Fundamental physical fields. Physical field Which fields are not fundamental

Natural scientists and philosophers of the past and present tried to explain the diversity of natural phenomena from a unified position. Likewise in physics, scientists sought to reduce real forces to a finite number of fundamental interactions. Currently, four types of interactions are called fundamental, to which all others are reduced.

1.
Strong or nuclear interaction U = De - a r /r. Here a=1/r o

R o ~10 -14 m is the characteristic distance at which the action of nuclear forces manifests itself. The interaction is short-range (at short distances) and has the nature of attraction.

2.
The electromagnetic interaction U cool = q 1 q 2 /r is long-range and has the nature of attraction in the case of opposite charges. The ratio of the intensities of electromagnetic and nuclear interactions is I em /I poison = 10 -2.

3.
Weak interaction – short-range I sl /I poison = 10 -14.

4.
Gravitational interaction – long-range

I grav /I poison = 10 -39. U grav = Gm 1 m 2 /r – the interaction is in the nature of attraction.

Real powers. Elasticity and friction forces

Elastic forces.

Elastic forces arise as a reaction to the deformation of a solid body. Let's define some concepts.

Deformation (e) – relative displacement of body points.

Elastic stress (s) is the pressure that arises in a solid body during its deformation s = F/S. Here S is the area on which the elastic force F acts. The relationship between stress and deformation is as follows:

S I – area

Corresponds to elastic

Deformations. Here

Hooke's law is true:

s=Ee, where E is the module

I II III elasticity.

II – region of inelastic

• 
  deformations.

III – area of ​​material destruction.

For rod-shaped bodies (rods, beams, pipes)

e = DL/L – relative elongation, E – Young’s modulus. Shear stresses s^ are related to shear strains e^ = DD/D (D is the diameter of the rod) through the shear modulus G: s^ = Ge^. Hydrodynamic pressure P is related to the relative change in volume through the modulus of compression K:

P = KDV/V. For isotropic bodies, there will be only two independent moduli of elasticity. The rest can be recalculated using known formulas, for example: E = 2G(1 + m). Here m is Poisson's ratio.

The nature of elastic forces is associated with fundamental electromagnetic interactions.

Friction forces

The forces that arise between the surfaces of contacting bodies and prevent their relative movement are called friction forces. By parallel transfer, the friction force is drawn from the center of gravity of the body. It is directed against the speed of relative movement of bodies.

External or dry friction is the friction that occurs between solid bodies. In turn, it is divided into static friction and kinematic friction (sliding and rolling). The static friction force is equal to the maximum force that must be applied to a solid body in order for its movement to begin. F tr = kN

Here N is the normal pressure force.

to Dependence of coefficient

friction from the speed of movement

body alignment is shown in

drawing. At small

travel speeds

V coefficient of friction varies

movement and rolling is less than the coefficient of static friction.

Static friction is associated with elastic deformation of interacting bodies. Sliding and rolling friction are associated with inelastic deformation of body surfaces and even their partial destruction. Therefore kinematic

friction is accompanied by acoustic emission - noise.

Rolling friction is associated with inelastic

deformation of bodies. Then

a horizontal component appears

deformation reaction forces N 2

on the surface under the front of the wheel - N 1

this is the rolling friction force.

Ways to reduce the coefficient of friction:

1.
Replacing sliding friction with rolling friction.

2.
Replacing dry friction with viscous friction.

3.
Improving the quality of surface treatment of rubbing parts.

4.
Replacing static friction with sliding friction and rolling friction through the use of sound and ultrasonic vibrations.

5.
Use of polymer-filled compositions based on fluoroplastic.

6. Gravitational interaction− the weakest of the four fundamental interactions. According to Newton's law of universal gravitation, the force of gravitational interaction F g of two point masses m 1 and m 2 is equal to

8. G = 6.67·10 -11 m 3 · kg –1 · cm –2 is the gravitational constant, r is the distance between the interacting masses m 1 and m 2. The ratio of the force of gravitational interaction between two protons to the force of Coulomb electrostatic interaction between them is 10 -36.
The quantity G 1/2 m is called the gravitational charge. The gravitational charge is proportional to the mass of the body. Therefore, for the non-relativistic case, according to Newton’s law, the acceleration caused by the force of gravitational interaction F g does not depend on the mass of the accelerated body. This statement amounts to equivalence principle .
The fundamental property of the gravitational field is that it determines the geometry of space-time in which matter moves. According to modern concepts, interaction between particles occurs through the exchange of particles between them - carriers of interaction. It is believed that the carrier of gravitational interaction is the graviton, a particle with spin J = 2. The graviton has not been detected experimentally. The quantum theory of gravity has not yet been created.

