Universal laws of physics. Why are the laws of physics needed in everyday life?

Let's understand this a little. By saying you can't win, Snow meant that since matter and energy are conserved, you can't gain one without losing the other (that is, E=mc²). This also means that you need to supply heat to run the engine, but in the absence of a perfectly closed system, some heat will inevitably be lost to the engine. open world, which will lead to the second law.

The second law - losses are inevitable - means that due to increasing entropy, you cannot return to your previous energy state. Energy concentrated in one place will always tend to places of lower concentration.

Finally, the third law - you cannot quit the game - refers to the lowest theoretically possible temperature - minus 273.15 degrees Celsius. When the system reaches absolute zero, the movement of molecules stops, which means entropy will reach its lowest value and there will not even be kinetic energy. But in real world It is impossible to reach absolute zero - you can only get very close to it.

Archimedes' force

After the ancient Greek Archimedes discovered his principle of buoyancy, he allegedly shouted “Eureka!” (Found it!) and ran naked through Syracuse. So says the legend. The discovery was so important. Legend also says that Archimedes discovered the principle when he noticed that the water in a bathtub rose when a body was immersed in it.

According to Archimedes' principle of buoyancy, the force acting on a submerged or partially submerged object is equal to the mass of the fluid that the object displaces. This principle has vital importance in density calculations, as well as the design of submarines and other ocean-going vessels.

Evolution and natural selection

Now that we have established some of the basic concepts about how the universe began and how physical laws affect our daily lives, let's turn our attention to the human form and find out how we got this far. According to most scientists, all life on Earth has a common ancestor. But in order for such a huge difference to arise between all living organisms, some of them had to turn into a separate species.

IN in a general sense, this differentiation occurred during the process of evolution. Populations of organisms and their traits have gone through mechanisms such as mutations. Those with traits that were more advantageous to survival, such as brown frogs, which are excellent at camouflage in the swamp, were naturally selected for survival. This is where the term natural selection comes from.

You can multiply these two theories for many, many times, and this is actually what Darwin did in the 19th century. Evolution and natural selection explain the enormous diversity of life on Earth.

Albert Einstein's general theory of relativity was and remains a major discovery that forever changed our view of the universe. Einstein's major breakthrough was the claim that space and time are not absolute, and that gravity is not simply a force applied to an object or mass. Rather, gravity is due to the fact that mass bends space and time itself (space-time).

To think about this, imagine driving across the Earth in a straight line in an easterly direction, say, from the Northern Hemisphere. After a while, if someone wants to accurately determine your location, you will be much further south and east of your original position. This is because the Earth is curved. To drive straight east, you need to take into account the shape of the Earth and drive at an angle slightly north. Compare a round ball and a sheet of paper.

Space is pretty much the same thing. For example, it will be obvious to passengers on a rocket flying around the Earth that they are flying in a straight line through space. But in reality, the spacetime around them is being bent by Earth's gravity, causing them to both move forward and remain in Earth's orbit.

Einstein's theory had a huge impact on the future of astrophysics and cosmology. She explained a small and unexpected anomaly in Mercury's orbit, showed how starlight bends, and laid the theoretical foundations for black holes.

Heisenberg Uncertainty Principle

The expansion of Einstein's theory of relativity taught us more about how the universe works and helped lay the foundation for quantum physics, leading to a completely unexpected embarrassment of theoretical science. In 1927, the realization that all laws of the universe are flexible in a given context led to a stunning discovery by the German scientist Werner Heisenberg.

By postulating his uncertainty principle, Heisenberg realized that it was impossible to simultaneously know two properties of a particle with a high level of accuracy. You can know the position of an electron with a high degree of accuracy, but not its momentum, and vice versa.

Niels Bohr later made a discovery that helped explain Heisenberg's principle. Bohr discovered that the electron has the qualities of both a particle and a wave. The concept became known as wave-particle duality and formed the basis of quantum physics. Therefore, when we measure the position of an electron, we define it as a particle at a certain point in space with an indefinite wavelength. When we measure a pulse, we treat the electron as a wave, which means we can know the amplitude of its length, but not its position.

A physical law is a quantitative or qualitative objective dependence of some physical quantities on others, found experimentally and established by generalizing experimental data.

Continuum model

A model according to which in physics matter is considered as a medium continuously distributed in space, having neither voids nor discontinuities and possessing the physical properties of real matter (solid body, droplet liquid, gas, plasma).

The use of a continuum model allows the use of the mathematical apparatus of differential and integral calculus.

Temperature

Temperature is a scalar physical quantity that characterizes the thermal state of the system. According to molecular kinetic theory, temperature is related to the intensity of movement of microstructural particles of matter. The numerical value of the temperature represents is the magnitude of the deviation of the thermal state of a body from thermal equilibrium with another body, the state of which is taken as the reference point.

The scale for measuring temperature is determined by the selected starting point. Currently, the SI system of units provides for the use of two temperature scales: thermodynamic (absolute scale) and international law k t h e s k u (MPSHT). On the first scale, absolute zero temperature is conventionally taken as the starting point. The unit of measurement of thermodynamic temperature is kelvin, designation: T.

On the second scale, the starting point is the state corresponding to the melting of ice in water, this is 273.15 K. The temperature on this scale is expressed in degrees Celsius (0 C) and is designated t.

The relationship between temperatures on established scales has the form:

T =t + 273,15.

A number of countries still use a non-systemic scale expressed in degrees Fahrenheit (0 F). Conversion of temperature from the Fahrenheit scale to the Celsius scale is carried out using the expression

t = (t F – 32).

Pressure

Pressure is a physical quantity that characterizes the stressed state of continuous media; numerically it is the intensity of normal forces with which one body acts on the surface of another.

Pressure is indicated p, its SI unit is pascal (Pa).

One pascal in a stationary medium is equal to the pressure caused by a normal force of 1 N acting on a surface equal to 1 m 2 (1 Pa = 1 N/m 2).

The following units can be used: bar (1 bar = 1 5 Pa), technical atmosphere (1 atm = 1 kgf/cm 2 = 0.98110 5 Pa), physical atmosphere (1 atm = 1.0110 5 Pa), millimeter of mercury (1 mm Hg = 133.3 Pa), millimeter of water column (1 mm water column = 9.81 Pa). p The pressure in the system, measured from zero value, is called absolute and is designated abs (p . Absolute atmospheric pressure is called barometric pressure ). bar. Pressure in the system exceeding atmospheric (barometric) is called excess pressure ( R Pressure in the system exceeding atmospheric (barometric) is called excess pressure ( hut), and what is missing to the atmospheric level is discharge ( once ), or vacuum pressure (p ).

wack 1.1. Annotation.

The laws of the theory of relativity and quantum mechanics, according to which the movement and interaction of elementary particles of matter occur, predetermine the formation and emergence of patterns of a wide range of phenomena studied by various natural sciences. These laws underlie modern high technologies and largely determine the state and development of our civilization. Therefore, familiarity with the basics of fundamental physics is necessary not only for students, but also for schoolchildren. Active possession of basic knowledge about the structure of the world is necessary for a person entering life in order to find his place in this world and successfully continue his education. It is addressed both to specialists in the field of particle physics and to a much wider audience: non-particle physicists, mathematicians, chemists, biologists, energy scientists, economists, philosophers, linguists,... To be sufficiently precise, I must use terms and formulas of fundamental physics. To be understood, I must constantly explain these terms and formulas. If particle physics is not your specialty, read first only those sections whose titles are not marked with asterisks. Then try reading sections with one asterisk *, two **, and finally three ***. I managed to talk about most of the sections without stars during the report, but I didn’t have time for the rest.

1.3. Physics of elementary particles. Particle physics is the foundation of all natural sciences. She studies the smallest particles of matter and the basic patterns of their movements and interactions. Ultimately, it is these patterns that determine the behavior of all objects on Earth and in the sky. Particle physics deals with such fundamental concepts as space and time; matter; energy, momentum and mass; spin. (Most readers have an idea of ​​space and time, have probably heard about the connection between mass and energy and have no idea what momentum has to do with it, and are unlikely to realize the most important role of spin in physics. Even among themselves they cannot yet agree on what to call matter experts.) Particle physics was created in the 20th century. Its creation is inextricably linked with the creation of two greatest theories in human history: the theory of relativity and quantum mechanics. The key constants of these theories are the speed of light c and Planck's constant h.

1.4. Theory of relativity. The special theory of relativity, which arose at the beginning of the 20th century, completed the synthesis of a number of sciences that studied such classical phenomena as electricity, magnetism and optics, creating mechanics at velocities of bodies comparable to the speed of light. (Newton's classical non-relativistic mechanics dealt with velocities v<<c.) Then in 1915 the general theory of relativity was created, which was intended to describe gravitational interactions, taking into account the finite speed of light c.

1.5. Quantum mechanics. Quantum mechanics, created in the 1920s, explained the structure and properties of atoms based on the dual wave-particle properties of electrons. She explained a huge range of chemical phenomena associated with the interaction of atoms and molecules. And it made it possible to describe the processes of emission and absorption of light by them. Understand the information that the light of the Sun and stars brings us.

1.6. Quantum field theory. The combination of the theory of relativity and quantum mechanics led to the creation of quantum field theory, which makes it possible to describe the most important properties of matter with a high degree of accuracy. Quantum field theory is, of course, too complex to be explained to schoolchildren. But in the middle of the 20th century, the visual language of Feynman diagrams emerged, which radically simplifies the understanding of many aspects of quantum field theory. One of the main goals of this talk is to show how Feynman diagrams can be used to easily understand a wide range of phenomena. At the same time, I will dwell in more detail on issues that are not known to all experts in quantum field theory (for example, about the connection between classical and quantum gravity), and will only briefly outline issues that are widely discussed in the popular scientific literature.

1.7. Identity of elementary particles. Elementary particles are the smallest indivisible particles of matter from which the entire world is built. The most amazing property that distinguishes these particles from ordinary non-elementary particles, for example, grains of sand or beads, is that all elementary particles of the same type, for example, all electrons in the Universe are absolutely (!) the same - identical. And as a result, their simplest bound states - atoms and the simplest molecules - are identical to each other.

1.8. Six elementary particles. To understand the basic processes occurring on Earth and the Sun, as a first approximation it is enough to understand the processes in which six particles participate: electron e, proton p, neutron n and electron neutrino ν e , as well as photon γ and graviton g̃. The first four particles have a spin of 1/2, a photon has a spin of 1, and a graviton has a spin of 2. (Particles with integer spin are called bosons, particles with half-integer spin are called fermions. Spin will be discussed in more detail below.) Protons and neutrons are usually called nucleons because Atomic nuclei are built from them, and nucleus in English is nucleus. Electrons and neutrinos are called leptons. They do not have strong nuclear interactions.

Due to the very weak interaction of gravitons, it is impossible to observe individual gravitons, but it is through these particles that gravity is realized in nature. Just as electromagnetic interactions are carried out through photons.

1.9. Antiparticles. The electron, proton and neutron have so-called antiparticles: positron, antiproton and antineutron. They are not part of ordinary matter, since when they meet the corresponding particles, they enter into reactions of mutual destruction - annihilation. Thus, an electron and a positron annihilate into two or three photons. The photon and graviton are truly neutral particles: they coincide with their antiparticles. Whether the neutrino is a truly neutral particle is still unknown.

