Universal laws of physics. The law of physics in everyday life: how much you give, you get so much

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 environment. The second law of thermodynamics expresses the tendency of a system consisting of a large number randomly 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).

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

Law of Archimedes

The law of hydro- and aerostatics: on a body immersed in a liquid or gas, a buoyant force acts vertically upwards, 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 submerged part of the body. Otherwise, the law can be formulated as follows: a body immersed in a liquid or gas loses as much in its weight as the liquid (or gas) displaced by it 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 gravity

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

Boyle's Law - Mariotte

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, the elastic deformations of a solid body are directly proportional to the external influences causing them.

Dalton's Law
One of the main 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. Opened in 1801 by J. Dalton.

Joule–Lenz law

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

Coulomb's law

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

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

Ohm's law

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

Wave reflection law

The incident beam, the reflected beam and the perpendicular raised to the point of incidence of the beam lie in the same plane, and the angle of incidence equal to the 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 refraction of light

The incident beam, the refracted beam and the perpendicular raised to the point of incidence of the beam 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 relative indicator refraction of the second medium relative to the first.

The law of rectilinear propagation of light

The law of geometric optics, which states that light travels in a straight line in a homogeneous medium. Explains, for example, the formation of shade and penumbra.

Law of conservation of charge
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, the law of conservation of charge allows the appearance of new charged particles, but the total electric charge of the particles that have appeared must always be zero.

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

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

Law of electromagnetic induction

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

The law of conservation and transformation of energy
The general law of nature: the energy of any closed system for all processes occurring in the system remains constant (conserved). 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 the 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 no other bodies act on it or the action of these bodies is compensated. Newton's second 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. 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 the substance released on the electrode during the passage of an electric current is directly proportional to the amount of electricity (charge) that has passed 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 the same electric 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 communicated to the system is spent on changing internal energy system U and the performance of work A by the system against external forces. The formula Q \u003d U + A underlies the operation of heat engines.

Bohr's postulates

Bohr's first postulate: an 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. 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 conductor with current in a magnetic field (or a moving charged particle). The rule says: if the left hand is positioned so that the outstretched fingers show the direction of the current (particle velocity), and the lines of force magnetic field(lines of magnetic induction) entered the palm, then the thumb set aside will indicate the direction of the force acting on the conductor (positive particle; in the case of a negative particle, the direction of the force is opposite).

Right hand rule
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 it includes the lines of magnetic induction, 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 the 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 that envelops all secondary waves. Huygens' principle explains the laws of reflection and refraction of light.

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

The principle of relativity
In any inertial frame of reference, all physical (mechanical, electromagnetic, etc.) phenomena proceed in the same way under the same conditions. 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 proceed in the same way under the same conditions.

Sound
Sound is called elastic waves that propagate in liquids, gases and solids and are perceived by the ear of humans and animals. 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 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 is called electromagnetic waves in the range of frequencies perceived by the human eye: 7.5 '1014–4.3 '1014 Hz. The wavelength varies from 760 nm (red light) to 380 nm (violet light).

It is natural and correct to be interested in the surrounding world and the laws of its functioning and development. That is why it is reasonable to pay attention to the natural sciences, for example, physics, which explains the very essence of the formation and development of the Universe. The basic physical laws are easy to understand. At a very young age, the school introduces children to these principles.

For many, this science begins with the textbook "Physics (Grade 7)". The basic concepts of and and thermodynamics are revealed to schoolchildren, they get acquainted with the core of the main physical laws. But should knowledge be limited to the school bench? What physical laws should every person know? This will be discussed later in the article.

science physics

Many of the nuances of the described science are familiar to everyone from early childhood. And this is due to the fact that, in essence, physics is one of the areas of natural science. It tells about the laws of nature, the action of which affects the life of everyone, and in many ways even provides it, about the features of matter, its structure and patterns of motion.

The term "physics" was first recorded by Aristotle in the fourth century BC. Initially, it was synonymous with the concept of "philosophy". After all, both sciences had a common goal - to correctly explain all the mechanisms of the functioning of the Universe. But already in the sixteenth century, due to scientific revolution physics became independent.

general law

Some basic laws of physics are applied in various branches of science. In addition to them, there are those that are considered to be common to all nature. It's about O

It implies that the energy of each closed system, when any phenomena occur in it, is necessarily conserved. Nevertheless, it is able to transform into another form and effectively change its quantitative content in various parts of the named system. At the same time, in an open system, the energy decreases, provided that the energy of any bodies and fields that interact with it increases.

In addition to the above general principle, physics contains the basic concepts, formulas, laws that are necessary for interpreting the processes taking place in the surrounding world. Exploring them can be incredibly exciting. Therefore, in this article the basic laws of physics will be briefly considered, and in order to understand them deeper, it is important to pay full attention to them.

Mechanics

Many basic laws of physics are revealed to young scientists in grades 7-9 of the school, where such a branch of science as mechanics is more fully studied. Its basic principles are described below.

1. Galileo's law of relativity (also called the mechanical law of relativity, or the basis of classical mechanics). The essence of the principle is that under similar conditions mechanical processes in any inertial frames of reference are completely identical.
2. Hooke's law. Its essence is that the greater the impact on an elastic body (spring, rod, cantilever, beam) from the side, the greater its deformation.

Newton's laws (represent the basis of classical mechanics):

1. The principle of inertia says that any body is capable of being at rest or moving uniformly and rectilinearly only if no other bodies affect it in any way, or if they somehow compensate for each other's action. To change the speed of movement, it is necessary to act on the body with some force, and, of course, the result of the action of the same force on bodies of different sizes will also differ.
2. The main pattern of dynamics states that the greater the resultant of the forces that are currently acting on given body, the greater its acceleration. And, accordingly, the greater the body weight, the lower this indicator.
3. Newton's third law says that any two bodies always interact with each other in an identical pattern: their forces are of the same nature, are equivalent in magnitude, and necessarily have the opposite direction along the straight line that connects these bodies.
4. The principle of relativity states that all phenomena occurring under the same conditions in inertial frames of reference proceed in an absolutely identical way.

Thermodynamics

The school textbook, which reveals to students the basic laws ("Physics. Grade 7"), introduces them to the basics of thermodynamics. We will briefly review its principles below.

The laws of thermodynamics, which are basic in this branch of science, are of a general nature and are not related to the details of the structure of a particular substance at the atomic level. By the way, these principles are important not only for physics, but also for chemistry, biology, aerospace engineering, etc.

For example, in the named industry there is a rule that cannot be logically determined that in a closed system, the external conditions for which are unchanged, an equilibrium state is established over time. And the processes that continue in it invariably compensate each other.

