Quantum physics is the theory of everything. On the way to a theory of everything. A new hypothesis - a new view of the world

I guess you could say that no one understands quantum mechanics

Physicist Richard Feynman

It is not an exaggeration to say that the invention of semiconductor devices was a revolution. Not only is this an impressive technological achievement, but it also paved the way for events that would change modern society forever. Semiconductor devices are used in all kinds of microelectronics devices, including computers, certain types of medical diagnostic and therapeutic equipment, and popular telecommunications devices.

But behind this technological revolution there is even more, a revolution in general science: the field quantum theory. Without this leap in understanding of the natural world, the development of semiconductor devices (and the more advanced electronic devices being developed) would never have succeeded. Quantum physics is an incredibly complex branch of science. This chapter provides only a brief overview. When scientists of Feynman's stature say that "nobody understands [it]", you can be sure that this is a truly complex topic. Without a basic understanding of quantum physics, or at least an understanding of the scientific discoveries that led to their development, it is impossible to understand how and why semiconductor electronic devices work. Most electronics textbooks try to explain semiconductors in terms of "classical physics", making them even more confusing to understand as a result.

Many of us have seen diagrams of atomic models that look like the figure below.

Rutherford atom: negative electrons orbiting a small positive nucleus

Tiny particles of matter called protons And neutrons, form the center of the atom; electrons revolve like planets around a star. The nucleus carries a positive electrical charge due to the presence of protons (neutrons have no electrical charge), while the balancing negative charge of the atom is found in the orbiting electrons. Negative electrons are attracted to positive protons, just as planets are attracted to the Sun by gravity, but the orbits are stable due to the movement of electrons. We owe this popular model of the atom to the work of Ernest Rutherford, who around 1911 experimentally determined that the positive charges of atoms were concentrated in a tiny, dense nucleus, rather than uniformly distributed across the diameter, as the researcher J. J. Thomson had previously assumed.

Rutherford's scattering experiment involves bombarding thin gold foil with positively charged alpha particles, as shown in the figure below. Young graduate students H. Geiger and E. Marsden obtained unexpected results. The trajectory of some alpha particles was deflected by a large angle. Some alpha particles were scattered in the opposite direction, at an angle of almost 180°. Most of the particles passed through the gold foil without changing their path, as if there was no foil at all. The fact that several alpha particles experienced large deviations in their trajectory indicates the presence of nuclei with a small positive charge.

Although Rutherford's model of the atom was supported better by experimental data than Thomson's model, it was still not ideal. Further attempts were made to determine the structure of the atom, and these efforts helped pave the way for the strange discoveries of quantum physics. Today our understanding of the atom is a little more complex. However, despite the revolution of quantum physics and its contributions to our understanding of atomic structure, Rutherford's image of the solar system as the structure of an atom has taken root in the popular consciousness to such an extent that it persists in fields of education, even if it is inappropriate.

Consider this short description of electrons in an atom, taken from a popular electronics textbook:

The spinning negative electrons are attracted to the positive nucleus, which leads us to the question of why electrons do not fly into the nucleus of the atom. The answer is that spinning electrons remain in their stable orbit due to two equal but opposite forces. The centrifugal force acting on the electrons is directed outward, and the force of attraction between the charges tries to pull the electrons towards the nucleus.

According to Rutherford's model, the author considers electrons to be solid pieces of matter occupying circular orbits, their inward attraction toward an oppositely charged nucleus balanced by their motion. The use of the term "centrifugal force" is technically incorrect (even for orbiting planets), but this is easily forgiven due to the popular acceptance of the model: in fact, there is no such thing as force. repulsiveany a rotating body from the center of its orbit. It seems that this is so because the inertia of the body strives to maintain its motion in a straight line, and since the orbit is a constant deviation (acceleration) from rectilinear motion, there is a constant inertial reaction to any force attracting the body to the center of the orbit (centripetal), be it then gravity, electrostatic attraction, or even the tension of a mechanical connection.

However, the real problem with this explanation is the idea of ​​electrons moving in circular orbits in the first place. It is a proven fact that accelerated electrical charges emit electromagnetic radiation, a fact that was known even in Rutherford's time. Since spinning motion is a form of acceleration (a spinning object in constant acceleration, moving the object away from normal straight-line motion), electrons in the spinning state should emit radiation, like dirt from a skidding wheel. Electrons accelerated along circular paths in particle accelerators called synchrotrons are known to do this, and the result is called synchrotron radiation. If electrons were to lose energy in this way, their orbits would eventually become disrupted, causing them to collide with a positively charged nucleus. However, this usually does not happen inside atoms. Indeed, electron "orbits" are remarkably stable over a wide range of conditions.

In addition, experiments with "excited" atoms have shown that electromagnetic energy is emitted by an atom only at certain frequencies. Atoms are "excited" by external stimuli such as light, as is known, to absorb energy and return electromagnetic waves at certain frequencies, like a tuning fork that does not ring at a certain frequency until it is struck. When the light emitted by an excited atom is divided into its component frequencies (colors) by a prism, individual color lines in the spectrum are detected, a pattern of spectral lines that is unique to the chemical element. This phenomenon is commonly used to identify chemical elements, and even to measure the proportions of each element in a compound or chemical mixture. According to Rutherford's solar system atomic model (relating to electrons as pieces of matter freely rotating in an orbit with some radius) and the laws of classical physics, excited atoms should return energy in an almost infinite range of frequencies, and not at selected frequencies. In other words, if Rutherford's model were correct, there would be no "tuning fork" effect, and the color spectrum emitted by any atom would appear as a continuous band of colors rather than as several individual lines.

A researcher named Niels Bohr attempted to improve Rutherford's model after studying it in Rutherford's laboratory for several months in 1912. Trying to reconcile the results of other physicists (notably Max Planck and Albert Einstein), Bohr proposed that each electron had a specific, specific amount of energy, and that their orbits were distributed in such a way that each of them could occupy specific places around the nucleus, like marbles , fixed on circular paths around the core, and not as freely moving satellites, as previously assumed (figure above). In deference to the laws of electromagnetism and accelerating charges, Bohr referred to "orbits" as stationary states to avoid the interpretation that they were mobile.

Although Bohr's ambitious attempt to rethink the structure of the atom so that it was more consistent with experimental data was an important milestone in physics, it was not completed. His mathematical analysis was better at predicting the results of experiments than analyzes carried out according to previous models, but there were still unanswered questions about Why electrons must behave in this strange way. The claim that electrons existed in stationary quantum states around the nucleus fit the experimental data better than Rutherford's model, but did not say what caused the electrons to adopt these special states. The answer to this question was to come from another physicist, Louis de Broglie, about ten years later.

De Broglie proposed that electrons, like photons (particles of light), have both the properties of particles and the properties of waves. Based on this assumption, he suggested that analyzing spinning electrons in terms of waves was better suited than in terms of particles and could provide more insight into their quantum nature. And indeed, another breakthrough was made in understanding.

The atom, according to de Broglie, consisted of standing waves, a phenomenon well known to physicists in various forms. Like the plucked string of a musical instrument (picture above), vibrating at a resonant frequency, with "knots" and "anti-knots" at stable locations along its length. De Broglie imagined electrons around atoms as waves bent into a circle (picture below).

Electrons can only exist in certain, specific "orbits" around the nucleus because these are the only distances at which the ends of the wave coincide. At any other radius, the wave will destructively collide with itself and thus cease to exist.

De Broglie's hypothesis provided both the mathematics and a convenient physical analogy to explain the quantum states of electrons within an atom, but his model of the atom was still incomplete. For several years, physicists Werner Heisenberg and Erwin Schrödinger, working independently of each other, worked on the concept of de Broglie's wave-particle duality to create more rigorous mathematical models of subatomic particles.

This theoretical progression from the primitive de Broglie standing wave model to the Heisenberg matrix and Schrödinger differential equation models was given the name quantum mechanics and introduced a rather shocking characteristic into the world of subatomic particles: the sign of probability, or uncertainty. According to the new quantum theory, it was impossible to determine the exact position and exact momentum of a particle at one moment. A popular explanation for this "uncertainty principle" was that there was measurement error (that is, by trying to accurately measure the position of an electron, you interfere with its momentum, and therefore cannot know what was there before you started measuring the position, and vice versa). The sensational conclusion of quantum mechanics is that particles do not have exact positions and momenta, and because of the relationship of these two quantities, their combined uncertainty will never decrease below a certain minimum value.