1.10. Nucleons and quarks. In the middle of the 20th century, it turned out that the nucleons themselves consist of more elementary particles - two types of quarks, which denote u And d: p = uud, n = ddu. The interaction between quarks is carried out by gluons. Antinucleons are made up of antiquarks.

1.11. Three generations of fermions. Along with u, d, e, ν e two other groups (or, as they say, generations) of quarks and leptons were discovered and studied: c, s, μ, ν μ and t, b, τ , ν τ . These particles are not included in the composition of ordinary matter, since they are unstable and quickly disintegrate into lighter particles of the first generation. But they played an important role in the first moments of the existence of the Universe.

For an even more complete and profound understanding of nature, we need even more particles with even more unusual properties. But perhaps in the future all this diversity will be reduced to a few simple and beautiful essences.

1.12. Hadrons. A large family of particles consisting of quarks and/or antiquarks and gluons are called hadrons. All hadrons, with the exception of nucleons, are unstable and therefore are not part of ordinary matter.

Often hadrons are also classified as elementary particles, since they cannot be broken down into free quarks and gluons. (I did the same, classifying the proton and neutron as the first six elementary particles.) If all hadrons are considered elementary, then the number of elementary particles will be measured in the hundreds.

1.13. Standard model and four types of interactions. As will be explained below, the elementary particles listed above make it possible, within the framework of the so-called “Standard Model of Elementary Particles,” to describe all hitherto known processes occurring in nature as a result of gravitational, electromagnetic, weak and strong interactions. But in order to understand how the first two of them work, four particles are enough: photon, graviton, electron and proton. Moreover, the fact that a proton consists of u- And d-quarks and gluons turns out to be insignificant. Of course, without weak and strong interactions it is impossible to understand either how atomic nuclei are structured or how our Sun works. But it is possible to understand how atomic shells, which determine all the chemical properties of elements, are structured, how electricity works and how galaxies are structured.

1.14. Beyond the known. We already know today that the particles and interactions of the Standard Model do not exhaust the treasures of nature.

It has been established that ordinary atoms and ions make up only less than 20% of all matter in the Universe, and more than 80% is so-called dark matter, the nature of which is still unknown. The most common belief is that dark matter consists of superparticles. It is possible that it consists of mirror particles.

Even more amazing is that all matter, both visible (light) and dark, carries only a quarter of the total energy of the Universe. Three quarters belong to the so-called dark energy.

1.15. Elementary particles "e to a degree” are fundamental. When my teacher Isaac Yakovlevich Pomeranchuk wanted to emphasize the importance of a question, he said that the question e is very important. Of course, most of the natural sciences, not just particle physics, are fundamental. Condensed matter physics, for example, is governed by fundamental laws that can be used without understanding how they follow from the laws of particle physics. But the laws of relativity and quantum mechanics " e“to a degree fundamental” in the sense that they cannot be contradicted by any of the less general laws.

1.16. Basic laws. All processes in nature occur as a result of local interactions and movements (propagations) of elementary particles. The basic laws governing these movements and interactions are very unusual and very simple. They are based on the concept of symmetry and the principle that everything that does not contradict symmetry can and should happen. Below, using the language of Feynman diagrams, we will trace how this is realized in gravitational, electromagnetic, weak and strong interactions of particles.

2. Particles and life

2.1. About civilization and culture. Foreign member of the RAS Valentin Telegdi (1922–2006) explained: “If a WC (water closet) is civilization, then the ability to use it is culture.”

ITEP employee A. A. Abrikosov Jr. wrote to me recently: “One of the goals of your report is to convince high audiences of the need to teach modern physics more widely. If so, then perhaps it would be worth giving a few everyday examples. What I mean is this:

We live in a world that, even at the everyday level, is unthinkable without quantum mechanics (QM) and the theory of relativity (TR). Cell phones, computers, all modern electronics, not to mention LED lights, semiconductor lasers (including pointers), and LCD displays are essentially quantum devices. It is impossible to explain how they work without the basic concepts of CM. How can you explain them without mentioning tunneling?

The second example, perhaps, I know from you. Satellite navigators are already installed in every 10th car. The accuracy of clock synchronization in a satellite network is no less than 10 −8 (this corresponds to an error of the order of a meter in localizing an object on the Earth’s surface). Such accuracy requires taking into account maintenance corrections to the clock rate on a moving satellite. They say that engineers could not believe it, so the first devices had a double program: with and without corrections. As it turns out, the first program works better. Here is a test of the theory of relativity at the everyday level.

Of course, chatting on the phone, driving a car and tapping computer keys is possible without high science. But academicians should hardly urge people not to study geography, because “there are cabbies.”

Otherwise, schoolchildren and then students have been talking about material points and Galilean relativity for five years, and suddenly, out of the blue, they declare that this is “not entirely true.”

It is difficult to switch from the visual Newtonian world to the quantum one even in physics and technology. Yours, AAA."

2.2. About fundamental physics and education. Unfortunately, the modern education system is a century behind modern fundamental physics. And most people (including most scientists) have no idea about the amazingly clear and simple picture (map) of the world that particle physics has created. This map makes it much easier to navigate all natural sciences. The purpose of my report is to convince you that some elements (concepts) of elementary particle physics, the theory of relativity and quantum theory can and should become the basis for teaching all natural science subjects not only in higher, but also in secondary and even primary schools. After all, fundamentally new concepts are most easily mastered in childhood. The child easily masters the language and gets used to using a mobile phone. Many children return the Rubik's cube to its original state in a matter of seconds, but even a day is not enough for me.

To avoid unpleasant surprises in the future, an adequate worldview must be established in kindergarten. Constants c And h should become tools of cognition for children.

2.3. About mathematics. Mathematics - the queen and servant of all sciences - should certainly serve as the main tool of knowledge. It gives such basic concepts as truth, beauty, symmetry, order. Concepts of zero and infinity. Mathematics teaches you to think and count. Fundamental physics is unthinkable without mathematics. Education is unthinkable without mathematics. Of course, it may be too early to study group theory at school, but it is necessary to teach to appreciate truth, beauty, symmetry and order (and at the same time some disorder).

It is very important to understand the transition from real (real) numbers (simple, rational, irrational) to imaginary and complex numbers. Probably only those students who want to work in the field of mathematics and theoretical physics should study hypercomplex numbers (quaternions and octonions). For example, I have never used octonions in my work. But I know that they make it easier to understand what many theoretical physicists consider to be the most promising exceptional symmetry group, E 8 .

2.4. About worldview and natural sciences. An idea of ​​the basic laws governing the world is necessary in all natural sciences. Of course, solid state physics, chemistry, biology, Earth sciences, and astronomy have their own specific concepts, methods, and problems. But it is very important to have a general map of the world and an understanding that on this map there are many blank spots of the unknown. It is very important to understand that science is not an ossified dogma, but a living process of approaching the truth at many points on the world map. Approaching the truth is an asymptotic process.

2.5. About true and vulgar reductionism. The idea that more complex structures in nature are composed of less complex structures and, ultimately, of simpler elements is commonly called reductionism. In this sense, what I am trying to convince you of is reductionism. But vulgar reductionism, which claims that all sciences can be reduced to the physics of elementary particles, is absolutely unacceptable. At each increasingly higher level of complexity, its own patterns are formed and emerge. To be a good biologist, you don't need to know particle physics. But to understand its place and role in the system of sciences, to understand the key role of constants c And h necessary. After all, science as a whole is a single organism.

2.6. About the humanities and social sciences. A general understanding of the structure of the world is very important for economics, history, cognitive sciences, such as the sciences of language, and philosophy. And vice versa - these sciences are extremely important for fundamental physics itself, which constantly refines its fundamental concepts. This will be clear from the discussion of the theory of relativity, to which I will now turn. I will especially say about the legal sciences, which are extremely important for the prosperity (not to mention the survival) of the natural sciences. I am convinced that social laws should not contradict the fundamental laws of nature. Human laws should not contradict the Divine Laws of Nature.

2.7. Micro-, Macro-, Cosmo-. Our ordinary world of large, but not gigantic, things is usually called the macroworld. The world of celestial objects can be called the cosmoworld, and the world of atomic and subatomic particles is called the microworld. (Since the sizes of atoms are on the order of 10−10 m, the microcosm means objects at least 4, or even 10 orders of magnitude smaller than a micrometer, and 1–7 orders of magnitude smaller than a nanometer. The fashionable nano region is located down the road from the micro to the macro.) In the 20th century, the so-called Standard Model of elementary particles was built, which allows you to simply and clearly understand many macro and cosmic laws based on micro laws.

2.8. Our models. Models in theoretical physics are built by discarding irrelevant circumstances. For example, in atomic and nuclear physics, gravitational interactions of particles are negligible and can be ignored. This model of the world fits into the special theory of relativity. In this model there are atoms, molecules, condensed bodies,... accelerators and colliders, but there is no Sun and stars.

Such a model would certainly be incorrect on very large scales where gravity is significant.

Of course, the existence of the Earth (and therefore gravity) is necessary for the existence of CERN, but for understanding the vast majority of experiments carried out at CERN (except for the search for microscopic “black holes” at the collider), gravity is unimportant.

2.9. Orders of magnitude. One of the difficulties in understanding the properties of elementary particles is due to the fact that they are very small and there are a lot of them. There are a huge number of atoms in a spoonful of water (about 10 23). The number of stars in the visible part of the Universe is not much less. There is no need to be afraid of large numbers. After all, handling them is not difficult, since multiplying numbers comes down mainly to adding their orders: 1 = 10 0, 10 = 10 1, 100 = 10 2. Multiply 10 by 100, we get 10 1+2 = 10 3 = 1000.

2.10. A drop of oil. If a drop of oil with a volume of 1 milliliter is dropped onto the surface of water, it will blur into a rainbow-colored spot with an area of ​​about several square meters and a thickness of about a hundred nanometers. This is only three orders of magnitude larger size and an atom. And the thickness of the film of a soap bubble in the thinnest places is on the order of the size of molecules.

2.11. Joules. A typical AA battery has a voltage of 1.5 volts (V) and contains 10 4 joules (J) of electrical energy. Let me remind you that 1 J = 1 coulomb × 1 V, and also that 1 J = kg m 2 / s 2 and that the acceleration of gravity is approximately 10 m / s 2. So 1 joule allows you to lift 1 kilogram to a height of 10 cm, and 10 4 J will lift 100 kg to 10 meters. This is how much energy an elevator consumes to take a schoolchild to the tenth floor. This is how much energy is in the battery.

2.12. Electrovolts. The unit of energy in particle physics is the electronvolt (eV): the energy of 1 eV is acquired by 1 electron passing through a potential difference of 1 volt. Since there are 6.24 × 10 18 electrons in one coulomb, then 1 J = 6.24 × 10 18 eV.

1 keV =10 3 eV, 1 MeV =10 6 eV, 1 GeV =10 9 eV, 1 TeV =10 12 eV.

Let me remind you that the energy of one proton in the CERN Large Hadron Collider should be equal to 7 TeV.

