The essence of string theory. Question: is this real? Dot, dot, comma

Theoretical physics is obscure to many, but at the same time is of paramount importance in the study of the world around us. The task of any theoretical physicist is to build a mathematical model, a theory capable of explaining certain processes in nature.

Need

As you know, the physical laws of the macrocosm, that is, the world in which we exist, differ significantly from the laws of nature in the microcosm - within which atoms, molecules and elementary particles live. An example would be a difficult-to-understand principle called carpuscular-wave dualism, according to which micro-objects (electron, proton and others) can be both particles and waves.

Like us, theoretical physicists want to describe the world briefly and clearly, which is the main purpose of string theory. With its help, it is possible to explain some physical processes, both at the level of the macroworld and at the level of the microworld, which makes it universal, uniting other previously unrelated theories (general relativity and quantum mechanics).

The essence

According to string theory, the entire world is built not from particles, as is believed today, but from infinitely thin objects 10-35 m long that have the ability to vibrate, which allows us to draw an analogy with strings. Using a complex mathematical mechanism, these vibrations can be associated with energy, and therefore with mass; in other words, any particle arises as a result of one or another type of vibration of a quantum string.

Issues and Features

Like any unconfirmed theory, string theory has a number of problems that indicate that it requires improvement. These problems include, for example, the following: as a result of calculations, mathematically, there was a new type of particles that cannot exist in nature - tachyons, the square of whose mass is less than zero, and the speed of movement exceeds the speed of light.

Another important problem, or rather feature, is the existence of string theory only in 10-dimensional space. Why do we perceive other dimensions? “Scientists have concluded that on very small scales these spaces fold and close in on themselves, making it impossible for us to identify them.

Development

There are two types of particles: fermions - particles of matter, and bosons - carriers of interaction. For example, a photon is a boson that carries electromagnetic interaction, a graviton is gravitational, or the same Higgs boson that carries interaction with the Higgs field. So, if string theory took into account only bosons, then superstring theory also took into account fermions, which made it possible to get rid of tachyons.

The final version of the superstring principle was developed by Edward Witten and is called "m-theory", according to which an 11th dimension should be introduced to unify all the different versions of superstring theory.

We can probably end here. Work to solve problems and refine the existing mathematical model is diligently carried out by theoretical physicists from around the world. Perhaps soon we will finally be able to understand the structure of the world around us, but looking back at the scope and complexity of the above, it is obvious that the resulting description of the world will not be understandable without a certain base of knowledge in the field of physics and mathematics.

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:

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 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 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 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 surprising 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 -

Superstring theory

Briefly about superstring theory

This theory looks so crazy that it is quite possible that it is correct!

Various versions of string theory are now considered as the main contenders for the title of a comprehensive, universal theory that explains the nature of everything that exists. And this is a kind of Holy Grail of theoretical physicists involved in the theory of elementary particles and cosmology. Universal theory (aka theory of everything) contains only a few equations that combine the entire 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 supersymmetry, as a result of which was born superstring theory, and to date this is the maximum that has been achieved in terms of unifying the theory of all four main interactions (forces acting in nature). The theory of supersymmetry itself is already built on the basis of an a priori modern concept, according to which any remote (field) interaction is caused by the exchange of interaction carrier particles of the corresponding kind between interacting particles (Standard Model). For clarity, interacting particles can be considered the “bricks” of the universe, and carrier particles can be considered cement.

Within the standard model, quarks act as building blocks, and interaction carriers act as gauge bosons, which these quarks exchange with each other. 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 in the composition of hadrons and bosons. Naturally, none of the predictions of the theory of supersymmetry have yet been tested in laboratory conditions, but the hypothetical hidden components of the material world already have names - for example, selectron(supersymmetric partner of the electron), squark etc. The existence of these particles, however, is unambiguously predicted by theories of this kind.

The picture of the Universe offered by these theories, however, is quite easy to visualize. On a scale of about 10–35 m, that is, 20 orders of magnitude smaller than the diameter of the same proton, which includes three bound quarks, the structure of matter differs from what we are 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, such a string can excite, in addition to the main tone, many overtones or harmonics Each harmonic has its own energy state. According to principle of relativity(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 the theory of superstrings 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 theory of multidimensional membranes- in essence, 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 reconcile 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 so far 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.

Introduction to Superstrings

translation by Sergei Pavlyuchenko

String theory is one of the most exciting and profound theories in modern theoretical physics. Unfortunately, this is still a rather difficult thing to understand, which can only be understood from the standpoint of quantum field theory. Knowledge of mathematics such as group theory, differential geometry, etc. will not harm understanding. Thus, for most it remains a “thing in itself”.

This introduction is intended as a "readable" concise introduction to the basic concepts of string theory for those interested. Unfortunately, we will have to pay rigor and completeness for the accessibility of presentation. We hope it will give you answers to the simplest questions about string theory, and you will be imbued with the beauty of this field of science.

String theory is a dynamically developing field of knowledge to this day; every day brings something new about her. We do not yet know for sure whether string theory describes our Universe and to what extent. But she can well describe it, as can be seen from this review.

The original version is at http://www.sukidog.com/jpierre/strings/index.html.

Why string theory?

Although the Standard Model describes most of the phenomena that we can observe using modern accelerators, many questions regarding Nature remain unanswered. The goal of modern theoretical physics is precisely to unify descriptions of the Universe. Historically, this path has been quite successful. For example, Einstein's Special Theory of Relativity combined electricity and magnetism into the electromagnetic force. The 1979 Nobel Prize-winning work of Glashow, Weinberg and Salam showed that the electromagnetic and weak forces can be combined into the electroweak force. Further, there is every reason to believe that all forces within the Standard Model will eventually unify. If we begin to compare the strong and electroweak interactions, then we will have to go to regions of increasingly higher energies until they become equal in strength in the region of GeV. Gravity will join at energies of the order of .

The purpose of string theory is precisely to explain the sign " ? " in the diagram above.

The characteristic energy scale for quantum gravity is called Planck mass and is expressed through Planck's constant, the speed of light and the gravitational constant as follows:

It can be assumed that in its final form, string theory will provide answers to the following questions:

• What is the origin of the 4 forces of Nature known to us?
• Why are the masses and charges of particles the way they are?
• Why do we live in a space with 4 spatial dimensions?
• What is the nature of space-time and gravity?

