String theory vs loop quantum theory of gravity. Loop quantum gravity - Notes in the margins - LiveJournal. Excerpt characterizing Loop Quantum Gravity

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Definition 1

Loop quantum theory represents the knowledge of loop gravity of quantums. Its founders were such scientists as T. Jacobson, C. Rovelli, A. Ashtekar and L. Smolin.

The essence of loop quantum theory

According to this theory, time and space consist of discrete quantum cells connected in a certain way to each other. This allows them to create a discrete structure on small time scales, and on large time scales the time space becomes continuous.

Thus, space is made up of very small cells, smoothly connected to each other, forming the surrounding space for us. At the moments when these bundles form knots and tangles, elementary particles are formed.

Thanks to loop quantum gravity, scientists were able to find out the fact that the initial singularity disappears under the influence of quantum effects. Thus, the Big Bang ceases to be a veil of mystery behind which one cannot look. Science now allows us to look at the events that took place in the Universe before him.

The main objects in loop quantum theory are special cells of space, whose state and behavior are controlled by a certain field that exists in them. Its value becomes the so-called “internal time” for such cells. In other words, the transition from a weak field to a stronger one presupposes the existence of a “past” capable of influencing a certain “future”.

Consequently, the theory equates space to atoms: the numbers obtained when determining the volume form a discrete set, which allows the volume to change in separate portions. This, in turn, deprives space of continuity and allows for the idea of ​​its existence in the format of certain quantum units of volume and area.

Specifics of loop quantum theory

In the case of describing quantum mechanical phenomena, physicists calculate the probability of various processes that occur under certain circumstances. The same thing happens when using the theory of loop quantum gravity to describe changes in the geometry of space or the movement of fields and particles in a spin network.

Scientist Thomas Tiemann was able to derive exact expressions for determining the quantum probability of spin network steps. The end result of such calculations was the emergence of a clear methodology for calculating the probability of any process whose origin is probable in this world within the framework of subordination to the laws of the above theory.

The theory of relativity assumes the inseparability of time and space from each other and their existence in the format of a single time space. Introducing the concept of time space into loop quantum theory, the spin networks that represent space become what is called "spin foam".

When one more measurement indicator is included - time - the lines of the spin network expand and transform into two-dimensional surfaces, while the nodes in the line dissolve. Transitions that provoke changes in the spin network are now presented in the form of special nodes, within which the foam lines are combined. A snapshot of an ongoing process is visually similar to an image of a cross-section of time space.

A similar slice of spin foam is a spin network, but one should not be mistaken about the movements of the slice plane in a continuous mode, similar to the smooth flow of time. Similar to the process of defining space as a discrete geometry of a spin network, time will be defined as a sequence of individual steps that are rearranged by the network.

Thus, certain conclusions can be drawn:

1. About the discreteness of time, that is, it does not flow like a river, but is more reminiscent of a ticking clock, the interval between ticks of which is approximately equal to Planck’s time. In other words, time in the Universe is measured by myriads of clocks: in the region where a quantum step is carried out in the spin foam, the clock produces one “tick”.
2. Loop quantum gravity contributes to characteristic predictions of new events and phenomena. In fact, it is considered completely compatible with the postulate of both a three-dimensional world and one time dimension.
3. While compatible with a wide range of different versions of the matter contained in the world, it does not require symmetries, dimensions, or degrees of freedom other than those explored by scientists.

At the same time, there are versions of loop quantum gravity that include supersymmetry and extend many of the results to higher dimensions. For this reason, when there are indications of the presence of supersymmetry or higher dimensions, problems do not arise for loop quantum theory. Instead, quantum loop gravity assumptions will apply to the structure of space over very small distances.

Thus, loop quantum gravity assumes the presence in reality of a smooth picture of the time space of classical general relativity only as a result of averaging of a discrete structure, within which regions and surfaces can have exclusively certain discrete quantized values ​​of volumes and areas.

