A new approach to the problem of quantum gravity, over which scientists have been struggling for many decades, returns to the basics and shows how the “bricks” from which space and time are built “add up” to each other.

How did space and time originate? How did they create the smooth 4D void that serves as the backdrop to our physical world? What do they look like on closer inspection? Questions like these arise at the forefront of modern science and push the exploration of quantum gravity - the still unfinished union of Einstein's general theory of relativity with quantum theory. The theory of relativity describes how space and time on a macroscopic scale can take on countless forms, creating what we call gravity or gravity. Quantum theory describes the laws of physics at the atomic and subatomic scales, completely ignoring the effects of gravity. The theory of quantum gravity must describe in quantum laws the nature of space-time on the smallest scales - the spaces between the smallest known elementary particles - and, perhaps, explain it through some fundamental components.

The main candidate for this role is often called superstring theory, but it has not yet answered any of the burning questions. Moreover, following its own internal logic, it uncovered even deeper layers of new exotic components and relationships between them, leading to a staggering variety of possible results.

MAIN PROVISIONS

It is well known that quantum theory and Einstein's general theory of relativity do not fit with each other. Physicists have long been trying to link them into a single theory of quantum gravity, but have not achieved much success.

The proposed new approach does not introduce any exotic provisions, but opens up a new way of applying known laws to individual elements of space-time. These elements come into agreement like molecules in a crystal.

Our approach shows how the four-dimensional spacetime we know can dynamically emerge from more fundamental components. Moreover, it suggests how this space-time on a microscopic scale gradually transitions from smooth continuity to bizarre fractality.

In recent years, our work has become a promising alternative to the well-trodden highway of theoretical physics. Following the simplest recipe - take a few fundamental components, assemble them in accordance with well-known quantum principles (without any exotics), mix well and let stand - you get quantum space-time. The process is simple enough to be simulated on a laptop computer.

In other words, if, considering the empty space-time (vacuum) as a kind of non-material substance, consisting of a very large number of microscopic structureless elements, we allow them to interact with each other in accordance with the simple rules of the theory of gravity and quantum theory, then these elements will spontaneously organize into a single a whole that in many respects will look the same as the observable universe. The process is similar to how molecules organize themselves into a crystalline or amorphous solid.

With this approach, space-time may look more like a regular mixed roast than an elaborate wedding cake. Moreover, unlike other approaches to quantum gravity, ours is very stable. When we change the details of our model, the result hardly changes. This resilience gives reason to hope that we are on the right track. If the result were sensitive to where we placed each piece of our vast ensemble, we would end up with an enormous number of equally probable baroque forms, which would eliminate the possibility of explaining why the universe turned out to be the way it is.

Similar mechanisms of self-assembly and self-organization operate in physics, biology and other fields of science. A beautiful example is the behavior of large flocks of birds, such as starlings. Individual birds interact with only a small number of neighbors; there is no leader who would explain to them what to do. Nevertheless, the pack forms and moves as a whole, possessing collective or derived properties that do not appear in the behavior of individual individuals.

A Brief History of Quantum Gravity

Previous attempts to explain the quantum structure of space-time as being formed in the process of spontaneous emergence did not bring noticeable success. They came from Euclidean quantum gravity. The research program was started in the late 1970s. and became popular thanks to the best-selling book Brief History of Time by physicist Stephen Hawking. This program is based on the principle of superposition, which is fundamental to quantum mechanics. Any object, classical or quantum, is in some state, characterized, for example, by position and speed. But if the state of a classical object can be described by a set of numbers peculiar only to it, then the state of a quantum object is much richer: it is the sum of all possible classical states.

THEORIES OF QUANTUM GRAVITATION

STRING THEORY
Supported by most theoretical physicists, this theory concerns not only quantum gravity, but all kinds of matter and forces. It is based on the notion that all particles (including hypothetical ones that carry gravity) are oscillating strings

LOOP QUANTUM GRAVITY
The main alternative to string theory. It involves a new method of applying the rules of quantum mechanics to Einstein's general theory of relativity. Space is divided into discrete "atoms" of volume

EUCLIDAN QUANTUM GRAVITY
An approach made famous by physicist Stephen Hawking is based on the assumption that spacetime emerges from a common quantum average of all possible shapes. In this theory, time is considered equal to spatial dimensions.

CAUSAL DYNAMIC TRIANGULATION
This approach, which is the subject of this article, is a modern version of the Euclidean approach. It is based on the approximation of space-time by a mosaic of triangles with the initial distinction between space and time. On a small scale, space-time acquires a fractal structure

For example, a classic billiard ball moves along a certain trajectory, and its position and speed can be precisely determined at any time. In the case of a much smaller electron, things are different. Its movement obeys quantum laws, according to which an electron can exist simultaneously in many places and have many speeds. In the absence of external influences from point A to point B, the electron does not move in a straight line, but along all possible paths simultaneously. A qualitative picture of all possible ways of its movement, collected together, turns into a rigorous mathematical "recipe" for quantum superposition, formulated by Nobel laureate Richard Feynman, and gives a weighted average of all individual possibilities.

Using the proposed recipe, one can calculate the probability of finding an electron in any particular range of positions and velocities away from the direct path along which it would have to move according to the laws of classical mechanics. A distinctive property of the quantum mechanical behavior of a particle is deviations from a single clear trajectory, the so-called. quantum fluctuations. The smaller the size of the considered physical system, the greater the role of quantum fluctuations.