All our daily actions come down to the fact that we, with the help of muscles, either set the surrounding bodies in motion and maintain this movement, or stop the moving bodies.

These bodies are tools (hammer, pen, saw), in games - balls, pucks, chess pieces. In production and agriculture, people also set tools in motion. True, nowadays the role of the worker is increasingly reduced to operating machinery. But in any machine you can find the semblance of simple manual labor tools. A sewing machine has a needle, a lathe's cutter is like a plane, and an excavator's bucket replaces a shovel.

Engines. The use of machines increases labor productivity many times due to the use of engines in them.

The purpose of any engine is to set bodies in motion and maintain this movement, despite braking by both ordinary friction and “working” resistance (the cutter should not just slide over the metal, but, cutting into it, remove chips; the plow should loosen land, etc.). In this case, a force must act on a moving body from the side of the engine, the point of application of which moves along with the body.

Everyday idea of ​​work. When a person (or any engine) acts with a certain force on a moving body, then we say that he does work. This everyday idea of ​​work formed the basis for the formation of one of the most important concepts of mechanics - the concept of the work of force.

Work is performed in nature whenever a force (or several forces) from another body (other bodies) acts on a body in the direction of its movement or against it. Thus, the force of gravity does work when raindrops or stones fall from a cliff. At the same time, work is also performed by the friction forces acting on the falling drops or on the stone from the air. The elastic force also performs work when a tree bent by the wind straightens.

Definition of work. Newton's second law in the form allows us to determine how the speed of a body changes in magnitude and direction if it is affected during time ∆ t force acts.

In many cases, it is important to be able to calculate the change in speed modulo if, when moving a body, a force acts on it. The effects on bodies of forces leading to a change in the modulus of their speed are characterized by a value that depends on both the forces and the movements of the bodies. In mechanics this quantity is called work of force.

In the general case, when a rigid body moves, the displacements of its different points are different, but when determining the work of a force, we understand the displacement of its point of application. During the translational motion of a rigid body, the movement of all its points coincides with the movement of the point of application of the force.

M. Faraday entered science solely thanks to his talent and diligence in self-education. Coming from a poor family, he worked in a bookbinding shop, where he became acquainted with the works of scientists and philosophers. The famous English physicist G. Davy (1778-1829), who contributed to M. Faraday's entry into the scientific community, once said that his greatest achievement in science was his “discovery” of M. Faraday. M. Faraday invented an electric motor and an electric generator, i.e. machines for producing electricity. He came up with the idea that electricity has a single physical nature, that is, regardless of how it is obtained: by the movement of a magnet or the passage of electrically charged particles in a conductor. To explain the interaction between electric charges at a distance, M. Faraday introduced the concept of a physical field. Physical field he represented the property of the space itself around an electrically charged body to have a physical effect on another charged body placed in this space. Using metal particles, he showed the location and presence of forces acting in space around a magnet (magnetic forces) and an electrically charged body (electric). M. Faraday outlined his ideas about the physical field in a letter-testament, which was opened only in 1938 in the presence of members of the Royal Society of London. In this letter, it was discovered that M. Faraday owned a technique for studying the properties of the field and in his theory, electromagnetic waves propagate at a finite speed. The reasons why he outlined his ideas about the physical field in the form of a letter of testament are perhaps the following. Representatives of the French school of physics demanded from him a theoretical proof of the connection between electric and magnetic forces. In addition, the concept of a physical field, according to M. Faraday, meant that the propagation of electric and magnetic forces occurs continuously from one point of the field to another and, therefore, these forces have the character of short-range forces, and not long-range, as C. Coulomb believed. M. Faraday has another fruitful idea. While studying the properties of electrolytes, he discovered that the electric charge of the particles that form electricity is not fractional. This idea was confirmed

determination of the electron charge already at the end of the 19th century.

D. Maxwell's theory of electromagnetic forces

Like I. Newton, D. Maxwell gave all the results of research into electric and magnetic forces a theoretical form. This happened in the 70s of the XIX century. He formulated his theory based on the laws of communication between the interaction of electric and magnetic forces, the content of which can be represented as follows:

1. Any electric current causes or creates a magnetic field in the space surrounding it. A constant electric current creates a constant magnetic field. But a constant magnetic field (fixed magnet) cannot create an electric field at all (neither constant nor alternating).