3. About the theory of relativity

3.1. Frames of reference. We describe all our experiments in one or another reference system. The reference system can be a laboratory, a train, an Earth satellite, the center of the galaxy... . The reference system can be any particle flying, for example, in a particle accelerator. Since all these systems move relative to each other, not all experiments in them will look the same. In addition, the gravitational influence of nearby massive bodies is also different. It is taking these differences into account that constitutes the main content of the theory of relativity.

3.2. Galileo's ship. Galileo formulated the principle of relativity, colorfully describing all kinds of experiments in the cabin of a smoothly sailing ship. If the windows are curtained, it is impossible to find out with the help of these experiments how fast the ship is moving and whether it is stationary. Einstein added finite speed of light experiments to this cabin. If you don't look out the window, you can't tell the ship's speed. But if you look at the shore, you can.

3.3. Distant stars*. It makes sense to provide a frame of reference in relation to which people could formulate the results of their experiments, regardless of where they are. For such a universal reference system, a system in which distant stars are motionless has long been accepted. And relatively recently (half a century ago) even more distant quasars were discovered and it turned out that in this system the relict microwave background should be isotropic.

3.4. In search of a universal reference system*. Essentially, the entire history of astronomy is a progression towards an increasingly universal frame of reference. From anthropocentric, where man is in the center, to geocentric, where the Earth rests in the center (Ptolemy, 87–165), to heliocentric, where the Sun rests in the center (Copernicus, 1473–1543), to galacentric, where the center of our Galaxy rests, to nebular, where the system of nebulae - clusters of galaxies rests; to the background, where the cosmic microwave background is isotropic. It is important, however, that the speeds of these reference systems are small compared to the speed of light.

3.5. Copernicus, Kepler, Galileo, Newton*. In the book of Nicolaus Copernicus “On the Rotations of the Celestial Spheres,” published in 1543, it is said: “All the movements noticeable in the Sun are not peculiar to it, but belong to the Earth and our sphere, together with which we revolve around the Sun, like any other planet; thus the Earth has several movements. The apparent forward and backward movements of the planets do not belong to them, but to the Earth. Thus, this movement alone is sufficient to explain a large number of irregularities visible in the sky.”

Copernicus and Kepler (1571–1630) gave a simple phenomenological description of the kinematics of these movements. Galileo (1564–1642) and Newton (1643–1727) explained their dynamics.

3.6. Universal space and time*. Spatial coordinates and time, referred to a universal reference system, can be called universal or absolute in complete harmony with the theory of relativity. It is only important to emphasize that the choice of this system is made and agreed upon by local observers. Any reference system that is progressively moving relative to the universal system is inertial: in it free movement is uniform and rectilinear.

3.7. "Theory of Invariance"*. Note that both Albert Einstein (1879–1955) and Max Planck (1858–1947) (who coined the term “theory of relativity” in 1907, referring to the theory put forward by Einstein in 1905) believed that the term “theory invariance" could more accurately reflect its essence. But, apparently, at the beginning of the 20th century it was more important to emphasize the relativity of such concepts as time and simultaneity in equal inertial reference systems than to single out one of these systems. The more important thing was that with the windows of Galileo’s cabin curtained, it was impossible to determine the speed of the ship. But now it’s time to open the curtains and look at the shore. In this case, of course, all the patterns established with the curtains closed will remain unshakable.

3.8. Letter to Chimmer*. In 1921, Einstein, in a letter to E. Chimmer, the author of the book “Philosophical Letters,” wrote: “As for the term “theory of relativity,” I admit that it is unfortunate and leads to philosophical misunderstandings.” But, according to Einstein, it is too late to change it, in particular because it is widespread. This letter was published in volume 12 of the 25-volume “Collected Works of Einstein,” published in the fall of 2009, published in Princeton.

3.9. Maximum speed in nature. The key constant of the theory of relativity is the speed of light c= 300,000 km/s = 3 × 10 8 m/s. (More accurately, c= 299,792,458 m/s. And this number now underlies the definition of the meter.) This speed is the maximum speed of propagation of any signals in nature. It exceeds the speed of massive objects with which we deal every day by many orders of magnitude. It is precisely its unusually large value that hinders the understanding of the main content of the theory of relativity. Particles moving at speeds on the order of the speed of light are called relativistic.

3.10. Energy, momentum and speed. The free movement of a particle is characterized by the energy of the particle E and its impulse p. According to the theory of relativity, the speed of a particle v is determined by the formula

One of the main reasons for the terminological confusion discussed in Sect. 3.14, is that when creating the theory of relativity they tried to preserve the Newtonian connection between momentum and speed p = mv, which contradicts the theory of relativity.

3.11. Weight. Particle mass m is determined by the formula

While the energy and momentum of a particle depend on the frame of reference, the magnitude of its mass m does not depend on the reference system. It is an invariant. Formulas (1) and (2) are basic in the theory of relativity.

Oddly enough, the first monograph on the theory of relativity, in which formula (2) appeared, was published only in 1941. It was “Field Theories” by L. Landau (1908–1968) and E. Lifshitz (1915–1985). I didn’t find it in any of Einstein’s works. It is not found in the wonderful book “The Theory of Relativity” by W. Pauli (1900–1958), published in 1921. But the relativistic wave equation containing this formula was in the book “Principles of Quantum Mechanics” by P. Dirac, published in 1930 ( 1902–1984), and even earlier in articles of 1926 by O. Klein (1894–1977) and V. Fok (1898–1974).

3.12. Massless photon. If the mass of a particle is zero, i.e. the particle is massless, then from formulas (1) and (2) it follows that in any frame of reference its speed is equal to c. Since the mass of a particle of light - a photon - is so small that it cannot be detected, it is generally accepted that it is equal to zero and that c- this is the speed of light.

3.13. Energy of rest. If the mass of the particle is different from zero, then consider the frame of reference in which the free particle is at rest and v = 0, p= 0. Such a frame of reference is called the rest frame of the particle, and the energy of the particle in this frame is called the rest energy and is denoted E 0. From formula (2) it follows that

This formula expresses the relationship between the rest energy of a massive particle and its mass, discovered by Einstein in 1905.

3.14. "The most famous formula." Unfortunately, very often Einstein’s formula is written in the form of “the most famous formula E = mc 2”, omitting the zero index of the rest energy, which leads to numerous misunderstandings and confusion. After all, this “famous formula” identifies energy and mass, which contradicts the theory of relativity in general and formula (2) in particular. From it follows the widespread misconception that the mass of a body, according to the theory of relativity, supposedly increases with its speed. In recent years, the Russian Academy of Education has done a lot to dispel this misconception.

3.15. Unit of speed*. In the theory of relativity, which deals with velocities comparable to the speed of light, it is natural to choose c as a unit of speed. This choice simplifies all formulas, since c/c= 1, and they should be put c= 1. In this case, speed becomes a dimensionless quantity, distance has the dimension of time, and mass has the dimension of energy.

In particle physics, particle masses are usually measured in electronvolts - eV and their derivatives (see Section 2.14). The mass of an electron is about 0.5 MeV, the mass of a proton is about 1 GeV, the mass of the heaviest quark is about 170 GeV, and the mass of a neutrino is about a fraction of an eV.

3.16. Astronomical distances*. In astronomy, distances are measured in light years. The size of the visible part of the Universe is about 14 billion light years. This number is even more impressive when compared with the time of 10 −24 s, during which light travels a distance on the order of the size of a proton. And throughout this colossal range the theory of relativity works.

3.17. Minkowski's world. In 1908, a few months before his untimely death, Herman Minkowski (1864–1909) prophetically said: “The views on space and time that I intend to develop before you arose on an experimental physical basis. This is their strength. Their tendency is radical. From now on, space in itself and time in itself must turn into fiction, and only some kind of combination of both must still retain independence.”

A century later, we know that time and space have not become fiction, but Minkowski's idea made it possible to very simply describe the movements and interactions of particles of matter.

3.18. Four-dimensional world*. In units in which c= 1, the idea of ​​Minkowski’s world, which combines time and three-dimensional space into a single four-dimensional world, looks especially beautiful. Energy and momentum are combined into a single four-dimensional vector, and mass, in accordance with equation (2), serves as the pseudo-Euclidean length of this energy-momentum 4-vector p = E, p:

A four-dimensional trajectory in the Minkowski world is called a world line, and individual points are called world points.

3.19. The dependence of the clock on its speed**. Numerous observations indicate that clocks run fastest when they are at rest relative to the inertial frame. Finite motion in an inertial reference system slows down their progress. The faster they move in space, the slower they go in time. The deceleration is absolute in the universal reference system (see sections 3.1–3.8). Its measure is the ratio E/m, which is often denoted by the letter γ.

3.20. Muons in a ring accelerator and at rest**. The existence of this slowdown can most clearly be seen by comparing the lifetimes of a muon at rest and a muon rotating in a ring accelerator. The fact that in the accelerator the muon does not move completely freely, but has centripetal acceleration ω 2 R, Where ω is the radial frequency of circulation, and R- orbital radius, gives only a negligible correction, since E/ω 2 R = ER>> 1. Motion in a circle, and not in a straight line, is absolutely essential for the direct comparison of a rotating muon with a stationary one. But with regard to the aging rate of a moving muon, a circular arc of a sufficiently large radius is indistinguishable from a straight line. This tempo is determined by the ratio E/m. (I emphasize that according to the special theory of relativity, the frame of reference in which a rotating muon is at rest is not inertial.)

3.21. Arc and chord**. From the point of view of an observer at rest in an inertial reference frame, a circular arc of a sufficiently large radius and its chord are practically indistinguishable: motion along the arc is almost inertial. From the point of view of an observer at rest relative to a muon flying in a circle, its motion is essentially non-inertial. After all, its speed changes sign in half a turn. (For a moving observer, distant stars are by no means motionless. The entire Universe is asymmetrical for him: the stars in front are blue and behind are red. While for us they are all the same - golden, because the speed solar system small.) And the non-inertiality of this observer is manifested in the fact that the constellations in front and behind change as the muon moves in the ring accelerator. We cannot consider observers at rest and observers in motion to be equivalent, since the first does not experience any acceleration, and the second, in order to return to the meeting place, must experience it.

3.22. GTO**. Theoretical physicists accustomed to language General theory relativity (GR), insist that all reference systems are equal. Not only inertial, but also accelerated. That space-time itself is curved. In this case, gravitational interaction ceases to be the same physical interaction as electromagnetic, weak and strong, but becomes an exclusive manifestation of curved space. As a result, all physics for them appears to be split into two parts. If we proceed from the fact that acceleration is always due to interaction, that it is not relative, but absolute, then physics becomes unified and simple.

3.23. "Lenkom". The use of the words “relativity” and “relativism” in relation to the speed of light is reminiscent of the name of the Lenkom theater or the Moskovsky Komsomolets newspaper, only genealogically related to the Komsomol. These are the paradoxes of language. The speed of light in vacuum is not relative. She is absolute. Physicists just need help from linguists.

4. About quantum theory

4.1. Planck's constant. If the key constant in relativity is the speed of light c, then in quantum mechanics the key constant is h= 6.63·10 −34 J· s, discovered by Max Planck in 1900. The physical meaning of this constant will become clear from the subsequent presentation. For the most part The so-called reduced Planck constant appears in the formulas of quantum mechanics:

ħ = h/2π= 1.05 10 −34 J × c= 6.58·10 −22 MeV·c.