This form of "uncertainty" connection exists in fields other than quantum mechanics. As discussed in the chapter "Mixed Frequency AC Signals" in Volume 2 of this book series, there are mutually exclusive relationships between confidence in a waveform's time domain data and its frequency domain data. Simply put, the more we know its component frequencies, the less accurately we know its amplitude over time, and vice versa. I quote myself:

A signal of infinite duration (infinite number of cycles) can be analyzed with absolute accuracy, but the fewer cycles available to the computer for analysis, the less accurate the analysis... The fewer periods of the signal, the less accurate its frequency. Taking this concept to its logical extreme, a short pulse (not even a full cycle of the signal) does not actually have a specific frequency, it is an infinite range of frequencies. This principle is common to all wave phenomena, and not just to alternating voltages and currents.

To accurately determine the amplitude of a changing signal, we must measure it in a very short period of time. However, doing this limits our knowledge of the frequency of the wave (a wave in quantum mechanics is not supposed to be like a sine wave; such similarity is a special case). On the other hand, to determine the frequency of a wave with great accuracy, we must measure it over a large number of periods, which means we will lose sight of its amplitude at any given moment. Thus, we cannot simultaneously know the instantaneous amplitude and all frequencies of any wave with unlimited accuracy. Another strange thing is that this uncertainty is much greater than that of the observer; it is in the very nature of the wave. This is not true, although it would be possible, given the appropriate technology, to provide accurate measurements of both instantaneous amplitude and frequency simultaneously. Literally, a wave cannot have precise instantaneous amplitude and precise frequency at the same time.

The minimum uncertainty in particle position and momentum expressed by Heisenberg and Schrödinger has nothing to do with a limitation in measurement; rather, it is an intrinsic property of the nature of particle-wave duality. Therefore, electrons do not actually exist in their "orbits" as precisely defined particles of matter, or even as precisely defined waveforms, but rather as "clouds" - the technical term wave function probability distributions as if each electron were "scattered" or "spread out" over a range of positions and momenta.

This radical view of electrons as vague clouds initially contradicts the original principle of electron quantum states: electrons exist in discrete, defined “orbits” around the nucleus of an atom. This new insight was, after all, the discovery that led to the formation and explanation of quantum theory. How strange it seems that a theory created to explain the discrete behavior of electrons ends up declaring that electrons exist as “clouds” rather than as individual pieces of matter. However, the quantum behavior of electrons does not depend on electrons having certain values ​​of coordinates and momentum, but on other properties called quantum numbers. In essence, quantum mechanics dispenses with the common concepts of absolute position and absolute moment, and replaces them with absolute concepts of types that have no analogues in general practice.

Even though electrons are known to exist in ethereal, "clouds" of distributed probability rather than as individual pieces of matter, these "clouds" have slightly different characteristics. Any electron in an atom can be described by four numerical measures (the previously mentioned quantum numbers), which are called main (radial), orbital (azimuthal), magnetic And spin numbers. Below is a brief overview of the meaning of each of these numbers:

Principal (radial) quantum number: indicated by a letter n, this number describes the shell in which the electron resides. The electron "shell" is a region of space around the nucleus of an atom in which electrons can exist, corresponding to the stable "standing wave" models of de Broglie and Bohr. Electrons can "jump" from shell to shell, but cannot exist between them.

The principal quantum number must be a positive integer (greater than or equal to 1). In other words, the electron's principal quantum number cannot be 1/2 or -3. These integers were not chosen arbitrarily, but through experimental evidence of the light spectrum: the different frequencies (colors) of light emitted by excited hydrogen atoms follow a mathematical relationship depending on the specific integer values, as shown in the figure below.

Each shell has the ability to hold several electrons. An analogy for electronic shells is the concentric rows of seats in an amphitheater. Just as a person sitting in an amphitheater must choose a row to sit in (he cannot sit between the rows), electrons must “choose” a specific shell in order to “sit.” Like the rows in an amphitheater, the outermost shells hold more electrons compared to shells closer to the center. Electrons also tend to find the smallest available shell, just as people in an amphitheater seek the seat closest to the center stage. The higher the shell number, the more energy the electrons on it have.

The maximum number of electrons that any shell can hold is described by the equation 2n 2, where n is the principal quantum number. Thus, the first shell (n = 1) can contain 2 electrons; second shell (n = 2) - 8 electrons; and the third shell (n = 3) - 18 electrons (picture below).

Electron shells in an atom were designated by letters rather than numbers. The first shell (n = 1) was designated K, the second shell (n = 2) L, the third shell (n = 3) M, the fourth shell (n = 4) N, the fifth shell (n = 5) O, the sixth shell ( n = 6) P, and the seventh shell (n = 7) B.

Orbital (azimuthal) quantum number: a shell consisting of subshells. Some may find it easier to think of subshells as simple sections of shells, like stripes dividing a road. Subshells are much stranger. Subshells are regions of space where electron "clouds" can exist, and in fact different subshells have different shapes. The first subshell is spherical (figure below (s)), which makes sense when visualized as an electron cloud surrounding the atomic nucleus in three dimensions.

The second subshell resembles a dumbbell, consisting of two “petals” connected at one point near the center of the atom (picture below (p)).

The third subshell usually resembles a set of four "petals" grouped around the nucleus of the atom. These subshell shapes resemble graphical representations of antenna patterns with onion-like lobes extending from the antenna in different directions (Figure below (d)).

Valid values ​​for the orbital quantum number are positive integers, as for the principal quantum number, but also include zero. These quantum numbers for electrons are denoted by the letter l. The number of subshells is equal to the principal quantum number of the shell. Thus, the first shell (n = 1) has one subshell numbered 0; the second shell (n = 2) has two subshells with numbers 0 and 1; the third shell (n = 3) has three subshells numbered 0, 1 and 2.

The old convention for describing subshells used letters rather than numbers. In this format, the first subshell (l = 0) was denoted s, the second subshell (l = 1) was denoted p, the third subshell (l = 2) was denoted d, and the fourth subshell (l = 3) was denoted f. The letters came from the words: sharp, principal, diffuse And fundamental. You can still see these notations in many periodic tables, used to represent the electron configuration of the outer ( valence) shells of atoms.

Magnetic quantum number: The magnetic quantum number for an electron classifies the orientation of the electron's subshell figure. The “petals” of the subshells can be directed in several directions. These different orientations are called orbitals. For the first subshell (s; l = 0), which resembles a sphere, the “direction” is not specified. For the second (p; l = 1) subshell in each shell, which resembles a dumbbell pointing in three possible directions. Imagine three dumbbells intersecting at the origin, each pointing along its own axis in a triaxial coordinate system.

Valid values ​​for a given quantum number consist of integers ranging from -l to l, and this number is denoted as m l in atomic physics and l z in nuclear physics. To calculate the number of orbitals in any subshell, you need to double the subshell number and add 1, (2∙l + 1). For example, the first subshell (l = 0) in any shell contains one orbital numbered 0; the second subshell (l = 1) in any shell contains three orbitals with numbers -1, 0 and 1; the third subshell (l = 2) contains five orbitals with numbers -2, -1, 0, 1 and 2; and so on.

Like the master quantum number, the magnetic quantum number arose directly from experimental data: the Zeeman effect, the splitting of spectral lines by exposing an ionized gas to a magnetic field, hence the name "magnetic" quantum number.

Spin quantum number: Like the magnetic quantum number, this property of the electrons of an atom was discovered through experiments. Careful observation of the spectral lines showed that each line was actually a pair of very closely spaced lines, it was assumed that this so-called fine structure was the result of each electron “rotating” on its axis, like a planet. Electrons with different "spin" would produce slightly different frequencies of light when excited. The concept of a spinning electron is now obsolete, being more suited to the (incorrect) view of electrons as individual particles of matter rather than as "clouds", but the name remains.

Spin quantum numbers are denoted as m s in atomic physics and s z in nuclear physics. Each orbital in each subshell can have two electrons in each shell, one with spin +1/2 and one with spin -1/2.

Physicist Wolfgang Pauli developed a principle that explains the ordering of electrons in an atom according to these quantum numbers. His principle, called Pauli's exclusion principle, states that two electrons in the same atom cannot occupy the same quantum states. That is, each electron in an atom has a unique set of quantum numbers. This limits the number of electrons that can occupy any one orbital, subshell, and shell.