Note 2

Loop quantum gravity makes it possible to obtain specific assumptions for the discrete geometry of quanta (we are talking about short distances). Moreover, such assumptions begin to be formed on the basis of first principles, and therefore they exclude elements of adjustment.

In this sense, approaches in loop quantum gravity have certain differences in comparison with other approaches that postulate some form of discrete structure in the format of the starting position and without deriving it as a consequence of combining general relativity with quantum theory.

Differences between string theory and loop quantum gravity theory

Scientists note the fundamental differences between loop quantum theory and other theories. In particular, superstring theory. In the latter, the main objects are multidimensional membranes and strings moving in the time and space initially prepared for them. At the same time, this theory does not allow us to name the factors of the emergence of this multidimensional space.

The above theories are based on one-dimensional extended objects corresponding in their duality to the flow of lines of the gauge quantized field. Their differences are observed in three relationships:

1. Strings are considered with the property of moving in a classical format, which is characterized by a fixed choice of metrics and other classical fields. The existence of loops is allowed to be considered at a more fundamental level, where other fields and the classical metric are absent.
2. The gauge field in the case of loops is considered in the format of the gauge field of all Lorentz transformations or only some of them. With open strings, such a field will correspond to the Yang-Mills field.
3. Loop quantum gravity allows quantization without corresponding assumptions. In fact, since global Lorentz invariance does not represent a symmetry of classical general relativity, it cannot be considered in cases of any exact quantization of this theory.

Eighty years have passed since physicists realized that the theories of quantum mechanics and gravity are incompatible, and the mystery of combining them remains unresolved. Over the past decades, researchers have studied this problem in two different ways - through and through quantum gravity - which the scientists who practice them consider incompatible. But some scientists argue that to advance it is necessary to join forces.

Two candidates for a “theory of everything,” long considered incompatible, may turn out to be two sides of the same coin.

Among the attempts to unify quantum theory and gravity, the one that has attracted the most attention is . Its premise is simple: everything is made of little strings. The strings can be closed or open; they can vibrate, stretch, combine or disintegrate. And in this diversity lie explanations for all observable phenomena, including matter and space-time.

Loop quantum gravity (LQG), on the contrary, gives less than value matter present in spacetime and focuses more on the properties of spacetime itself. In the PKG theory, space-time is a network. The smooth background of Einstein's theory of gravity is replaced by nodes and links that are assigned quantum properties. Thus, the space consists of separate pieces. The PKG mainly studies these pieces.

This approach for a long time was considered incompatible with string theory. Indeed, their differences are obvious and profound. For starters, PCG studies chunks of space-time, and string theory studies the behavior of objects in space-time. These areas also share technical challenges. String theory requires that there be 10 dimensions in space; PKG does not work in higher dimensions. String theory assumes the existence of supersymmetry, in which all particles have as yet undiscovered partners. Supersymmetry is not characteristic of PCG.

These and other differences have divided the theoretical physics community into two camps.

"The conferences are divided," says Dorge Pullin, a physicist at Louisiana State University and co-author of a textbook on PCG. – Loop players go to loop conferences, string players go to string conferences. Now they don’t even go to physics conferences. I think it's quite unfortunate."

But some factors may move these camps closer. New theoretical discoveries have revealed possible similarities between PKG and string theory. A new generation of string theorists has moved beyond string theory and began searching for methods and tools that could be useful in creating a “theory of everything.” And the recent paradox of information loss in black holes has made everyone feel more humble.

Moreover, in the absence of experimental confirmation of string theory or PKG, mathematical proof that they are two sides of the same coin would argue that physicists are moving towards a "theory of everything" in search of a "theory of everything" in the right direction. The combination of PKG and string theory would make the new theory unique.