In Euclidean quantum gravity, the principle of superposition applies to the entire universe as a whole. In this case, the superposition does not consist of different trajectories of the particle, but of the possible paths of the evolution of the universe in time, in particular, the forms of space-time. To reduce the problem to a solution, physicists usually consider only the general shape and size of spacetime, and not every conceivable distortion of it (see: Jonathan J. Halliwell. Quantum Cosmology and the Creation of the Universe // Scientific American , December 1991).

In the 1980s–1990s research in the field of Euclidean quantum gravity has come a long way, associated with the development of powerful computer simulation tools. The models used represented the geometries of curved space-time using elementary "bricks", which, for convenience, were considered triangular. Triangular meshes can effectively approximate curved surfaces, which is why they are often used in computer animation. In the case of space-time modeling, these elementary "building blocks" are generalizations of triangles in relation to four-dimensional space and are called 4-simplices. Just as gluing triangles together with their edges creates curved 2D surfaces, gluing the "faces" of 4D simplices (which are 3D tetrahedra) creates a 4D space-time model.

The "bricks" themselves have no direct physical meaning. If space-time could be viewed under a super-powerful microscope, no triangles would be visible. They are only approximations. The only information that makes physical sense is contained in their collective behavior in the notion that each of them has shrunk to size zero. In this limit, the geometry of the "bricks" (be they triangular, cubic, pentagonal, or any mixture of these shapes) does not matter.

Insensitivity to a variety of small scale details is often referred to as versatility. A well-known phenomenon in statistical physics, which studies the movement of molecules in gases and liquids: molecules behave in almost the same way, whatever their composition. Universality is associated with the properties of systems consisting of a large number of individual elements, and manifests itself on a scale much larger than the scale of a single component. A similar statement for a flock of birds is that the coloration, size, wingspan, and age of individual birds have nothing to do with the behavior of the flock as a whole. On a macroscopic scale, very few microscopic details show up.

cringe

With the help of computer models, researchers of quantum gravity began to study the effects of superposition of space-time forms, which are not amenable to study by the methods of classical relativity, in particular, strongly curved at very small distances. This so-called non-perturbing regime is of most interest to physicists, but is almost impossible to analyze without the use of computers.

DESCRIPTION OF THE FORM OF SPACE

MOSAIC FROM TRIANGLES
To determine how space shapes itself, physicists first need a way to describe its shape. They describe it in terms of triangles and their high-dimensional counterparts, the mosaic of which makes it possible to approximate curved shapes. The curvature at a particular point is determined by the total angle subtracted by the triangles that surround that point. In the case of a flat surface, this angle is exactly 360°, but in the case of curved surfaces, it can be smaller or larger.

Unfortunately, simulations have shown that Euclidean quantum gravity does not take into account important components of behavior. All nonperturbing superpositions in the four-dimensional universe turned out to be unstable in principle. The small-scale quantum fluctuations of curvature that characterize the various superimposed universes that contribute to the average do not cancel out but mutually reinforce each other, causing all of space to shrink into a small ball with an infinite number of dimensions. In such a space, the distance between any two points always remains very small, even if its volume is huge. In some cases, space goes to the other extreme, becoming extremely thin and extended, like a polymer with many branches. None of these possibilities are similar to our real universe.

Before we return once more to the assumptions that led physicists to a dead end, let's consider one oddity of the result. The "bricks" are four-dimensional, but together they form either a space with an infinite number of dimensions (a shrinking universe) or a two-dimensional space (a polymer universe). Once the assumption of large quantum fluctuations in the vacuum let the genie out of the bottle, it became possible to change the most fundamental concepts, such as dimension. Perhaps the classical theory of gravity, in which the number of dimensions is always assumed to be certain, could not have foreseen such a result.

One consequence may be somewhat disappointing to fans of science fiction. Science fiction writers often use the concept of space-time tunnels, as if they allow areas that are far apart to be brought closer to each other. They captivate with the promising possibility of time travel and transmission of signals at speeds exceeding the speed of light. Despite the fact that nothing like this has ever been observed, physicists admit that such tunnels may be rehabilitated in the framework of the not yet created theory of quantum gravity. In light of the negative result of computer simulations of Euclidean quantum gravity, the possibility of the existence of such tunnels seems extremely unlikely. Space-time tunnels have so many variations that they must dominate the superposition, making it unstable, so that the quantum universe can never grow beyond a small but highly interconnected totality.

APPLICATION OF QUANTUM RULES TO SPACE-TIME

AVERAGE
Space-time can take on a great many different forms. According to quantum theory, the shape we are most likely to see is a superposition, or a weighted average of all possible shapes. When composing shapes from triangles, theorists assign a weight to each of them, depending on the specific way these triangles are connected when constructing a given shape. The authors found that in order for the resulting average to be consistent with the observed real Universe, triangles must obey certain rules, in particular, contain built-in "arrows" indicating the direction of time

What could be the root of the trouble? Looking for gaps and "loose ends" in the Euclidean approach, we came up with a key idea - one component that is absolutely necessary for the possibility of preparing our mixed roast: the code of the universe must include the principle of causality, i.e. the structure of the vacuum must provide the possibility of an unambiguous distinction between cause and effect. Causality is an integral part of the classical particular and general theories of relativity.

Causality is not included in Euclidean quantum gravity. The definition of "Euclidean" means that space and time are considered equivalent. The universes included in the Euclidean superposition have four spatial dimensions instead of one temporal and three spatial ones. Since the Euclidean universes do not have a separate concept of time, they do not have a structure that allows events to be arranged in a certain order. The inhabitants of such universes cannot have the concepts of "cause" and "effect". Hawking and other Euclidean scientists have said that "time is imaginary" in both the mathematical and colloquial senses. They hoped that causality would arise as a macroscopic property from microscopic quantum fluctuations that did not individually have signs of a causal structure. However, computer simulation dashed their hopes.