  Fundamentals of String Theory

  We are used to thinking about elementary particles (such as electrons) as point-like 0-dimensional objects. A somewhat more general concept is fundamental strings as 1-dimensional objects. They are infinitely thin, and their length is on the order of . But this is simply negligible compared to the lengths with which we usually deal, so we can consider them to be practically point-like. But as we'll see, their string nature is quite important.

  There are strings open And closed. As they move through space-time, they cover a surface called world sheet.

  

  These strings have specific vibrational modes that determine the particle's inherent quantum numbers, such as mass, spin, etc. The basic idea is that each mode carries a set of quantum numbers corresponding to a specific type of particle. This is the final unification - all particles can be described through one object - a string!

  As an example, consider a closed string that looks like this:

  Such a string corresponds to the massless graviton with spin 2 - a particle that transfers gravitational interaction. By the way, this is one of the features of string theory - it naturally and inevitably includes gravity as one of the fundamental interactions.

  Strings interact by fission and fusion. For example, the annihilation of two closed strings into one closed string looks like this:

  
  

  Note that the surface of the world sheet is a smooth surface. This implies another “good” property of string theory - it does not contain a number of divergences inherent in quantum field theory with point particles. Feynman diagram for the same process

  

  contains a topological singularity at the interaction point.

  If we “glue” two simple string interactions together, we get a process in which two closed strings interact through union into an intermediate closed string, which then again splits into two:
  

  This major contribution to the interaction process is called arboreal approach. In order to calculate quantum mechanical amplitudes of processes using perturbation theory, add contributions from higher order quantum processes. Perturbation theory gives good results because the contributions get smaller and smaller as we use higher and higher orders. Even if you calculate only the first few diagrams, you can get fairly accurate results. In string theory, higher orders correspond to a larger number of holes (or "handles") on the world sheets.
  
  

  The good thing about this approach is that each order of the perturbation theory corresponds to only one diagram (for example, in field theory with point particles, the number of diagrams grows exponentially in higher orders). The bad news is that accurate calculations of diagrams with more than two holes are very difficult due to the complexity of the mathematical apparatus used when working with such surfaces. Perturbation theory is very useful in studying weakly coupled processes, and most of the discoveries in particle physics and string theory come from it. However, all this is still far from over. Answers to the deepest questions of the theory can only be obtained after an accurate description of this theory has been completed.

  D-branes

  Strings can have completely arbitrary boundary conditions. For example, a closed string has periodic boundary conditions (the string “turns into itself”). Open strings can have two types of boundary conditions - conditions Neumann and conditions Dirichlet. In the first case, the end of the string can move freely, although without carrying away any momentum. In the second case, the end of the string can move along some manifold. This diversity is called D-brane or Dp-brane(when using the second notation, “p” is an integer characterizing the number of spatial dimensions of the manifold). An example is two strings with one or both ends attached to a 2-dimensional D-brane or D2-brane:

  

  D-branes can have a number of spatial dimensions from -1 to the number of spatial dimensions of our spacetime. For example, in superstring theory there are 10 dimensions - 9 spatial and one time. Thus, in superstrings the maximum that can exist is a D9-brane. Note that in this case the ends of the strings are fixed on a manifold covering all space, so they can move everywhere, so in effect the Neumann condition is imposed! In the case p=-1, all spatial and temporal coordinates are fixed, and such a configuration is called instanton or D-instanton. If p=0, then all spatial coordinates are fixed, and the end of the string can only exist at one single point in space, so D0-branes are often called D particles. In exactly the same way, D1-branes are called D-strings. By the way, the word “brane” itself comes from the word “membrane,” which refers to 2-dimensional branes, or 2-branes.

  In reality, D-branes are dynamic; they can fluctuate and move. For example, they interact gravitationally. In the diagram below you can see how one closed string (in our case a graviton) interacts with a D2-brane. Of particular note is the fact that upon interaction the closed string becomes open with both ends on the D-brane.
  
  
  So, string theory is more than just string theory!

  Additional dimensions

  Superstrings exist in 10-dimensional space-time, while we live in 4-dimensional spacetime. And if superstrings describe our Universe, we need to somehow connect these two spaces. To do this, let's collapse 6 dimensions to a very small size. If the size of the compact dimension turns out to be on the order of the size of the strings (), then due to the smallness of this dimension we simply will not be able to see it directly. Ultimately, we will get our (3+1)-dimensional space, in which each point of our 4-dimensional Universe corresponds to a tiny 6-dimensional space. This is shown very schematically in the picture below:

  

  This is actually a fairly old idea that dates back to the work of Kaluza and Klein in the 1920s. In this case, the mechanism described above is called Kaluza-Klein theory or compactification. Kaluza's work itself shows that if we take relativity in 5-dimensional space-time, then fold one dimension into a circle, we get 4-dimensional space-time with relativity plus electromagnetism! And this happens because electromagnetism is U(1) gauge theory. U(1) is a group of rotations around a point in the plane. The Kaluza-Klein mechanism gives a simple geometric interpretation of this circle - this is the very folded fifth dimension. Although folded measurements are small for direct detection, they can nevertheless have a deep physical meaning. [Accidentally leaked to the press, Kaluza and Klein's work sparked much speculation about the fifth dimension.]

  How can we find out if there really are extra dimensions and how can we “feel” them if we have accelerators with high enough energies? From quantum mechanics it is known that if space is periodic, then momentum is quantized: , whereas if space is unlimited, then the spectrum of momentum values ​​is continuous. If you decrease the radius of compactification (the size of additional dimensions), then the range of permissible momentum values ​​will increase. This is how a tower of momentum states is obtained - the Kaluza Klein tower.

  

  And if the radius of the circle is taken to be very large (we “decompact” the measurement), then the range of possible values ​​of the momentum will be quite narrow, but will be “almost continuous”. Such a spectrum will be similar to the mass spectrum of the world without compactifications. For example, states that are massless in a larger number of dimensions in a smaller number of dimensions will look exactly like the tower of states described above. Then a “set” of particles with masses equally spaced from each other should be observed. True, in order to “see” the most massive particles, accelerators are needed that are much better than those that we currently have.