Another rule of thermodynamics confirms the desire of a system, which consists of a colossal number of particles characterized by chaotic motion, to independently transition from less probable states for the system to more probable ones.

And the Gay-Lussac law (also called it states that for a gas of a certain mass under conditions of stable pressure, the result of dividing its volume by absolute temperature will certainly become a constant value.

Another important rule of this industry is the first law of thermodynamics, which is also called the principle of conservation and transformation of energy for a thermodynamic system. According to him, any amount of heat that was communicated to the system will be spent exclusively on the metamorphosis of its internal energy and the performance of its work in relation to any acting external forces. It is this regularity that became the basis for the formation of a scheme for the operation of heat engines.

Another gas regularity is Charles' law. It states that the greater the pressure of a certain mass of an ideal gas, while maintaining a constant volume, the greater its temperature.

Electricity

Opens for young scientists interesting basic laws of physics 10th grade school. At this time, the main principles of nature and the laws of action of electric current, as well as other nuances, are studied.

Ampère's law, for example, states that conductors connected in parallel, through which current flows in the same direction, inevitably attract, and in the case of the opposite direction of current, respectively, repel. Sometimes the same name is used for a physical law that determines the force acting in an existing magnetic field on a small section of a conductor that is currently conducting current. It is called so - the power of Ampere. This discovery was made by a scientist in the first half of the nineteenth century (namely, in 1820).

The law of conservation of charge is one of the basic principles of nature. It states that the algebraic sum of all electric charges arising in any electrically isolated system is always conserved (becomes constant). Despite this, the named principle does not exclude the appearance of new charged particles in such systems as a result of certain processes. Nevertheless, the total electric charge of all newly formed particles must necessarily be equal to zero.

Coulomb's law is one of the fundamental in electrostatics. It expresses the principle of the force of interaction between fixed point charges and explains the quantitative calculation of the distance between them. Coulomb's law makes it possible to substantiate the basic principles of electrodynamics in an experimental way. It says that fixed point charges will certainly interact with each other with a force that is the higher, the greater the product of their magnitudes and, accordingly, the less, the less square the distances between the charges under consideration and the medium in which the described interaction occurs.

Ohm's law is one of the basic principles of electricity. It says that the greater the strength of the direct electric current acting in a certain section of the circuit, the greater the voltage at its ends.

They call the principle that allows you to determine the direction in the conductor of a current moving under the influence of a magnetic field in a certain way. To do this, it is necessary to position the right hand so that the lines of magnetic induction figuratively touch the open palm, and extend the thumb in the direction of the conductor. In this case, the remaining four straightened fingers will determine the direction of movement of the induction current.

Also, this principle helps to find out the exact location of the lines of magnetic induction of a straight conductor that conducts current at the moment. It works like this: place the thumb of the right hand in such a way that it points and figuratively grasp the conductor with the other four fingers. The location of these fingers will demonstrate the exact direction of the lines of magnetic induction.

The principle of electromagnetic induction is a pattern that explains the process of operation of transformers, generators, electric motors. This law is as follows: in a closed circuit, the generated induction is the greater, the greater the rate of change of the magnetic flux.

Optics

The branch "Optics" also reflects a part of the school curriculum (basic laws of physics: grades 7-9). Therefore, these principles are not as difficult to understand as it might seem at first glance. Their study brings with it not just additional knowledge, but a better understanding of the surrounding reality. The main laws of physics that can be attributed to the field of study of optics are as follows:

1. Huynes principle. It is a method that allows you to efficiently determine at any given fraction of a second the exact position of the wave front. Its essence is as follows: all points that are in the path of the wave front in a certain fraction of a second, in fact, become sources of spherical waves (secondary) in themselves, while the placement of the wave front in the same fraction of a second is identical to the surface , which goes around all spherical waves (secondary). This principle is used to explain the existing laws related to the refraction of light and its reflection.
2. The Huygens-Fresnel principle reflects an effective method for resolving issues related to wave propagation. It helps to explain the elementary problems associated with the diffraction of light.
3. waves. It is equally used for reflection in the mirror. Its essence lies in the fact that both the falling beam and the one that was reflected, as well as the perpendicular constructed from the point of incidence of the beam, are located in a single plane. It is also important to remember that in this case the angle at which the beam falls is always absolutely equal to the angle of refraction.
4. The principle of refraction of light. This is a change in trajectory electromagnetic wave(light) at the moment of movement from one homogeneous medium to another, which differs significantly from the first in a number of refractive indices. The speed of propagation of light in them is different.
5. The law of rectilinear propagation of light. At its core, it is a law related to the field of geometric optics, and is as follows: in any homogeneous medium (regardless of its nature), light propagates strictly rectilinearly, along shortest distance. This law simply and clearly explains the formation of a shadow.

Atomic and nuclear physics

The basic laws of quantum physics, as well as the basics of atomic and nuclear physics are studied in high school high school and higher educational institutions.

Thus, Bohr's postulates are a series of basic hypotheses that have become the basis of the theory. Its essence is that any atomic system can remain stable only in stationary states. Any radiation or absorption of energy by an atom necessarily occurs using the principle, the essence of which is as follows: the radiation associated with transport becomes monochromatic.

These postulates belong to the standard school curriculum studying the basic laws of physics (Grade 11). Their knowledge is mandatory for the graduate.

Basic laws of physics that a person should know

Some physical principles, although they belong to one of the branches of this science, are nevertheless of a general nature and should be known to everyone. We list the basic laws of physics that a person should know:

• Archimedes' law (applies to the areas of hydro-, as well as aerostatics). It implies that any body that has been immersed in a gaseous substance or in a liquid is subject to a kind of buoyant force, which is necessarily directed vertically upwards. This force is always numerically equal to the weight of the liquid or gas displaced by the body.
• Another formulation of this law is as follows: a body immersed in a gas or liquid will certainly lose as much weight as the mass of the liquid or gas in which it was immersed. This law became the basic postulate of the theory of floating bodies.
• The law of universal gravitation (discovered by Newton). Its essence lies in the fact that absolutely all bodies are inevitably attracted to each other with a force that is the greater, the greater the product of the masses of these bodies and, accordingly, the less, the smaller the square of the distance between them.

These are the 3 basic laws of physics that everyone who wants to understand the mechanism of the functioning of the surrounding world and the features of the processes occurring in it should know. It is quite easy to understand how they work.

The value of such knowledge

The basic laws of physics must be in the baggage of knowledge of a person, regardless of his age and type of activity. They reflect the mechanism of existence of all today's reality, and, in essence, are the only constant in a continuously changing world.

