Large string theory. Quantum string theory

Science is an immense field and a huge amount of research and discoveries is carried out every day, and it is worth noting that some theories seem to be interesting, but at the same time they do not have real confirmation and seem to “hang in the air.”

What is string theory?

The physical theory that represents particles in the form of vibration is called string theory. These waves have only one parameter - longitude, and no height or width. In figuring out what string theory is, we need to look at the main hypotheses it describes.

It is assumed that everything around us is made up of filaments that vibrate and membranes of energy.
Tries to combine general relativity and quantum physics.
String theory offers a chance to unify all the fundamental forces of the Universe.
Predicts symmetric coupling between different types of particles: bosons and fermions.
Provides a chance to describe and imagine dimensions of the Universe that have not previously been observed.

String theory - who discovered it?

Quantum string theory was first created in 1960 to explain phenomena in hadronic physics. At this time it was developed by: G. Veneziano, L. Susskind, T. Goto and others.
The scientist D. Schwartz, J. Scherk and T. Enet told what string theory is, since they were developing the bosonic string hypothesis, and this happened 10 years later.
In 1980, two scientists: M. Green and D. Schwartz identified the theory of superstrings, which had unique symmetries.
Research on the proposed hypothesis is still ongoing, but it has not yet been proven.

String theory - philosophy

There is a philosophical direction that has a connection with string theory, and it is called the monad. It involves the use of symbols in order to compact any amount of information. The monad and string theory make use of opposites and dualities in philosophy. The most popular simple monad symbol is Yin-Yang. Experts have proposed depicting string theory on a volumetric, and not on a flat, monad, and then strings will be a reality, although their length will be miniscule.

If a volumetric monad is used, then the line dividing Yin-Yang will be a plane, and when using a multidimensional monad, a volume curled into a spiral is obtained. There is no work yet on philosophy relating to multidimensional monads - this is an area for future study. Philosophers believe that cognition is an endless process and when trying to create a unified model of the universe, a person will be surprised more than once and change his basic concepts.

Disadvantages of String Theory

Since the hypothesis proposed by a number of scientists is unconfirmed, it is quite understandable that there are a number of problems indicating the need for its refinement.

The string theory has errors, for example, during calculations a new type of particle was discovered - tachyons, but they cannot exist in nature, since the square of their mass is less than zero, and the speed of movement is greater than the speed of light.
String theory can only exist in ten-dimensional space, but then the relevant question is: why doesn’t a person perceive other dimensions?

String theory - proof

The two main physical conventions on which scientific evidence is based are actually opposed to each other, since they represent the structure of the universe at the micro level differently. To try them on, the theory of cosmic strings was proposed. In many respects, it looks reliable, not only in words, but also in mathematical calculations, but today a person does not have the opportunity to practically prove it. If strings exist, they are at the microscopic level, and there is no technical capability yet to recognize them.

String theory and God

The famous theoretical physicist M. Kaku proposed a theory in which he uses the string hypothesis to prove the existence of God. He came to the conclusion that everything in the world operates according to certain laws and rules established by a single Mind. According to Kaku, string theory and the hidden dimensions of the Universe will help create an equation that unifies all the forces of nature and allows us to understand the mind of God. He focuses his hypothesis on tachyon particles, which move faster than light. Einstein also said that if such parts were discovered, it would be possible to move time back.

After conducting a series of experiments, Kaku concluded that human life is governed by stable laws and does not react to cosmic accidents. The string theory of life exists and it is associated with an unknown force that controls life and makes it whole. In his opinion, this is what it is. Kaku is sure that the Universe is vibrating strings that emanate from the mind of the Almighty.

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 the way 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 / ©Bruno P. Ramos

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 / ©John Stembridge/Atlas of Lie Groups Project

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

Graph of Euler's beta function with real arguments / ©Flickr

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.

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.

Interactions between different particles in the Standard Model / ©Wikimedia Commons

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.

©Wikimedia Commons

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 no surprise 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.

American theoretical physicist John Schwartz and Michael Green

©California Institute of Technology/elementy.ru

What reasons are there to think that gravity obeys the laws of quantum mechanics? For the discovery of these “foundations” the Nobel Prize in Physics was awarded in 2011. It consisted in the fact that the expansion of the Universe is not slowing down, as was once thought, but, on the contrary, is accelerating. This acceleration is explained by the action of a special “antigravity”, which is somehow characteristic of the empty space of the vacuum of space. On the other hand, at the quantum level, nothing absolutely “empty” can be - in a vacuum, subatomic particles constantly appear and immediately disappear. This “flickering” of particles is believed to be responsible for the existence of “anti-gravity” dark energy that fills empty space.

At one time, it was Albert Einstein, who until the end of his life never accepted the paradoxical principles of quantum mechanics (which he himself predicted), suggested the existence of this form of energy. Following the tradition of classical Greek philosophy, Aristotle, with its belief in the eternity of the world, Einstein refused to believe what his own theory predicted, namely, that the universe had a beginning. To “perpetuate” the universe, Einstein even introduced a certain cosmological constant into his theory, and thus described the energy of empty space. Fortunately, a few years later it became clear that the Universe is not a frozen form at all, that it is expanding. Then Einstein abandoned the cosmological constant, calling it “the greatest miscalculation of his life.”

Today science knows that dark energy still exists, although its density is much lower than what Einstein assumed (the problem of dark energy density, by the way, is one of the greatest mysteries of modern physics). But no matter how small the value of the cosmological constant is, it is quite enough to verify that quantum effects in gravity exist.

Subatomic nesting dolls

Despite everything, in the early 1980s, string theory still had intractable 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, different musical notes, different 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, it is not at all necessary to see strings “with your own eyes.” Proving string theory requires, rather, something else—what sounds like science fiction—confirmation of the existence of extra dimensions of space.

What are we talking 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 / ©Wikimedia Commons

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 within 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 have again given 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.

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 would suggest.

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:

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

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 has noted, “The moment you are introduced to string theory and realize that almost all of 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 have convinced many physicists that string theory can fulfill its promise and become the final 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).

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

Let's start from the beginning. 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 people:

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 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 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 which bar it will take place in, 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 at lunchtime.

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 will 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 can 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 -

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 imagine gravity. The phone falls from your 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 this, you need very heavy objects. We feel the gravity of the Earth, which is 7.5 × 10 22 times heavier than a person, and we do not notice the gravity 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 a children's park and place a heavy stone on the trampoline. A crater will appear on the rubber of the trampoline. If you put a small ball on the trampoline, it will roll down the funnel towards the stone. This is roughly how the planets form a funnel in space, and we, like balls, fall onto them.

Planets so massive they bend 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 earth's gravity is 10 38 times less than the force holding the particles of the atomic nucleus. 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 folds space itself and draws in everything nearby. Even light flies into 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 carried out calculations, but they didn’t add up. Calculations showed that the graviton energy grows to infinity. But this shouldn’t happen.

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

Problems with divergences in calculations disappeared when the graviton was considered not as a particle, but as a string. Strings have a finite length and energy, so the graviton's energy 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 us understand how the universe came to be. 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 powerful as other forces, so knowing the effects of gravity is important to understanding the early universe.

Success in describing quantum gravity is a step towards creating 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 what its end will be.

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.

Physics contradiction

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.

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.

2D Universe. Polyhedron graph E8 Theory of Everything

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

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

Standard model

Interactions between different particles in the Standard Model
Graviton

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.

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, different musical notes, different 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.

Fifth dimension

What are we talking 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.

Ten dimensions

How the world works

Superstring theory

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