  Strings have another remarkable property - they can “wind” around a compactified dimension, which leads to the appearance negotiable mods in the mass spectrum. A closed string can wrap around a compactified dimension an integer number of times. Similar to the Kaluza-Klein case, they contribute to the momentum as . The significant difference lies precisely in a different connection with the compactification radius. In this case, for small sizes of extra dimensions, reversal modes become very easy!
  
  

  Now we need to move to our 4-dimensional space. To do this we need a 10-dimensional superstring theory on a 6-dimensional compact manifold. Naturally, the picture described above becomes more complex. The easiest way is to assume that all these 6 dimensions are 6 circles, so they all represent a 6-dimensional torus. Moreover, this scheme allows one to preserve supersymmetry. It is believed that some supersymmetry also exists in our 4-dimensional space on energy scales of the order of 1 TeV (it is at these energies that supersymmetry has recently been sought at modern accelerators). In order to preserve minimal supersymmetry, N=1 in 4-dimensionality, it is necessary to compactify on a special 6-dimensional manifold called Calabi-Yau manifold.

  The properties of Calabi-Yo manifolds can have important applications to low-energy physics—to the particles we observe, their masses and quantum numbers, and the number of generations of particles. The problem here is that, generally speaking, there are a huge number of Calabi-Yo varieties, and we don't know which one to use. This is the meaning, having in fact one 10-dimensional string theory, we get that the 4-dimensional theory becomes not the only possible one, at least at our (still incomplete) level of understanding. The “string people” (scientists working in the field of string theories) have hopes that with a complete non-perturbative string theory (a theory that is NOT built on the perturbations described a little above), we will be able to explain how the Universe went from 10- dimensional physics, which may have taken place during the high-energy period immediately after the Big Bang, to the 4-dimensional physics we are dealing with now. [In other words, we will find a unique Calabi-Yo manifold.] Andrew Strominger showed that Calabi-Yo manifolds can be continuously related to each other by conical transformations and thus one can move between different Calabi-Yo manifolds by changing the parameters of the theory. But this suggests the possibility that different 4-dimensional theories arising from different Calabi-Yo manifolds are different phases of the same theory.

  Duality

  The five superstring theories described above turn out to be very different from the point of view of the weakly coupled perturbative theory (the perturbation theory developed above). But in fact, as it has become clear in the last few years, they are all connected by various string dualities. Let's call the theory dual if they describe the same physics.

  The first type of duality we will discuss here is T-duality. This type of duality connects a theory compactified on a circle of radius with a theory compactified on a circle of radius . Thus, if in one theory space is folded into a circle of small radius, then in the other it will be rolled into a circle of large radius, but both of them will describe the same physics! Type IIA and type IIB superstring theories are connected through T-duality, SO(32) and E8 x E8 heterotic theories are also connected through it.

  Another duality we will look at is S-duality. Simply put, this duality links the strong coupling limit of one theory with the weak coupling limit of another theory. (Note that the loosely coupled descriptions of both theories can be very different.) For example, SO(32) Heterotic string theory and Type I theory are S-dual in 10-dimension. This means that in the strong coupling limit SO(32) the Heterotic theory becomes a Type I theory in the weak coupling limit and vice versa. You can find evidence of duality between the strong and weak limits by comparing the spectra of light states in each of the pictures and finding that they are consistent with each other. For example, in Type I string theory there is a D-string that is heavy when coupled weakly and light when coupled strongly. This D-string carries the same light fields as the SO(32) Heterotic String world sheet, so when Type I theory is coupled very strongly, the D-string becomes very light, and we will simply see the description become the same, as well as through a loosely coupled Heterotic string. Another S-duality in the 10th dimension is the self-duality of IIB strings: the strongly coupled limit of the IIB string is simply another IIB theory, but weakly coupled. The IIB theory also has a D-string (though it is more supersymmetric than the D-strings of the Type I theory, so the physics is different) that becomes light when strongly coupled, but this D-string is also the other fundamental string of the theory ii Type IIB.

  

  The dualities between different string theories are evidence that they are all simply different limits of the same theory. Each of the limits has its own applicability, and different limits of different descriptions overlap. What is this M-theory shown in the picture? Read on!

  M-theory

  At low energies, M-theory is described by a theory called 11-dimensional supergravity. This theory has a membrane and five-branes as solitons, but no strings. How can we get the strings we already love here? It is possible to compactify 11-dimensional M-theory on a circle of small radius to obtain 10-dimensional theory. Then if our membrane had the topology of a torus, then by folding one of these circles, we will get a closed string! In the limit where the radius is very small, we get a Type IIA superstring.

  

  But how do we know that M-theory on the circle will produce a Type IIA superstring, and not IIB or heterotic superstrings? The answer to this question can be obtained after a careful analysis of the massless fields that we obtain as a result of the compactification of 11-dimensional supergravity on a circle. Another simple test would be to find that the M-theory D-brane is unique to the IIA theory. Recall that IIA theory contains D0, D2, D4, D6, D8-branes and an NS five-brane. The following table summarizes the above:
  

  Here the D6 and D8-branes are omitted. The D6-brane can be interpreted as a “Kalutza-Klein monopole”, which is a special solution of 11-dimensional supergravity when compactified onto a circle. The D8-brane has no clear interpretation in terms of M-theory, it is still an open question.

  Another way to obtain a consistent 10-dimensional theory is to compactify the M-theory into a small segment. This means that we assume that one of the dimensions (the 11th) has a finite length. In this case, the ends of the segment determine the boundaries of 9 spatial dimensions. An open membrane can be built at these boundaries. Since the intersection of the membrane with the boundary is a string, we can see that the (9+1)-dimensional “worldvolume” can contain strings “sticking out” from the membrane. After all this, in order to avoid anomalies, it is necessary that each of the boundaries carry an E8 gauge group. Therefore, if we make the space between the boundaries very small, we get a 10-dimensional theory with strings and an E8 x E8 gauge group. And this is an E8 x E8 heterotic string!

  

  Thus, considering different conditions and different dualities between string theories, we will come to the conclusion that at the basis of all this lies one theory - M-theory. Moreover, five superstring theories and 11-dimensional supergravity are its classical limits. Initially, we tried to obtain the corresponding quantum theories by “expanding” the classical limits using perturbative theory (perturbation theory). However, perturbative theory has its limits of applicability, so by studying the non-perturbative aspects of these theories, using dualities, supersymmetry, etc. we come to the conclusion that they are all united by one single quantum theory. This uniqueness is very attractive, so work on constructing a complete quantum M-theory is in full swing.
  