This shows the arrangement of electrons in a hydrogen atom:

With one proton in the nucleus, the atom accepts one electron for its electrostatic balance (the positive charge of the proton is exactly balanced by the negative charge of the electron). This electron is located in the lower shell (n = 1), the first subshell (l = 0), in the only orbital (spatial orientation) of this subshell (m l = 0), with a spin value of 1/2. The general method of describing this structure is done by listing the electrons according to their shells and subshells according to a convention called spectroscopic designation. In this notation, the shell number is shown as an integer, the subshell as a letter (s,p,d,f), and the total number of electrons in the subshell (all orbitals, all spins) as a superscript. Thus, hydrogen, with its single electron placed in the base level, is described as 1s 1.

Moving on to the next atom (in order of atomic number), we get the element helium:

A helium atom has two protons in the nucleus, which requires two electrons to balance the double positive electrical charge. Since two electrons - one with spin 1/2 and the other with spin -1/2 - are in the same orbital, the electronic structure of helium does not require additional subshells or shells to hold the second electron.

However, an atom requiring three or more electrons will need additional subshells to hold all the electrons, since only two electrons can be found in the bottom shell (n = 1). Consider the next atom in the sequence of increasing atomic numbers, lithium:

The lithium atom uses part of the L shell capacity (n = 2). This shell actually has a total capacity of eight electrons (maximum shell capacity = 2n 2 electrons). If we consider the structure of an atom with a completely filled L shell, we see how all combinations of subshells, orbitals and spins are occupied by electrons:

Often, when assigning a spectroscopic designation to an atom, any completely filled shells are skipped, and unfilled shells and higher-level filled shells are designated. For example, the element neon (shown in the figure above), which has two completely filled shells, can be spectrally described simply as 2p 6 rather than 1s 22 s 22 p 6. Lithium, with its fully filled K shell and a single electron in the L shell, can be described simply as 2s 1 rather than 1s 22 s 1 .

Skipping completely filled lower-level shells is not just for recording convenience. It also illustrates a basic principle of chemistry: the chemical behavior of an element is primarily determined by its unfilled shells. Both hydrogen and lithium have one electron in their outer shells (as 1 and 2s 1, respectively), that is, both elements have similar properties. Both are highly reactive, and react in almost the same ways (binding with similar elements under similar conditions). It doesn't really matter that lithium has a completely filled K-shell underneath an almost empty L-shell: the unfilled L-shell is the one that determines its chemical behavior.

Elements that have completely filled outer shells are classified as noble and are characterized by an almost complete lack of reaction with other elements. These elements were classified as inert when they were thought not to react at all, but they are known to form compounds with other elements under certain conditions.

Since elements with similar electron configurations in their outer shells have similar chemical properties, Dmitri Mendeleev organized the chemical elements in the table accordingly. This table is known as , and modern tables follow this general form, shown in the figure below.

Dmitri Mendeleev, a Russian chemist, was the first to develop the periodic table of elements. Even though Mendeleev organized his table according to atomic mass rather than atomic number, and created a table that was not as useful as modern periodic tables, his development stands as an excellent example of scientific proof. After seeing patterns of periodicity (similar chemical properties according to atomic mass), Mendeleev hypothesized that all elements should fit into this ordered pattern. When he discovered "empty" places in the table, he followed the logic of the existing order and assumed the existence of as yet unknown elements. The subsequent discovery of these elements confirmed the scientific correctness of Mendeleev's hypothesis, and further discoveries led to the type of periodic table that we use today.

Like this must work science: hypotheses lead to logical conclusions and are accepted, modified or rejected depending on the consistency of experimental data with their conclusions. Any fool can formulate an after-the-fact hypothesis to explain the available experimental data, and many do. What distinguishes a scientific hypothesis from ex post facto speculation is the prediction of future experimental data that has not yet been collected, and the possible disconfirmation of that data as a result. Boldly pursue a hypothesis to its logical conclusion(s), and attempting to predict the results of future experiments is not a dogmatic leap of faith, but rather a public test of that hypothesis, an open challenge to opponents of the hypothesis. In other words, scientific hypotheses are always "risky" because they attempt to predict the results of experiments that have not yet been performed, and therefore can be falsified if the experiments do not go as expected. Thus, if a hypothesis correctly predicts the results of repeated experiments, it is disproved as false.

Quantum mechanics, first as a hypothesis and then as a theory, has proven extremely successful in predicting the results of experiments, hence gaining a high degree of scientific credibility. Many scientists have reason to believe that it is an incomplete theory, since its predictions are more true at microphysical scales than at macroscopic scales, but it is nevertheless an extremely useful theory for explaining and predicting the interactions of particles and atoms.

As you have seen in this chapter, quantum physics is important in describing and predicting many different phenomena. In the next section we will see its importance in the electrical conductivity of solids, including semiconductors. Simply put, nothing in chemistry or solid state physics makes sense of the popular theoretical structure of electrons existing as individual particles of matter orbiting the nucleus of an atom like miniature satellites. When electrons are viewed as "wave functions" existing in specific, discrete states that are regular and periodic, then the behavior of matter can be explained.

Let's sum it up

Electrons in atoms exist in "clouds" of distributed probability, rather than as discrete particles of matter orbiting a nucleus like miniature satellites, as common examples suggest.

Individual electrons around the nucleus of an atom tend to achieve unique "states" described by four quantum numbers: principal (radial) quantum number, known as shell; orbital (azimuthal) quantum number, known as subshell; magnetic quantum number, describing orbital(subshell orientation); And spin quantum number, or simply spin. These states are quantum, that is, “between them” there are no conditions for the existence of an electron, except for the states that fit into the quantum numbering scheme.

Glacial (radial) quantum number (n) describes the base level or shell in which an electron resides. The larger this number, the larger the radius of the electron cloud from the atomic nucleus, and the greater the energy of the electron. Principal quantum numbers are integers (positive integers)

Orbital (azimuthal) quantum number (l) describes the shape of the electron cloud in a particular shell or level and is often known as a "subshell". In any shell there are as many subshells (electron cloud forms) as the principal quantum number of the shell. Azimuthal quantum numbers are positive integer numbers starting from zero and ending with a number less than the principal quantum number by one (n - 1).

Magnetic quantum number (m l) describes what orientation the subshell (electron cloud shape) has. Subshells can allow as many different orientations as twice the subshell number (l) plus 1, (2l+1) (that is, for l=1, m l = -1, 0, 1), and each unique orientation is called an orbital. These numbers are integers starting from the negative value of the subshell number (l) through 0 and ending with the positive value of the subshell number.

Spin quantum number (ms) describes another property of an electron and can take values ​​+1/2 and -1/2.

Pauli's exclusion principle says that two electrons in an atom cannot share the same set of quantum numbers. Therefore, there can be no more than two electrons in each orbital (spin=1/2 and spin=-1/2), 2l+1 orbitals in each subshell, and n subshells in each shell, and no more.

Spectroscopic designation is a convention for indicating the electronic structure of an atom. Shells are shown as whole numbers followed by subshell letters (s, p, d, f) with superscript numbers indicating the total number of electrons found in each corresponding subshell.

The chemical behavior of an atom is determined solely by electrons in unfilled shells. Low level shells that are completely filled have little or no effect on the chemical binding characteristics of the elements.

Elements with completely filled electron shells are almost completely inert and are called noble elements (formerly known as inert).

The golden autumn foliage of the trees shone brightly. The rays of the evening sun touched the thinned tops. The light broke through the branches and created a spectacle of bizarre figures flashing on the wall of the university “camper.”

Sir Hamilton's thoughtful gaze slowly slid, watching the play of chiaroscuro. A real melting pot of thoughts, ideas and conclusions was going on in the head of the Irish mathematician. He understood perfectly well that the explanation of many phenomena using Newtonian mechanics is like a play of shadows on a wall, deceptively intertwining figures and leaving many questions unanswered. “Perhaps it is a wave... or perhaps a stream of particles,” the scientist thought, “or light is a manifestation of both phenomena. Like figures woven from shadow and light.”

The beginning of quantum physics

It is interesting to watch great people and try to understand how great ideas are born that change the course of evolution of all mankind. Hamilton is one of those who stood at the origins of quantum physics. Fifty years later, at the beginning of the twentieth century, many scientists were studying elementary particles. The knowledge gained was contradictory and uncompiled. However, the first shaky steps were taken.