A COMPLETELY NEW DIMENSION IN SPACE

In ordinary life, the dimension of space is the minimum number of dimensions required to determine the position of a point, such as longitude, latitude and height. This definition is based on the assumption that space is continuous and subject to the laws of classical physics. And if the space behaves not so simply? What if its form is determined by quantum processes that do not manifest themselves in ordinary life? In such cases, physicists and mathematicians must develop a more sophisticated notion of dimension. The number of dimensions may not even necessarily be an integer, as in the case of fractals - structures that have the same appearance at all scales.

GENERALIZED DIMENSIONAL DEFINITIONS

Hausdorff dimension
The definition formulated at the beginning of the 20th century. German mathematician Felix Hausdorff, proceeds from the dependence of the volume V of the region on its linear size r. In ordinary three-dimensional space, V is proportional to $r^3$. The exponent in this relationship is the number of measurements. "Volume" can be considered other indicators of the total size, such as area. In the case of the Sierpinski gasket, V is proportional to $r^(1.5850)$. This circumstance reflects the fact that this figure does not fill the entire area

Spectral dimension
This definition characterizes the spread of an object or phenomenon in the environment over time, whether it is a drop of ink in a vessel with water or a disease in a population. Each water molecule or individual in a population has a certain number of nearest neighbors, which determines the rate of ink diffusion or disease spread. In a 3D environment, the size of an ink cloud grows in proportion to time to the power of 3/2. In Sierpiński's pad, the ink must seep through the sinuous shape, so it spreads more slowly - proportional to time to the power of 0.6826, which corresponds to a spectral dimension of 1.3652

Application of definitions
In the general case, different ways of calculating the dimension give different numbers of dimensions, since they start from different characteristics of the geometry. For some geometric shapes, the number of dimensions is not constant. In particular, diffusion can be a more complex function than time to some constant degree.
When modeling quantum gravity, the emphasis is on the spectral dimension. A small amount of some substance is introduced into one elementary brick of the quantum space-time model. From this brick, it spreads randomly. The total number of space-time bricks that this substance reaches in a certain period of time determines the spectral dimension

Instead of neglecting causality when linking separate universes in the expectation that it would emerge from the collective wisdom of superposition, we chose to include causality at a much earlier stage. We called our method dynamic triangulation. We have assigned to each simplex an arrow of time pointing from the past to the future. Then we introduced the causal “gluing” rule: two simplexes must be glued in such a way that their arrows are aligned. The concept of time in the simplices to be glued together must be the same: time must flow at a constant speed in the direction of these arrows, never stopping or turning back. In the course of time, space must retain its overall shape, not break up into separate parts and not create space-time tunnels.

Having formulated this strategy in 1998, we showed on extremely simplified models that the rules for gluing simplices lead to a macroscopic form different from Euclidean quantum gravity. This was encouraging, but did not mean that the accepted gluing rules were sufficient to ensure the stability of the entire four-dimensional universe. So we held our breath when, in 2004, our computer was almost ready to give us the first calculations of the causal superposition of four-dimensional simplices. Will this space-time behave at large distances like an extended four-dimensional object, and not like a shriveled ball or polymer?

Imagine our delight when the number of dimensions of the calculated universe turned out to be 4 (more precisely, 4.02 ± 0.1). This was the first time that the number of dimensions equal to the observed was deduced from the fundamental principles. Today, introducing the concept of causality into the quantum gravity model is the only known way to deal with the instabilities of the superposition of space-time geometries.

Space-time in general

This simulation was the first in an ongoing series of computational experiments in which we attempt to deduce the physical and geometric properties of quantum spacetime through computer simulations. Our next step was to study the shape of space-time at large distances and check its correspondence to the real world, i.e. predictions of the general theory of relativity. In the case of nonperturbative models of quantum gravity, which do not contain an a priori assumption about the shape of spacetime, such a test is very difficult - so much so that in most approaches to quantum gravity, including string theory, except for special cases, the success achieved is insufficient to carry it out.

DEEPING INTO SPACE-TIME

According to the authors' calculations, the spectral dimension of space-time decreases from four (in the limit of a large scale) to two (in the limit of a small scale), and the continuous space-time breaks up, turning into a branched fractal. Physicists are not yet able to understand whether this conclusion means that in the end space-time consists of localized "atoms", or whether it is built from microscopic structures that are very loosely related to the usual concept of geometry.

As it turned out, in order for our model to work, it is necessary from the very beginning to introduce the so-called cosmological constant - an invisible and non-material substance contained in space even in the absence of any other forms of matter and energy. This need is good news, as cosmologists have found experimental confirmation of the existence of this constant. Moreover, the obtained form of space-time corresponded to the de Sitter geometry, i.e. solving Einstein's equations for a universe containing nothing but the cosmological constant. It is truly remarkable that the assembly of an ensemble of microscopic "bricks" in an almost random way - without any assumption of symmetry or preferred geometric structure - led to a space-time that has, on a large scale, the highly symmetrical shape of the de Sitter universe.