In many phenomena, the quantity plays an important role ħc= 1.97·10−11 MeV cm.

4.2. Electron spin. Let's start with the well-known naive comparison of an atom with a planetary system. The planets rotate around the Sun and around their own axis. Similarly, electrons rotate around the nucleus and around their own axis. The rotation of an electron in its orbit is characterized by the orbital angular momentum L(it is often and not quite correctly called orbital angular momentum). The rotation of an electron around its own axis is characterized by its own angular momentum - spin S. It turned out that all electrons in the world have a spin equal to (1/2) ħ . For comparison, we note that the “spin” of the Earth is 6 10 33 m 2 kg/s = 6 10 67 ħ .

4.3. Hydrogen atom. In fact, an atom is not a planetary system, and an electron is not an ordinary particle moving in an orbit. An electron, like all other elementary particles, is not a particle at all in the everyday sense of the word, which implies that the particle must move along a certain trajectory. In the simplest atom - a hydrogen atom, if it is in its ground state, i.e. not excited, the electron rather resembles a spherical cloud with a radius of the order of 0.5 × 10 −10 m. As the atom is excited, the electron goes into higher and higher states , having an increasingly larger size.

4.4. Quantum numbers of electrons. Without taking spin into account, the motion of an electron in an atom is characterized by two quantum numbers: the principal quantum number n and orbital quantum number l, and n ≥ l. If l= 0, then the electron is a spherically symmetric cloud. The larger n, the larger the size of this cloud. The more l, the more the electron’s motion resembles the motion of a classical particle in its orbit. Binding energy of an electron located in a hydrogen atom on a shell with a quantum number n, is equal

Where α =e 2/ħc≈ 1/137, a e- electron charge.

4.5. Multielectron atoms. Spin plays a key role in filling the electron shells of multielectron atoms. The fact is that two electrons with identically directed self-rotation (identical spins) cannot be on the same shell with these values n And l. This is prohibited by the so-called Pauli principle (1900–1958). Essentially, the Pauli principle determines the periods of Mendeleev's Periodic Table of Elements (1834–1907).

4.6. Bosons and fermions. All elementary particles have spin. So, the photon spin is equal to 1 in units ħ , the graviton spin is 2. Particles with integer spin in units ħ are called bosons. Particles with half-integer spin are called fermions. Bosons are collectivists: “they strive to all live in the same room,” to be in the same quantum state. A laser is based on this property of photons: all photons in a laser beam have exactly the same impulses. Fermions are individualists: “each of them needs a separate apartment.” This property of electrons determines the patterns of filling the electron shells of atoms.

4.7. "Quantum Centaurs". Elementary particles are like quantum centaurs: half-particles are half-waves. Due to their wave properties, quantum centaurs, unlike classical particles, can pass through two slits at once, resulting in an interference pattern on a screen behind them. All attempts to fit quantum centaurs into the Procrustean bed of classical physics concepts have proven fruitless.

4.8. Uncertainty relations. Constant ħ determines the features of not only rotational, but also translational motion of elementary particles. The uncertainties in the position and momentum of the particle must satisfy the so-called Heisenberg uncertainty relations (1901–1976), such as

A similar relationship exists for energy and time:

4.9. Quantum mechanics. Both spin quantization and uncertainty relations are particular manifestations of the general laws of quantum mechanics, created in the 20s of the 20th century. According to quantum mechanics, any elementary particle, for example, an electron, is both an elementary particle and an elementary (single-particle) wave. Moreover, unlike an ordinary wave, which is the periodic movement of a colossal number of particles, an elementary wave is a new, previously unknown type of movement of an individual particle. Elementary wavelength λ of a particle with momentum p equal to λ = h/|p|, and the elementary frequency ν , corresponding to energy E, is equal ν = E/h.

4.10. Quantum field theory. So, at first we were forced to admit that particles can be arbitrarily light and even massless, and that their speeds cannot exceed c. Then we were forced to admit that particles are not particles at all, but peculiar hybrids of particles and waves, the behavior of which is united by quantum h. The unification of relativity and quantum mechanics was carried out by Dirac (1902–1984) in 1930 and led to the creation of a theory called quantum field theory. It is this theory that describes the basic properties of matter.

4.11. Units in which c, ħ = 1. In what follows, as a rule, we will use units in which the unit of speed is taken to be c, and per unit of angular momentum (action) - ħ . In these units, all formulas are significantly simplified. In them, in particular, the dimensions of energy, mass and frequency are the same. These units are accepted in high-energy physics, since quantum and relativistic phenomena are significant in it. In cases where it is necessary to emphasize the quantum nature of a particular phenomenon, we will explicitly write out ħ . We will do the same with c.

4.12. Einstein and quantum mechanics*. Einstein, in a sense, having given birth to quantum mechanics, did not reconcile himself with it. And until the end of his life he tried to build a “unified theory of everything” based on classical field theory, ignoring ħ . Einstein believed in classical determinism and the inadmissibility of randomness. He repeated about God: “He does not play dice.” And he could not come to terms with the fact that the instant of decay of an individual particle cannot, in principle, be predicted, although the average lifetime of a particular type of particle is predicted within the framework of quantum mechanics with unprecedented accuracy. Unfortunately, his biases shaped the views of too many people.

5. Feynman diagrams

5.1. The simplest diagram. Particle interactions can be conveniently viewed using diagrams proposed by Richard Feynman (1918–1988) in 1949. In Fig. Figure 1 shows the simplest Feynman diagram describing the interaction of an electron and a proton through the exchange of a photon.

The arrows in the figure indicate the direction of time flow for each particle.

5.2. Real particles. Each process is represented by one or more Feynman diagrams. The outer lines in the diagram correspond to incoming (before interaction) and outgoing (after interaction) particles that are free. Their 4-momenta p satisfy the equation

They are called real particles and are said to be on the mass surface.

5.3. Virtual particles. The inner lines of the diagrams correspond to particles in a virtual state. For them

They are called virtual particles and are said to be off-shell. The propagation of a virtual particle is described by a mathematical quantity called a propagator.

This common terminology may lead a newbie to believe that virtual particles are less material than real particles. In reality they are equally are material, but we perceive real particles as matter and radiation, and virtual ones mainly as force fields, although this distinction is largely arbitrary. It is important that the same particle, for example, a photon or an electron, can be real under some conditions and virtual under others.

5.4. Peaks. The vertices of the diagram describe local acts elementary interactions between particles. At each vertex the 4-momentum is conserved. It is easy to see that if three lines of stable particles meet at one vertex, then at least one of them must be virtual, that is, it must be outside the mass surface: “Bolivar cannot demolish three.” (For example, a free electron cannot emit a free photon and still remain a free electron.)

Two real particles interact at a distance, exchanging one or more virtual particles.

5.5. Spreading. If real particles are said to move, then virtual particles are said to propagate. The term "propagation" emphasizes the fact that a virtual particle can have many trajectories, and it may be that none of them are classical, like a virtual photon with zero energy and non-zero momentum, describing the static Coulomb interaction.

5.6. Antiparticles. A remarkable property of Feynman diagrams is that they describe both particles and their corresponding antiparticles in a unified way. In this case, the antiparticle looks like a particle moving backward in time. In Fig. Figure 2 shows a diagram depicting the birth of a proton and antiproton during the annihilation of an electron and a positron.

Moving backward in time applies equally to fermions and bosons. It makes unnecessary the interpretation of positrons as unfilled states in a sea of ​​electrons with negative energy, which Dirac resorted to when he introduced the concept of an antiparticle in 1930.

5.7. Schwinger and Feynman diagrams. Schwinger (1918–1994), who did not care for computational difficulties, did not like Feynman diagrams and wrote somewhat condescendingly about them: “Like the computer chip in more recent years, the Feynman diagram brought calculations to the masses.” Unfortunately, unlike the chip, Feynman diagrams did not reach the broadest masses.

5.8. Feynman and Feynman diagrams. For unknown reasons, Feynman's diagrams did not even make it to the famous Feynman Lectures on Physics. I am convinced that they need to be brought to students high school, explaining to them the basic ideas of particle physics. This is the simplest view of the microcosm and the world as a whole. If a student knows the concept of potential energy (for example, Newton's law, or Coulomb's law), then Feynman diagrams allow him to obtain an expression for this potential energy.

5.9. Virtual particles and physical force fields. Feynman diagrams are the simplest language of quantum field theory. (At least in cases where the interaction is not very strong and perturbation theory can be used.) Most books on quantum field theory treat particles as quantum excitations of fields, which requires familiarity with the formalism of secondary quantization. In the language of Feynman diagrams, fields are replaced by virtual particles.

Elementary particles have both corpuscular and wave properties. Moreover, in the real state they are particles of matter, and in the virtual state they are also carriers of forces between material objects. After the introduction of virtual particles, the concept of force becomes unnecessary, and the concept of field, if you were not familiar with it before, should perhaps be introduced after the concept of a virtual particle has been mastered.

5.10. Elementary interactions*. Elementary acts of emission and absorption of virtual particles (vertices) are characterized by such interaction constants as electric charge e in the case of a photon, weak charges e/sin θ W in the case of the W boson and e/sin θ W cos θ W in the case of the Z boson (where θW- Weinberg angle), color charge g in the case of gluons, and the quantity √G in the case of graviton, where G- Newton's constant. (See Ch. 6–10.) Electromagnetic interaction is discussed below in Ch. 7. Weak interaction - in Ch. 8. Strong - in ch. 9.

We'll start in the next chapter. 6 with gravitational interaction.

6. Gravitational interaction

6.1. Gravitons. I'll start with particles that have not yet been discovered and certainly will not be discovered in the foreseeable future. These are particles of the gravitational field - gravitons. Not only gravitons have not yet been discovered, but also gravitational waves (and this is at a time when electromagnetic waves literally permeate our lives). This is due to the fact that at low energies the gravitational interaction is very weak. As we will see, the theory of gravitons allows us to understand all the known properties of gravitational interaction.

6.2. Exchange of gravitons. In the language of Feynman diagrams, the gravitational interaction of two bodies is carried out by the exchange of virtual gravitons between the elementary particles that make up these bodies. In Fig. 3, a graviton is emitted by a particle with 4-momentum p 1 and absorbed by another particle with 4-momentum p 2 . Due to the conservation of 4-momentum, q=p 1 − p′ 1 =p′ 2 −p 2 , where q is the 4-momentum of the graviton.

The propagation of a virtual graviton (like any virtual particle, it has a propagator) is depicted in the figure by a spring.

6.3. A hydrogen atom in the Earth's gravitational field. In Fig. Figure 4 shows the sum of diagrams in which a hydrogen atom with 4-momentum p 1 exchanges gravitons with all atoms of the Earth having a total 4-momentum p 2 . And in this case, q = p 1 − p′ 1 = p′ 2 − p 2 , where q is the total 4-momentum of virtual gravitons.

6.4. About the mass of the atom. In the future, when considering gravitational interaction, we will neglect the mass of the electron in comparison with the mass of the proton, and also neglect the difference in the masses of the proton and neutron and the binding energy of nucleons in atomic nuclei. So the mass of an atom is approximately the sum of the masses of the nucleons in the atomic nucleus.