Understanding the microworld at the beginning of the twentieth century

In 1901, the first model of the atom was presented and its inconsistency was shown from the position of conventional electrodynamics. During the same period, Max Planck and Niels Bohr published many works on the nature of the atom. Despite their complete understanding of the structure of the atom did not exist.

A few years later, in 1905, the little-known German scientist Albert Einstein published a report on the possibility of the existence of a light quantum in two states - wave and corpuscular (particles). In his work, arguments were given to explain the reason for the failure of the model. However, Einstein's vision was limited by the old understanding of the atomic model.

After numerous works by Niels Bohr and his colleagues, a new direction was born in 1925 - a kind of quantum mechanics. The common expression “quantum mechanics” appeared thirty years later.

What do we know about quanta and their quirks?

Today, quantum physics has come quite far. Many different phenomena have been discovered. But what do we really know? The answer is presented by one modern scientist. “You can either believe in quantum physics or not understand it,” is the definition. Think about it for yourself. It will be enough to mention such a phenomenon as quantum entanglement of particles. This phenomenon plunged the scientific world into a state of complete bewilderment. An even bigger shock was that the paradox that arose was incompatible with Einstein.

The effect of quantum entanglement of photons was first discussed in 1927 at the Fifth Solvay Congress. A heated argument arose between Niels Bohr and Einstein. The paradox of quantum entanglement has completely changed the understanding of the essence of the material world.

It is known that all bodies consist of elementary particles. Accordingly, all phenomena of quantum mechanics are reflected in the ordinary world. Niels Bohr said that if we do not look at the Moon, then it does not exist. Einstein considered this unreasonable and believed that an object exists independently of the observer.

When studying the problems of quantum mechanics, one should understand that its mechanisms and laws are interconnected and do not obey classical physics. Let's try to understand the most controversial area - quantum entanglement of particles.

Quantum entanglement theory

To begin with, it is worth understanding that quantum physics is like a bottomless well in which you can find anything. The phenomenon of quantum entanglement at the beginning of the last century was studied by Einstein, Bohr, Maxwell, Boyle, Bell, Planck and many other physicists. Throughout the twentieth century, thousands of scientists around the world actively studied and experimented with this.

The world is subject to the strict laws of physics

Why such interest in the paradoxes of quantum mechanics? Everything is very simple: we live subject to certain laws of the physical world. The ability to “bypass” predestination opens a magical door behind which everything becomes possible. For example, the concept of "Schrodinger's Cat" leads to the control of matter. Teleportation of information caused by quantum entanglement will also become possible. The transmission of information will become instantaneous, regardless of distance.
This issue is still under study, but has a positive trend.

Analogy and understanding

What is unique about quantum entanglement, how to understand it, and what happens when it happens? Let's try to figure it out. To do this, you will need to conduct some kind of thought experiment. Imagine that you have two boxes in your hands. Each of them contains one ball with a stripe. Now we give one box to the astronaut, and he flies off to Mars. Once you open a box and see that the stripe on the ball is horizontal, then the ball in another box will automatically have a vertical stripe. This will be quantum entanglement expressed in simple words: one object predetermines the position of another.

However, it should be understood that this is only a superficial explanation. In order to obtain quantum entanglement, the particles must have the same origin, like twins.

It is very important to understand that the experiment will be disrupted if someone before you had the opportunity to look at at least one of the objects.

Where can quantum entanglement be used?

The principle of quantum entanglement can be used to transmit information over long distances instantly. Such a conclusion contradicts Einstein's theory of relativity. It says that the maximum speed of movement is inherent only in light - three hundred thousand kilometers per second. Such transfer of information makes it possible for physical teleportation to exist.

Everything in the world is information, including matter. Quantum physicists came to this conclusion. In 2008, based on a theoretical database, it was possible to see quantum entanglement with the naked eye.

This once again suggests that we are on the threshold of great discoveries - movement in space and time. Time in the Universe is discrete, so instantaneous movement over vast distances makes it possible to get into different time densities (based on the hypotheses of Einstein and Bohr). Perhaps in the future this will be a reality just like the mobile phone is today.

Aetherdynamics and quantum entanglement

According to some leading scientists, quantum entanglement is explained by the fact that space is filled with a kind of ether - black matter. Any elementary particle, as we know, exists in the form of a wave and a corpuscle (particle). Some scientists believe that all particles reside on a “canvas” of dark energy. This is not easy to understand. Let's try to figure it out another way - by association.

Imagine yourself on the seashore. Light breeze and weak wind. Do you see the waves? And somewhere in the distance, in the reflections of the sun's rays, a sailboat is visible.
The ship will be our elementary particle, and the sea will be the ether (dark energy).
The sea can be in motion in the form of visible waves and drops of water. In the same way, all elementary particles can be simply the sea (its integral part) or a separate particle - a drop.

This is a simplified example, everything is somewhat more complicated. Particles without the presence of an observer are in the form of a wave and do not have a specific location.

A white sailboat is a distinct object; it differs from the surface and structure of the sea water. In the same way, there are “peaks” in the ocean of energy, which we can perceive as a manifestation of the forces known to us that shaped the material part of the world.

The microworld lives by its own laws

The principle of quantum entanglement can be understood if we take into account the fact that elementary particles are in the form of waves. Having no specific location and characteristics, both particles reside in an ocean of energy. At the moment the observer appears, the wave “transforms” into an object accessible to touch. The second particle, observing the equilibrium system, acquires opposite properties.

The described article is not aimed at succinct scientific descriptions of the quantum world. The ability of an ordinary person to comprehend is based on the accessibility of understanding the presented material.

Particle physics studies the entanglement of quantum states based on the spin (rotation) of an elementary particle.

In scientific language (simplified) - quantum entanglement is defined by different spins. In the process of observing objects, scientists saw that only two spins can exist - along and across. Oddly enough, in other positions the particles do not “pose” to the observer.

A new hypothesis - a new view of the world

The study of microcosm - the space of elementary particles - has given rise to many hypotheses and assumptions. The effect of quantum entanglement prompted scientists to think about the existence of some kind of quantum microlattice. In their opinion, at each node - the point of intersection - there is a quantum. All energy is an integral lattice, and the manifestation and movement of particles is possible only through the nodes of the lattice.

The size of the “window” of such a lattice is quite small, and measurement with modern equipment is impossible. However, in order to confirm or refute this hypothesis, scientists decided to study the movement of photons in a spatial quantum lattice. The point is that a photon can move either straight or in zigzags - along the diagonal of the lattice. In the second case, having covered a greater distance, he will spend more energy. Accordingly, it will differ from a photon moving in a straight line.

Perhaps over time we will learn that we live in a spatial quantum lattice. Or it may turn out to be incorrect. However, it is the principle of quantum entanglement that indicates the possibility of the existence of a lattice.

In simple terms, in a hypothetical spatial “cube” the definition of one face carries with it a clear opposite meaning of the other. This is the principle of preserving the structure of space - time.

Epilogue

To understand the magical and mysterious world of quantum physics, it is worth taking a close look at the development of science over the past five hundred years. Previously, it was believed that the Earth was flat, not spherical. The reason is obvious: if you take its shape as round, then the water and people will not be able to hold on.

As we can see, the problem existed in the lack of a complete vision of all the forces at play. It is possible that modern science does not have enough vision of all the acting forces to understand quantum physics. Gaps in vision give rise to a system of contradictions and paradoxes. Perhaps the magical world of quantum mechanics contains the answers to the questions posed.

How do modern theoretical physicists develop new theories that describe the world? What do they add to quantum mechanics and general relativity to create a “theory of everything”? What limitations are discussed in articles talking about the absence of “new physics”? All these questions can be answered if you understand what it is action- an object that underlies all existing physical theories. In this article I will explain what physicists mean by action, and also show how it can be used to construct a real physical theory using just a few simple assumptions about the properties of the system in question.

I warn you right away: the article will contain formulas and even simple calculations. However, they can be skipped without much harm to understanding. Generally speaking, I present formulas here only for those interested readers who certainly want to figure it out on their own.

Equations

Physics describes our world using equations that link together various physical quantities - speed, force, magnetic field strength, and so on. Almost all such equations are differential, that is, they contain not only functions that depend on quantities, but also their derivatives. For example, one of the simplest equations describing the motion of a point body contains the second derivative of its coordinate:

Here I denoted the second derivative with respect to time by two points (accordingly, one point will denote the first derivative). Of course, this is Newton’s second law, which he discovered at the end of the 17th century. Newton was one of the first to recognize the need to write the equations of motion in this form, and also developed the differential and integral calculus necessary to solve them. Of course, most physical laws are much more complex than Newton's second law. For example, the system of equations of hydrodynamics is so complex that scientists still do not know whether it is solvable in the general case or not. The problem of the existence and smoothness of solutions to this system is even included in the list of “Millennium Problems,” and the Clay Mathematical Institute awarded a prize of one million dollars for its solution.