An unexpected connection

Attempts to solve some problems of PKG led to the first unexpected connection with string theory. Physicists studying PKG do not have a clear understanding of how to move from pieces of a spacetime network to a large-scale description of spacetime that matches Einstein's general relativity, our best theory of gravity. Moreover, their theory cannot accommodate the special case in which gravity can be neglected. This is the problem that besets any attempt to use space-time piece by piece: in SRT linear dimensions of an object decrease depending on the movement of the observer relative to the object. Compression also affects the size of pieces of space-time, which are perceived differently by observers moving at different speeds. This discrepancy leads to problems with the central principle of Einstein's theory - that the laws of physics do not depend on the speed of the observer.

“It's difficult to introduce discrete structures without running into SRT problems,” says Pullin.

In a 2014 paper written with colleague Rudolfo Gambini, a physicist at the Universidad Republican de Uruguay in Montevideo, Pullin writes that aligning PKG with STR inevitably entails the appearance of interactions similar to those present in string theory.

That the two approaches had something in common had seemed likely to Pullin since a seminal discovery in the late 1990s by Juan Malzadena, a physicist at the Institute for Advanced Study in Princeton, New Jersey. Malzadena, in anti-De Sitter spacetime (AdS), reconciled the theory of gravity and conformal field theory (CFT) at the boundary of spacetime. Using the AdS/CFT approach, the theory of gravity can be described using a more understandable field theory.

The full version of dualism is still a hypothesis, but it has a well-understood limiting case that string theory does not deal with. Because strings do not play a role in this case, it can be used in any theory of quantum gravity. Pullin sees a common ground here.

PKG as imagined by an artist

Hermann Verlinde, a theoretical physicist at Princeton University who frequently works with string theory, says it is plausible that PKG methods could shed light on the gravitational side of dualism. In a recent paper he described simplified model AdS/CFT in two dimensions for space and one for time, or, as physicists say, in the case of “2+1”. He discovered that the AdS space can be described using networks such as those used in PCG. Despite the fact that the entire design still works in “2+1”, it offers A New Look to gravity. Verlinde hopes to generalize the model to more measurements. “PKG was looked at too narrowly. My approach includes other areas as well. In an intellectual sense, this is a look into the future,” he said.

But even if it is possible to combine the methods of PKG and string theory to move forward with AdS space, the question remains: how useful will such a combination be? AdS space has a negative cosmological constant (this number describes the geometry of the Universe on large scales), while our Universe has a positive one. We do not live in a mathematical construct described by the AdS space.

Verlinde's approach is pragmatic. “For example, for a positive cosmological constant, we may need a new theory. The question then is how different it will be from this one. AdS is the best hint yet of the structure we are looking for, and we need to perform some trick to arrive at a positive constant.” He believes that scientists are not wasting their time with this theory: “Although AdS does not describe our world, it will give us lessons that will lead us in the right direction.”

Unification in the territory of a black hole

Verlinde and Pullin point to another possibility for the string theory and PKG communities to unite: the mysterious fate of information falling into a black hole. In 2012, four researchers from the University of California drew attention to a contradiction in the prevailing theory. They argued that if a black hole allowed information to escape from it, it would destroy the fine structure of empty space around the horizon black hole, and will create a high-energy barrier - a “firewall”. But such a barrier is incompatible with the equivalence principle underlying general relativity, which states that an observer cannot tell whether he has crossed the horizon. This incompatibility has upset string theorists, who thought they understood the connection between black holes and information, and were forced to grab their notebooks again.

But this problem is important not only for string theorists. “This whole firewall debate has been mostly in the string theorist community, which I don't understand,” Verlinde said. “Issues of quantum information, entanglement and the construction of mathematical Hilbert space are what the PCG experts have been working on.”

At this time, an event occurred unnoticed by most string specialists - the fall of the barrier erected by supersymmetry and additional dimensions. Thomas Tiemann's group at the University of Erlangen-Nuremberg (Germany) has extended PKG to higher dimensions and included supersymmetry - concepts that were previously the exclusive domain of string theory.