6.5. Gain*. The number of nucleons of the Earth N E ≈ 3.6·10 51 is equal to the product of the number of nucleons in one gram of terrestrial matter, i.e. Avogadro's number N A ≈ 6·10 23, by the mass of the Earth in grams ≈ 6·10 27. Therefore, the diagram in Fig. 4 represents the sum of 3.6 10 51 diagrams in Fig. 3, which is marked by thickening of the lines of the Earth and virtual gravitons in Fig. 4. In addition, the “graviton spring”, in contrast to the propagator of one graviton, is shown in Fig. 4 grey. It seems to contain 3.6·10 51 gravitons.

6.6. Newton's apple in the Earth's gravitational field. In Fig. 5, all apple atoms with a total 4-momentum p 1 interact with all Earth atoms with a total 4-momentum p 2 .

6.7. Number of charts*. Let me remind you that one gram of ordinary matter contains N A = 6·10 23 nucleons. The number of nucleons in a 100-gram apple N a = 100N A = 6·10 25. The mass of the Earth is 6·10 27 g, and therefore the number of nucleons of the Earth N E = 3.6·10 51. Of course, the thickening of the lines in Fig. 5 in no way corresponds to the huge number of apple nucleons N a , Earth nucleons N E and the much larger, simply fantastic number of Feynman diagrams N d = N a N E = 2.2·10 77 . After all, every nucleon of an apple interacts with every nucleon of the Earth. To emphasize the enormous number of diagrams, the spring in Fig. 5 is made dark.

Although the interaction of a graviton with an individual elementary particle is very small, the sum of the diagrams for all the Earth's nucleons creates a significant attraction that we feel. Universal gravity pulls the Moon toward the Earth, both of them toward the Sun, all the stars in our Galaxy, and all galaxies toward each other.

6.8. Feynman amplitude and its Fourier transform***.

The Feynman diagram of the gravitational interaction of two slow bodies with masses m 1 and m 2 corresponds to the Feynman amplitude

Where G- Newton's constant, a q- 3-momentum carried by virtual gravitons. (Value 1/q 2, Where q- 4-pulse, called a graviton propagator. In the case of slow bodies, energy is practically not transferred and therefore q 2 = −q 2 .)

To move from momentum space to configuration (coordinate) space, we need to take the Fourier transform of the amplitude A( q)

Value A( r) gives the potential energy of gravitational interaction of non-relativistic particles and determines the movement of a relativistic particle in a static gravitational field.

6.9. Newton's potential*. The potential energy of two bodies with masses m 1 and m 2 is equal to

Where G- Newton's constant, a r- distance between bodies.

This energy is contained in the “spring” of virtual gravitons in Fig. 5. Interaction, the potential of which decreases as 1/ r, is called long-range. Using the Fourier transform, we can see that gravity is long-range, because the graviton is massless.

6.10. Yukawa type potential**. Indeed, if the graviton had a non-zero mass m, then the Feynman amplitude for its exchange would have the form

and a potential like the Yukawa potential with a range of action would correspond to it r ≈ 1/m:

6.11. About potential energy**. In Newton's non-relativistic mechanics, the kinetic energy of a particle depends on its speed (momentum), and the potential energy only on its coordinates, i.e., on its position in space. In relativistic mechanics, such a requirement cannot be preserved, since the interaction of particles itself often depends on their velocities (moments) and, consequently, on kinetic energy. However, for ordinary, fairly weak gravitational fields, the change in the kinetic energy of the particle is small compared to its total energy, and therefore this change can be neglected. The total energy of a nonrelativistic particle in a weak gravitational field can be written as ε = E kin + E 0 + U.

6.12. The universality of gravity. Unlike all other interactions, gravity has the remarkable property of universality. The interaction of a graviton with any particle does not depend on the properties of this particle, but depends only on the amount of energy that the particle possesses. If this particle is slow, then its rest energy E 0 = mc 2, contained in its mass, far exceeds its kinetic energy. And therefore its gravitational interaction is proportional to its mass. But for a fast enough particle, its kinetic energy is much greater than its mass. In this case, its gravitational interaction is practically independent of mass and is proportional to its kinetic energy.

6.13. Graviton spin and the universality of gravity**. More precisely, graviton emission is proportional not to simple energy, but to the energy-momentum tensor of the particle. And this, in turn, is due to the fact that the spin of the graviton is equal to two. Let the 4-momentum of the particle before the emission of the graviton be p 1 and after emission p 2. Then the graviton momentum is equal to q = p 1 − p 2. If you enter the designation p = p 1 + p 2, then the vertex of graviton emission will have the form

where h αβ is the graviton wave function.

6.14. Interaction of graviton with photon**. This is especially clearly seen in the example of a photon, whose mass is zero. It has been experimentally proven that when a photon flies from the lower floor of a building to the upper floor, its momentum decreases under the influence of the Earth's gravity. It has also been proven that a ray of light from a distant star is deflected by the gravitational attraction of the Sun.

6.15. Interaction of a photon with the Earth**. In Fig. Figure 6 shows the exchange of gravitons between the Earth and the photon. This figure conventionally represents the sum of the figures of graviton exchanges of a photon with all nucleons of the Earth. On it, the earth's vertex is obtained from the nucleon vertex by multiplying by the number of nucleons in the Earth N E with the corresponding replacement of the 4-momentum of the nucleon by the 4-momentum of the Earth (see Fig. 3).

6.16. Interaction of graviton with graviton***. Since gravitons carry energy, they themselves must emit and absorb gravitons. We have never seen individual real gravitons and will never see them. Nevertheless, the interaction between virtual gravitons leads to observable effects. At first glance, the contribution of three virtual gravitons to the gravitational interaction of two nucleons is too small to be detected (see Fig. 7).

6.17. Secular precession of Mercury**. However, this contribution is manifested in the precession of the perihelion of Mercury's orbit. The secular precession of Mercury is described by the sum of single-loop graviton diagrams of the attraction of Mercury to the Sun (Fig. 8).

6.18. Gain for Mercury**. The mass ratio of Mercury and Earth is 0.055. So the number of nucleons in Mercury N M = 0,055 N E= 2·10 50 . Mass of the Sun M S= 2·10 33 g. So the number of nucleons in the Sun N S = N A M S= 1.2·10 57 . And the number of diagrams describing the gravitational interaction of nucleons of Mercury and the Sun, N dM= 2.4·10 107 .

If the potential energy of attraction of Mercury to the Sun is equal to U = GM S M M/r, then after taking into account the discussed correction for the interaction of virtual gravitons with each other, it is multiplied by a factor of 1 − 3 GM S/r. We see that the correction to potential energy is −3 G 2 M S 2 M M /r 2.

6.19. Mercury's orbit**. Mercury's orbital radius a= 58·10 6 km. The orbital period is 88 Earth days. Orbital eccentricity e= 0.21. Due to the discussed correction, during one revolution the semi-major axis of the orbit rotates through an angle of 6π GM S/a(1 − e 2), i.e., about one tenth of an arc second, and in 100 Earth years it rotates by 43 "".

6.20. Gravitational Lamb shift**. Anyone who has studied quantum electrodynamics will immediately see that the diagram in Fig. 7 is similar to a triangular diagram describing the frequency (energy) shift of level 2 S 1/2 relative to level 2 P 1/2 in the hydrogen atom (where the triangle consists of one photon and two electron lines). This shift was measured in 1947 by Lamb and Rutherford and found to be 1060 MHz (1.06 GHz).

This measurement marked the beginning chain reaction theoretical and experimental work that led to the creation of quantum electrodynamics and Feynman diagrams. The precession frequency of Mercury is 25 orders of magnitude lower.

6.21. Classical or quantum effect?**. It is well known that the Lamb shift of level energy is a purely quantum effect, while the precession of Mercury is a purely classical effect. How can they be described by similar Feynman diagrams?

To answer this question, we need to remember the relationship E = ħω and take into account that the Fourier transform in the transition from momentum space to configuration space in Sect. 6.8 contains e iqr / ħ . In addition, it should be taken into account that in the electromagnetic Lamb shift triangle there is only one line of a massless particle (photon), and the other two are electron propagators. Therefore, the characteristic distances in it are determined by the mass of the electron (the Compton wavelength of the electron). And in the precession triangle of Mercury there are two propagators of a massless particle (graviton). This circumstance, due to the three-graviton vertex, leads to the fact that the gravitational triangle makes a contribution at incomparably greater distances than the electromagnetic triangle. This comparison demonstrates the power of quantum field theory in the method of Feynman diagrams, which makes it easy to understand and calculate wide circle phenomena, both quantum and classical.

7. Electromagnetic interaction

7.1. Electrical interaction. The electrical interaction of particles is carried out by the exchange of virtual photons, as in Fig. 19.

Photons, like gravitons, are also massless particles. So the electrical interaction is also long-range:

Why is it not as universal as gravity?

7.2. Positive and negative charges. Firstly, because there are electric charges of two signs. And secondly, because there are neutral particles that have no electric charge(neutron, neutrino, photon...). Particles with charges of opposite signs, like an electron and a proton, attract each other. Particles with the same charges repel each other. As a result, atoms and the bodies consisting of them are basically electrically neutral.

7.3. Neutral particles. Neutron contains u-quark with charge +2 e/3 and two d-quark with charge − e/3. So the total charge of the neutron is zero. (Recall that a proton contains two u-quark and one d-quark.) Truly elementary particles that do not have an electric charge are the photon, graviton, neutrino, Z-boson and Higgs boson.

7.4. Coulomb potential. Potential energy of attraction between an electron and a proton located at a distance r from each other, equal

7.5. Magnetic interaction. Magnetic interaction is not as long-range as electrical interaction. It falls like 1/ r 3. It depends not only on the distance between the two magnets, but also on their relative orientation. Fine famous example- interaction of the compass needle with the field of the Earth's magnetic dipole. Potential energy of interaction of two magnetic dipoles μ 1 and μ 2 is equal

Where n = r/r.

7.6. Electromagnetic interaction. The greatest achievement of the 19th century was the discovery that electric and magnetic forces are two different manifestations of the same electromagnetic force. In 1821, M. Faraday (1791–1867) investigated the interaction of a magnet and a conductor with a current. A decade later he laid down the laws electromagnetic induction when two conductors interact. In subsequent years, he introduced the concept of the electromagnetic field and expressed the idea of ​​​​the electromagnetic nature of light. In the 1870s, J. Maxwell (1831–1879) realized that electromagnetic interactions were responsible for a wide class of optical phenomena: the emission, transformation, and absorption of light, and wrote equations describing the electromagnetic field. Soon G. Hertz (1857–1894) discovered radio waves, and V. Roentgen (1845–1923) discovered X-rays. Our entire civilization is based on manifestations of electromagnetic interactions.

7.7. Combining the theory of relativity and quantum mechanics. The most important stage in the development of physics was 1928, when an article by P. Dirac (1902–1984) appeared, in which he proposed a quantum and relativistic equation for the electron. This equation contained the magnetic moment of the electron and indicated the existence of the electron's antiparticle - the positron, discovered a few years later. After this, quantum mechanics and relativity theory were combined into quantum field theory.