However, how do physicists find these differential equations? For a long time, the only source of new theories was experiment. In other words, the scientist first took measurements of several physical quantities, and only then tried to determine how they were related. For example, it was in this way that Kepler discovered the three famous laws of celestial mechanics, which later led Newton to his classical theory of gravitation. It turned out that the experiment seemed to be “running ahead of the theory.”

In modern physics, things are arranged a little differently. Of course, experiment still plays a very important role in physics. Without experimental confirmation, any theory is just a mathematical model - a toy for the mind that has no relation to the real world. However, now physicists obtain equations that describe our world not by empirical generalization of experimental facts, but derive them “from first principles,” that is, based on simple assumptions about the properties of the system being described (for example, space-time or the electromagnetic field). Ultimately, only the parameters of the theory are determined from experiment - arbitrary coefficients that enter into the equation derived by the theorist. In this case, the key role in theoretical physics is played by principle of least action, first formulated by Pierre Maupertuis in the mid-18th century and finally generalized by William Hamilton in the early 19th century.

Action

What is action? In the most general formulation, an action is a functional that associates the trajectory of the system (that is, a function of coordinates and time) with a certain number. And the principle of least action states that true trajectory the action will be minimal. To understand the meaning of these buzzwords, consider the following illustrative example, taken from the Feynman Lectures on Physics.

Let's say we want to find out which trajectory a body placed in a gravitational field will move. For simplicity, we will assume that the movement is completely described by the height x(t), that is, the body moves along a vertical line. Suppose that we know about motion only that the body starts at the point x 1 at a time t 1 and comes to the point x 2 at a time t 2, and the total travel time is T = t 2 − t 1 . Consider the function L, equal to the difference in kinetic energy TO and potential energy P: L = TO − P. We will assume that the potential energy depends only on the particle coordinate x(t), and kinetic - only from its speed ẋ (t). We also define action- functionality S, equal to the average value L during the entire movement: S = ∫ L(x, ẋ , t)d t.

Obviously the meaning S will significantly depend on the shape of the trajectory x(t) - in fact, that’s why we call it a functional, not a function. If the body rises too high (trajectory 2), the average potential energy will increase, and if it begins to loop too often (trajectory 3), the kinetic energy will increase - we assumed that the total time of movement is exactly equal to T, which means the body needs to increase speed in order to make it through all the turns. In reality the functionality S reaches a minimum on some optimal trajectory, which is a section of a parabola passing through the points x 1 and x 2 (trajectory 1). By a happy coincidence, this trajectory coincides with the trajectory predicted by Newton's second law.

Examples of trajectories connecting points x 1 and x 2. The trajectory obtained by variation of the true trajectory is marked in gray. The vertical direction corresponds to the axis x, horizontal - axis t

Is this a coincidence? Of course, this is no coincidence. To show this, let's assume we know the true trajectory and consider it variations. Variation δ x(t) is an addition to the trajectory x(t), which changes its shape, but leaves the start and end points in their places (see picture). Let's see what significance the action takes on trajectories that differ from the true trajectory by an infinitesimal variation. Unfolding function L and calculating the integral by parts, we find that the change S proportional to the variation δ x:

Here we benefit from the fact that the variation at points x 1 and x 2 is equal to zero - this made it possible to discard terms that appear after integration by parts. The resulting expression is very similar to the formula for the derivative, written in terms of differentials. Indeed, the expression δ S/δ x sometimes called variational derivative. Continuing this analogy, we conclude that when adding a small additive δ x to the true trajectory the action should not change, that is, δ S= 0. Since the addition can be almost arbitrary (we fixed only its ends), this means that the integrand also vanishes. Thus, knowing the action, we can obtain a differential equation that describes the motion of the system - the Euler-Lagrange equation.

Let's return to our problem with a body moving in a gravity field. Let me remind you that we defined the function L as the difference between the kinetic and potential energy of a body. Substituting this expression into the Euler-Lagrange equation, we actually obtain Newton's second law. In fact, our guess about the form of the function L turned out to be very successful:

It turns out that with the help of an action you can write down the equations of motion in a very brief form, as if “packing” all the features of the system inside a function L. This in itself is quite interesting. However, action is not just a mathematical abstraction; it has a deep physical meaning. In general, a modern theoretical physicist first writes down the action, and only then derives the equations of motion and studies them. In many cases, an action for a system can be constructed by making only the simplest assumptions about its properties. Let's see how this can be done with a few examples.

Free relativistic particle

When Einstein built his special theory of relativity (STR), he postulated several simple statements about the properties of our space-time. Firstly, it is homogeneous and isotropic, that is, it does not change with finite displacements and rotations. In other words, it doesn't matter where you are - on Earth, on Jupiter or in the Small Magellanic Cloud galaxy - the laws of physics work the same at all these points. In addition, you will not notice any difference if you move uniformly in a straight line - this is Einstein's principle of relativity. Secondly, no body can exceed the speed of light. This leads to the fact that the usual rules for recalculating velocities and time when transitioning between different reference systems - Galilean transformations - need to be replaced with more correct Lorentz transformations. As a result, the truly relativistic quantity, the same in all reference systems, becomes not the distance, but the interval - the proper time of the particle. Interval s 1 − s 2 between two given points can be found using the following formula where c- speed of light:

As we saw in the previous part, it is enough for us to write down the action for a free particle in order to find its equation of motion. It is reasonable to assume that the action is a relativistic invariant, that is, it looks the same in different frames of reference, since the physical laws in them are the same. In addition, we would like the action to be written down as simply as possible (we will leave complex expressions for later). The simplest relativistic invariant that can be associated with a point particle is the length of its world line. Choosing this invariant as an action (so that the dimension of the expression is correct, we multiply it by the coefficient − mc) and varying it, we get the following equation:

Simply put, the 4-acceleration of a free relativistic particle must be equal to zero. 4-acceleration, like 4-velocity, are generalizations of the concepts of acceleration and velocity to four-dimensional space-time. As a result, a free particle can only move along a given straight line with a constant 4-speed. In the limit of low speeds, the change in the interval practically coincides with the change in time, and therefore the equation we obtained goes into Newton’s second law, already discussed above: mẍ= 0. On the other hand, the condition for the 4-acceleration to be zero is satisfied for a free particle in the general theory of relativity, only in it space-time already begins to bend and the particle will not necessarily move along a straight line even in the absence of external forces.

Electromagnetic field

As is known, the electromagnetic field manifests itself in interaction with charged bodies. Typically this interaction is described using the electric and magnetic field strength vectors, which are related by a system of four Maxwell equations. The almost symmetrical appearance of Maxwell's equations suggests that these fields are not independent entities - what appears to us to be an electric field in one frame of reference can turn into a magnetic field if we move to another frame.

In fact, consider a wire along which electrons flow at the same and constant speed. In the frame of reference associated with electrons, there is only a constant electric field, which can be found using Coulomb's law. However, in the original reference frame, the movement of electrons creates a constant electric current, which in turn induces a constant magnetic field (Bio-Savart's law). At the same time, in accordance with the principle of relativity, in the reference systems we have chosen, the laws of physics must coincide. This means that both electric and magnetic fields are parts of some one, more general entity.

Tensors

Before we move on to the covariant formulation of electrodynamics, it is worth saying a few words about the mathematics of special and general relativity. The most important role in these theories is played by the concept of a tensor (and in other modern theories too, to be honest). To put it very roughly, the rank tensor ( n, m) can be thought of as ( n+m)-dimensional matrix, the components of which depend on coordinates and time. In addition to this, the tensor must change in a certain clever way when moving from one reference system to another or when the coordinate grid changes. How exactly, determines the number of contravariant and covariant indices ( n And m respectively). At the same time, the tensor itself as a physical entity does not change under such transformations - just as the 4-vector, which is a special case of a rank 1 tensor, does not change under them.