The dynamic emergence of a four-dimensional universe of almost regular geometric shape from the basic principles has become a central achievement of our modeling. The question of whether this outstanding result can be understood within the framework of ideas about the interaction of some not yet established "atoms" of space-time is the goal of our ongoing research. Since we have seen that our model of quantum gravity has passed a number of classical tests, it is time to turn to experiments of a different kind - to reveal the distinctive quantum structure of space-time that Einstein's classical theory could not reveal. In one of these experiments, we modeled the diffusion process: we introduced a suitable analogue of an ink drop into a superposition of universes and observed how it propagates and is perturbed by quantum fluctuations. Finding the size of the ink cloud over time allowed us to determine the number of dimensions in space (see sidebar).

The result was stunning: the number of measurements depends on the scale. In other words, if diffusion continued for a short time, then the number of dimensions of space-time turned out to be different than when the diffusion process went on for a long time. Even those of us who specialized in quantum gravity could hardly imagine how the number of dimensions of space-time could change continuously depending on the resolution of our "microscope". Obviously, the space-time for small objects is very different from that for large ones. For small objects, the universe is like a fractal structure - an unusual kind of space in which the concept of size simply does not exist. It is self-similar, i.e. looks the same in all scales. This means that there are no objects of characteristic size that could serve as something like a scale bar.

How small is "small"? Up to a size of about $10^(–34)$m, the quantum universe as a whole is well described by the classical four-dimensional de Sitter geometry, although the role of quantum fluctuations increases with decreasing distance. The fact that the classical approximation remains valid down to such small distances is surprising. Very important consequences flow from it both for the earliest stages of the history of the universe, and for its very distant future. In both these limits, the universe is practically empty. At the very beginning, quantum fluctuations were so great that matter was barely detectable. She was a tiny raft on a rippling ocean. Billions of years after us, due to the rapid expansion of the Universe, the matter will be so rarefied that it will play a very small role or even will not play a role at all. Our approach allows us to explain the shape of space in both limiting cases.

WHAT IS CAUSE?

Causality is the principle that events occur in a certain sequence in time, and not in disorder, which makes it possible to distinguish between cause and effect. In the approach to quantum gravity adopted by the authors, the difference between cause and effect appears as a fundamental property in nature, and not a derived property.

On even smaller scales, the quantum fluctuations of space-time increase so much that classical intuitions about geometry completely lose their meaning. The number of dimensions is reduced from the classical four to approximately two. However, as far as we can tell, space-time remains continuous and does not contain any tunnels. It is not as exotic as the seething space-time foam that physicist John Wheeler and many others have seen. The geometry of space-time obeys unusual and non-classical laws, but the concept of distance remains applicable. Now we are trying to penetrate into an even smaller area. One possibility is that the universe becomes self-similar and looks the same at all scales below a certain limit. If so, then the universe is not made up of strings or atoms of space-time, but is a world of endless boredom: a structure found just below the threshold, as it goes deeper into a region of ever smaller dimensions, will simply repeat itself ad infinitum.

It is hard to imagine how physicists can manage with fewer components and technical means than we used to build a quantum universe with realistic properties. We still have a lot of tests and experiments to do, for example, in order to understand the behavior of matter in the universe and its influence on its overall shape. Our main goal, as with any theory of quantum gravity, is to predict the observable consequences of the microscopic quantum structure. This will be the decisive criterion for the correctness of our model as a theory of quantum gravity.

Translation: I.E. Satsevich

ADDITIONAL LITERATURE

• Planckian Birth of a Quantum de Sitter Universe. J. Ambjorn, A. Gorlich, J. Jurkiewicz and R. Loll in Physical Review Letters, Vol. 100, article no. 091304; March 7, 2008. Preprint available
• The Complete Idiot's Guide to String Theory. George Musser. Alpha, 2008.
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop. R. Loll in Classical and Quantum Gravity, Vol. 25, no. 11, article no. 114006; June 7, 2008. Preprint available
• Renata Loll website

Jan Ambjorn, Renate Loll and Jerzy Jurkewicz developed their approach to the problem of quantum gravity in 1998. Ambjorn is a member of the Royal Danish Academy, a professor at the Niels Bohr Institute in Copenhagen and Utrecht University in the Netherlands. He is known as a master of Thai cuisine - a circumstance that publishers tend to note first. Renata Loll is a professor at the University of Utrecht, where she leads one of the largest quantum gravity research teams in Europe. Previously she worked at the Max Planck Institute for Gravity Physics in Holm (Germany). In rare leisure hours, chamber music is played. Jerzy Yurkiewicz is the head of the Department of Complex Systems Theory at the Physical Institute of the Jagiellonian University in Krakow. Among his previous jobs is the Niels Bohr Institute in Copenhagen, where he was captivated by the beauty of sailing.

Two English physicists, one of whom studies elementary particles (Brian Cox), and the other is a professor at the Department of Theoretical Physics at the University of Manchester (Jeff Forshaw), introduce us to the fundamental model of the world.

Using accessible language, numerous drawings and good analogies, the authors were able to explain the concepts of quantum physics that are difficult to understand.

Brian Cox, Jeff Forshaw:

The goal of this book is to demystify quantum theory, a theoretical construct that has confused too many, including even the pioneers of the industry. We intend to use a modern perspective, using the lessons learned over the centuries of hindsight and theory development. However, at the start of the journey, we will be transported to the beginning of the 20th century and explore some of the problems that forced physicists to radically deviate from what was previously considered the mainstream of science.

1. Something strange is coming

Quantum theory is perhaps the best example of how the infinitely difficult to understand by most people becomes extremely useful. It is difficult to understand because it describes a world in which a particle can actually be in several places at the same time and move from one place to another, thereby exploring the entire Universe. We found that everything is made up of many tiny particles that move according to the laws of quantum theory. These laws are so simple that they can be written on the back of an envelope. And the fact that an entire library is not required to explain the deep nature of things is in itself one of the greatest mysteries of the world.