The basic laws, concepts of physics open up new opportunities for studying the world around us. Their knowledge helps to understand the mechanism of the existence of the Universe and the movement of all space bodies. It turns us not just onlookers of daily events and processes, but allows us to be aware of them. When a person clearly understands the basic laws of physics, that is, all the processes taking place around him, he gets the opportunity to control them in the most effective way, making discoveries and thereby making his life more comfortable.

Results

Some are forced to study in depth the basic laws of physics for the exam, others - by occupation, and some - out of scientific curiosity. Regardless of the goals of studying this science, the benefits of the knowledge gained can hardly be overestimated. There is nothing more satisfying than understanding the basic mechanisms and laws of the existence of the surrounding world.

Don't be indifferent - develop!

1.1. Annotation. The laws of relativity and quantum mechanics, according to which there is movement and interaction elementary particles matter, predetermine the formation and appearance of patterns of the widest 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, acquaintance 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.

1.2. What is the main difficulty of this report. It is addressed both to specialists in the field of elementary particle physics and to a much wider audience: physicists who do not deal with elementary particles, mathematicians, chemists, biologists, energy scientists, economists, philosophers, linguists, ... To be sufficiently precise, I must use the terms and formulas of fundamental physics. To be understood, I must constantly explain these terms and formulas. If elementary particle physics is not your specialty, read first only those sections whose titles are not marked with asterisks. Then try to read sections with one asterisk *, two **, and finally three ***. I managed to talk about most of the sections without asterisks during the report, but there was no time for the rest.

1.3. Physics of elementary particles. Particle physics is the foundation of all natural sciences. It studies the smallest particles of matter and the basic patterns of their movements and interactions. Ultimately, it is these regularities 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 about space and time, they may have heard about the connection between mass and energy and have no idea what momentum has to do with it, and they hardly guess about the most important role of spin in physics. They can’t even agree among themselves on what to call matter yet experts.) Particle physics was created in the 20th century. Its creation is inextricably linked with the creation of two of the greatest theories in the history of mankind: 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 speeds 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 designed to describe gravitational interactions, taking into account the finiteness of the 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 allowed 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 unification of the theory of relativity and quantum mechanics led to the creation quantum theory field, 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 complicated to explain to schoolchildren. But in the middle of the 20th century, a visual language of Feynman diagrams appeared in it, which radically simplifies the understanding of many aspects of quantum field theory. One of the main aims of this talk is to show how the widest range of phenomena can be simply understood with the help of Feynman diagrams. At the same time, I will dwell in more detail on issues that are far from known to all experts in quantum field theory (for example, on the relationship between classical and quantum gravity), and I will only sparingly outline issues widely discussed in popular scientific literature.

1.7. Identity of elementary particles. Elementary particles are called the smallest indivisible particles of matter, from which the whole 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 kind, for example, all electrons in the Universe are absolutely (!) The same - identical. And as a consequence, their simplest bound states are identical to each other - atoms and the simplest molecules.

1.8. Six elementary particles. To understand the main processes occurring on the Earth and on the Sun, it is enough to understand, as a first approximation, 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 spin 1/2, the photon has spin 1, and the graviton has 2. (Particles with integer spin are called bosons, particles with half-integer spin are called fermions. More on spin will be discussed later.) Protons and neutrons are usually called nucleons because atomic nuclei are built from them, and the nucleus in English is the nucleus. The electron and neutrino are called leptons. They do not have strong nuclear forces.

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

1.9. Antiparticles. The electron, proton and neutron have so-called antiparticles: positron, antiproton and antineutron. They are not included in the composition of ordinary matter, since when they meet with the corresponding particles, they enter into reactions of mutual annihilation with them - 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 became clear that the nucleons themselves consist of more elementary particles - quarks of two types, 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. As well as u, d, e, v 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 decay 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 deep understanding of nature, even more particles with even more unusual properties are needed. But, perhaps, in the future, all this diversity will be reduced to a few simple and beautiful entities.

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 do not enter into the composition of ordinary matter.

Often, hadrons are also referred to as elementary particles, since they cannot be divided into free quarks and gluons. (So ​​did I, referring the proton and neutron to the first six elementary particles.) If all hadrons are considered elementary, then the number of elementary particles will be measured in 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 the processes known so far that occur 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: a photon, a graviton, an electron, and a proton. Moreover, the fact that the 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 arranged, or how our Sun works. But how atomic shells are arranged, which determine all the chemical properties of elements, how electricity works and how galaxies are arranged, one can understand.

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 the so-called dark matter, the nature of which is still unknown. The most common opinion is that dark matter consists of superparticles. It is possible that it consists of mirror particles.

Even more striking is the fact that all matter, both visible (light) and dark, carries only a quarter of the entire 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 Isaak Yakovlevich Pomeranchuk wanted to emphasize the importance of a question, he said that the question e is important in degree. Of course, most of the natural sciences, and not just elementary particle physics, are fundamental. Condensed matter physics, for example, is subject to fundamental laws that can be used without having to figure out 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 none of the less general laws can contradict them.

1.16. Basic laws. All processes in nature occur as a result of local interactions and movements (distributions) 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 the gravitational, electromagnetic, weak and strong interactions of particles.

2. Particles and life

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

ITEP researcher A. A. Abrikosov Jr. wrote to me recently: “One of the goals of your report is to convince a high audience of the need to teach modern physics more widely. If so, then perhaps it would be worthwhile to give a few everyday examples. I mean the following:

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

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

Of course, talking on the phone, driving a car and typing computer keys is possible without high science. But it is unlikely that academicians should urge not to study geography, because "there are cabs."

And then they talk to schoolchildren, and then to students for five years about material points and Galilean relativity, and suddenly, for no reason at all, they say that this is “not quite true.”

It is difficult to change from the visual Newtonian world to the quantum one, even at the Physicotechnical Institute. Yours, AAA."

2.2. On fundamental physics and education. Unfortunately, the modern education system has lagged behind modern fundamental physics by a whole century. And most people (including the majority of scientists) have no idea about that amazingly clear and simple picture (map) of the world that elementary particle physics has created. This map makes it much easier to navigate in 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 elementary school. After all, fundamentally new concepts are most easily mastered precisely in childhood. The child easily masters the language, masters with a mobile phone. Many children return the Rubik's cube to its original state in a matter of seconds, and even a day is not enough for me.

In order to avoid unpleasant surprises in the future, it is necessary to lay an adequate worldview in kindergarten. Constants c and h should become tools of knowledge for children.

2.3. About mathematics. Mathematics - the queen and servant of all sciences - must 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 in school, but it is necessary to teach you to appreciate truth, beauty, symmetry and order (and some disorder at the same time).

