which almost completely described our world, but not completely.

Physicists, going through versions of string theory in the hope of finding a universal true formula, have created 5 different self-sufficient versions. Some of their properties reflected the physical reality of the world, others did not correspond to reality.

M-theory

At a conference in 1995, physicist Edward Witten proposed a bold solution to the five-hypothesis problem. Based on the newly discovered duality, they all became special cases of a single overarching concept, called M-theory of superstrings by Witten. One of its key concepts was branes (short for membrane), fundamental objects with more than 1 dimension. Although the author did not propose a complete version, which still does not exist, M-theory of superstrings briefly consists of the following features:

• 11-dimensionality (10 spatial plus 1 time dimension);
• dualities that lead to five theories explaining the same physical reality;
• Branes are strings with more than 1 dimension.

Consequences

As a result, instead of one, 10,500 solutions emerged. For some physicists, this caused a crisis, while others accepted the anthropic principle, which explains the properties of the universe by our presence in it. It remains to be seen that theorists will find another way to navigate superstring theory.

Some interpretations suggest that our world is not the only one. The most radical versions allow for the existence of an infinite number of universes, some of which contain exact copies of ours.

Einstein's theory predicts the existence of a collapsed space called a wormhole or Einstein-Rosen bridge. In this case, two distant areas are connected by a short passage. Superstring theory allows not only this, but also the connection of distant points of parallel worlds. It is even possible to transition between universes with different laws of physics. However, it is likely that the quantum theory of gravity will make their existence impossible.

Many physicists believe that the holographic principle, when all the information contained in a volume of space corresponds to the information recorded on its surface, will allow a deeper understanding of the concept of energy threads.

Some believe that superstring theory allows for multiple dimensions of time, which could lead to travel across them.

In addition, the hypothesis offers an alternative to the big bang model, in which our universe was created by the collision of two branes and goes through repeated cycles of creation and destruction.

The ultimate fate of the universe has always occupied physicists, and the final version of string theory will help determine the density of matter and the cosmological constant. Knowing these values, cosmologists will be able to determine whether the universe will shrink until it explodes, so that it all starts again.

No one knows what it might lead to until it is developed and tested. Einstein, having written the equation E=mc 2, did not assume that it would lead to the emergence of nuclear weapons. The creators of quantum physics did not know that it would become the basis for the creation of lasers and transistors. And although it is not yet known what such a purely theoretical concept will lead to, history indicates that something outstanding will certainly result.

You can read more about this hypothesis in Andrew Zimmerman's book, Superstring Theory for Dummies.