2. In two places at the same time

The most unusual predictions of quantum theory usually show up in the behavior of small objects. But since large objects are made up of small ones, under certain circumstances quantum physics is required to explain the properties of one of the largest objects in the universe, the stars.

3. What is a particle?

Having established that the description of the electron mimics the behavior of waves in many respects, we must develop more precise concepts of the waves themselves. Let's start by describing what happens in a water tank when two waves meet, mix, and interfere with each other. Let's represent the wave highs as clocks with a 12 o'clock hand and the lows as clocks with a 6 o'clock hand. We can also represent wave positions intermediate between the minimum and maximum by drawing clocks with intermediate times, as in the case of phases between new and full moon.

4. Anything That Can Happen Really Happens

Heisenberg uncertainty principle

In his original work, Heisenberg was able to appreciate the relationship between the accuracy of measuring the position and momentum of a particle. The Heisenberg Uncertainty Principle is one of the most misunderstood parts of quantum theory, the path down which all sorts of charlatans and purveyors of nonsense push their philosophical nonsense.

Derivation of the Heisenberg Uncertainty Principle from the Theory of Clock Faces

Three dials, showing the same time and located on the same line, describe the particle, which at the initial moment is somewhere in the area of ​​these dials. We are interested in what are the chances of finding a particle at point X at some subsequent time.

A Brief History of Planck's Constant

Planck destroyed the first stones in the foundation of Maxwell's concept of light, showing that the energy of light emitted by a heated body can only be described if it is emitted in quanta.

Back to the Heisenberg Uncertainty Principle

The theory of quantum mechanics that we developed suggests that if you place a grain of sand at some point, it can later end up anywhere else in the universe. But it is obvious that this does not happen with real grains of sand. The first question to be answered is: how many times will the hands of the clock turn if we move a particle with the mass of a grain of sand a distance of, say, 0.001 mm in one second?

5. Movement as an illusion

Having set the initial group with the help of clocks showing different, and not the same time, we came to the description of a moving particle. Interestingly, we can make a very important connection between shifted clocks and wave behavior.

Wave Packs

A particle with a well-known momentum is described by a large group of dials. More precisely, a particle with exactly known momentum will be described by an infinitely long group of clocks, which means an infinitely long wave packet.

6. Music of atoms

Now we can apply our accumulated knowledge to solve the question that baffled Rutherford, Bohr and other scientists in the first decades of the 20th century: what exactly happens inside the atom? …Here we will try for the first time with the help of our theory to explain the phenomena of the real world.

atomic box

We seem to have worked out a correct view of atoms. But still, something is not quite right. The last piece of the puzzle is missing, without which it is impossible to explain the structure of atoms heavier than hydrogen. More prosaically, we also fail to explain why we do not actually fall through the ground, which creates problems for our wonderful theory of nature.

7. The universe on a pinhead (and why we don't fall through the ground)

Matter can only be stable if electrons obey the so-called Pauli principle, one of the most amazing phenomena in our quantum universe.

8. Interdependence

Until now, we have paid close attention to the quantum physics of isolated particles and atoms. However, our physical experience is connected with the perception of many atoms grouped together, and therefore it is time to start understanding what happens when atoms group together.

9. Modern world

The transistor is the most important invention of the last 100 years: the modern world is built on and shaped by semiconductor technology.

10. Interaction

Let's start with the formulation of the laws of the first open quantum field theory - quantum electrodynamics, abbreviated as QED. The origins of this theory date back to the 1920s, when Dirac was particularly successful in putting Maxwell's electromagnetic theory on a quantum footing.

The problem of measurement in quantum theory

We can move forward believing that the world has changed irreversibly as a result of the measurement, even though nothing of the sort actually happened. But all this is not so important when it comes to the serious task of calculating the probability that something will happen when setting up an experiment.

antimatter

Electrons moving backward in time look like "electrons with a positive charge". Such particles do exist and are called "positrons".

11. Empty space is not so empty.

The vacuum is a very interesting place, full of possibilities and obstacles in the path of particles.

Standard Model of Particle Physics

The Standard Model does contain a cure for the disease of high probability, and this cure is known as the Higgs mechanism. If it is true, then the Large Hadron Collider should detect another natural particle, the Higgs boson, after which our views on the contents of empty space should change dramatically.

Origin of mass

The question of the origin of mass is especially remarkable in that the answer to it is valuable beyond our obvious desire to know what mass is. Let's try to explain this rather mysterious and strangely constructed sentence in more detail.

Epilogue: Death of the Stars

As they die, many stars end up as superdense balls of nuclear matter entwined with many electrons. These are the so-called white dwarfs. This will be the fate of our Sun when it runs out of nuclear fuel in about 5 billion years.

For further reading

We have used many other works in the preparation of this book, and some of them deserve special mention and recommendation.

Cox B., Forshaw D. The quantum universe.
How is it that we cannot see. M.: MIF. 2016.

Brian Cox, Jeff Forshaw

quantum universe. How is it that we cannot see

Scientific editors Vyacheslav Maracha and Mikhail Pavlov

Published with permission from Apollo's Children Ltd and Jeff Forshow and Diane Banks Associates Ltd.

Legal support for the publishing house is provided by Vegas Lex law firm.