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

2.4. About worldview and natural sciences. The idea of ​​the basic laws that govern 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 there are many blank spots of the unknown on this map. It is very important to understand that science is not an ossified dogma, but a living process of approaching the truth in many points of the world map. Approximation to the truth is an asymptotic process.

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

2.6. On the humanities and social sciences. A general idea of ​​the structure of the world is very important for economics, and for history, and for cognitive sciences, such as the sciences of language, and for philosophy. And vice versa - these sciences are extremely important for the most fundamental physics, which constantly refines its fundamental concepts. This will be seen from the consideration of the theory of relativity, to which I now turn. I will especially mention 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 macrocosm. The world of celestial objects can be called the cosmic world, and the world of atomic and subatomic particles is called the microworld. (Since the sizes of atoms are of the order of 10 −10 m, then the microworld 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 nano fashion area is located along the road from the micro to 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 non-essential circumstances. For example, in atomic and nuclear physics, the gravitational interactions of particles are negligible, and they can be ignored. Such a model of the world fits into the special theory of relativity. This model has atoms, molecules, condensed bodies,... accelerators and colliders, but no Sun and stars.

Such a model would certainly be wrong on very large scales where gravity is essential.

Of course, for the existence of CERN, the existence of the Earth (and, consequently, of gravity) is necessary, but for understanding the vast majority of experiments conducted at CERN (except for searches at the collider for microscopic "black holes"), gravity is not essential.

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. Big numbers are not to be feared. After all, it is not difficult to deal with them, since the multiplication of numbers comes down mainly to the addition of their orders: 1 \u003d 10 0, 10 \u003d 10 1, 100 \u003d 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, then it will spread into a rainbow 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 than the size of an atom. And the thickness of the soap bubble film in the thinnest places is of the order of the size of the 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 \u003d 1 pendant × 1 V, and also that 1 J \u003d kg m 2 / s 2 and that the acceleration of gravity is about 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 student to the tenth floor. That's how much energy is in the battery.

2.12. Electronvolts. The unit of energy in elementary particle physics is the electron volt (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 pendant, 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. Reference systems. We describe all our experiments in one or another reference system. The reference system can be a laboratory, a train, a satellite of the Earth, the center of a galaxy... . Any particle flying, for example, in a particle accelerator, can also be a reference system. Since all these systems move relative to each other, not all experiments will look the same in them. In addition, the gravitational influence of the nearest massive bodies is also different in them. It is the consideration of these differences that constitutes the main content of the theory of relativity.

3.2. Ship of Galileo. 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 standing still. Einstein added experiments with the finite speed of light to this cabin. If you do not look out the window, you cannot know the speed of the ship. But if you look at the shore, you can.

3.3. Distant stars*. It is reasonable to single out such 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 the relic microwave background should be isotropic in this system.

3.4. In search of a universal frame of reference*. In essence, the entire history of astronomy is an advance towards an ever more universal frame of reference. From anthropocentric, where man is in the center, to geocentric, where the Earth is at rest in the center (Ptolemy, 87–165), to heliocentric, where the Sun is at rest in the center (Copernicus, 1473–1543), to halacentric, 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 essential, however, that the velocities of these frames of reference 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 says: “All the movements noticed by the Sun are not characteristic of 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 motions. 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 the 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 related to the 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 frame of reference that is progressively moving relative to the universal frame is inertial: the free motion in it is uniform and rectilinear.

3.7. "Invariance Theory"*. Note that both Albert Einstein (1879-1955) and Max Planck (1858-1947) (who introduced the term "theory of relativity" in 1907, calling it 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 frames of reference than to single out one of these frames. It was more important that with the curtained windows of Galileo's cabin it was impossible to determine the speed of the ship. But now it's time to part the curtains and look at the shore. At the same time, 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 unsuccessful and leads to philosophical misunderstandings." But to change it, according to Einstein, it is already too late, in particular, because it is widespread. This letter was published in the 12th volume of the 25-volume Collected Works of Einstein published in Princeton, published in the fall of 2009.

3.9. Maximum speed in nature. The key constant of the theory of relativity is the speed of light c\u003d 300,000 km / s \u003d 3 × 10 8 m / s. (More accurately, c= 299 792 458 m/s. And this number now underlies the definition of a meter.) This speed is the maximum speed of propagation of any signals in nature. It is many orders of magnitude higher than the speed of massive objects that we deal with every day. It is its unusually large value that hinders the understanding of the main content of the theory of relativity. Particles moving at speeds of the order of the speed of light are called relativistic.

3.10. Energy, momentum and speed. The free motion of a particle is characterized by the energy of the particle E and her momentum 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 lies in the fact that when creating the theory of relativity, they tried to preserve the Newtonian relationship between momentum and velocity 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. She is an invariant. Formulas (1) and (2) are fundamental 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 did not find it in any of Einstein's works. It is not in the remarkable 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 the articles of 1926 by O. Klein (1894–1977) and W. Fock (1898–1974).

3.12. Massless photon. If the mass of the particle is zero, i.e., the particle is massless, then from formulas (1) and (2) it follows that in any frame of reference its velocity 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 is the speed of light.

3.13. Peace energy. If the mass of the particle is nonzero, then consider a frame of reference in which the free particle is at rest and near it 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 denoted E0. 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=mc2”, 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 a widespread misconception that the mass of a body, according to the theory of relativity, allegedly grows with an increase in its speed. In recent years, the Russian Academy of Education has done much 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 we should put in them c= 1. In this case, the speed becomes a dimensionless quantity, the distance has the dimension of time, and the mass has the dimension of energy.

In elementary 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 fractions 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 to the 10 −24 s time it takes for light to travel a distance on the order of the size of a proton. And in all this colossal range, the theory of relativity works.

3.17. The world of Minkowski. In 1908, a few months before his untimely death, Hermann 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 trend is radical. From now on, space by itself and time by itself must turn into fictions, and only some kind of combination of both must still retain independence.

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

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

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

3.19. The dependence of the clock rate on their speed**. Numerous observations indicate that clocks run fastest when they are at rest with respect to the inertial frame. The finite motion in the inertial frame of reference slows down their progress. The faster they move in space, the slower they go in time. The deceleration is absolute in the universal frame of reference (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 deceleration can be most clearly 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 revolution, and R is the radius of the orbit, gives only a negligible correction, since E/ω 2 R = ER>> 1. Movement along a circle, and not along a straight line, is absolutely essential for a direct comparison of a rotating muon with a muon at rest. But as far as the aging rate of a moving muon is concerned, a circular arc of sufficiently large radius is indistinguishable from a straight line. This rate is determined by the ratio e/m. (I emphasize that according to special theory relativity, the frame of reference in which the rotating muon rests is not inertial.)