  

  Black holes

  The classical description of gravity - the General Theory of Relativity (GTR) - contains solutions called "black holes" (BH). There are quite a few types of black holes, but they all show similar general properties. The event horizon is a surface in space-time that, simply put, separates the region inside the black hole from the region outside it. The gravitational attraction of a black hole is so strong that nothing, not even light, having penetrated under the horizon, can escape back. Thus, classical black holes can only be described using parameters such as mass, charge and angular momentum.

  (explanation of Penrose diagram a)

  Black holes are good laboratories for studying string theories, since the effects of quantum gravity are important even for fairly large black holes. Black holes aren't really "black" because they radiate! Using semiclassical arguments, Stephen Hawking showed that black holes emit thermal radiation from their horizon. Since string theory, among other things, is also a theory of quantum gravity, it is able to consistently describe black holes. And then there are black holes that satisfy the equation of motion for strings. These equations are similar to the equations from General Relativity, but they have some additional fields that came there from the strings. In superstring theories there are special solutions such as black holes, which themselves are also supersymmetric.

  One of the most dramatic results in string theory was the derivation of the formula for Bekenstein-Hawking entropy A black hole obtained from considering the microscopic string states that form the black hole. Bekenstein noted that black holes obey the “law of areas,” dM = K dA, where “A” is the area of ​​the horizon and “K” is a constant of proportionality. Since the total mass of a black hole is its rest energy, the situation is very similar to thermodynamics: dE = T dS, as shown by Bekenstein. Hawking later showed in a semiclassical approximation that the temperature of a black hole is T = 4k, where "k" is a constant called "surface gravity". Thus, the entropy of a black hole can be rewritten as . Moreover, recently Strominger and Vafa showed that this entropy formula can be obtained microscopically (down to a factor of 1/4) using the degeneracy of quantum states of strings and D-branes corresponding to certain supersymmetric BHs in string theory. By the way, D-branes give a description at small distances as if they were weakly coupled. For example, the BHs considered by Strominger and Vafa are described by 5-branes, 1-branes, and open strings "living" on the 1-brane, all folded into a 5-dimensional torus, effectively yielding a 1-dimensional object - the BH.

  

  In this case, Hawking radiation can be described within the framework of the same structure, but if open strings can “travel” in both directions. Open strings interact with each other and radiation is emitted in the form of closed strings.

  

  Precise calculations show that for the same types of black holes, string theory makes the same predictions as semiclassical supergravity, including a nontrivial frequency-dependent correction called the “gray parameter” ( greybody factor).

  Quantum gravity discovered on Earth?
  

  << Вчера

  Tomorrow >>

  
  Explanation: Are there separate portions of gravity? The theory known as quantum mechanics describes the laws that govern the universe at small distances, while Einstein's General Theory of Relativity explains the nature of gravity and the universe on large scales. Until now, no theory has been created that can unite them. Research recently conducted in France may have shown that gravity is a quantum field. It is stated that Earth's gravitational field showed its quantum nature. In an experiment carried out by Valery Nezvizhevsky and his colleagues, it was shown that ultracold neutrons moving in a gravitational field are detected only at discrete altitudes. Scientists around the world are awaiting independent confirmation of these results. The figure shows in false color the surface that could form during the evolution of a one-dimensional string. By describing elementary particles as tiny strings, many physicists are working to develop a truly quantum theory of gravity.

  (Editor's note: The experiments of French and Russian physicists described in this note, published in Nature 415 , 297 (2002) have nothing to do with quantum gravity. Their explanation(both given by the authors of the experiments and given in the New Scientist magazine and on the Physicsweb.org website) completely different.

  Experimenters search for new forces predicted by superstring theories

  Researchers at the University of Colorado at Boulder were able to conduct the most sensitive experiment to date to assess the gravitational interaction between masses separated by a distance of only twice the thickness of a human hair, but they did not observe any of the predicted new forces.

  The results obtained make it possible to exclude some variants of the superstring theory, in which the corresponding parameter for the influence of new forces from the “collapsed” measurements is in the range from 0.1 to 0.01 mm.

  String theory, considered the most promising approach to the long-awaited grand unification—a single account of all known forces and matter—believes that everything in the universe is made up of tiny loops of vibrating strings. According to various versions of superstring theory, there must be at least six or seven extra spatial dimensions beyond the three that are accessible to us, and theorists believe that these extra dimensions are collapsed into small spaces. This "compactification" gives rise to what are called moduli fields, which describe the size and shape of the folded dimensions at each point in spacetime.

  The modulus regions exert forces comparable in strength to ordinary gravity, and according to recent predictions, they can be detected at distances as small as 0.1 mm. The limit of sensitivity achieved in previous experiments made it possible to test the force of attraction between two masses separated by only 0.2 mm, so the question remained open. However, it remains open now.

  “If these forces really exist, then we now know that they should manifest themselves at shorter distances than we tested,” explains the head of the laboratory, professor at the University of Colorado John Price. “However, these results do not in themselves refute the theory "You just need to keep in mind that the effect will have to be looked for at shorter distances and using settings with higher sensitivity." In addition, the researchers claim that such experiments themselves are not intended to confirm or refute the superstring theory. “The ideas we're testing are just some of the possible scenarios inspired by strings, not precise predictions of the theory itself,” John Price told Space.com. “There's no way yet for string theory to make those kinds of precise predictions.” , and I would say that no one knows whether string theory will ever be capable of this." However, experiments at smaller distances may still “add more patches to the quilt of physics,” and so it is important to continue this kind of research because “something new and “very fundamental” may be discovered.”

  The experimental setup of researchers from the University of Colorado, called a high-frequency resonator, consisted of two thin tungsten plates (20 mm long and 0.3 mm thick). One of these plates was made to vibrate at a frequency of 1000 Hz. The movements of the second plate, caused by the influence of the first, were measured by very sensitive electronics. We are talking about forces measured in femtonewtons (10–15 n), or one millionth of the weight of a grain of sand. The force of gravity acting at such short distances turned out to be quite traditional, described by Newton’s famous law.