2. The resulting alternating magnetic field creates an alternating electric field, which, in turn, creates an alternating magnetic field,

3. The electric field lines are closed on electric charges.

4. The magnetic field lines are closed on themselves and never end, i.e., magnetic charges do not exist in nature.

In D. Maxwell's equations there was a certain constant value C, which indicated that the speed of propagation of electromagnetic waves in a physical field is finite and coincides with the speed of propagation of light in a vacuum, equal to 300 thousand km/s.

Basic concepts and principles of electromagnetism.

D. Maxwell's theory was perceived by some scientists with great doubt. For example, G. Helmholtz (1821-1894) adhered to the point of view according to which electricity is a “weightless fluid” spreading at infinite speed. At his request, G. Hertz (1857-

1894) began an experiment proving the fluid nature of electricity.

By this time, O. Fresnel (1788-1827) showed that light propagates not as longitudinal, but as transverse waves. In 1887, G. Hertz managed to construct an experiment. Light in the space between electric charges propagated in transverse waves at a speed of 300 thousand km/s. This allowed him to say that his experiment eliminates doubts about the identity of light, thermal radiation and wave electromagnetic motion.

This experiment became the basis for the creation of an electromagnetic physical picture of the world, one of the adherents of which was G. Helmholtz. He believed that all physical forces that dominate nature should be explained on the basis of attraction and repulsion. However, creating an electromagnetic picture of the world has encountered difficulties.

1. The main concept of Galileo-Newton mechanics was the concept of matter,

having mass, but it turns out that matter can have a charge.

Charge is the physical property of a substance to create a physical field around itself that has a physical effect on other charged bodies and substances (attraction, repulsion).

2. The charge and mass of a substance can have different values, i.e. they are discrete quantities. At the same time, the concept of a physical field presupposes the transfer of physical interaction continuously from one point to another. This means that electric and magnetic forces are short-range forces because there is no empty space in the physical field that is not filled with electromagnetic waves.

3. In Galileo-Newtonian mechanics, infinitely high speed is possible

physical interaction, it is also stated here that electromagnetic

waves propagate with high but finite speed.

4. Why do the force of gravity and the force of electromagnetic interaction act independently of each other? As we move away from the Earth, gravity decreases and weakens, and electromagnetic signals act in a spacecraft in exactly the same way as on Earth. In the 19th century an equally convincing example could be given without a spaceship.

5. Opening in 1902 P. Lebedev (1866-1912) - a professor at Moscow University - light pressure sharpened the question of the physical nature of light: is it a stream of particles or only electromagnetic waves of a certain length? Pressure, as a physical phenomenon, is associated with the concept of matter, with discreteness - more precisely. Thus, the pressure of light indicated the discrete nature of light as a stream of particles.

6. The similarity of the decrease of gravitational and electromagnetic forces - according to the law

“inversely proportional to the square of the distance” - raised a legitimate question: why the square of the distance, and, for example, not the cube? Some scientists began to talk about the electromagnetic field as one of the states of the “ether” that fills the space between planets and stars.

All these difficulties occurred due to the lack of knowledge about the structure of the atom at that time, but M. Faraday was right when he said that, without knowing how the atom is structured, we can study the phenomena in which its physical nature is expressed. Indeed, electromagnetic waves carry significant information about the processes occurring inside the atoms of chemical elements and molecules of matter. They provide information about the distant past and present of the Universe: about the temperature of cosmic bodies, their chemical composition, distance to them, etc.

7. The following scale of electromagnetic waves is currently used:

radio waves with a wavelength from 104 to 10 -3 m;

infrared waves - from 10-3 to 810-7 m;

visible light - from 8 10-7 to 4 10-7 m;

ultraviolet waves - from 4 10-7 to 10-8 m;

X-ray waves (rays) - from 10-8 to 10-11 m;

gamma radiation - from 10-11 to 10-13 m.

8. As for the practical aspects of the study of electric and magnetic forces, it was carried out in the 19th century. at a rapid pace: the first telegraph line between cities (1844), laying of the first transatlantic cable (1866), telephone (1876), incandescent lamp (1879), radio receiver (1895).

The minimum portion of electromagnetic energy is photon. This is the smallest indivisible amount of electromagnetic radiation.