© Brian Cox and Jeff Forshaw, 2011

© Translation into Russian, edition in Russian, design. LLC "Mann, Ivanov and Ferber", 2016

* * *

1. Something strange is coming

Quantum. This word simultaneously appeals to the senses, confuses and fascinates. Depending on one's point of view, this is either evidence of the vast advances of science, or a symbol of the limitations of human intuition, which is forced to struggle with the inevitable strangeness of the subatomic realm. For a physicist, quantum mechanics is one of the three great pillars on which the understanding of nature rests (the other two are Einstein's general and special theories of relativity). Einstein's theories deal with the nature of space and time and the force of gravity. Quantum mechanics takes care of everything else, and it can be said that, no matter how emotionally appealing, confusing or fascinating, it is just a physical theory describing how nature actually behaves. But even if measured by this very pragmatic criterion, it is striking in its accuracy and explanatory power. There is one experiment from the field of quantum electrodynamics, the oldest and best understood of modern quantum theories. It measures how an electron behaves near a magnet. Theoretical physicists worked hard for years with pen and paper, and later with computers, to predict exactly what such studies would reveal. Practitioners invented and set up experiments to find out more details from nature. Both camps, independently of each other, gave results with an accuracy similar to measuring the distance between Manchester and New York with an error of a few centimeters. It is noteworthy that the figures obtained by the experimenters fully corresponded to the results of the calculations of theorists; measurements and calculations were in complete agreement.

This is not only impressive but surprising, and if model building were the sole concern of quantum theory, you might rightly ask what the problem is. Science doesn't have to be useful, of course, but many of the technological and social changes that have revolutionized our lives have come from fundamental research conducted by modern scientists who are driven only by a desire to better understand the world around them. Thanks to these curiosity-driven discoveries across all branches of science, we have extended lifespans, international air travel, freedom from the need to farm for our own survival, and a broad, inspiring, and eye-opening picture of our place in an endless sea of ​​stars. But all this is, in a sense, by-products. We explore out of curiosity, not because we want to gain a better understanding of reality or develop better trinkets.

Quantum theory is perhaps the best example of how what is infinitely difficult for most people to understand becomes extremely useful. It is difficult to understand because it describes a world in which a particle can actually be in several places at the same time and move from one place to another, thereby exploring the entire Universe. It is useful because understanding the behavior of the smallest building blocks of the universe strengthens the understanding of everything else. It puts a limit to our arrogance, because the world is much more complex and diverse than it seemed. Despite all this complexity, we found that everything is made up of many tiny particles that move in accordance with the laws of quantum theory. These laws are so simple that they can be written on the back of an envelope. And the fact that an entire library is not required to explain the deep nature of things is in itself one of the greatest mysteries of the world.

So, the more we learn about the elementary nature of the universe, the simpler it seems to us. Gradually, we will come to understand all the laws and how these little building blocks interact to form the world. But as fascinated as we are by the simplicity that underlies the universe, we must remember that although the basic rules of the game are simple, their consequences are not always easy to calculate. Our daily experience of knowing the world is determined by the relationships of many billions of atoms, and it would be simply foolish to try to deduce the principles of the behavior of people, animals and plants from the nuances of the behavior of these atoms. Having recognized this, we do not diminish its importance: behind all phenomena, in the end, the quantum physics of microscopic particles is hidden.

Imagine the world around us. You are holding a book made of paper - ground wood pulp. Trees are machines capable of taking atoms and molecules, breaking them down, and reorganizing them into colonies of billions of individual pieces. They do this thanks to a molecule known as chlorophyll, which is made up of over a hundred carbon, hydrogen, and oxygen atoms that are curved in a special way and bonded to a few more magnesium and hydrogen atoms. Such a combination of particles is able to capture light that has flown 150,000,000 km from our star - a nuclear chamber with a volume of a million planets like the Earth - and transport this energy deep into cells, where it creates new molecules from carbon dioxide and water and releases a giving our life is oxygen.

It is these molecular chains that form the superstructure that holds together the trees, the paper in this book, and all life. You are able to read a book and understand the words because you have eyes that can turn the scattered light from the pages into electrical impulses that can be interpreted by the brain, the most complex structure in the universe that we know of. We have found that all things in the world are nothing more than a collection of atoms, and the widest variety of atoms consists of only three particles - electrons, protons and neutrons. We also know that protons and neutrons themselves are made up of smaller entities called quarks, and that's where it all ends - at least that's what we think now. All of this is based on quantum theory.

Thus, modern physics draws a picture of the Universe in which we live with exceptional simplicity; elegant phenomena occur somewhere where they cannot be seen, giving rise to the diversity of the macrocosm. Perhaps this is the most remarkable achievement of modern science - reducing the incredible complexity of the world, including humans themselves, to a description of the behavior of a handful of tiny subatomic particles and four forces acting between them. The best descriptions of three of these four forces—the strong and weak nuclear forces that exist inside the atomic nucleus, and the electromagnetic force that holds atoms and molecules together—are provided by quantum theory. Only the force of gravity - the weakest, but perhaps the most familiar force of all - does not currently have a satisfactory quantum description.

It is worth admitting that quantum theory has a somewhat strange reputation, and a lot of real nonsense is covered by its name. Cats can be both alive and dead at the same time; particles are in two places at the same time; Heisenberg claims that everything is uncertain. All this is indeed true, but the conclusions that often follow from this - since something strange happens in the microcosm, then we are shrouded in a haze of fog - are definitely wrong. Extrasensory perception, mystical healings, vibrating bracelets that protect against radiation, and who knows what else regularly sneaks into the pantheon of the possible under the guise of the word "quantum". This nonsense is caused by inability to think clearly, self-deception, genuine or feigned misunderstanding, or some particularly unfortunate combination of all of the above. Quantum theory accurately describes the world with mathematical laws as specific as those used by Newton or Galileo. This is why we can calculate the magnetic field of an electron with incredible accuracy. Quantum theory offers a description of nature that, as we will learn, has tremendous predictive and explanatory power and extends to everything from silicon chips to stars.