3.21. Arc and chord**. From the point of view of an observer at rest in an inertial frame of reference, the arc of a circle with a sufficiently large radius and its chord are practically indistinguishable: the 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 stationary. The entire Universe is asymmetric for him: the stars in front are blue and behind are red. While for us they are all the same - golden, because the speed of the solar system is low.) And the non-inertiality of this observer manifests itself in that the constellations in front and behind change as the muon moves in the ring accelerator. We cannot consider the resting and moving observers to be equivalent, since the first does not experience any acceleration, and the second, in order to return to the meeting point, must experience it.

3.22. general relativity**. Theoretical physicists, accustomed to the language of the General Theory of Relativity (GR), insist that all frames of reference are equal. Not only inertial, but also accelerated. That space-time itself is curved. In this case, the gravitational interaction ceases to be the same physical interaction as the electromagnetic, weak and strong, and becomes an exceptional manifestation of curved space. As a result, the whole physics for them appears as if 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 theater "Lenkom" or the newspaper "Moskovsky Komsomolets", only genealogically connected with the Komsomol. These are language paradoxes. The speed of light in vacuum is not relative. She is absolute. Just physicists need the help of linguists.

4. About quantum theory

4.1. Planck's constant. If in the theory of relativity the key constant is the speed of light c, then the key constant in quantum mechanics is h= 6.63 10 −34 J s, discovered by Max Planck in 1900 physical meaning this constant will become clear from what follows. 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 s.

In many phenomena an important role is played by the quantity ħc= 1.97 10 −11 MeV cm.

4.2. Spin of an electron. Let's start with the well-known naive comparison of the atom with the planetary system. The planets revolve around the Sun and around their own axis. Similarly, electrons revolve around the nucleus and around their own axis. The rotation of an electron in orbit is characterized by the orbital angular momentum L(it is often and not quite correctly called the 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, the atom is not planetary system, and the 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 - the 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 passes into higher and higher states , which are getting larger.

4.4. Quantum numbers of electrons. Without taking into account the spin, the motion of an electron in an atom is characterized by two quantum numbers: the principal quantum number n and orbital quantum number l, moreover 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 motion of an electron is similar to the motion of a classical particle in orbit. The binding energy of an electron located in a hydrogen atom on a shell with a quantum number n, is equal to

where α =e 2/ħc≈ 1/137, a e is the charge of an electron.

4.5. Multi-electron atoms. Spin plays a key role in filling the electron shells of multielectron atoms. The fact is that two electrons with the same direction of their own rotation (the same direction of spins) cannot be on the same shell with the given values n and l. This is prohibited by the so-called Pauli principle (1900–1958). Essentially, the Pauli principle defines the periods Periodic table elements of Mendeleev (1834–1907).

4.6. Bosons and fermions. All elementary particles have spin. So, the spin of a photon is 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 tend 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 momentum. 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 - 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 the screen behind them. All attempts to put the quantum centaurs in the Procrustean bed of the concepts of classical physics have proved fruitless.

4.8. Uncertainty relations. Constant ħ determines the features of not only the rotational, but also the translational motion of elementary particles. The position and momentum uncertainties 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 general patterns quantum mechanics, created in the 20s of the XX 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 a periodic motion of a colossal number of particles, an elementary wave is a new, previously unknown type of motion of an individual particle. Elementary wavelength λ of a particle with momentum p is equal to λ = h/|p|, and the elementary frequency ν corresponding to the energy E, is equal to 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 velocities 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 combined by a quantum h. The unification of the theory of relativity and quantum mechanics was carried out by Dirac (1902-1984) in 1930 and led to the creation of a theory that was 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 such units in which the unit of velocity is taken to be c, and per unit of angular momentum (action) - ħ . In these units, all formulas are greatly 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 essential in it. In those cases when 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 certain sense, having given birth to quantum mechanics, did not reconcile himself to it. And until the end of his life he tried to build a "unified theory of everything" on the basis of classical field theory, ignoring ħ . Einstein believed in classical determinism and in 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 moment of decay of an individual particle cannot be predicted in principle, although the average lifetime of one or another type of particle is predicted within the framework of quantum mechanics with unprecedented accuracy. Unfortunately, his addictions determined the views of so many people.

5. Feynman diagrams

5.1. The simplest diagram. Particle interactions are conveniently viewed using diagrams proposed by Richard Feynman (1918–1988) in 1949. 1 shows the simplest Feynman diagram describing the interaction of an electron and a proton by exchanging a photon.

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

5.2. real particles. Each process corresponds to one or more Feynman diagrams. The outer lines on 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 the novice to the idea that virtual particles are less material than real particles. In reality, they are equally 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 certain conditions and virtual under others.

5.4. Vertices. The tops of the chart 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, i.e., must be outside the mass shell: "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 be moving, then virtual particles are said to be propagate. The term "propagation" emphasizes the fact that a virtual particle can have many trajectories, and it may be that none of them is classical, like a virtual photon with zero energy and non-zero momentum, which describes the static Coulomb interaction.

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

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

5.7. Schwinger and Feynman diagrams. Schwinger (1918–1994), who had no problem with computational difficulties, disliked Feynman diagrams and wrote somewhat condescendingly about them: “Like a computer chip in more recent years, the Feynman diagram brought computation to the masses.” Unfortunately, unlike the chip, the Feynman diagrams did not reach the widest masses.

5.8. Feynman and Feynman diagrams. For unknown reasons, Feynman diagrams did not even make it to the famous Feynman Lectures on Physics. I am convinced that they need to be brought to high school students, explaining to them the basic ideas of elementary 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 one can use perturbation theory.) In most books on quantum field theory, particles are treated as quantum excitations of fields, which requires familiarity with the formalism of second quantization. In the language of Feynman diagrams, the fields are replaced by virtual particles.

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

5.10. Elementary Interactions*. The elementary acts of emission and absorption of virtual particles (vertices) are characterized by such interaction constants as the 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 a graviton, where G is Newton's constant. (See ch. 6–10.) The electromagnetic interaction is discussed below in ch. 7. Weak interaction - in Ch. 8. Strong - in Ch. 9.

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

6. Gravitational interaction

6.1. Gravitons. I'll start with particles that haven't been discovered yet and probably won't be discovered in the foreseeable future. These are particles of the gravitational field - gravitons. Not only gravitons, but also gravitational waves have not yet been discovered (and this is while 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 makes it possible to understand all the known properties of the 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. On fig. 3 graviton is emitted by a particle with 4-momentum p 1 and is absorbed by another particle with 4-momentum p 2 . Due to the conservation of the 4-momentum, q=p 1 − p′ 1 =p′ 2 −p 2 , where q is the 4-momentum of the graviton.