  Professor Price expects to continue the experiments to try to measure forces at even shorter distances. To take the next step, the Colorado experimenters remove the gold-plated sapphire shield between the tungsten strips that blocked electromagnetic forces and replace it with thinner copper-beryllium foil, allowing the masses to move closer together. They also plan to cool the experimental setup to reduce interference from thermal fluctuations.

  Regardless of the fate of superstring theory, the ideas of extra dimensions, introduced almost a hundred years ago (at that time many physicists made fun of them), are becoming unusually popular due to the crisis of standard physical models that are unable to explain the new observations. Among the most glaring facts is the accelerated expansion of the Universe, which has many confirmations. A mysterious new force, called dark energy for now, is pushing our space apart, acting like some kind of antigravity. Nobody knows what kind of physical phenomenon lies behind this. What cosmologists do know is that while gravity holds galaxies together at the "local" level, mysterious forces push them apart. O on a larger scale.

  Dark energy can be explained by interactions between dimensions, those that we see and those that are still hidden from us, some theorists believe. At the annual meeting of the AAAS (American Association for the Advancement of Science) held in Denver earlier this month, top cosmologists and physicists expressed cautious optimism about this.

  "There is some hope that this new approach will solve the whole set of problems at once," says physicist Sean Carroll, an assistant professor at the University of Chicago.

  All these problems inevitably cluster around gravity, the force of which was calculated by Newton more than three centuries ago. Gravity was the first of the fundamental forces to be described mathematically, but it is still the most poorly understood. Quantum mechanics, developed in the 20s of the last century, describes well the behavior of objects at the atomic level, but is not very “friendly” with gravity. The fact is that although gravity acts over large distances, it is still very weak compared to the other three fundamental forces (electromagnetic, strong and weak interactions that dominate the microcosm). Understanding gravity at the quantum level is expected to link quantum mechanics with a complete description of other forces.

  In particular, scientists for a long time could not determine whether Newton's law (the inverse proportionality of force to the square of distance) is valid at very small distances, in the so-called quantum world. Newton developed his theory for astronomical distances, such as the interactions of the Sun with the planets, but now it turns out that it is also valid in the microcosm.

  "What's happening right now in particle physics, gravitational physics and cosmology is very reminiscent of when quantum mechanics started to come together," says Maria Spiropulu, a researcher at the University of Chicago and organizer of the AAAS Workshop on Extra Dimensional Physics. (physics of extra dimensions).

  For the first time it was possible to measure the speed of gravity

  

  Russian physicist Sergei Kopeikin, working at the University of Missouri in Columbia, and American Edward Fomalont from the National Radio Astronomy Observatory in Charlottesville, Virginia, said that they were the first to measure the speed of gravity with acceptable accuracy. Their experiment confirms the opinion of most physicists: the speed of gravity is equal to the speed of light. This idea underlies modern theories, including Einstein’s General Theory of Relativity, but so far no one has been able to measure this quantity directly in an experiment. The research was released Tuesday at the 201st meeting of the American Astronomical Society in Seattle. The results were previously submitted for publication in a scientific journal, but were criticized by some experts. Kopeikin himself considers the criticism unfounded.

  Newton's theory of gravity assumes that the effects of gravity are instantaneous, but Einstein proposed that gravity travels at the speed of light. This postulate became one of the foundations of his Theory of Relativity in 1915.

  The equality of the speed of gravity and the speed of light means that if the Sun were to suddenly disappear from the center of the solar system, the Earth would remain in its orbit for approximately 8.3 minutes - the time it takes light to travel from the Sun to the Earth. After these few minutes, the Earth, feeling liberated from the sun's gravity, would leave its orbit and fly away into space in a straight line.

  How can you measure the "speed of gravity"? One way to solve this problem is to try to detect gravitational waves - small "ripples" in the space-time continuum that diverge from any accelerating masses. Various installations for capturing gravitational waves have already been built in large numbers, but none of them has so far been able to register such an effect due to its exceptional weakness.

  Kopeikin went a different route. He rewrote the equations of General Relativity to express the gravitational field of a moving body in terms of its mass, velocity, and gravitational velocity. It was decided to use Jupiter as a massive body. A rather rare opportunity occurred in September 2002, when Jupiter passed in front of a quasar (such events occur approximately once every 10 years), intensely emitting radio waves. Kopeikin and Fomalont combined observations from a dozen radio telescopes in different parts of the globe, from Hawaii to Germany (using both the 25-meter radio telescopes of the National Radio Astronomy Observatory and the 100-meter German instrument in Effelsberg) to measure the minute apparent change in the position of the quasar caused by bending of radio waves from this source in the gravitational field of Jupiter. By studying the nature of the influence of Jupiter's gravitational field on passing radio waves, knowing its mass and speed of movement, it is possible to calculate the speed of gravity.

  The joint work of earth-based radio telescopes made it possible to achieve an accuracy 100 times greater than that achievable with the Hubble Space Telescope. The displacements measured in the experiment were very tiny - changes in the position of the quasar (the angular distance between it and the reference quasar was measured) were within 50 millionths of an arcsecond. The equivalent of such measurements could be the size of a silver dollar on the Moon or the thickness of a human hair from a distance of 250 miles, astronomers say (Western sources, apparently, did not think to pay attention to the meaning of the Russian surname of one of the authors of the studies, otherwise they would not have compared the sizes with a dollar, and with our monetary unit...).

  The result obtained: gravity is transmitted at 0.95 speed of light, the possible experimental error is plus or minus 0.25. "We now know that the speed of gravity is probably equal to the speed of light," Fomalont said. "And we can confidently rule out any result that is twice that."

  Steven Carlip, a physics professor at the University of California, said the experiment was a "good demonstration" of Einstein's principle. He says the experiment was preceded by measurements of the deflection of light by the Sun, but these were much less precise. Moreover, new measurements of gravitational speed in the very near future will have to clarify this value. A number of gravitational wave interferometers have been commissioned in recent months, one of which should finally detect gravitational waves directly and thereby measure their speed - an important fundamental constant of our Universe.