A sensation at the beginning of the 21st century. is the creation by Russian scientists from Troitsk (Moscow region) of a polymer made of carbon atoms, which has the properties of a magnet. It was generally believed that the presence of metals in a substance was responsible for magnetic properties. Testing of this polymer for metallicity showed that there is no presence of metals in it.

The field variable can be considered formally in the same way as in ordinary quantum mechanics the spatial coordinate is considered, and the quantum operator of the corresponding name is associated with the field variable.

Field paradigm, which represents the entire physical reality at a fundamental level reduced to a small number of interacting (quantized) fields, is not only one of the most important in modern physics, but, perhaps, certainly dominant.

The physical field can thus be characterized as a distributed dynamic system with an infinite number of degrees of freedom.

The role of the field variable for fundamental fields is often played by potential (scalar, vector, tensor), sometimes by a quantity called field strength. (For quantized fields, in a sense, the corresponding operator is also a generalization of the classical concept of a field variable).

Also field in physics they call a physical quantity considered as depending on location: as a complete set, generally speaking, of different values ​​of this quantity for all points of some extended continuous body - a continuous medium, describing in its totality the state or movement of this extended body. Examples of such fields could be:

• temperature (generally speaking different at different points, as well as at different times) in some medium (for example, in a crystal, liquid or gas) - (scalar) temperature field,
• the velocity of all elements of a certain volume of liquid is a vector field of velocities,
• vector field of displacements and tensor field of stresses during deformation of an elastic body.

The dynamics of such fields are also described by partial differential equations, and historically, starting from the 18th century, such fields were the first to be considered in physics.

The modern concept of a physical field grew out of the idea of ​​an electromagnetic field, first realized in a physically concrete and relatively close to modern form by Faraday, and mathematically consistently implemented by Maxwell - initially using a mechanical model of a hypothetical continuous medium - the ether, but then went beyond the use of a mechanical model.

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  Among the fields in physics, the so-called fundamental ones are distinguished. These are fields that, in accordance with the field paradigm of modern physics, form the basis of the physical picture of the world; all other fields and interactions are derived from them. They include two main classes of fields that interact with each other:

  • fundamental fermionic fields, which primarily represent the physical basis for the description of matter,
  • fundamental bosonic fields (including gravitational, which is a tensor gauge field), which are an extension and development of the concept of Maxwellian electromagnetic and Newtonian gravitational fields; The theory is built on them.

  There are theories (for example, string theory, various other unification theories) in which the role of fundamental fields is occupied by slightly different, even more fundamental from the point of view of these theories, fields or objects (and the current fundamental fields appear or should appear in these theories to some approximation as a “phenomenological” consequence). However, such theories are not yet sufficiently confirmed or generally accepted.

  Story

  Historically, among the fundamental fields, the fields responsible for electromagnetic (electric and magnetic fields, then combined into an electromagnetic field) and gravitational interaction were first discovered (precisely as physical fields). These fields were discovered and studied in sufficient detail already in classical physics. At first, these fields (within the framework of the Newtonian theory of gravitation, electrostatics and magnetostatics) looked to most physicists more like formal mathematical objects introduced for formal convenience, and not as a full-fledged physical reality, despite attempts at deeper physical understanding, which remained, however, rather vague or not bearing too significant fruits. But starting with Faraday and Maxwell, the approach to the field (in this case, the electromagnetic field) as a completely meaningful physical reality began to be applied systematically and very fruitfully, including a significant breakthrough in the mathematical formulation of these ideas.

  On the other hand, as quantum mechanics developed, it became increasingly clear that matter (particles) has properties that are theoretically inherent specifically in fields.

  Current state

  Thus, it turned out that the physical picture of the world can be reduced in its foundation to quantized fields and their interaction.

  To some extent, mainly within the framework of the formalism of integration over trajectories and Feynman diagrams, the opposite movement also occurred: fields could be significantly represented as almost classical particles (more precisely, as a superposition of an infinite number of almost classical particles moving along all conceivable trajectories) , and the interaction of fields with each other is like the birth and absorption of each other by particles (also with a superposition of all conceivable variants of this). And although this approach is very beautiful, convenient and allows, in many ways, psychologically to return to the idea of ​​a particle having a well-defined trajectory, it, nevertheless, cannot cancel the field view of things and is not even a completely symmetrical alternative to it (and therefore still closer to a beautiful, psychologically and practically convenient, but still just a formal device, than to a completely independent concept). There are two key points here:

  1. the superposition procedure cannot be “physically” explained in any way in terms of truly classical particles; it just added to an almost classical “corpuscular” picture, without being its organic element; at the same time, from a field point of view, this superposition has a clear and natural interpretation;
  2. the particle itself, moving along one separate trajectory in the path integral formalism, although very similar to the classical one, is still not completely classical: to the usual classical movement along a certain trajectory with a certain momentum and coordinate at each specific moment, even for one single trajectory - you have to add the concept of phase (that is, some wave property), which is completely alien to this approach in its pure form, and this moment (although it is really reduced to a minimum and it’s quite easy to just not think about it) also does not have any organic internal interpretation; but within the framework of the usual field approach such an interpretation again exists, and it is again organic.

  Thus, we can conclude that the approach of integration along trajectories is, although very psychologically convenient (after all, say, a point particle with three degrees of freedom is much simpler than the infinite-dimensional field that describes it) and has proven practical productivity, but still only a certain reformulation, albeit a rather radical, field concept, and not its alternative.

  And although in words in this language everything looks very “corpuscular” (for example: “the interaction of charged particles is explained by the exchange of another particle - the carrier of interaction” or “the mutual repulsion of two electrons is due to the exchange of a virtual photon between them”), however, behind this there are such typical field reality, like the propagation of waves, albeit quite well hidden for the sake of creating an effective calculation scheme, and in many ways providing additional opportunities for qualitative understanding.

  List of fundamental fields

  Fundamental bosonic fields (fields that carry fundamental interactions)

  These fields within the standard model are gauge fields. The following types are known:

  • Electroweak
    • Electromagnetic field (see also Photon)
    • The field is a carrier of the weak interaction (see also W- and Z-bosons)
  • Gluon field (see also Gluon)

  Hypothetical fields

  In a broad sense, hypothetical can be considered any theoretical objects (for example, fields) that are described by theories that do not contain internal contradictions, that do not clearly contradict observations, and that at the same time are capable of producing observable consequences that allow one to make a choice in favor of these theories over those which are now accepted. Below we will talk (and this generally corresponds to the usual understanding of the term) mainly about hypotheticality in this narrower and stricter sense, implying the validity and falsifiability of the assumption that we call a hypothesis.

  In theoretical physics, many different hypothetical fields are considered, each of which belongs to a very specific specific theory (in their type and mathematical properties, these fields can be completely or almost the same as known non-hypothetical fields, and can be more or less very different; in In both cases, their hypothetical nature means that they have not yet been observed in reality, have not been discovered experimentally; in relation to some hypothetical fields, the question may arise as to whether they can be observed in principle, and even whether they can exist at all - for example, if a theory in which they are present suddenly turns out to be internally contradictory).

  The question of what should be considered a criterion that allows one to transfer a certain specific field from the category of hypothetical to the category of real is quite subtle, since confirmation of a particular theory and the reality of certain objects contained in it are often more or less indirect. In this case, the matter usually comes down to some kind of reasonable agreement of the scientific community (whose members are more or less fully aware of what degree of confirmation we are actually talking about).

  Even in theories that are considered to be fairly well confirmed, there is a place for hypothetical fields (here we are talking about the fact that different parts of the theory have been tested with varying degrees of thoroughness, and some fields that play an important role in them, in principle, have not yet appeared in experiment quite definitely, that is, for now they look exactly like a hypothesis invented for certain theoretical purposes, while other fields appearing in the same theory have already been studied well enough to talk about them as reality).

  An example of such a hypothetical field is the Higgs field, which is important in the Standard Model, the remaining fields of which are by no means hypothetical, and the model itself, albeit with inevitable reservations, is considered to describe reality (at least to the extent that reality is known).

  There are many theories containing fields that have (yet) never been observed, and sometimes these theories themselves give such estimates that their hypothetical fields apparently (due to the weakness of their manifestation following from the theory itself) cannot in principle be detected in the foreseeable future (for example, a torsion field). Such theories (if they do not contain, in addition to practically unverifiable ones, also a sufficient number of easier-to-verifiable consequences) are not considered to be of practical interest, unless some non-trivial new method of testing them emerges, allowing one to bypass obvious limitations. Sometimes (as, for example, in many alternative theories of gravity - for example, the Dicke field) such hypothetical fields are introduced, about the strength of which the theory itself cannot say anything at all (for example, the coupling constant of this field with others is unknown and can be quite large , and as small as desired); There is also usually no rush to test such theories (since there are many such theories, and each of them has not proven its usefulness in any way, and is not even formally falsifiable), except in cases where one of them does not begin to seem promising for some reason. resolution of some current difficulties (however, screening out theories on the basis of non-falsifiability - especially due to uncertain constants - is sometimes abandoned here, since a serious good theory can sometimes be tested in the hope that its effect will be discovered, although there are no guarantees of this; This is especially true when there are few candidate theories at all or some of them look particularly fundamentally interesting; also in cases where it is possible to test theories of a wide class all at once according to known parameters, without spending special effort on testing each one separately).