Recently, Norbert Bodendorfer, a former student of Tiemann working at the University of Warsaw, applied loop quantification methods from PCG to AdS space. He argues that PKG is useful for dealing with AdS/CFT duality in cases where string theorists cannot make gravitational calculations. Bodendorfer believes that the gap that existed between the PKG and the strings is disappearing.

“Sometimes I got the impression that string theorists have very little understanding of PKG and don’t want to talk about it,” he said. “But younger specialists demonstrate open-mindedness. They are very interested in what is happening at the intersection of regions.”

“The biggest difference is how we define our questions,” says Verlinde. “The problem is more sociological than scientific, unfortunately.” He doesn't think the two approaches conflict: “I've always thought of string theory and PKG as being part of the same description. PKG is a method, not a theory. This is a method of thinking about quantum mechanics and geometry. This is a method that string theorists can, and already do, use. These things are not mutually exclusive."

But not everyone is convinced. Moshe Rozali, a string theorist at the University of British Columbia, remains skeptic about PKG: “The reason I don't work on PKG is because it has problems with SRT,” he says. “If your approach is disrespectful of the symmetries in special relativity from the very beginning, you will need a miracle at one of the intermediate steps.” However, according to Rosalie, some of the mathematical tools that come from PCG can be useful.

“I don’t think it is possible to combine PKG and string theory. But people usually need methods, and in that sense they are similar. Mathematical methods may intersect."

Also, not all adherents of PCG expect a merger of the two theories.

Carlo Rovelli, physicist at the University of Marseille and founder of the PCG theory believes in the dominance of his theory.

“The string community is not as arrogant as it was ten years ago, especially after the severe disappointment of the lack of supersymmetric particles,” he says. – It is possible that the two theories could be part of one solution... but I think it’s unlikely. In my opinion, string theory has failed to deliver what it promised in the 1980s and is one of those ideas that look nice but don't describe the real world, of which the history of science has been replete. I don’t understand how people can still place their hopes in her.”

Pullin believes that it is premature to declare victory:

“Adherents of PCG say that their theory is the only correct one. I won't sign up for this. It seems to me that both theories are extremely incomplete."

Despite more than half a century of attempts, gravity is the only fundamental interaction for which a generally accepted consistent quantum theory has not yet been constructed. At low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as the exchange of gravitons - spin-2 gauge bosons.

However, in Lately Three promising approaches to solving the problem of quantizing gravity have been developed: string theory, loop quantum gravity and causal dynamic triangulation.

String theory

In it, instead of particles and background space-time, there are strings and their multidimensional analogues - branes. For high-dimensional problems, branes are high-dimensional particles, but from the point of view of the particles moving inside these branes, they are space-time structures. A variant of string theory is M-theory.

Loop quantum gravity

It attempts to formulate a quantum field theory without reference to the space-time background; according to this theory, space and time consist of discrete parts. These small quantum cells of space are connected to each other in a certain way, so that on small scales of time and length they create a motley, discrete structure of space, and on large scales they smoothly transform into continuous smooth space-time. Although many cosmological models can describe the behavior of the universe only from Planck time after Big Bang, loop quantum gravity can describe the explosion process itself, and even look ahead. Loop quantum gravity allows us to describe all standard model particles without requiring the introduction of the Higgs boson to explain their masses.

• Translation

Two candidates for a “theory of everything,” long considered incompatible, may turn out to be two sides of the same coin.

Eighty years have passed since physicists realized that the theories of quantum mechanics and gravity are incompatible, and the mystery of combining them remains unresolved. Over the past decades, researchers have studied this problem in two different ways - through string theory and through quantum gravity - which the scientists who practice them consider incompatible. But some scientists argue that to advance it is necessary to join forces.

Among the attempts to unify quantum theory and gravity, string theory has received the most attention. Its premise is simple: everything is made of little strings. The strings can be closed or open; they can vibrate, stretch, combine or disintegrate. And in this diversity lie explanations for all observable phenomena, including matter and space-time.