The fact that electromagnetic interactions are caused by the emission and absorption of virtual photons became completely clear only in the middle of the 20th century with the advent of Feynman diagrams, i.e. after the concept of a virtual particle was clearly formed.

8. Weak interaction

8.1. Nuclear interactions. At the beginning of the 20th century, the atom and its nucleus were discovered and α -, β - And γ - rays emitted by radioactive nuclei. As it turned out, γ -rays are photons of very high energy, β -rays are high-energy electrons, α -rays - helium nuclei. This led to the discovery of two new types of interactions - strong and weak. Unlike gravitational and electromagnetic interactions, strong and weak interactions are short-range.

They were later found to be responsible for the conversion of hydrogen into helium in our Sun and other stars.

8.2. Charged currents*. The weak interaction is responsible for the transformation of a neutron into a proton with the emission of an electron and an electron antineutrino. A large class of weak interaction processes is based on the transformation of quarks of one type into quarks of another type with the emission (or absorption) of virtual W-bosons: u, c, t ↔ d, s, b. Similarly for emission and absorption W-bosons, transitions occur between charged leptons and the corresponding neutrinos:

e ↔ ν e, μ ↔ ν μ , τ ↔ ν τ . Transitions of the type also occur equally dˉu ↔ W and eˉν e ↔ W. In all these transitions involving W-bosons involve so-called charged currents that change the charges of leptons and quarks by one. The weak interaction of charged currents is short-range and is described by the Yukawa potential e−mWr/r, so its effective radius is r ≈ 1/mW.

8.3. Neutral currents*. In the 1970s, processes of weak interaction between neutrinos, electrons and nucleons, caused by so-called neutral currents, were discovered. In the 1980s, it was experimentally established that the interactions of charged currents occur through the exchange W-bosons, and the interaction of neutral currents - through exchange Z- bosons.

8.4. Violation P- And C.P.-parity*. In the second half of the 1950s, spatial parity violation was discovered P and charge parity C in weak interactions. In 1964, weak decays were discovered that violate the conservation C.P.-symmetry. Currently, the mechanism of violation C.P.-symmetry is studied in the decays of mesons containing b-quarks.

8.5. Neutrino oscillations*. For the past two decades, the attention of physicists has been focused on measurements carried out at underground kiloton detectors in Kamioka (Japan) and Sudbury (Canada). These measurements showed that between the three types of neutrinos ν e , ν μ , ν τ Mutual transitions (oscillations) occur in a vacuum. The nature of these oscillations is being clarified.

8.6. Electroweak interaction. In the 1960s, the theory was formulated that the electromagnetic and weak forces are different manifestations of a single electroweak force. If there were strict electroweak symmetry, then the masses W- And Z-bosons would be equal to zero like the photon mass.

8.7. Electroweak symmetry breaking. In the Standard Model, the Higgs boson breaks electroweak symmetry and thus explains why the photon is massless and weak bosons are massive. He also gives masses to leptons, quarks and himself.

8.8. What you need to know about the Higgs. One of the main goals of the LHC Large Hadron Collider is the discovery of the Higgs boson (called simply the Higgs and denoted h or H) and subsequent establishment of its properties. First of all, measuring its interactions with W- And Z-bosons, with photons, as well as its self-interactions, i.e., the study of vertices containing three and four Higgs: h 3 and h 4, and its interactions with leptons and quarks, especially the top quark. Within the Standard Model, there are clear predictions for all of these interactions. Their experimental verification is of great interest from the point of view of the search for “new physics” beyond the Standard Model.

8.9. What if there is no Higgs? If it turns out that in the mass range of the order of several hundred GeV the Higgs does not exist, then this will mean that at energies above TeV there lies a new, completely unknown region where interactions W- And Z-bosons become nonperturbatively strong, i.e., they cannot be described by perturbation theory. Research in this area will bring many surprises.

8.10. Lepton colliders of the future. To carry out this entire research program, in addition to the LHC, it may be necessary to build lepton colliders:

ILC (International Linear Collider) with a collision energy of 0.5 TeV,

or CLIC (Compact Linear Collider) with a collision energy of 1 TeV,

or MC (Muon Collider) with a collision energy of 3 TeV.

8.11. Linear electron-positron colliders. ILC - International Linear Collider, which collides electrons with positrons, as well as photons with photons. The decision to build it can be made only after it becomes clear whether the Higgs exists and what its mass is. One of the proposed ILC construction sites is in the vicinity of Dubna. CLIC - Compact Linear Electron-Positron Collider. The project is being developed at CERN.

8.12. Muon collider. MS - The muon collider was first conceived by G. I. Budker (1918–1977). In 1999, the fifth international Conference"Physical potential and development of muon colliders and neutrino factories." The MS project is currently being developed at Fermi National Laboratory and could be implemented in 20 years.

9. Strong interaction

9.1. Gluons and quarks. The strong force keeps nucleons (protons and neutrons) inside the nucleus. It is based on the interaction of gluons with quarks and the interaction of gluons with gluons. It is the self-interaction of gluons that leads to the fact that despite the fact that the mass of the gluon is zero, just as the masses of the photon and graviton are equal to zero, the exchange of gluons does not lead to gluon long-range interaction, similar to photon and graviton. Moreover, it leads to the absence of free gluons and quarks. This is due to the fact that the sum of one-gluon exchanges is replaced by a gluon tube or thread. The interaction of nucleons in the nucleus is similar to van der Waals forces between neutral atoms.

9.2. Confinement and asymptotic freedom. The phenomenon of gluons and quarks not escaping from hadrons is called confinement. Downside The dynamics leading to confinement is that at very short distances deep inside hadrons, the interaction between gluons and quarks gradually decreases. Quarks seem to become free at short distances. This phenomenon is called asymptotic freedom.

9.3. Quark colors. The phenomenon of confinement is a consequence of the fact that each of the six quarks exists as if in the form of three “color” varieties. Quarks are usually “colored” yellow, blue and red. Antiques are painted in additional colors: purple, orange, green. All these colors represent the peculiar charges of quarks - “multidimensional analogues” of electric charge, responsible for strong interactions. Of course, there is no connection, other than a metaphorical one, between the colors of quarks and ordinary optical colors.

9.4. Gluon colors. The family of colored gluons is even more numerous: there are eight of them, two of which are identical to their antiparticles, and the remaining six are not. The interactions of color charges are described by quantum chromodynamics and determine the properties of the proton, neutron, all atomic nuclei and the properties of all hadrons. The fact that gluons carry color charges leads to the phenomenon of confinement of gluons and quarks, which means that colored gluons and quarks cannot escape from hadrons. The nuclear forces between colorless (white) hadrons are faint echoes of the powerful color interactions within the hadrons. This is similar to the smallness of molecular bonds compared to intraatomic ones.

9.5. Hadron masses. The masses of hadrons in general and nucleons in particular are determined by the gluon self-action. Thus, the mass of all visible matter, which makes up 4–5% of the energy of the Universe, is due precisely to the self-action of gluons.

10. Standard model and beyond

10.1. 18 Standard Model particles. All known fundamental particles naturally fall into three groups:

6 leptons(spin 1/2):
3 neutrinos: ν e, ν μ , ν τ ;
3 charged leptons: e, μ , τ ;
6 quarks(spin 1/2):
u,c, t,
d, s, b;
6 bosons:
g̃ - graviton (spin 2),
γ , W, Z, g- gluons (spin 1),
h- Higgs (spin 0).

10.2. Beyond the Standard Model. 96% of the energy in the Universe lies outside the Standard Model, waiting to be discovered and studied. There are several basic assumptions about what the new physics might look like (see points 10.3–10.6 below).

10.3. Great Unification. A huge number of works, mostly theoretical, are devoted to the unification of strong and electroweak interactions. Most of them assume that it occurs at energies of the order of 10 16 GeV. Such a union should lead to proton decay.

10.4. Supersymmetric particles. According to the idea of ​​supersymmetry, which first arose at the Lebedev Physical Institute, each “our” particle has a superpartner whose spin differs by 1/2: 6 squarks and 6 sleptons with spin 0, higgsino, photino, wine and zino with spin 1/2, gravitino with spin 3/2. The masses of these superpartners must be significantly greater than those of our particles. Otherwise they would have been opened long ago. Some of the superpartners may be discovered when the Large Hadron Collider becomes operational.

10.5. Superstrings. The hypothesis of supersymmetry is developed by the hypothesis of the existence of superstrings that live at very short distances of the order of 10 −33 cm and corresponding energies of 10 19 GeV. Many theoretical physicists hope that it is on the basis of ideas about superstrings that they will be able to construct a unified theory of all interactions that does not contain free parameters.

10.6. Mirror particles. According to the idea of ​​mirror matter, which first arose at ITEP, each of our particles has a mirror twin, and there is a mirror world that is only very weakly connected with our world.

10.7. Dark matter. Only 4–5% of the total energy in the Universe exists as the mass of ordinary matter. About 20% of the energy of the universe is contained in the so-called dark matter, which is thought to consist of superparticles, or mirror particles, or some other unknown particles. If dark matter particles are much heavier than ordinary particles, and if, when colliding with each other in space, they annihilate into ordinary photons, then these high-energy photons can be detected by special detectors in space and on Earth. Finding out the nature of dark matter is one of the main tasks of physics.

10.8. Dark energy. But the overwhelming majority of the energy of the Universe (about 75%) is due to the so-called dark energy. It is “spilled” through the vacuum and pushes clusters of galaxies apart. Its nature is still unclear.

11. Elementary particles in Russia and the world

11.1. Decree of the President of the Russian Federation. On September 30, 2009, the Decree of the President of the Russian Federation “On additional measures for the implementation of a pilot project to create the National Research Center “Kurchatov Institute”” was issued. The decree provides for the participation of the following organizations in the project: St. Petersburg Institute of Nuclear Physics, Institute of High Energy Physics and Institute of Theoretical and Experimental Physics. The decree also provides for “the inclusion of the specified institution, as the most significant scientific institution, in the departmental structure of federal budget expenditures as the main manager budget funds" This Decree can contribute to the return of elementary particle physics to the number of priority areas for the development of science in our country.

11.2. US Congressional Hearings 1. On October 1, 2009, a hearing was held in the Subcommittee on Energy and Environment of the Committee on Science and Technology of the US House of Representatives on the topic “Investigations into the Nature of Matter, Energy, Space and Time.” The Department of Energy's 2009 appropriation for this program is $795.7 million. Harvard University professor Lisa Randall presented views on matter, energy and the origin of the Universe from the point of view of the future string theory. Director of the Fermi National Laboratory (Batavia) Pierre Oddone spoke about the state of particle physics in the USA, and in particular, about the upcoming completion of the Tevatron and the beginning of joint work between FNAL and the underground laboratory DUSEL to study the properties of neutrinos and rare processes. He emphasized the importance of the participation of American physicists in high energy physics projects in Europe (LHC), Japan (JPARC), China (PERC) and the international space project (GLAST, recently named after Fermi).