The tensor components are numbered using indices. For convenience, upper and lower indices are distinguished in order to immediately see how the tensor is transformed when changing coordinates or a reference system. So, for example, the tensor component T rank (3, 0) is written as Tαβγ , and the tensor U rank (2, 1) - as Uα β γ . According to established tradition, the components of four-dimensional tensors are numbered with Greek letters, and three-dimensional ones with Latin letters. However, some physicists prefer to do the opposite (for example, Landau).

In addition, for the sake of brevity, Einstein suggested not writing the sum sign "Σ" when folding tensor expressions. Convolution is the summation of a tensor over two given indices, one of which must be “upper” (contravariant) and the other “lower” (covariant). For example, to calculate the trace of a matrix - a tensor of rank (1, 1) - you need to fold it along two available indices: Tr[ A μ ν ] = Σ A μ μ = Aμ μ . You can raise and lower indices using the metric tensor: T αβ γ = T αβμ g μγ .

Finally, it is convenient to introduce an absolutely antisymmetric pseudotensor ε μνρσ - a tensor that changes sign for any permutation of indices (for example, ε μνρσ = −ε νμρσ) and whose component ε 1234 = +1. It is also called the Levi-Civita tensor. When rotating the coordinate system ε μνρσ behaves like an ordinary tensor, but during inversions (replacement like x → −x) it is converted differently.

Indeed, the electric and magnetic field vectors are combined into a structure that is invariant under Lorentz transformations - that is, does not change during the transition between different (inertial) reference systems. This is the so-called electromagnetic field tensor Fμν. It would be most clear to write it in the form of the following matrix:

Here the components of the electric field are indicated by the letter E, and the components of the magnetic field - the letter H. It is easy to see that the electromagnetic field tensor is antisymmetric, that is, its components located on opposite sides of the diagonal are equal in magnitude and have opposite signs. If we want to obtain Maxwell's equations "from first principles", we need to write down the action of electrodynamics. To do this, we must construct the simplest scalar combination of the tensor objects we have, somehow related to the field or to the properties of spacetime.

If you think about it, we have little choice - only the field tensor can act as “building blocks” Fμν, metric tensor gμν and the absolutely antisymmetric tensor ε μνρσ. From them, only two scalar combinations can be assembled, and one of them is a total derivative, that is, it can be ignored when deriving the Euler-Lagrange equations - after integration, this part will simply go to zero. By choosing the remaining combination as an action and varying it, we get a pair of Maxwell's equations - half of the system (first line). It would seem that we were missing two equations. However, we don't actually need to write out the action to derive the remaining equations - they follow directly from the antisymmetry of the tensor Fμν (second line):

Once again we have obtained the correct equations of motion by choosing the simplest possible combination as our action. True, since we did not take into account the existence of charges in our space, we obtained equations for a free field, that is, for an electromagnetic wave. When adding charges to the theory, their influence must also be taken into account. This is done by turning on the 4-current vector in action.

Gravity

The real triumph of the principle of least action in its time was the construction of the general theory of relativity (GTR). Thanks to him, the laws of motion were first derived, which scientists could not obtain by analyzing experimental data. Or they could, but didn’t have time. Instead, Einstein (and Hilbert, if you like) derived the equations into metrics, starting from assumptions about the properties of space-time. From this moment on, theoretical physics began to “overtake” experimental physics.

In general relativity, the metric ceases to be constant (as in special relativity) and begins to depend on the density of the energy placed in it. Let me note that it is more correct to talk about energy rather than mass, although these two quantities are related by the relation E = mc 2 in its own frame of reference. Let me remind you that the metric specifies the rules by which the distance between two points (strictly speaking, infinitely close points) is calculated. It is important that the metric does not depend on the choice of coordinate system. For example, a flat three-dimensional space can be described using a Cartesian or spherical coordinate system, but in both cases the space metric will be the same.

To write down the action for gravity, we need to construct some invariant from the metric that will not change when the coordinate grid changes. The simplest such invariant is the determinant of the metric. However, if we include only this in action, we will not get differential equation, since this expression does not contain derivatives of the metric. And if the equation is not differential, it cannot describe situations in which the metric changes over time. Therefore, we need to add the simplest invariant to the action, which contains derivatives gμν. Such an invariant is the so-called Ricci scalar R, which is obtained by convolution of the Riemann tensor Rμνρσ, describing the curvature of space-time:

Robert Couse-Baker / flickr.com

Theory of everything

Finally, it's time to talk about the "theory of everything." This is the name of several theories that try to unify General Relativity and the Standard Model - the two main currently known physical theories. Scientists make such attempts not only for aesthetic reasons (the fewer theories needed to understand the world, the better), but also for more compelling reasons.

Both GTR and the Standard Model have limits of applicability, after which they stop working. For example, GTR predicts the existence of singularities - points at which the energy density, and therefore the curvature of space-time, tends to infinity. Not only are infinities in themselves unpleasant - in addition to this problem, the Standard Model states that energy cannot be localized at a point, it must be spread over some, albeit small, volume. Therefore, near the singularity the effects of both General Relativity and the Standard Model should be large. At the same time, general relativity has still not been able to be quantized, and the Standard Model is constructed under the assumption of flat space-time. If we want to understand what happens around singularities, we need to develop a theory that includes both of these theories.

Bearing in mind how successful the principle of least action has been in the past, scientists base all their attempts to build a new theory on it. Remember, we considered only the simplest combinations when we built the action for various theories? Then our actions were crowned with success, but this does not mean at all that the simplest action is the most correct. Generally speaking, nature is not obliged to adjust its laws to simplify our lives.

Therefore, it is reasonable to include the following, more complex invariant quantities in action and see what this leads to. This is somewhat reminiscent of successively approximating a function by polynomials of increasingly higher degrees. The only problem here is that all such corrections come into play with certain unknown coefficients that cannot be calculated theoretically. Moreover, since the Standard Model and General Relativity in general still work well, these coefficients should be very small - therefore, they are difficult to determine from experiment. Numerous works reporting on “constraints on new physics” are precisely aimed at determining the coefficients at higher orders of the theory. So far they have only been able to find upper bounds.

In addition, there are approaches that introduce new, non-trivial concepts. For example, string theory suggests that the properties of our world can be described using vibrations of not point objects, but extended objects - strings. Unfortunately, experimental confirmation of string theory has not yet been found. For example, she predicted some excitations at accelerators, but they never manifested themselves.

In general, it does not yet seem that scientists are close to discovering a “theory of everything.” Probably, theorists will still have to come up with something significantly new. However, there is no doubt that the first thing they will do is write down the action for the new theory.

***

If all these arguments seemed complicated to you and you skimmed through the article without reading, here is a brief summary of the facts that were discussed in it. Firstly, all modern physical theories rely in one way or another on the concept actions- a quantity that describes how much the system “likes” a particular trajectory of movement. Secondly, the equations of motion of the system can be obtained by searching for the trajectory on which the action takes least meaning. Third, an action can be constructed using just a few basic assumptions about the properties of the system. For example, that the laws of physics coincide in reference systems that move at different speeds. Fourth, some of the candidates for a “theory of everything” are obtained by simply adding terms to the action of the Standard Model and General Relativity that violate some of the assumptions of these theories. For example, Lorentz invariance. If after reading the article you remember the statements listed, that’s already good. And if you also understand where they come from, that’s just great.

Dmitry Trunin

Physics is the most mysterious of all sciences. Physics gives us an understanding of the world around us. The laws of physics are absolute and apply to everyone without exception, regardless of person or social status.

This article is intended for persons over 18 years of age

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Fundamental discoveries in the field of quantum physics

Isaac Newton, Nikola Tesla, Albert Einstein and many others are the great guides of humanity in the wonderful world of physics, who, like prophets, revealed to humanity the greatest secrets of the universe and the possibilities of controlling physical phenomena. Their bright heads cut through the darkness of ignorance of the unreasonable majority and, like a guiding star, showed the way to humanity in the darkness of the night. One of such guides in the world of physics was Max Planck, the father of quantum physics.

Max Planck is not only the founder of quantum physics, but also the author of the world famous quantum theory. Quantum theory is the most important component of quantum physics. In simple words, this theory describes the movement, behavior and interaction of microparticles. The founder of quantum physics also brought us many other scientific works that became the cornerstones of modern physics:

• theory of thermal radiation;
• special theory of relativity;
• research in thermodynamics;
• research in the field of optics.