Loop quantum gravity (LQG), in contrast, places less emphasis on the matter present in spacetime and focuses more on the properties of spacetime itself. In the PKG theory, space-time is a network. The smooth background of Einstein's theory of gravity is replaced by nodes and links that are assigned quantum properties. Thus, the space consists of separate pieces. The PKG mainly studies these pieces.

This approach has long been considered incompatible with string theory. Indeed, their differences are obvious and profound. For starters, PCG studies chunks of space-time, and string theory studies the behavior of objects in space-time. These areas also share technical challenges. String theory requires that there be 10 dimensions in space; PKG does not work in higher dimensions. String theory assumes the existence of supersymmetry, in which all particles have as yet undiscovered partners. Supersymmetry is not characteristic of PCG.

These and other differences have divided the theoretical physics community into two camps. "The conferences are divided," says Dorge Pullin, a physicist at Louisiana State University and co-author of a textbook on PCG. – Loop players go to loop conferences, string players go to string conferences. Now they don’t even go to physics conferences. I think it's quite unfortunate."

But some factors may move these camps closer. New theoretical discoveries have revealed possible similarities between PKG and string theory. A new generation of string theorists has moved beyond string theory and began searching for methods and tools that could be useful in creating a “theory of everything.” And the recent paradox of information loss in black holes has made everyone feel more humble.

Moreover, in the absence of experimental evidence for string theory or PKG, mathematical proof that they are two sides of the same coin would provide evidence that physicists are moving in the right direction in their quest for a “theory of everything.” The combination of PKG and string theory would make the new theory unique.

An unexpected connection

Attempts to solve some problems of PKG led to the first unexpected connection with string theory. Physicists studying PKG do not have a clear understanding of how to move from pieces of a spacetime network to a large-scale description of spacetime that matches Einstein's general relativity, our best theory of gravity. Moreover, their theory cannot accommodate the special case in which gravity can be neglected. This is the problem that besets any attempt to use space-time in pieces: in SRT, the linear dimensions of an object decrease depending on the movement of the observer relative to the object. Compression also affects the size of pieces of space-time, which are perceived differently by observers moving at different speeds. This discrepancy leads to problems with the central principle of Einstein's theory - that the laws of physics do not depend on the speed of the observer.

“It's difficult to introduce discrete structures without running into SRT problems,” says Pullin. In a 2014 paper written with colleague Rudolfo Gambini, a physicist at the Universidad Republican de Uruguay in Montevideo, Pullin writes that aligning PKG with STR inevitably entails the appearance of interactions similar to those present in string theory.

That the two approaches had something in common had seemed likely to Pullin since a seminal discovery in the late 1990s by Juan Malzadena, a physicist at the Institute for Advanced Study in Princeton, New Jersey. Malzadena, in anti-De Sitter spacetime (AdS), reconciled the theory of gravity and conformal field theory (CFT) at the boundary of spacetime. Using the AdS/CFT approach, the theory of gravity can be described using a more understandable field theory.

The full version of dualism is still a hypothesis, but it has a well-understood limiting case that string theory does not deal with. Because strings do not play a role in this case, it can be used in any theory of quantum gravity. Pullin sees a common ground here.

PKG as imagined by an artist

Hermann Verlinde, a theoretical physicist at Princeton University who frequently works with string theory, says it is plausible that PKG methods could shed light on the gravitational side of dualism. In a recent paper, he described a simplified AdS/CFT model in two dimensions for space and one for time, or, as physicists say, in the “2+1” case. He discovered that the AdS space can be described using networks such as those used in PCG. Even though the entire design is still working in 2+1, it offers a new way of thinking about gravity. Verlinde hopes to generalize the model to more dimensions. “PKG was looked at too narrowly. My approach includes other areas as well. In an intellectual sense, this is a look into the future,” he said.

But even if it is possible to combine the methods of PKG and string theory to move forward with AdS space, the question remains: how useful will such a combination be? AdS space has a negative cosmological constant (this number describes the geometry of the Universe on large scales), while our Universe has a positive one. We do not live in a mathematical construct described by the AdS space.