11.3. US Congressional Hearings 2. Jefferson National Laboratory Director Hugh Montgomery spoke about the Laboratory's contributions to nuclear physics, accelerator technology, and educational programs. Director of the High Energy Physics Science Division at the Department of Energy, Dennis Kovar, spoke about three main areas of high energy physics:

1) accelerator research at maximum energies,

2) accelerator studies at maximum intensities,

3) ground-based and satellite space exploration in order to clarify the nature of dark matter and dark energy,

and three main directions in nuclear physics:

1) study of strong interactions of quarks and gluons,

2) the study of how atomic nuclei were formed from protons and neutrons,

3) study of weak interactions involving neutrinos.

12. About fundamental science

12.1. What is fundamental science? From the above text it is clear that I, like most scientists, call fundamental science that part of science that establishes the most fundamental laws of nature. These laws lie at the foundation of the pyramid of science or its individual floors. They determine the long-term development of civilization. There are, however, people who call fundamental science those branches of science that have the greatest direct impact on momentary achievements in the development of civilization. I personally think that these sections and areas are better called applied science.

12.2. Roots and fruits. If fundamental science can be compared to the roots of a tree, then applied science can be compared to its fruits. Major technological breakthroughs such as the creation mobile phones or fiber optic communications, these are the fruits of science.

12.3. A. I. Herzen about science. In 1845, Alexander Ivanovich Herzen (1812–1870) published the remarkable “Letters on the Study of Nature” in the journal Otechestvennye zapiski. At the end of his first letter, he wrote: “Science seems difficult not because it is really difficult, but because you cannot reach its simplicity otherwise than by breaking through the darkness of ready-made concepts that prevent you from seeing directly. Let those who come forward know that the entire arsenal of rusty and worthless tools that we inherited from scholasticism is worthless, that it is necessary to sacrifice the views formed outside of science, that without throwing everything away half a lie, with which for clarity they clothe half-truths“You cannot enter into science, you cannot reach the whole truth.”

12.4. About the reduction of school programs. Modern physics programs at school may well include active mastery of elements of the theory of elementary particles, the theory of relativity and quantum mechanics, if they reduce those sections that are mainly descriptive in nature and increase the child’s “erudition” rather than understanding the world around them and the ability to live and create.

12.5. Conclusion. It would be right for the Presidium of the Russian Academy of Sciences to note the importance of early familiarization of young people with a worldview based on the achievements of the theory of relativity and quantum mechanics, and to instruct the Commissions of the Presidium of the Russian Academy of Sciences on textbooks (chaired by Vice-President V.V. Kozlov) and on education (chaired by Vice President -President V. A. Sadovnichy) to prepare proposals for improving the teaching of modern fundamental physics in secondary and higher schools.

Second law of thermodynamics

According to this law, a process whose only result is the transfer of energy in the form of heat from a colder body to a hotter one is impossible without changes in the system itself and the environment. The second law of thermodynamics expresses the tendency of a system consisting of large quantity chaotically moving particles, to a spontaneous transition from less probable states to more probable states. Prohibits the creation of a perpetual motion machine of the second kind.

Avogardo's Law
Equal volumes of ideal gases at the same temperature and pressure contain the same number of molecules. The law was discovered in 1811 by the Italian physicist A. Avogadro (1776–1856).

Ampere's law
The law of interaction between two currents flowing in conductors located at a short distance from each other states: parallel conductors with currents in the same direction attract, and with currents in the opposite direction they repel. The law was discovered in 1820 by A. M. Ampere.

Archimedes' Law

The law of hydro- and aerostatics: a body immersed in a liquid or gas is acted upon by a buoyant force directed vertically upward, equal to the weight of the liquid or gas displaced by the body, and applied at the center of gravity of the immersed part of the body. FA = gV, where g is the density of the liquid or gas, V is the volume of the immersed part of the body. Otherwise, the law can be formulated as follows: a body immersed in a liquid or gas loses as much weight as the liquid (or gas) it displaces weighs. Then P = mg – FA. The law was discovered by the ancient Greek scientist Archimedes in 212 BC. e. It is the basis of the theory of floating bodies.

Law of Gravity

The law of universal gravitation, or Newton's law of gravitation: all bodies attract each other with a force directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them.

Boyle–Mariotte law

One of the laws of an ideal gas: at a constant temperature, the product of the gas pressure and its volume is a constant value. Formula: pV = const. Describes an isothermal process.

Hooke's law
According to this law, elastic deformations of a solid body are directly proportional to the external influences that cause them.

Dalton's law
One of the basic gas laws: the pressure of a mixture of chemically non-interacting ideal gases is equal to the sum of the partial pressures of these gases. Discovered in 1801 by J. Dalton.

Joule–Lenz law

Describes thermal effect electric current: the amount of heat released in a conductor when a direct current passes through it is directly proportional to the square of the current, the resistance of the conductor and the time of passage. Discovered by Joule and Lenz independently of each other in the 19th century.

Coulomb's law

The basic law of electrostatics, expressing the dependence of the force of interaction between two stationary point charges on the distance between them: two stationary point charges interact with a force directly proportional to the product of the magnitudes of these charges and inversely proportional to the square of the distance between them and the dielectric constant of the medium in which the charges are located. The value is numerically equal to the force acting between two stationary point charges of 1 C each located in a vacuum at a distance of 1 m from each other. Coulomb's law is one of the experimental justifications of electrodynamics. Opened in 1785.

Lenz's Law
According to this law, the induced current always has such a direction that its own magnetic flux compensates for the changes in the external magnetic flux that caused this current. Lenz's law is a consequence of the law of conservation of energy. Installed in 1833 by E. H. Lenz.

Ohm's law

One of the basic laws of electric current: the strength of direct electric current in a section of a circuit is directly proportional to the voltage at the ends of this section and inversely proportional to its resistance. Valid for metal conductors and electrolytes whose temperature is maintained constant. In the case of a complete circuit, it is formulated as follows: the strength of a direct electric current in the circuit is directly proportional to the emf of the current source and inversely proportional to the total resistance of the electric circuit. Discovered in 1826 by G.S. Ohm.

Law of Wave Reflection

The incident ray, the reflected ray and the perpendicular raised to the point of incidence of the ray lie in the same plane, and the angle of incidence is equal to angle refraction. The law is valid for mirror reflection.

Pascal's law
The basic law of hydrostatics: the pressure produced by external forces on the surface of a liquid or gas is transmitted equally in all directions.

Law of light refraction

The incident ray, the refracted ray and the perpendicular restored to the point of incidence of the ray lie in the same plane, and for these two media the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value, called the relative refractive index of the second medium relative to the first.

Law of rectilinear propagation of light

The law of geometric optics, which states that light propagates rectilinearly in a homogeneous medium. Explains, for example, the formation of shadow and penumbra.

Law of conservation of charge
One of fundamental laws nature: the algebraic sum of the electric charges of any electrically isolated system remains unchanged. In an electrically isolated system, the law of conservation of charge allows for the appearance of new charged particles, but the total electric charge of the appearing particles must always be equal to zero.

Law of conservation of momentum
One of the basic laws of mechanics: the momentum of any closed system, during all processes occurring in the system, remains constant (conserved) and can only be redistributed between parts of the system as a result of their interaction.

Charles's Law
One of the basic gas laws: the pressure of a given mass of ideal gas at constant volume is directly proportional to the temperature.

Law of Electromagnetic Induction

Describes the phenomenon of the appearance of an electric field when a magnetic field changes (the phenomenon of electromagnetic induction): the electromotive force of induction is directly proportional to the rate of change of magnetic flux. The proportionality coefficient is determined by the system of units, the sign is determined by Lenz’s rule. The law was discovered by M. Faraday.

Law of conservation and transformation of energy
General law of nature: the energy of any closed system remains constant (conserved) during all processes occurring in the system. Energy can only be converted from one form to another and redistributed between parts of the system. For an open system, an increase (decrease) in its energy is equal to a decrease (increase) in the energy of bodies and physical fields interacting with it.

Newton's laws
Classical mechanics is based on Newton's 3 laws. Newton's first law (law of inertia): a material point is in a state of rectilinear and uniform motion or rest if other bodies do not act on it or the action of these bodies is compensated. Newton's second law (fundamental law of dynamics): the acceleration received by a body is directly proportional to the resultant of all forces acting on the body, and inversely proportional to the mass of the body. Newton's third law: the actions of two bodies are always equal in magnitude and directed in opposite directions.

Faraday's laws
Faraday's first law: the mass of a substance released on the electrode during the passage of an electric current is directly proportional to the amount of electricity (charge) passing through the electrolyte (m = kq = kIt). Faraday's second law: the ratio of the masses of various substances undergoing chemical transformations on the electrodes when identical electrical charges pass through the electrolyte is equal to the ratio of chemical equivalents. The laws were established in 1833–1834 by M. Faraday.

First law of thermodynamics
The first law of thermodynamics is the law of conservation of energy for a thermodynamic system: the amount of heat Q imparted to the system is spent on changing the internal energy of the system U and performing work A against the system external forces. The formula Q = U + A underlies the operation of heat engines.

Bohr's postulates

Bohr's first postulate: an atomic system is stable only in stationary states that correspond to a discrete sequence of atomic energy values. Each change in this energy is associated with a complete transition of the atom from one stationary state to another. Bohr's second postulate: the absorption and emission of energy by an atom occurs according to the law according to which the radiation associated with the transition is monochromatic and has a frequency: h = Ei – Ek, where h is Planck’s constant, and Ei and Ek are the energies of the atom in stationary states.

Left hand rule
Determines the direction of the force that acts on a current-carrying conductor (or a moving charged particle) located in a magnetic field. The rule says: if the left hand is positioned so that the outstretched fingers indicate the direction of the current (particle speed), and the magnetic field lines (magnetic induction lines) enter the palm, then the extended thumb will indicate the direction of the force acting on the conductor (positive particle; in In the case of a negative particle, the direction of the force is opposite).

Rule right hand
Determines the direction of the induction current in a conductor moving in a magnetic field: if the palm of the right hand is positioned so that the lines of magnetic induction enter it, and the bent thumb is directed along the movement of the conductor, then four outstretched fingers will show the direction of the induction current.

Huygens' principle
Allows you to determine the position of the wave front at any time. According to Huygens' principle, all points through which the wave front passes at time t are sources of secondary spherical waves, and the desired position of the wave front at time t coincides with the surface enveloping all secondary waves. Huygens' principle explains the laws of reflection and refraction of light.

Huygens–Fresnel principle
According to this principle, at any point located outside an arbitrary closed surface covering a point source of light, the light wave excited by this source can be represented as a result of the interference of secondary waves emitted by all points of the specified closed surface. The principle allows you to solve the simplest problems of light diffraction.

The principle of relativity
In any inertial reference systems, all physical (mechanical, electromagnetic, etc.) phenomena under the same conditions proceed in the same way. It is a generalization of Galileo's principle of relativity.

Galileo's principle of relativity

The mechanical principle of relativity, or the principle of classical mechanics: in any inertial frame of reference, all mechanical phenomena occur in the same way under the same conditions.

Sound
Sound refers to elastic waves that propagate in liquids, gases and solids and are perceived by the human and animal ears. A person has the ability to hear sounds with frequencies in the range of 16–20 kHz. Sound with frequencies up to 16 Hz is usually called infrasound; with frequencies of 2·104–109 Hz – ultrasound, and with frequencies of 109–1013 Hz – hypersound. The science that studies sounds is called acoustics.