The distribution of a virtual graviton (it, like any virtual particle, corresponds to a propagator) is shown in the figure by a spring.

6.3. Hydrogen atom in the Earth's gravitational field. On fig. Figure 4 shows the sum of diagrams in which a hydrogen atom with a 4-momentum p 1 exchanges gravitons with all the Earth's atoms with 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. On the mass of an atom. In the future, when considering the gravitational interaction, we will neglect the mass of an electron compared to the mass of a proton, as well as the difference in the masses of a proton and a neutron and the binding energy of nucleons in atomic nuclei. So the mass of an atom is roughly 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. the Avogadro number N A ≈ 6 10 23 , by the mass of the Earth in grams ≈ 6 10 27 . Therefore, the diagram in Fig. 4 is the sum of the 3.6·10 51 diagrams of fig. 3, which is marked by the 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 made in fig. 4 grey. It seems to contain 3.6·10 51 gravitons.

6.6. Newton's apple in the gravitational field of the Earth. On fig. 5, all the atoms of the apple, which have a total 4-momentum p 1 , interact with all the atoms of the Earth, which have 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 is N a = 100N A = 6 10 25 . The mass of the Earth is 6 10 27 g, and consequently, the number of nucleons of the Earth N E = 3.6 10 51 . Of course, the thickening of the lines in Fig. 5 does not in any way correspond 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, each nucleon of the apple interacts with each nucleon of the Earth. To emphasize the colossal number of diagrams, the spring in fig. 5 is made dark.

Although the interaction of a graviton with a single elementary particle is very small, the sum of the diagrams for all the nucleons of the Earth creates a significant attraction that we feel. Universal gravity pulls the Moon to the Earth, both of them to the Sun, all the stars in our Galaxy, and all the galaxies to 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/q2, where q- 4-momentum, called graviton propagator. In the case of slow bodies, energy is practically not transferred, and therefore q2 = −q 2 .)

To pass from the momentum space to the configuration (coordinate) space, one must take the Fourier transform of the amplitude A( q)

Value A( r) gives the potential energy of the gravitational interaction of non-relativistic particles and determines the motion 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

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

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

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

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

6.11. About potential energy**. In Newton's nonrelativistic mechanics kinetic energy particle depends on its speed (momentum), and the potential depends only on its coordinates, i.e., on its position in space. In relativistic mechanics, such a requirement cannot be maintained, since the very interaction of particles often depends on their velocities (momentums) and, consequently, on kinetic energy. However, for ordinary, rather weak gravitational fields, the change in the particle's kinetic energy 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. Universality of gravity. Unlike all other interactions, gravity has a 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 sufficiently fast particle, its kinetic energy is much greater than its mass. In this case, its gravitational interaction practically does not depend on the mass and is proportional to its kinetic energy.

6.13. Graviton spin and the universality of gravity**. More precisely, the emission of a graviton 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 momentum of the graviton is q = p 1 − p 2. If we introduce the notation p = p 1 + p 2 , then the graviton emission vertex will look like

where h αβ is the graviton wave function.

6.14. Interaction of a graviton with a photon**. This is especially clearly seen in the example of a photon, whose mass is equal to 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 beam of light from a distant star is deflected by the gravitational pull of the Sun.

6.15. Interaction of a photon with the Earth**. On fig. 6 shows the exchange of gravitons between the Earth and a photon. This figure conditionally represents the sum of figures of graviton exchanges of a photon with all nucleons of the Earth. On it, the earth's vertex is obtained from the nucleon one 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 a graviton with a graviton***. Since gravitons carry energy, they themselves must emit and absorb gravitons. We have not seen individual real gravitons and will never see them. Nevertheless, the interaction between virtual gravitons leads to the observed 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. Mercury's secular precession**. However, this contribution manifests itself in the precession of the perihelion of Mercury's orbit. The secular precession of Mercury is described by the sum of one-loop graviton diagrams of Mercury's attraction to the Sun (Fig. 8).

6.18. Gain for Mercury**. The ratio of the masses of Mercury and the Earth is 0.055. So the number of nucleons in Mercury NM = 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 the nucleons of Mercury and the Sun, NdM= 2.4 10 107 .

If the potential energy of attraction of Mercury to the Sun is 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 the coefficient 1 − 3 GM S/r. We see that the potential energy correction is −3 G 2 M S 2 M M /r 2.

6.19. Orbit of Mercury**. Mercury orbit radius a= 58 10 6 km. The orbital period is 88 Earth days. Orbital eccentricity e= 0.21. Due to the correction under discussion, in 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 a second of arc, and rotates by 43 "" in 100 Earth years.

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 Riserford and found to be 1060 MHz (1.06 GHz).

This measurement started 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 less.

6.21. Classical or quantum effect?**. It is well known that the Lamb shift of the 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 relation E = ħω and take into account that the Fourier transform during the transition from momentum to configuration space in Sec. 6.8 contains e iqr / ħ . In addition, it should be taken into account that in the Lamb shift electromagnetic 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 peak, leads to the fact that the gravitational triangle makes a contribution at incomparably greater distances than the electromagnetic one. This comparison shows the power of quantum field theory in the method of Feynman diagrams, which make it easy to understand and calculate a wide range of 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. nineteen.

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. First, because there are electric charges of two signs. And secondly, because there are neutral particles that do not have any electric charge(neutron, neutrino, photon...). Particles with charges of opposite signs, like an electron and a proton, are attracted to each other. Particles with the same charge repel each other. As a result, atoms and the bodies composed 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 a photon, a graviton, a neutrino, Z-boson and Higgs boson.

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

7.5. Magnetic interaction. The magnetic interaction is not as long-range as the electrical one. It falls off like 1/ r 3 . It depends not only on the distance between the two magnets, but also on their mutual orientation. A well-known example is the interaction of a compass needle with the field of the Earth's magnetic dipole. Potential energy of interaction of two magnetic dipoles μ 1 and μ 2 equals

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) studied the interaction of a magnet and a conductor with current. A decade later, he established the laws of electromagnetic induction in the interaction of two conductors. In later years, he introduced the concept electromagnetic field and expressed the idea of ​​the electromagnetic nature of light. In the 1870s, J. Maxwell (1831-1879) realized that the electromagnetic interaction is 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. Unification of 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 an antiparticle of the electron - the positron, discovered a few years later. After that, quantum mechanics and the theory of relativity merged 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 very high energy photons. β rays are high energy electrons α rays are helium nuclei. This led to the discovery of two new types of interactions - strong and weak. Unlike gravity and electromagnetic interactions, strong and weak interactions are short-range.