The purpose of this book is to demystify quantum theory, a theoretical construct that has confused too many, including even the pioneers of the industry. We intend to use a modern perspective, using the lessons learned over the centuries of hindsight and theory development. However, at the start of the journey, we will be transported to the beginning of the 20th century and explore some of the problems that forced physicists to radically deviate from what was previously considered the mainstream of science.

Depending on one's point of view, quantum theory is either a testament to the vast advances of science, or a symbol of the limitations of human intuition, which is forced to contend with the strangeness of the subatomic realm. For a physicist, quantum mechanics is one of the three great pillars on which the understanding of nature is based (along with Einstein's general and special theories of relativity). For those who have always wanted to understand at least something in the fundamental model of the world, scientists Brian Cox and Jeff Forshaw explain in their book "The Quantum Universe", which was published by MIF. T & P publish a short passage about the essence of the quantum and the origins of the theory.

Einstein's theories deal with the nature of space and time and the force of gravity. Quantum mechanics takes care of everything else, and it can be said that no matter how emotionally appealing, confusing or fascinating, it is just a physical theory describing how nature actually behaves. But even if measured by this very pragmatic criterion, it is striking in its accuracy and explanatory power. There is one experiment from the field of quantum electrodynamics, the oldest and best understood of modern quantum theories. It measures how an electron behaves near a magnet. Theoretical physicists worked hard for years with pen and paper, and later with computers, to predict exactly what such studies would reveal. Practitioners invented and set up experiments to find out more details from nature. Both camps, independently of each other, gave results with an accuracy similar to measuring the distance between Manchester and New York with an error of a few centimeters. It is noteworthy that the figures obtained by the experimenters fully corresponded to the results of the calculations of theorists; measurements and calculations were in complete agreement.

Quantum theory is perhaps the best example of how what is infinitely difficult for most people to understand becomes extremely useful. It is difficult to understand because it describes a world in which a particle can actually be in several places at the same time and move from one place to another, thereby exploring the entire Universe. It is useful because understanding the behavior of the smallest building blocks of the universe strengthens the understanding of everything else. It puts a limit to our arrogance, because the world is much more complex and diverse than it seemed. Despite all this complexity, we found that everything is made up of many tiny particles that move in accordance with the laws of quantum theory. These laws are so simple that they can be written on the back of an envelope. And the fact that an entire library is not required to explain the deep nature of things is in itself one of the greatest mysteries of the world.

Imagine the world around us. Let's say you are holding a book made of paper - ground wood pulp. Trees are machines capable of taking atoms and molecules, breaking them down and reorganizing them into colonies of billions of individual pieces. They do this thanks to a molecule known as chlorophyll, which is made up of over a hundred carbon, hydrogen, and oxygen atoms that are curved in a special way and bonded to a few more magnesium and hydrogen atoms. Such a combination of particles is able to capture light that has flown 150,000,000 km from our star - a nuclear chamber with a volume of a million planets like the Earth - and transport this energy deep into the cells, where it creates new molecules from carbon dioxide and water and releases giving our life is oxygen.

It is these molecular chains that form the superstructure that holds together the trees, the paper in this book, and all life. You are able to read a book and understand the words because you have eyes and they can turn the scattered light from the pages into electrical impulses that can be interpreted by the brain, the most complex structure in the universe that we even know about. We have found that all things in the world are nothing more than a collection of atoms, and the widest variety of atoms consists of only three particles - electrons, protons and neutrons. We also know that the protons and neutrons themselves are made up of smaller entities called quarks, and they are the end of everything - at least that's what we think now. All of this is based on quantum theory.

Thus, modern physics draws a picture of the Universe in which we live with exceptional simplicity; elegant phenomena occur somewhere where they cannot be seen, giving rise to the diversity of the macrocosm. Perhaps this is the most remarkable achievement of modern science - the reduction of the incredible complexity of the world, including humans themselves, to a description of the behavior of a handful of tiny subatomic particles and four forces acting between them. The best descriptions of three of these four forces - the strong and weak nuclear forces that exist inside the atomic nucleus, and the electromagnetic force that holds atoms and molecules together - are provided by quantum theory. Only the force of gravity - the weakest, but perhaps the most familiar force of all - does not currently have a satisfactory quantum description.

It is worth admitting that quantum theory has a somewhat strange reputation, and a lot of real nonsense is covered by its name. Cats can be both alive and dead at the same time; particles are in two places at the same time; Heisenberg claims that everything is uncertain. All this is indeed true, but the conclusions that often follow from this - once something strange happens in the microcosm, then we are shrouded in a haze of fog - are definitely wrong. Extrasensory perception, mystical healings, vibrating bracelets that protect against radiation, and who knows what else regularly sneaks into the pantheon of the possible under the guise of the word "quantum". This nonsense is caused by inability to think clearly, self-deception, genuine or feigned misunderstanding, or some particularly unfortunate combination of all of the above. Quantum theory accurately describes the world with mathematical laws as specific as those used by Newton or Galileo. This is why we can calculate the magnetic field of an electron with incredible accuracy. Quantum theory offers a description of nature that, as we will learn, has tremendous predictive and explanatory power and extends to everything from silicon chips to stars.