Light
Light in the narrow sense of the term refers to electromagnetic waves in the frequency range perceived by the human eye: 7.5 ‘1014–4.3 ‘1014 Hz. Wavelengths range from 760 nm (red light) to 380 nm (violet light).

BASIC LAWS OF PHYSICS

[ Mechanics | Thermodynamics | Electricity | Optics | Atomic physics]

ENERGY OF CONSERVATION AND TRANSFORMATION LAW - common law nature: the energy of any closed system remains constant (conserved) during all processes occurring in the system. Energy can only be converted from one form to another and redistributed between parts of the system. For an open system, an increase (decrease) in its energy is equal to a decrease (increase) in the energy of bodies and physical fields interacting with it.

1. MECHANICS

ARCHIMEDES LAW - the law of hydro- and aerostatics: a body immersed in a liquid or gas is acted upon by a buoyant force directed vertically upward, numerically equal to the weight of the liquid or gas displaced by the body, and applied at the center of gravity of the immersed part of the body. FA= gV, where r is the density of the liquid or gas, V is the volume of the immersed part of the body. Otherwise, it can be formulated as follows: a body immersed in a liquid or gas loses as much weight as the liquid (or gas) it displaces weighs. Then P= mg - FA Another group is open. scientist Archimedes in 212. BC. It is the basis of the theory of floating bodies.

UNIVERSAL GRAVITATION LAW - Newton's law of gravity: all bodies are attracted to each other with a force directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them: , where M and m are the masses of interacting bodies, R is the distance between these bodies, G is gravitational constant (in SI G=6.67.10-11 N.m2/kg2.

GALILEO PRINCIPLE OF RELATIVITY, mechanical principle of relativity - the principle of classical mechanics: in any inertial frames of reference, all mechanical phenomena proceed in the same way under the same conditions. Wed. relativity principle.

HOOK'S LAW - a law according to which elastic deformations are directly proportional to the external influences causing them.

MOMENTUM CONSERVATION LAW - a law of mechanics: the momentum of any closed system, during all processes occurring in the system, remains constant (conserved) and can only be redistributed between parts of the system as a result of their interaction.

NEWTON'S LAWS - three laws underlying Newtonian classical mechanics. 1st law (law of inertia): a material point is in a state of rectilinear and uniform motion or rest if other bodies do not act on it or the action of these bodies is compensated. 2nd law (basic law of dynamics): the acceleration received by a body is directly proportional to the resultant of all forces acting on the body, and inversely proportional to the mass of the body (). 3rd law: two material points interact with each other by forces of the same nature equal in magnitude and opposite in direction along the straight line connecting these points ().

RELATIVITY PRINCIPLE - one of the postulates of the relativity theory, which states that in any inertial frames of reference all physical (mechanical, electromagnetic, etc.) phenomena under the same conditions proceed in the same way. Is a generalization of Galileo's principle of relativity to everything physical phenomena(except for gravity).

2. MOLECULAR PHYSICS AND THERMODYNAMICS

AVOGADRO'S LAW is one of the basic laws of ideal gases: equal volumes of different gases at the same temperature and pressure contain the same number of molecules. Opened in 1811 in Italy. physicist A. Avogadro (1776-1856).

BOYLE-MARIOTTE LAW - one of the laws of an ideal gas: for a given mass of a given gas at a constant temperature, the product of pressure and volume is a constant value. Formula: pV=const. Describes an isothermal process.

THE SECOND LAW OF THERMODYNAMICS is one of the basic laws of thermodynamics, according to which a periodic process is impossible, the only result of which is the performance of work equivalent to the amount of heat received from the heater. Another formulation: a process is impossible, the only result of which is the transfer of energy in the form of heat from a less heated body to a more heated one. V.Z.T. expresses the desire of a system consisting of a large number of chaotically moving particles to spontaneously transition from less probable states to more probable states. Prohibits the creation of a perpetual motion machine of the second kind.

GAY-LUSSAC'S LAW - gas law: for a given mass of a given gas at constant pressure, the ratio of volume to absolute temperature is a constant value, where = 1/273 K-1 is the temperature coefficient of volumetric expansion.

DALTON'S LAW is one of the basic gas laws: the pressure of a mixture of chemically non-interacting ideal gases is equal to the sum of the partial pressures of these gases.

PASCAL'S LAW is the basic law of hydrostatics: the pressure produced by external forces on the surface of a liquid or gas is transmitted equally in all directions.

THE FIRST LAW OF THERMODYNAMICS is one of the basic laws of thermodynamics, which is the law of conservation of energy for a thermodynamic system: the amount of heat Q imparted to the system is spent on changing the internal energy of the system U and performing work A by the system against external forces. Formula: Q= U+A. It underlies the operation of heat engines.

CHARLES' LAW is one of the basic gas laws: the pressure of a given mass of ideal gas at a constant volume is directly proportional to the temperature: where p0 is the pressure at 00C, =1/273.15 K-1 is the temperature coefficient of pressure.

3. ELECTRICITY AND MAGNETISM

AMPERE LAW - the law of interaction of two conductors with currents; Parallel conductors with currents in the same direction attract, and parallel conductors with currents in the opposite direction repel. A.z. also called the law that determines the force acting in a magnetic field on a small segment of a conductor carrying current. Opened in 1820 A.-M. Ampere.

JOULE-LENZ LAW - a law that describes the thermal effect of electric current. According to D. - L.z. the amount of heat released in a conductor when a direct current passes through it is directly proportional to the square of the current, the resistance of the conductor and the passage time.

CHARGE CONSERVATION LAW is one of the fundamental laws of nature: the algebraic sum of electric charges of any electrically isolated system remains unchanged. In an electrically isolated system Z.s.z. allows the appearance of new charged particles (for example, during electrolytic dissociation, ionization of gases, the creation of particle-antiparticle pairs, etc.), but the total electric charge of the appearing particles must always be equal to zero.

COULLOMB'S LAW is the basic law of electrostatics, expressing the dependence of the force of interaction between two stationary point charges on the distance between them: two stationary point charges interact with a force directly proportional to the product of the magnitudes of these charges and inversely proportional to the square of the distance between them and the dielectric constant of the medium in which the charges are located. In SI it has the form: . The value is numerically equal to the force acting between two stationary point charges of 1 C each, located in a vacuum at a distance of 1 m from each other. K.z. is one of the experimental justifications of electrodynamics.

LEFT HAND RULE - a rule that determines the direction of the force that acts on a current-carrying conductor (or a moving charged particle) located in a magnetic field. It says: if the left hand is positioned so that the outstretched fingers indicate the direction of the current (particle velocity), and the magnetic field lines (magnetic induction lines) enter the palm, then the extended thumb will indicate the direction of the force acting on the conductor (positive particle; in In the case of a negative particle, the direction of the force is opposite).

LENZA RULE (LAW) - a rule that determines the direction of induction currents arising during electromagnetic induction. According to L.p. the induced current always has such a direction that its own magnetic flux compensates for the changes in the external magnetic flux that caused this current. L.p. - a consequence of the law of conservation of energy.

OMA LAW is one of the basic laws of electric current: the strength of direct electric current in a section of a circuit is directly proportional to the voltage at the ends of this section and inversely proportional to its resistance. Valid for metal conductors and electrolytes whose temperature is maintained constant. In the case of a complete circuit, it is formulated as follows: the strength of a direct electric current in the circuit is directly proportional to the emf of the current source and inversely proportional to the total resistance of the electric circuit.

RIGHT HAND RULE - a rule that determines 1) the direction of the induction current in a conductor moving in a magnetic field: if the palm of the right hand is positioned so that the magnetic induction lines enter it, and the bent thumb is directed along the movement

conductor, then four outstretched fingers will show the direction of the induction current; 2) the direction of the magnetic induction lines of a straight conductor with current: if the thumb of the right hand is positioned in the direction of the current, then the direction of grasping the conductor with four fingers will show the direction of the magnetic induction lines.

FARADAY'S LAWS - the basic laws of electrolysis. Faraday's first law: the mass of a substance released on the electrode during the passage of an electric current is directly proportional to the amount of electricity (charge) passing through the electrolyte (m=kq=kIt). Second F.Z.: the ratio of the masses of various substances undergoing chemical transformations on the electrodes when identical electrical charges pass through the electrolyte is equal to the ratio of chemical equivalents. Installed in 1833-34 by M. Faraday. The generalized law of electrolysis has the form: , where M is the molar (atomic) mass, z is the valency, F is the Faraday constant. F.p. is equal to the product of the elementary electric charge and Avogadro's constant. F=e.NA. Determines the charge, the passage of which through the electrolyte leads to the release of 1 mole of a monovalent substance at the electrode. F=(96484.56 0.27) Cell/mol. Named in honor of M. Faraday.

ELECTROMAGNETIC INDUCTION LAW - a law that describes the phenomenon of the occurrence of an electric field when a magnetic field changes (the phenomenon of electromagnetic induction): the electromotive force of induction is directly proportional to the rate of change of magnetic flux. The proportionality coefficient is determined by the system of units, the sign is Lenz's rule. Formula in SI: , where Ф is the change in magnetic flux, and t is the time period during which this change occurred. Discovered by M. Faraday.

4. OPTICS

HUYGEN'S PRINCIPLE is a method that allows one to determine the position of the wave front at any time. According to g.p. all points through which the wave front passes at time t are sources of secondary spherical waves, and the desired position of the wave front at time t t coincides with the surface enveloping all secondary waves. Allows you to explain the laws of reflection and refraction of light.

HUYGENS - FRESNEL - PRINCIPLE - an approximate method for solving problems of wave propagation. G.-F. p. states: at any point located outside an arbitrary closed surface covering a point source of light, the light wave excited by this source can be represented as the result of the interference of secondary waves emitted by all points of the specified closed surface. Allows you to solve the simplest problems of light diffraction.

WAVE REFLECTIONS LAW - the incident beam, the reflected beam and the perpendicular, restored to the point of incidence of the beam, lie in the same plane, and the angle of incidence is equal to the angle of refraction. The law is valid for mirror reflection.

REFRACTION OF LIGHT - change in the direction of propagation of light ( electromagnetic wave) when passing from one medium to another, which differs from the first in refractive index. For refraction, the law is satisfied: the incident ray, the refracted ray and the perpendicular restored to the point of incidence of the ray lie in the same plane, and for these two media the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value, called the relative refractive index of the second medium relative to the first.

RECTILINEAR PROPAGATION OF LIGHT LAW - a law of geometric optics, which states that light propagates in a homogeneous medium in a straight line. Explains, for example, the formation of shadow and penumbra.

6. ATOMIC AND NUCLEAR PHYSICS.

BOHR POSTULATES - basic assumptions introduced without proof by N. Bohr, and forming the basis of BOHR THEORY: 1) The atomic system is stable only in stationary states, which correspond to a discrete sequence of atomic energy values. Each change in this energy is associated with a complete transition of the atom from one stationary state to another. 2) The absorption and emission of energy by an atom occurs according to the law, according to which the radiation associated with the transition is monochromatic and has a frequency: h = Ei-Ek, where h is the Planck constant, and Ei and Ek are the energies of the atom in stationary states