Verlinde's approach is pragmatic. “For example, for a positive cosmological constant, we may need a new theory. The question then is how different it will be from this one. AdS is the best hint yet of the structure we are looking for, and we need to perform some trick to arrive at a positive constant.” He believes that scientists are not wasting their time with this theory: “Although AdS does not describe our world, it will give us lessons that will lead us in the right direction.”

Unification in the territory of a black hole

Verlinde and Pullin point to another possibility for the string theory and PKG communities to unite: the mysterious fate of information falling into a black hole. In 2012, four researchers from the University of California drew attention to a contradiction in the prevailing theory. They argued that if a black hole allowed information to escape from it, it would destroy the fine structure of empty space around the black hole's horizon, and create a high-energy barrier - a "firewall". But such a barrier is incompatible with the equivalence principle underlying general relativity, which states that an observer cannot tell whether he has crossed the horizon. This incompatibility has upset string theorists, who thought they understood the connection between black holes and information, and were forced to grab their notebooks again.

But this problem is important not only for string theorists. “This whole firewall debate has been mostly in the string theorist community, which I don't understand,” Verlinde said. “Issues of quantum information, entanglement and the construction of mathematical Hilbert space are what the PCG experts have been working on.”

At this time, an event occurred unnoticed by most string specialists - the fall of the barrier erected by supersymmetry and additional dimensions. Thomas Tiemann's group at the University of Erlangen-Nuremberg (Germany) has extended PKG to higher dimensions and included supersymmetry - concepts that were previously the exclusive domain of string theory.

Recently, Norbert Bodendorfer, a former student of Tiemann working at the University of Warsaw, applied loop quantification methods from PCG to AdS space. He argues that PKG is useful for dealing with AdS/CFT duality in cases where string theorists cannot make gravitational calculations. Bodendorfer believes that the gap that existed between the PKG and the strings is disappearing. “Sometimes I got the impression that string theorists have very little understanding of PKG and don’t want to talk about it,” he said. “But younger specialists demonstrate open-mindedness. They are very interested in what is happening at the intersection of regions.”

“The biggest difference is how we define our questions,” says Verlinde. “The problem is more sociological than scientific, unfortunately.” He doesn't think the two approaches conflict: “I've always thought of string theory and PKG as being part of the same description. PKG is a method, not a theory. This is a method of thinking about quantum mechanics and geometry. This is a method that string theorists can, and already do, use. These things are not mutually exclusive."

But not everyone is convinced. Moshe Rozali, a string theorist at the University of British Columbia, remains skeptical about the PKG: “The reason I don't work on the PKG is because it has problems with SRT,” he says. “If your approach is disrespectful of the symmetries in special relativity from the very beginning, you will need a miracle at one of the intermediate steps.” However, according to Rosalie, some of the mathematical tools that come from PCG can be useful. “I don’t think it is possible to combine PKG and string theory. But people usually need methods, and in that sense they are similar. Mathematical methods may overlap.”

Also, not all adherents of PCG expect a merger of the two theories. Carlo Rovelli, physicist at the University of Marseille and founder of the PCG theory believes in the dominance of his theory. “The string community is not as arrogant as it was ten years ago, especially after the disappointment of the lack of supersymmetric particles,” he says. – It is possible that the two theories could be part of one solution... but I think it’s unlikely. In my opinion, string theory has failed to deliver what it promised in the 1980s and is one of those ideas that look nice but don't describe the real world, of which the history of science has been replete. I don’t understand how people can still place their hopes in her.”

Pullin believes that it is premature to declare victory: “Adherents of the PCG say that their theory is the only correct one. I won't sign up for this. It seems to me that both theories are extremely incomplete."