Later it was found that they are responsible for the conversion of hydrogen into helium in our Sun and other stars.

8.2. Charged currents*. The weak force 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, there are transitions between charged leptons and the corresponding neutrinos:

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

8.3. Neutral currents*. In the 1970s, processes of weak interaction between neutrinos, electrons and nucleons were discovered, due to the so-called neutral currents. 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 - by exchanging Z-bosons.

8.4. Violation P- and CP-parity*. In the second half of the 1950s, parity violation was discovered P and charge parity C in weak interactions. In 1964, weak decays were discovered that violate the conservation CP-symmetries. At present, the mechanism of violation CP-symmetries are studied in the decays of mesons containing b-quarks.

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

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

8.7. Violation of electroweak symmetry. In the framework of the Standard Model, the Higgs boson breaks the electroweak symmetry and thus explains why the photon is massless and weak bosons are massive. It also gives masses to leptons, quarks, and itself.

8.8. What you need to know about the Higgs. One of the main tasks of the Large Hadron Collider LHC is the discovery of the Higgs boson (which is simply called Higgs and denoted h or H) and the subsequent establishment of its properties. First of all, the measurement of 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 with 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, on the other hand, it turns out that Higgs does not exist in the mass interval of the order of several hundred GeV, then this will mean that at energies above TeV there is a new, absolutely unexplored 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, in which electrons collide with positrons, as well as photons with photons. The decision to build it can only be made 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 and 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" took place in San Francisco. The MS project is currently being developed at the 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-action 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 ones. 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 the van der Waals forces between neutral atoms.

9.2. Confinement and asymptotic freedom. The phenomenon of confinement of gluons and quarks from hadrons is called confinement. reverse side The dynamics leading to confinement is that at very small distances deep inside hadrons, the interaction between gluons and quarks gradually falls off. Quarks seem to become free at small distances. This phenomenon is called the term asymptotic freedom.

9.3. Quark colors. The phenomenon of confinement is a consequence of the fact that each of the six quarks exists, as it were, in the form of three "color" varieties. Quarks are usually "colored" in yellow, blue and red colors. Antiquarks are painted in additional colors: purple, orange, green. All these colors denote the peculiar charges of quarks - "multidimensional analogues" of the electric charge responsible for strong interactions. Of course, there is no connection, except metaphorical, 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, of which two are identical to their antiparticles, and the remaining six are not. 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 gluon-quark confinement, 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 hadrons. This is similar to the smallness of molecular bonds compared to intraatomic ones.

9.5. Masses of hadrons. The masses of hadrons in general and nucleons in particular are due to 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 particles of the Standard Model. 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 of the Universe is outside the Standard Model and is waiting to be discovered and studied. There are several basic assumptions about what the new physics might look like (see sections 10.3–10.6 below).

10.3. Great union. A huge number of works, mostly theoretical, have been devoted to the unification of the 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 the decay of the proton.

10.4. supersymmetric particles. According to the idea of ​​supersymmetry, first born at FIAN, each “our” particle has a superpartner whose spin differs by 1/2: 6 squarks and 6 sliptons with spin 0, higgsino, photino, wine and zino with spin 1/2, gravitino co spin 3/2. The masses of these superpartners must be substantially larger than those of our particles. Otherwise, they would have 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 small 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 it will be possible 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, first born at ITEP, each of our particles has a mirror twin, and there is a mirror world that is only very loosely connected to our world.

10.7. Dark matter. Only 4–5% of all energy in the universe exists as a 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, colliding with each other in space, they annihilate into ordinary photons, then these high-energy photons can be registered by special detectors in space and on Earth. Elucidation of the nature of dark matter is one of the main tasks of physics.

10.8. Dark energy. But the vast majority of the energy of the Universe (about 75%) is due to the so-called dark energy. It is "poured" through the vacuum and pushes the clusters of galaxies apart. Its nature is not yet clear.

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 a National research center Kurchatov Institute. The decree provides for the participation of the following organizations in the project: the St. Petersburg Institute of Nuclear Physics, the Institute of High Energy Physics and the Institute of Theoretical and Experimental Physics. The decree also provides for "inclusion of the specified institution, as the most significant institution of science, in the departmental structure of federal budget expenditures as the main manager of budgetary 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. Hearings in the US Congress 1. On October 1, 2009, hearings were held in the Subcommittee on Energy and the Environment of the Committee on Science and Technology of the US House of Representatives on the topic "Research on 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 outlined views on matter, energy and the origin of the universe in terms of 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 start of joint work of the FNAL and the DUSEL underground laboratory to study the properties of neutrinos and rare processes. He stressed 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. Hearings in the US Congress 2. Director of the Jefferson National Laboratory Hugh Montgomery spoke about the contribution of this Laboratory to nuclear physics, to accelerator technologies and to educational programs. Dennis Kovar, Director of the High Energy Physics Division of the Department of Energy, spoke about the three main areas of high energy physics:

1) accelerator studies at maximum energies,

2) accelerator studies at maximum intensities,

3) ground-based and satellite space exploration in order to elucidate 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 that part of science that establishes the most fundamental laws of nature as fundamental science. 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 sections of science that have the greatest direct impact on momentary achievements in the development of civilization. It seems to me personally that these sections and directions 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 mobile phones or fiber optic communications are the fruits of science.

12.3. A. I. Herzen on science. In 1845, Alexander Ivanovich Herzen (1812–1870) published in the journal Otechestvennye Zapiski the remarkable Letters on the Study of Nature. At the end of the first letter, he wrote: “Science seems difficult, not because it really is difficult, but because otherwise you won’t reach its simplicity, as breaking through the darkness of those 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 have inherited from scholasticism is worthless, that it is necessary to sacrifice views formulated outside of science, that, without discarding all half lies, with which, for clarity, they clothe half-truths one cannot enter into science, one cannot reach the whole truth.

12.4. On 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 we reduce those sections in them that are mainly descriptive in nature and increase the “erudition” of the child, rather than understanding the world around and 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 instruct the Commissions of the Presidium of the Russian Academy of Sciences on textbooks (chairman - vice-president V.V. Kozlov) and on education (chairman - vice-president -President V. A. Sadovnichiy) to prepare proposals for improving the teaching of modern fundamental physics in secondary and higher schools.

The session is approaching, and it's time for us to move from theory to practice. Over the weekend, we sat down and thought that many students would do well to have a collection of basic physics formulas handy. Dry formulas with explanation: short, concise, nothing more. A very useful thing when solving problems, you know. Yes, and at the exam, when exactly what was cruelly memorized the day before can “jump out” of my head, such a selection will serve you well.

Most of the tasks are usually given in the three most popular sections of physics. This Mechanics, thermodynamics and Molecular physics, electricity. Let's take them!