As often happens, the emergence of quantum theory provoked the discovery of natural phenomena that could not be described by the scientific paradigms of that time. For quantum theory, there were many such discoveries, moreover, of a diverse nature. A series of unexplained results generated excitement and confusion, and eventually sparked a period of experimental and theoretical innovation that truly deserves the popular term "golden age." The names of the main characters are forever rooted in the minds of any physics student and are mentioned more often than others in university courses to this day: Rutherford, Bohr, Planck, Einstein, Pauli, Heisenberg, Schrödinger, Dirac. Perhaps there will never again be a period in history when so many names will be associated with the greatness of science while moving towards a single goal - the creation of a new theory of atoms and forces that govern the physical world. In 1924, looking back over the previous decades of quantum theory, Ernest Rutherford, the New Zealand-born physicist who discovered the atomic nucleus, wrote: “1896 … marked the beginning of what has been quite aptly called the heroic age of physical science. Never before in the history of physics has there been such a period of feverish activity, during which some fundamentally significant discoveries were replaced by others at breakneck speed.

Only until June 30, T&P readers have a discount on paper and electronic versions of the book. Discounts are activated when you click on the links.

The term "quantum" appeared in physics in 1900 thanks to the work of Max Planck. He tried to theoretically describe the radiation emitted by heated bodies - the so-called "radiation of a completely black body." By the way, the scientist was hired for this purpose by a company engaged in electric lighting: this is how the doors of the universe sometimes open for the most prosaic reasons. Planck found that the properties of black body radiation can only be explained by assuming that light is emitted in small portions of energy, which he called quanta. The word itself means "packages", or "discrete". Initially, he thought it was just a mathematical trick, but Albert Einstein's 1905 work on the photoelectric effect supported the quantum hypothesis. The results were compelling because small amounts of energy could be synonymous with particles.

The idea that light is made up of a stream of small bullets has a long and illustrious history, dating back to Isaac Newton and the birth of modern physics. However, in 1864, the Scottish physicist James Clark Maxwell seemed to finally dispel all existing doubts in a series of works that Albert Einstein later described as "the most profound and fruitful that physics has known since Newton." Maxwell showed that light is an electromagnetic wave propagating in space, so the idea of ​​light as a wave had an irreproachable and seemingly undeniable origin. However, in a series of experiments that Arthur Compton and his colleagues conducted at Washington University in St. Louis, they succeeded in separating light quanta from electrons. Both of them behaved more like billiard balls, which clearly confirmed that Planck's theoretical assumptions had a solid foundation in the real world. In 1926 light quanta were called photons. The evidence was irrefutable: light behaves both as a wave and as a particle. This meant the end of classical physics - and the end of the formative period of quantum theory.

In this book, authoritative scientists Brian Cox and Jeff Forshaw introduce readers to quantum mechanics - the fundamental model of the world. They tell what observations led physicists to the quantum theory, how it was developed, and why scientists, despite all its strangeness, are so confident in it. The book is intended for everyone who is interested in quantum physics and the structure of the Universe.

Something strange is coming.
Quantum. This word simultaneously appeals to the senses, confuses and fascinates. Depending on one's point of view, this is either evidence of the vast advances of science, or a symbol of the limitations of human intuition, which is forced to struggle with the inevitable strangeness of the subatomic realm. For a physicist, quantum mechanics is one of the three great pillars on which the understanding of nature rests (the other two are Einstein's general and special theories of relativity). Einstein's theories deal with the nature of space and time and the force of gravity. Quantum mechanics takes care of everything else, and it can be said that, no matter how emotionally appealing, confusing or fascinating, it is just a physical theory describing how nature actually behaves. But even if measured by this very pragmatic criterion, it is striking in its accuracy and explanatory power. There is one experiment from the field of quantum electrodynamics, the oldest and best understood of modern quantum theories. It measures how an electron behaves near a magnet. Theoretical physicists worked hard for years with pen and paper, and later with computers, to predict exactly what such studies would reveal. Practitioners invented and set up experiments to find out more details from nature. Both camps, independently of each other, gave results with an accuracy similar to measuring the distance between Manchester and New York with an error of a few centimeters. It is noteworthy that the figures obtained by the experimenters fully corresponded to the results of the calculations of theorists; measurements and calculations were in complete agreement.
This is not only impressive but surprising, and if model building were the sole concern of quantum theory, you might rightly ask what the problem is. Science, of course, does not have to be useful, but many of the technological and social changes that have revolutionized our lives have come out of fundamental research conducted by modern scientists, who are guided only by the desire to better understand the world around them. Thanks to these curiosity-driven discoveries across all branches of science, we have extended lifespans, international air travel, freedom from the need to farm for our own survival, and a broad, inspiring, and eye-opening picture of our place in an endless sea of ​​stars. But all this is, in a sense, by-products. We explore out of curiosity, not because we want to gain a better understanding of reality or develop better trinkets.

Content
Something strange is coming
In two places at the same time
What is a particle?
Everything that can happen really happens
Movement as an illusion
Music of atoms
The universe on a pinhead (and why we don't fall through the ground)
Interdependence
Modern world
Interaction
Empty Space Isn't So Empty Epilogue: Death of the Stars
For further reading.

Free download e-book in a convenient format, watch and read:
Download the book The Quantum Universe, How What We Can't See Works, Cox B., Forshaw J., 2016 - fileskachat.com, fast and free download.

Download epub
Below you can buy this book at the best discounted price with delivery throughout Russia.