  However, it should be noted that the experiment itself is not an unambiguous confirmation of Einstein’s theory of gravity. With the same success it can be considered a confirmation of existing alternative theories. For example, Academician Logunov’s relativistic theory of gravity (RTG), which became known to the general public about ten years ago, does not diverge from general relativity in this regard. There are also gravitational waves in RTGs, although, as is known, there are no black holes. And yet another “refutation” of Newton’s theory of gravity is not of particular value. Nevertheless, the result is important from the point of view of “closing” some versions of modern theories and supporting others - it is associated with cosmological theories of multiple universes and the so-called string theory or superstrings, but it is too early to draw final conclusions, the researchers say. In the latest so-called unified M-theory, which is a development of the theory of superstrings, in addition to “strings”, new multidimensional objects have appeared - branes. Superstring theories by their nature include gravity, since calculations based on them invariably predict the existence of the graviton, a weightless hypothetical particle with a spin of 2. It is assumed that there are additional spatial dimensions, only “collapsed”. And gravity could take a "shortcut" through these extra dimensions, seemingly traveling faster than the speed of light, but without violating the equations of General Relativity.

  Two relativistic physicists present their views on the Universe,
  its evolution and the role of quantum theory

  IN Scientific American these lectures were published with abbreviations, the corresponding places in the text are marked with ellipses

  Introduction

  In 1994, Stephen Hawking and Roger Penrose gave a series of public lectures on general relativity at the Isaac Newton Institute of Mathematical Sciences at the University of Cambridge. Our magazine presents excerpts from these lectures, published this year by Princeton University Press under the title "The Nature of Space and Time," which compare the views of these two scientists. Although both belong to the same school of physics (Penrose assisted Hawking's doctoral dissertation at Cambridge), their views on the role of quantum mechanics in the evolution of the universe are very different from each other. In particular, Hawking and Penrose have different ideas about what happens to the information stored in a black hole and why the beginning of the universe is different from its end.

  One of Hawking's major discoveries, made in 1973, was the prediction that, due to quantum effects, black holes could emit particles. As a result of this process, the black hole evaporates, and ultimately it is possible that nothing will remain of its original mass. But during their formation, black holes absorb a lot of particles falling on it with different types, properties and configurations. Although quantum theory requires that such information be stored, the details of what happens to it next remain a topic of intense debate. Hawking and Penrose both believe that when a black hole emits, it loses the information it contained. But Hawking insists that this loss is irreplaceable, while Penrose argues that it is balanced by spontaneous measurements of quantum states that feed information back into the black hole.

  Both scientists agree that a future theory of quantum gravity is needed to describe nature. But their views differ on some aspects of this theory. Penrose believes that even if the fundamental interactions of elementary particles are symmetric with respect to time reversal, then quantum gravity should break such symmetry. Time asymmetry would then explain why the universe began so uniformly (as shown by the microwave background radiation produced by the big bang), while at the end the universe must be heterogeneous.

  Penrose tries to include a similar asymmetry in his hypothesis about Weyl curvature. Space-time, according to Albert Einstein, is curved by the presence of matter. But spacetime can also have some inherent deformation, referred to as Weyl curvature. Gravitational waves and black holes, for example, allow spacetime to bend even in regions that are empty. In the early universe, the Weyl curvature was probably zero, but in a dying universe, as Penrose argues, a large number of black holes will cause the Weyl curvature to increase. This will be the difference between the beginning and the end of the universe.

  Hawking agrees that the big bang and the final collapse ("Big crunch") will be different, but he does not consider time asymmetry to be a law of nature. The main reason for this difference, he thinks, is the path on which the development of the universe is programmed. He postulates a kind of democracy, declaring that there cannot be a single point in space in the universe; and therefore, the universe cannot have a boundary. It is this proposal of no boundary that Hawking claims explains the homogeneity of the microwave background radiation.

  The two physicists also have fundamentally different views on the interpretation of quantum mechanics. Hawking believes that the only purpose of theory is to make predictions that are consistent with experimental data. Penrose believes that a simple comparison of predictions with experiments is not enough to explain reality. He points out that quantum theory, which requires superposition of wave functions, is a concept that can lead to absurdities. These scientists thus take to a new level the well-known debate between Einstein and Bohr about the bizarre consequences of quantum theory.

  Stephen Hawking on quantum black holes:

  The quantum theory of black holes... appears to introduce a new level of unpredictability in physics beyond the usual quantum mechanical uncertainty. This is because black holes seem to have internal entropy and lose information from our region of the universe. I must say that these claims are highly controversial: many scientists working in the field of quantum gravity, including almost all those who came to it from particle physics, instinctively reject the idea that information about the state of a quantum system can be lost. However, this view has not had much success in explaining how information can escape a black hole. Ultimately, I believe that they will be forced to accept my proposal that information is irretrievably lost, just as they were forced to accept that black holes emit, which contradicts all their preconceptions...

  The fact that gravity is attractive means that in the universe there is a tendency for matter to gather in one place, a tendency for objects like stars and galaxies to form. Further compression of these objects can be restrained for some time by thermal pressure, in the case of stars, or by rotation and internal motions, in the case of galaxies. However, eventually the heat or angular momentum will be carried away and the object will begin to shrink again. If the mass is less than about one and a half solar masses, the compression can be stopped by the pressure of a degenerate gas of electrons or neutrons. The object will stabilize to become a white dwarf or a neutron star, respectively. However, if the mass is greater than this limit, then there is nothing that can stop the steady compression. Once the compression of an object approaches a certain critical size, the gravitational field on its surface will be so strong that the light cones will be tilted inward.... We can see that even the light rays going outward are curved towards each other, so that they they come closer together rather than apart. This means that there is some closed surface....

  Thus, there must be a region of space-time from which it is impossible to escape to an infinite distance. This region is called a black hole. Its boundary is called the event horizon, it is a surface formed by light rays that are unable to escape to infinity....

  A large amount of information is lost when a cosmic body collapses to form a black hole. A collapsing object is described by a very large number of parameters. Its state is determined by the types of matter and the multipole moments of their mass distribution. Despite this, the forming black hole is completely independent of the type of matter and quickly loses all multipole moments except the first two: monopole, which is mass, and dipole, which is angular momentum.

  This loss of information really did not matter in classical theory. We can say that all the information regarding the collapsing object ends up inside the black hole. For an observer outside the black hole, it would be very difficult to determine what the collapsing object looks like. However, in classical theory this was still possible in principle. The observer would never actually lose sight of the collapsing object. Instead, it would appear to him that the object was slowing down in its contraction and becoming increasingly fainter as it approached the event horizon. This observer could still see what the collapsing object was made of and how its mass was distributed.