Basic formulas in physics dynamics, kinematics, statics

Let's start with the simplest. Good old favorite rectilinear and uniform movement.

Kinematic formulas:

Of course, let's not forget about the movement in a circle, and then move on to the dynamics and Newton's laws.

After the dynamics, it's time to consider the conditions for the equilibrium of bodies and liquids, i.e. statics and hydrostatics

Now we give the basic formulas on the topic "Work and energy". Where would we be without them!

Basic formulas of molecular physics and thermodynamics

Let's finish the section of mechanics with formulas for vibrations and waves and move on to molecular physics and thermodynamics.

Efficiency, Gay-Lussac's law, the Clapeyron-Mendeleev equation - all these sweet formulas are collected below.

By the way! There is a discount for all our readers 10% on the any kind of work.

Basic formulas in physics: electricity

It's time to move on to electricity, although thermodynamics loves it less. Let's start with electrostatics.

And, to the drum roll, we finish with the formulas for Ohm's law, electromagnetic induction and electromagnetic oscillations.

That's all. Of course, a whole mountain of formulas could be given, but this is useless. When there are too many formulas, you can easily get confused, and then completely melt the brain. We hope that our cheat sheet of basic formulas in physics will help you solve your favorite problems faster and more efficiently. And if you want to clarify something or have not found the formula you need: ask the experts student service. Our authors keep hundreds of formulas in their heads and click tasks like nuts. Contact us, and soon any task will be "too tough" for you.

BASIC LAWS OF PHYSICS

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

ENERGIES OF CONSERVATION AND TRANSFORMATION LAW - the general law of nature: the energy of any closed system for all processes occurring in the system remains constant (conserved). 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 the 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 subjected to a buoyant force directed vertically upwards, 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 submerged part of the body. Otherwise, it can be formulated as follows: a body immersed in a liquid or gas loses as much in its weight as the liquid (or gas) displaced by it weighs. Then P= mg - FA Other gr. scientist Archimedes in 212. BC. It is the basis of the theory of swimming 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 the interacting bodies, R is the distance between these bodies, G is the gravitational constant (in SI G=6.67.10-11 N.m2/kg2.

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

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

MOMENTUM CONSERVATION LAW - the law of mechanics: the momentum of any closed system in 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 no other bodies act on it or the action of these bodies is compensated. 2nd law (basic law of dynamics): the acceleration received by the 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 theory of relativity, stating that in any inertial reference frames all physical (mechanical, electromagnetic, etc.) phenomena under the same conditions proceed in the same way. It is Galileo's generalization of the principle of relativity to all physical phenomena (except gravity).

2. MOLECULAR PHYSICS AND THERMODYNAMICS

AVOGADRO LAW - 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 by the Italian. 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. Formula: pV=const. Describes an isothermal process.

SECOND LAW OF THERMODYNAMICS - 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 hotter one. V.z.t. expresses the tendency of a system consisting of a large number of 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.

GAY-LUSSAC 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 \u003d 1/273 K-1 is the temperature coefficient of volume expansion.

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.

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.

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

CHARLES LAW - one of the main gas laws: the pressure of a given mass of an ideal gas at a constant volume is directly proportional to the temperature: where p0 is the pressure at 00C, \u003d 1/273.15 K-1 is the temperature coefficient of pressure.

3. ELECTRICITY AND MAGNETISM

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

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

CHARGE CONSERVATION LAW - 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 particles that appear must always be equal to zero.

Coulomb LAW - the basic law of electrostatics, expressing the dependence of the interaction force of two fixed point charges on the distance between them: two fixed 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 permittivity of the medium in which the charges are located. In SI it looks like: . The value is numerically equal to the force acting between two fixed point charges of 1 C each, located in vacuum at a distance of 1 m from each other. K.z. is one of the experimental substantiations of electrodynamics.

LEFT HAND RULE - a rule that determines the direction of the force that acts on a conductor with current in a magnetic field (or a moving charged particle). It says: if the left hand is positioned so that the outstretched fingers show the direction of the current (velocity of the particle), and the lines of force of the magnetic field (lines of magnetic induction) enter the palm, then the retracted 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).

LENTZ RULE (LAW) - a rule that determines the direction of induction currents that occur during electromagnetic induction. According to L.p. the inductive 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.

OHMA LAW - one of the basic laws of electric current: the strength of direct electric current in a circuit section is directly proportional to the voltage at the ends of this section and inversely proportional to its resistance. Valid for metallic conductors and electrolytes, the temperature of which is maintained constant. In the case of a complete circuit, it is formulated as follows: the strength of the direct electric current in the circuit is directly proportional to the emf of the current source and inversely proportional to the impedance 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 it includes lines of magnetic induction, 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 lines of magnetic induction of a rectilinear conductor with current: if the thumb of the right hand is placed in the direction of the current, then the direction of grasping the conductor with four fingers will show the direction of the lines of magnetic induction.

FARADAY'S LAWS - the basic laws of electrolysis. Faraday's first law: the mass of the substance released on the electrode during the passage of an electric current is directly proportional to the amount of electricity (charge) that has passed through the electrolyte (m=kq=kIt). The second FZ: the ratio of the masses of various substances undergoing chemical transformations on the electrodes when the same electric 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 valence, F is the Faraday constant. F.p. is equal to the product of the elementary electric charge and the Avogadro 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 on the electrode. F=(96484.56 0.27) cells/mol. Named after M. Faraday.

ELECTROMAGNETIC INDUCTION LAW - a law describing the phenomenon of the occurrence of an electric field when the magnetic field changes (the phenomenon of electromagnetic induction): the electromotive force of induction is directly proportional to the rate of change of the magnetic flux. The coefficient of proportionality is determined by the system of units, the sign is the Lenz rule. The formula in SI is: where Ф is the change in the magnetic flux, and t is the time interval during which this change occurred. Discovered by M. Faraday.

4. OPTICS

HUYGENS PRINCIPLE - a method that allows you 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. The item says: at any point 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 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 raised 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 - a change in the direction of propagation of light (an electromagnetic wave) during the transition from one medium to another, which differs from the first refractive index. For refraction, the law is fulfilled: the incident beam, the refracted beam and the perpendicular raised to the point of incidence of the beam 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 DISTRIBUTION OF LIGHT - the law of geometric optics, which consists in the fact that in a homogeneous medium light propagates in a straight line. Explains, for example, the formation of shade and penumbra.

6. ATOMIC AND NUCLEAR PHYSICS.

BOHR POSTULATES - the main assumptions introduced without proof by N.Bohr and underlying the BOHR THEORY: 1) 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. 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