Quantum physics' theories about the behavior and interactions of microparticles became the basis for condensed matter physics, particle physics, and high-energy physics. Quantum theory explains to us the essence of many phenomena in our world - from the functioning of electronic computers to the structure and behavior of celestial bodies. Max Planck, the creator of this theory, thanks to his discovery, allowed us to comprehend the true essence of many things at the level of elementary particles. But the creation of this theory is far from the only merit of the scientist. He became the first to discover the fundamental law of the Universe - the law of conservation of energy. Max Planck's contribution to science is difficult to overestimate. In short, his discoveries are invaluable for physics, chemistry, history, methodology and philosophy.

Quantum field theory

In a nutshell, quantum field theory is a theory for describing microparticles, as well as their behavior in space, interaction with each other and interconversion. This theory studies the behavior of quantum systems within the so-called degrees of freedom. This beautiful and romantic name doesn’t really mean anything to many of us. For dummies, degrees of freedom are the number of independent coordinates that are needed to indicate the motion of a mechanical system. In simple terms, degrees of freedom are characteristics of motion. Interesting discoveries in the field of interaction of elementary particles were made by Steven Weinberg. He discovered the so-called neutral current - the principle of interaction between quarks and leptons, for which he received the Nobel Prize in 1979.

Max Planck's quantum theory

In the nineties of the eighteenth century, the German physicist Max Planck began studying thermal radiation and eventually obtained a formula for the distribution of energy. The quantum hypothesis, which was born in the course of these studies, laid the foundation for quantum physics, as well as quantum field theory, discovered in 1900. Planck's quantum theory is that in thermal radiation the energy produced is not emitted and absorbed constantly, but episodically, quantumly. The year 1900, thanks to this discovery made by Max Planck, became the year of the birth of quantum mechanics. It is also worth mentioning Planck's formula. In short, its essence is as follows - it is based on the relationship between body temperature and its radiation.

Quantum mechanical theory of atomic structure

The quantum mechanical theory of atomic structure is one of the basic theories of concepts in quantum physics, and in physics in general. This theory allows us to understand the structure of all material things and lifts the veil of secrecy over what things actually consist of. And the conclusions based on this theory are quite unexpected. Let us briefly consider the structure of the atom. So, what is an atom actually made of? An atom consists of a nucleus and a cloud of electrons. The basis of an atom, its nucleus, contains almost the entire mass of the atom itself - more than 99 percent. The nucleus always has a positive charge, and this determines the chemical element of which the atom is a part. The most interesting thing about the nucleus of an atom is that it contains almost the entire mass of the atom, but at the same time occupies only one ten-thousandth of its volume. What follows from this? And the conclusion that emerges is quite unexpected. This means that there is only one ten-thousandth of the dense substance in an atom. And what takes up everything else? And everything else in the atom is an electron cloud.

An electronic cloud is not a permanent and, in fact, not even a material substance. An electron cloud is just the probability of electrons appearing in an atom. That is, the nucleus occupies only one ten thousandth in the atom, and the rest is emptiness. And if we consider that all the objects around us, from specks of dust to celestial bodies, planets and stars, are made of atoms, then it turns out that everything material is actually more than 99 percent composed of emptiness. This theory seems completely incredible, and its author, at the very least, a mistaken person, because the things that exist around have a solid consistency, have weight and can be touched. How can it consist of emptiness? Has an error crept into this theory of the structure of matter? But there is no mistake here.

All material things appear dense only due to the interaction between atoms. Things have a solid and dense consistency only due to attraction or repulsion between atoms. This ensures the density and hardness of the crystal lattice of chemical substances, from which everything material consists. But, an interesting point is that when, for example, environmental temperature conditions change, the bonds between atoms, that is, their attraction and repulsion, can weaken, which leads to a weakening of the crystal lattice and even to its destruction. This explains the change in the physical properties of substances when heated. For example, when iron is heated, it becomes liquid and can be shaped into any shape. And when ice melts, the destruction of the crystal lattice leads to a change in the state of the substance, and from solid it turns into liquid. These are clear examples of weakening bonds between atoms and, as a result, weakening or destruction of the crystal lattice, and allow the substance to become amorphous. And the reason for such mysterious metamorphoses is precisely that substances consist of only one ten-thousandth of dense matter, and the rest is emptiness.

And substances seem solid only because of strong bonds between atoms, when they weaken, the substance changes. Thus, the quantum theory of atomic structure allows us to look at the world around us in a completely different way.

The founder of atomic theory, Niels Bohr, put forward an interesting concept that electrons in an atom do not emit energy constantly, but only at the moment of transition between the trajectories of their movement. Bohr's theory helped explain many intra-atomic processes, and also made breakthroughs in the field of science such as chemistry, explaining the boundaries of the table created by Mendeleev. According to , the last element capable of existing in time and space has a serial number of one hundred thirty-seven, and elements starting from one hundred and thirty-eight cannot exist, since their existence contradicts the theory of relativity. Also, Bohr's theory explained the nature of such physical phenomena as atomic spectra.

These are the interaction spectra of free atoms that arise when energy is emitted between them. Such phenomena are typical for gaseous, vaporous substances and substances in the plasma state. Thus, quantum theory made a revolution in the world of physics and allowed scientists to advance not only in the field of this science, but also in the field of many related sciences: chemistry, thermodynamics, optics and philosophy. And also allowed humanity to penetrate into the secrets of the nature of things.

There is still a lot that humanity needs to turn over in its consciousness in order to realize the nature of atoms and understand the principles of their behavior and interaction. Having understood this, we will be able to understand the nature of the world around us, because everything that surrounds us, from specks of dust to the sun itself, and we ourselves, all consists of atoms, the nature of which is mysterious and amazing and conceals a lot of secrets.

English physicist Isaac Newton published a book in which he explained the movement of objects and the principle of gravity. “Mathematical principles of natural philosophy” gave things in the world established places. The story goes that at the age of 23, Newton went into an orchard and saw an apple falling from a tree. At that time, physicists knew that the Earth somehow attracts objects using gravity. Newton developed this idea.

According to John Conduitt, Newton's assistant, upon seeing an apple falling to the ground, Newton had the idea that the gravitational force "was not limited to a certain distance from the earth, but extended much further than was generally believed." According to Conduitt, Newton asked the question: why not all the way to the Moon?

Inspired by his insights, Newton developed a law of gravity that worked equally well for apples on Earth and for planets orbiting the Sun. All these objects, despite their differences, are subject to the same laws.

"People thought he explained everything that needed explaining," Barrow says. “His achievement was great.”

The problem is that Newton knew there were holes in his work.

For example, gravity doesn't explain how small objects are held together because the force isn't that strong. Moreover, although Newton could explain what was happening, he could not explain how it worked. The theory was incomplete.

There was a bigger problem. Although Newton's laws explained the most common phenomena in the universe, in some cases objects violated his laws. These situations were rare and usually involved high speeds or increased gravity, but they did happen.

One such situation was the orbit of Mercury, the planet closest to the Sun. Like any other planet, Mercury revolves around the Sun. Newton's laws could be applied to calculate the movements of the planets, but Mercury did not want to play by the rules. Stranger still, its orbit had no center. It became clear that the universal law of universal gravitation was not so universal, and not a law at all.

More than two centuries later, Albert Einstein came to the rescue with his theory of relativity. Einstein's 2015 idea provided a deeper understanding of gravity.

Theory of relativity

The key idea is that space and time, which appear to be different things, are actually intertwined. Space has three dimensions: length, width and height. Time is the fourth dimension. All four are connected in the form of a giant space cage. If you've ever heard the phrase "space-time continuum," that's what we're talking about.

Einstein's big idea was that objects like planets that are heavy or moving quickly can bend spacetime. A bit like a tight trampoline, if you put anything heavy on the fabric it will create a hole. Any other objects will roll down the slope towards the object in the depression. This is why, according to Einstein, gravity attracts objects.

The idea is strange in its essence. But physicists are convinced that this is so. It also explains Mercury's strange orbit. According to the general theory of relativity, the gigantic mass of the Sun bends space and time around it. Being the closest planet to the Sun, Mercury experiences much greater curvature than other planets. The equations of general relativity describe how this warped space-time affects Mercury's orbit and help predict the planet's position.

However, despite its success, the theory of relativity is not a theory of everything, just like Newton's theories. Just as Newton's theory doesn't work for truly massive objects, Einstein's theory doesn't work on the microscale. Once you start looking at atoms and anything smaller, matter starts to behave very strangely.