  However, from the point of view of quantum theory, everything changes completely. During collapse, the object would emit only a limited number of photons before crossing the event horizon. These photons would be completely insufficient to convey to us all the information regarding the collapsing object. This means that in quantum theory there is no way in which an external observer could determine the state of such an object. One would think that this wouldn't matter too much because the information would still be inside the black hole, even if it couldn't be measured from the outside. But this is exactly the case where the second effect of the quantum theory of black holes manifests itself....

  Quantum theory forces black holes to emit and lose mass. And apparently they eventually disappear completely - along with the information inside them. I want to make the case that this information is indeed lost and not returned in any form. As I will show later, with this loss of information, uncertainty enters into physics at a higher level than the usual uncertainty associated with quantum theory. Unfortunately, unlike the Heisenberg uncertainty relation, this new level of uncertainty will be quite difficult to confirm experimentally in the case of black holes.

  Roger Penrose on quantum theory and space-time:

  Quantum theory, special relativity, general relativity and quantum field theory are the greatest physical theories of the 20th century. These theories are not independent of each other: general relativity was built on the basis of special relativity, and quantum field theory has special relativity and quantum theory as its basis.

  It was commonly said that quantum field theory was the most accurate physical theory that had ever existed, being accurate to 11 decimal places. However, I would like to point out that general relativity has now been tested to within 14 decimal places (and this accuracy is obviously limited only by the accuracy of the clocks running on Earth). I'm talking about the binary pulsar Hulse-Taylor PSR 1913+16, a pair of neutron stars rotating relative to each other, one of which is a pulsar. General relativity predicts that such an orbit slowly contracts (and its period decreases) because energy is lost due to the emission of gravitational waves. This process has indeed been observed experimentally, and the complete description of its motion, observed for 20 years... is in agreement with the general theory of relativity (which includes Newton's theory) with the remarkable accuracy noted above. The researchers of this star system rightfully received Nobel Prizes for their work. Quantum theorists have always argued, citing the accuracy of their theory, that general relativity should take its example, but I now think that quantum field theory should take its example.

  Although these four theories have achieved great success, they are not free from problems.... General relativity predicts the existence of singularities in space-time. There is a "measurement problem" in quantum theory, which I will describe later. It may turn out that the solution to the problems of these theories is to recognize the fact that they are incomplete theories. For example, many are anticipating that quantum field theory could somehow “smear” the singularities of the general theory of relativity....

  Now I would like to say a few words regarding the loss of information in black holes, which I believe relates to the last statement. I agree with almost everything Stephen said regarding this. But while Stephen regards the loss of information in black holes as a new uncertainty in physics, at a higher level than quantum mechanical uncertainty, I see it as just "additional" uncertainty.... It is possible that a small amount of information is lost in the time of evaporation of the black hole... but this effect will be much less than the loss of information during the collapse (for which I accept any reasonable picture of the final disappearance of the black hole to describe).

  As a thought experiment, consider a closed system in a large box and consider the motion of matter inside the box in phase space. In regions of phase space corresponding to the locations of the black hole, the trajectories describing the physical evolution of the system will converge, and the phase volumes filled by these trajectories will shrink. This occurs as a result of information loss at the black hole singularity. This reduction is in direct contradiction with the law of classical mechanics, known as Liouville's theorem, which states that the phase volumes carried by phase trajectories remain constant.... Thus, the space-time of a black hole violates the conservation of such volumes. However, in my picture, this loss of phase space volume is balanced by a process of spontaneous quantum measurements, which results in the restoration of information and an increase in volume in phase space. As I understand it, this happens because the uncertainty associated with the loss of information in black holes is, as it were, “additional” to quantum mechanical uncertainty: each of them is only one side of the same coin....

  Now let's look at the Schrödinger's cat thought experiment. He describes the unenviable position of a cat in a box, in which an emitted photon falls on a translucent mirror, and the transmitted part of its wave function is recorded by a sensor. If the sensor detects a photon, the gun goes off, killing the cat. If the sensor does not detect the photon, then the cat remains alive and well. (I know that Stephen does not approve of the mistreatment of cats, even in thought experiments!) The wave function of such a system is a superposition of these two possibilities.... But why are only the macroscopic alternatives "cat dead" and "cat alive" available to our perception? and not macroscopic superpositions of such states? ...

  I suggest that with the use of general relativity, the use of superpositions of alternative space-time geometries faces serious difficulties. It is possible that the superposition of two different geometries is unstable and decays into one of these two alternatives. Such geometries could be, for example, the space and time of a living or dead cat. To refer to this decay of a superposition into one of the alternative states, I use the term objective reduction, which I like because it has a good acronym (OR). What does the Planck length of 10-33 centimeters have to do with this? This length is a natural criterion for determining whether the geometries are truly different worlds. The Planck scale also determines the time scale at which reduction into various alternatives occurs.

  Hawking on quantum cosmology:

  I end this lecture by discussing an issue about which Roger and I have different views: the arrow of time. There is a very clear distinction between the forward and backward directions of time in our part of the universe. You only need to rewind any movie to see this difference. Instead of cups falling off the table and breaking into small pieces, we would see these fragments come back together and jump back onto the table. Isn't real life anything like that?

  Local laws of physical fields satisfy the requirement of symmetry in time, or, to be more precise, CPT invariance (Charge-Parity-Time). Thus, the observed difference between past and future comes from the boundary conditions of the universe. Let's consider a model in which a spatially closed universe expands to its maximum size and then collapses again. As Roger pointed out, the universe will be very different at the end points of this story. At its beginning, the universe, we now think, will be quite smooth and regular. However, when it starts to collapse again, we expect it to be extremely disordered and irregular. Since there are many more disordered configurations than ordered ones, this means that the initial conditions must be chosen extremely precisely.

  As a result, the boundary conditions must be different at these times. Roger's assumption is that the Weyl tensor should vanish only at one end of time. The Weyl tensor is that part of the curvature of space-time that is not determined by the local distribution of matter through Einstein's equations. This curvature is extremely small in the ordered early stage, and very large in the collapsing universe. Thus, this proposal would allow us to distinguish both ends of time from each other and explain the existence of the arrow of time.