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I was prompted to write a note about loop quantum gravity by several things. And one of them is on this topic, from which a person “not in the subject” will hardly understand at all what it’s about we're talking about. This is simply brilliant and completely useless for Wikipedia:

In a 2005 paper, Sundance Bilson-Thompson proposed a model (apparently based on more general theory braids (mathematical braids) by M. Khovanov), in which the Harari rishons were transformed into extended ribbon-like objects called ribbons. This could potentially explain the reasons for the self-organization of subcomponents elementary particles, leading to the emergence of a color charge, while in the previous preon (Rishon) model the basic elements were point particles, and the color charge was postulated. Bilson-Thompson calls his extended ribbons "gelons" and his model a gelon. This model leads to the interpretation of electric charge as a topological entity that arises when ribbons are twisted.

No shit here to a normal person It’s not clear, but here’s the thing.

The first known theory of gravity was created by Aristotle. He believed that bodies fall at different speeds, directly proportional to mass and inversely proportional to the density of the medium. This is almost true in the presence of friction. However, the theory still did not have much practical meaning at that time.

The scientific theory of gravity was created by Newton, everyone studied it at school, so I won’t remind you. Newton described the law according to which bodies attract each other. But by the 20th century, physicists switched from deriving laws to searching for causes. The important question is not “how”, but “why”. And none other than Einstein proposed a theory of gravity based on Riemannian geometry: gravity is determined by the curvature of four-dimensional space-time. Physics turned out to be modeled by rather abstract geometry. The theory is elegant and confirmed experimentally.

However, physicists did not stop there. The fact is that in the 20-30s quantum mechanics was developed, which quite quickly developed into quantum field theory. The point is that physical quantities are no longer continuous, but take on stepwise, discrete values. For example, energy. In quantum field theory, quanta, some indivisible “pieces,” became “carriers” of fundamental interactions. The simplest thing is photons in electrodynamics (or photons of light, for example). Or gluons - in the strong interaction of quarks. But the essence is similar. Moreover, the theories were built in such a way that at the micro level it was possible to “work” at the quantum level, but with a continuous transition to the macro level, all the typical properties of the field were obtained. In physics, 4 types of fundamental fields (interactions) are known, and three of them are quantized. But not gravity. Moreover, the problems of quantizing the gravitational field turned out to be so fundamental that physicists began to look for other ways to “link” together all the fundamental fields (why? to explain how the world works), and string theories and other Theories of Everything appeared, based on exotic spaces and symmetries.

All these theories had one property that was very beloved by mathematicians - the geometry of space was considered continuous and smooth. Actually, this is how it is in Riemannian geometry, used by Einstein. In the mid-80s, Lee Smolin and his colleagues risked abandoning smoothness and continuity, and for the first time they managed to build a consistent quantum model of gravity, provided that space was also quantized! That is, it consists of “cells” of Planck length (ten minus 33 cm), connected in a bizarre way. For ease of presentation, instead of cells, they began to consider nodes, and their connections form what they began to call spin network. This allows you to specify any, no matter how curved, geometry. Unexpectedly, a seemingly abstract mathematical discipline - topology - suddenly became in demand here, since it is she who studies this kind of objects.

But the spin network is only an instantaneous “snapshot” of the state. In reality, at every moment in time something happens in the world, and this is expressed in the transformation of the network. Network plus time is called spin foam, because over time the network is constantly “seething”, experiencing endless transformations. The time “turned out” to be discrete too, with an interval between “ticks” of ten minus 43 cm.

Like any good theory (and this, by the way, is different from String Theory), the quantum theory of gravity allows for experiments that can confirm or refute it. At the moment, modern equipment does not allow such experiments to be carried out - the effects that the “grain” of space gives are too small - but the technology and imagination of scientists do not stand still. In any case, such experiments do not seem impossible.

It has also recently been proven that loop quantum gravity “in the limit” leads to the Einstein model (however, otherwise it would not make sense). It is interesting that, unlike Einstein’s theory, in “our” theory the Universe exists before the Big Bang.

Now it's time to return to what Wikipedia writes about. In fact, about the important things. The fact that the theory of loop quantum gravity allows us to deduce