Until the end of the 19th century, the atom was considered the smallest unit of matter. Born from the Greek word atomos, which meant “indivisible,” an atom, by definition, was not supposed to break down into smaller particles. But in the 1870s, scientists discovered particles that were 2,000 times lighter than atoms. By weighing beams of light in a vacuum tube, they found extremely light particles with a negative charge. This is how the first subatomic particle was discovered: the electron. Over the next half century, scientists discovered that the atom has a compound nucleus around which electrons scurry. This nucleus is made up of two types of subatomic particles: neutrons, which are neutrally charged, and protons, which are positively charged.

But that's not all. Since then, scientists have found ways to divide matter into smaller and smaller pieces, continuing to refine our understanding of fundamental particles. By the 1960s, scientists had found dozens of elementary particles, compiling a long list of the so-called particle zoo.

As far as we know, of the three components of the atom, the electron remains the only fundamental particle. Neutrons and protons split into tiny quarks. These elementary particles obey a completely different set of laws, different from those that trees or planets obey. And these new laws - which were much less predictable - spoiled the physicists' mood.

In quantum physics, particles do not have a specific place: their location is a bit blurred. It's as if each particle has a certain probability of being in a certain place. This means that the world is inherently a fundamentally uncertain place. Quantum mechanics is difficult to even understand. As Richard Feynman, an expert in quantum mechanics, once said, “I think I can say with confidence that no one understands quantum mechanics.”

Einstein was also concerned about the fuzziness of quantum mechanics. Despite the fact that he essentially partially invented it, Einstein himself never believed in quantum theory. But in their palaces - large and small - both quantum mechanics and quantum mechanics have proven their right to undivided power, being extremely accurate.

Quantum mechanics explained the structure and behavior of atoms, including why some are radioactive. It also forms the basis of modern electronics. You couldn't read this article without her.

General relativity predicted the existence of black holes. These massive stars that collapsed in on themselves. Their gravitational pull is so powerful that not even light can escape.

The problem is that these two theories are incompatible, so they cannot be true at the same time. General relativity says that the behavior of objects can be accurately predicted, whereas quantum mechanics says that you can only know the probability of what objects will do. It follows from this that there remain some things that physicists have not yet described. Black holes, for example. They are massive enough for relativity to apply, but small enough for quantum mechanics to apply. Unless you end up close to a black hole, this incompatibility will not affect your daily life. But it has puzzled physicists for most of the last century. It is this kind of incompatibility that makes us look for a theory of everything.

Einstein spent most of his life trying to find such a theory. Not a fan of the randomness of quantum mechanics, he wanted to create a theory that would unify gravity and the rest of physics, so that quantum weirdness would remain a secondary consequence.

His main goal was to make gravity work with electromagnetism. In the 1800s, physicists discovered that electrically charged particles can attract or repel. That's why some metals are attracted to magnets. Apparently, if there are two kinds of forces that objects can exert on each other, they can be attracted by gravity and attracted or repelled by electromagnetism.

Einstein wanted to combine these two forces into a “unified field theory.” To do this, he stretched spacetime into five dimensions. Along with three spatial and one time dimensions, he added a fifth dimension, which should be so small and curled up that we could not see it.

It didn't work, and Einstein spent 30 years searching in vain. He died in 1955, and his unified field theory was never revealed. But in the next decade, a serious challenger to this theory emerged: string theory.

String theory

The idea behind string theory is quite simple. The basic ingredients of our world, like electrons, are not particles. These are tiny loops or "strings". It's just that because the strings are so small, they appear to be dots.

Like the strings on a guitar, these loops are under tension. This means they vibrate at different frequencies depending on their size. These vibrations determine what kind of “particle” each string will represent. Vibrating the string in one way will give you an electron. For others, something else. All the particles discovered in the 20th century are the same kind of strings, just vibrating differently.

It's quite difficult to immediately understand why this is a good idea. But it is suitable for all forces operating in nature: gravity and electromagnetism, plus two more discovered in the 20th century. Strong and weak nuclear forces operate only within the tiny nuclei of atoms, so they could not be detected for a long time. A strong force holds the core together. A weak force usually does nothing, but if it gets strong enough, it breaks the nucleus into pieces: that's why some atoms are radioactive.

Any theory of everything will have to explain all four. Fortunately, the two nuclear forces and electromagnetism are completely described by quantum mechanics. Each force is carried by a specialized particle. But there is not a single particle that endures gravity.

Some physicists think it exists. And they call it “graviton”. Gravitons have no mass, a special spin, and they move at the speed of light. Unfortunately, they have not yet been found. This is where string theory comes into play. It describes a string that looks exactly like a graviton: has the correct spin, has no mass, and moves at the speed of light. For the first time in history, the theory of relativity and quantum mechanics found common ground.

In the mid-1980s, physicists were fascinated by string theory. “We realized in 1985 that string theory solved a bunch of problems that had been bugging people for the last 50 years,” says Barrow. But she also had problems.

First, "we don't understand what string theory is in the right detail," says Philip Candelas of the University of Oxford. “We don’t have a good way to describe it.”

In addition, some of the forecasts look strange. While Einstein's unified field theory relies on an extra hidden dimension, the simplest forms of string theory need 26 dimensions. They are needed to connect mathematical theory with what we already know about the Universe.

More advanced versions, known as “superstring theories,” make do with ten dimensions. But even this does not fit with the three dimensions that we observe on Earth.

“This can be dealt with by assuming that only three dimensions have expanded in our world and become large,” says Barrow. “Others are present but remain fantastically small.”

Because of these and other problems, many physicists don't like string theory. And they propose another theory: loop quantum gravity.

Loop quantum gravity

This theory does not set out to unify and include everything that exists in particle physics. Instead, loop quantum gravity simply attempts to derive a quantum theory of gravity. It is more limited than string theory, but not as cumbersome. Loop quantum gravity suggests that spacetime is divided into small pieces. From a distance it appears to be a smooth sheet, but upon closer inspection one can see a bunch of dots connected by lines or loops. These little fibers that weave together offer an explanation for gravity. This idea is as incomprehensible as string theory, and has similar problems: there is no experimental evidence.

Why are these theories still discussed? Perhaps we just don't know enough. If big things turn up that we've never seen before, we can try to understand the big picture and figure out the missing pieces of the puzzle later.

"It's tempting to think we've discovered everything," Barrow says. “But it would be very strange if by 2015 we had made all the necessary observations to get a theory of everything.” Why should this be so?

There is another problem. These theories are difficult to test, in large part because they have extremely brutal mathematics. Candelas tried to find a way to test string theory for years, but never succeeded.

“The main obstacle to the advancement of string theory remains the lack of development of mathematics that should accompany physics research,” says Barrow. “It’s at an early stage, there’s still a lot to explore.”

Even so, string theory remains promising. "For many years people have tried to integrate gravity with the rest of physics," Candelas says. - We had theories that explained electromagnetism and other forces well, but not gravity. With string theory we are trying to combine them.”

The real problem is that a theory of everything may simply be impossible to identify.

When string theory became popular in the 1980s, there were actually five versions of it. "People started to worry," Barrow says. “If this is the theory of everything, why are there five of them?” Over the next decade, physicists discovered that these theories could be converted into one another. They are simply different ways of seeing the same thing. The result was M-theory, put forward in 1995. This is a deep version of string theory, including all earlier versions. Well, at least we are back to a unified theory. M-theory requires only 11 dimensions, which is much better than 26. However, M-theory does not offer a unified theory of everything. She offers billions of them. In total, M-theory offers us 10^500 theories, all of which will be logically consistent and capable of describing the Universe.

This seems worse than useless, but many physicists believe it points to a deeper truth. Perhaps our Universe is one of many, each of which is described by one of trillions of versions of M-theory. And this gigantic collection of universes is called "".

At the beginning of time, the multiverse was like "a big foam of bubbles of different shapes and sizes," says Barrow. Each bubble then expanded and became a universe.

"We're in one of those bubbles," Barrow says. As the bubbles expanded, other bubbles, new universes, could form inside them. “In the process, the geography of such a universe became seriously complicated.”

The same physical laws apply in every bubble universe. That's why everything in our universe behaves the same. But in other universes there may be different laws. This gives rise to a strange conclusion. If string theory really is the best way to unify relativity and quantum mechanics, then both will and will not be the theory of everything.

On the one hand, string theory can give us a perfect description of our universe. But it will also inevitably lead to the fact that each of the trillions of other universes will be unique. A major change in thinking will be that we stop waiting for a unified theory of everything. There may be many theories of everything, each of which will be correct in its own way.