  I think Roger's proposal is Weylian in two senses of the word. Firstly, it is not CPT-invariant. Roger sees this property as an advantage, but I feel that symmetries should not be abandoned without good reasons. Secondly, if the Weyl tensor were exactly equal to zero at an early stage of the universe, then it would remain homogeneous and isotropic throughout subsequent time. Roger's Weyl hypothesis cannot explain either the fluctuations of the microwave background or the disturbances caused by galaxies and bodies like ourselves.

  Despite all this, I think Roger has pointed out a very important difference between these two time boundaries. But the fact that the smallness of the Weyl tensor in one of the boundaries should not be accepted by us ad hoc, but should be obtained from the more fundamental principle of “no boundaries”....

  How can two time boundaries be different? Why should disturbances be small in one of them, but not in the other? The reason for this is that the field equations have two possible complex solutions.... Obviously, one solution corresponds to one end of time, and the other to the other.... At one end of time, the universe was very smooth, and the Weyl tensor was small . However, it could not exactly be equal to zero, since this leads to a violation of the uncertainty relation. Instead, there must be small fluctuations that can later develop into galaxies and bodies like ourselves. In contrast to the beginning, the end of the universe should be very irregular and chaotic, and the Weyl tensor very large. This would explain why the arrow of time takes place and why cups fall off the table and break much more readily than they are restored and bounce back up.

  Penrose on quantum cosmology:

  From what I understand of Stephen's concept, I conclude that our disagreement on this issue (Weyl's curvature hypothesis) is extremely large... For an initial singularity, the Weyl curvature is approximately zero.... Stephen argued that in the initial state small quantum fluctuations must take place, and therefore the hypothesis of zero Weyl curvature is classical and unacceptable. But I think there is some freedom as to the precise formulation of this hypothesis. Small perturbations are of course acceptable from my point of view in the quantum regime. We only need to significantly limit these fluctuations around zero....

  It is possible that the James-Hartley-Hawking "no boundaries" principle is a good candidate for describing the structure of the initial state. However, it seems to me that something else is needed to explain the final state. In particular, a theory explaining the structure of singularities would have to include the breaking of CPT and other symmetries in order to be compatible with the Weyl curvature hypothesis. Such a violation of time symmetry could be quite small; and could be implicitly contained in a new theory that goes beyond the boundaries of quantum mechanics.

  Hawking on physical reality:

  These lectures made the difference between Roger and me very clear. He is a Platonist, and I am a positivist. He is seriously concerned that Schrödinger's cat is in a quantum state in which he is half alive and half dead. He senses a discrepancy with reality in this. But such things don't bother me. I do not demand that theory correspond to reality, because I do not know what reality is. Reality is not a quality that you can test with litmus paper. All I care about is that the theory predicts the results of the measurements. Quantum theory does this very successfully....

  Roger feels that...wave function collapse introduces CPT symmetry breaking into physics. He sees such disruptions at work in at least two areas of physics: cosmology and black holes. I agree that we can use time asymmetry when asking questions about observations. But I completely reject the idea that there are some physical processes that lead to a reduction in the wave function, or that this has anything to do with quantum gravity or consciousness. This all has to do with magic and magic, but not with science.

  Penrose on physical reality:

  Quantum mechanics has only been around for 75 years. This is not very much, especially when compared, for example, with Newton’s theory of gravity. So I wouldn't be surprised if quantum mechanics is modified for very large objects.

  At the beginning of this debate Stephen suggested that he was a positivist and I was a platonist. I am glad that he is a positivist, but for myself I can say that I am rather a realist. Also, if you compare this debate with the famous Bohr-Einstein debate some 70 years ago, I think Stephen is playing the role of Bohr and I am playing the role of Einstein! For Einstein, it was necessary that there be something similar to the real world, which is not necessarily described by a wave function, while Bohr emphasized that the wave function does not describe the real world, but only the knowledge necessary to predict the results of an experiment.

  It is now believed that Bohr's arguments were more powerful, and that Einstein (according to his biography written by Abraham Pais) could have been fishing since 1925. Indeed, he did not make much contribution to quantum mechanics, although his insightful criticism was very useful for the latter. I believe that the reason for this was that quantum theory was missing some important components. One of these components was the radiation of black holes discovered by Stephen 50 years later. Information leakage associated with the radiation of a black hole is a phenomenon that may take quantum theory to a new level.

  Stephen Hawking believes there may not be a definitive theory of the universe

  A television lecture given by the famous physicist Stephen Hawking from England to several audiences at the Massachusetts Institute of Technology (MIT) described scientists' search for a complete theory of the Universe. And in conclusion, the author of the bestselling scientific books A Brief History of Time and The Theory of Everything, a professor of mathematics at the University of Cambridge, suggested that “it is possible [such a theory ] is impossible."

  “Some people will be very disappointed to learn that there is no definitive theory,” Hawking said. “I was in that camp too, but now I’ve changed my mind. We will always be challenged by new scientific discoveries. Without it, civilization will stagnate.” "The search can continue for a very long time."

  The television program, during which some technical difficulties arose with the image and sound, was also broadcast via the Internet. It was organized by the Cambridge-MIT Institute (CMI) - a three-year strategic alliance between the University of Cambridge in England and the Massachusetts Institute of Technology.

  Hawking essentially summarized the history of particle physics, focusing on the key figures and theories in the field, from Aristotle to Stephen Weinberg, a Nobel laureate born in 1933.

  The equations of Maxwell and Dirac, for example, “govern almost all of physics and all of chemistry and biology,” Hawking reasoned. “So, knowing these equations, we could in principle predict human behavior, although I cannot claim that I myself had there is great success in this matter,” he concluded to laughter from the audience.

  The human brain contains too many particles to solve all the equations needed to predict someone's behavior. Perhaps someday in the foreseeable future we will learn to predict the behavior of the nematode worm.

  All theories developed to date to explain the universe "are either contradictory or incomplete," Hawking said. And he suggested why it is impossible in principle to develop one complete theory of the Universe. He based his argument on the work of Kurt Gödel, a Czech mathematician who wrote the famous theorem that, within any branch of mathematics, certain propositions can never be proven or disproved.

  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, we got 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 provide 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 contract until it explodes and start 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.