  It should also be noted that it is customary to call hypothetical only those fields that do not have observable manifestations at all (or have them insufficiently, as in the case of the Higgs field). If the existence of a physical field is firmly established by its observable manifestations, and we are only talking about improving its theoretical description (for example, about replacing the Newtonian gravitational field with the field of the metric tensor in General Relativity), then it is usually not accepted to talk about one or the other as hypothetical ( although for the early situation in general relativity one could talk about the hypothetical nature of the tensor nature of the gravitational field).

  In conclusion, let us mention such fields, the type of which is quite unusual, that is, theoretically quite conceivable, but no fields of such types have ever been observed in practice (and in some cases, at the early stages of the development of their theory, doubts about its consistency could arise). These include, first of all, tachyon fields. Actually, tachyon fields can rather be called only potentially hypothetical (that is, not reaching the status educated guess), since the known concrete theories in which they play a more or less significant role, for example, string theory, have not themselves achieved the status of being sufficiently confirmed.

  Even more exotic (for example, Lorentz-non-invariant - violating the principle of relativity) fields (despite being abstractly theoretically quite conceivable) in modern physics can be classified as standing quite far beyond the scope of a reasoned assumption, that is, strictly speaking, they are not considered even as

  Material from Wikipedia - the free encyclopedia

  The physical field can thus be characterized as a distributed dynamic system with an infinite number of degrees of freedom.

  The role of the field variable for fundamental fields is often played by potential (scalar, vector, tensor), sometimes by a quantity called field strength. (For quantized fields, in a sense, the corresponding operator is also a generalization of the classical concept of a field variable).

  Also field in physics they call a physical quantity considered as depending on place: as a complete set, generally speaking, of different values ​​of this quantity for all points of some extended continuous body - a continuous medium, describing in its entirety the state or movement of this extended body. Examples of such fields could be:

  • temperature (generally speaking different at different points, as well as at different times) in some medium (for example, in a crystal, liquid or gas) - (scalar) temperature field,
  • the velocity of all elements of a certain volume of fluid is a vector field of velocities,
  • vector field of displacements and tensor field of stresses during deformation of an elastic body.

  The dynamics of such fields are also described by partial differential equations, and historically, such fields were the first to be considered in physics, starting from the 18th century.

  The modern concept of a physical field grew out of the idea of ​​an electromagnetic field, first realized in a physically concrete and relatively close to modern form by Faraday, mathematically consistently implemented by Maxwell - initially using a mechanical model of a hypothetical continuous medium - the ether, but then went beyond the use of a mechanical model.

  Fundamental fields

  Among the fields in physics, the so-called fundamental ones are distinguished. These are fields that, in accordance with the field paradigm of modern physics, form the basis of the physical picture of the world; all other fields and interactions are derived from them. They include two main classes of fields that interact with each other:

  • fundamental fermion fields, primarily representing the physical basis for the description of matter,
  • fundamental bosonic fields (including gravitational, which is a tensor gauge field), which are an extension and development of the concept of Maxwellian electromagnetic and Newtonian gravitational fields; The theory is built on them.

  There are theories (for example, string theory, various other unification theories) in which the role of fundamental fields is occupied by slightly different, even more fundamental from the point of view of these theories, fields or objects (and the current fundamental fields appear or should appear in these theories to some approximation as a “phenomenological” consequence). However, such theories are not yet sufficiently confirmed or generally accepted.

  Story

  Historically, among the fundamental fields, the fields responsible for electromagnetic (electric and magnetic fields, then combined into an electromagnetic field) and gravitational interaction were first discovered (precisely as physical fields). These fields were discovered and studied in sufficient detail already in classical physics. At first, these fields (within the framework of the Newtonian theory of gravitation, electrostatics and magnetostatics) looked to most physicists more like formal mathematical objects introduced for formal convenience, and not as a full-fledged physical reality, despite attempts at deeper physical understanding, which remained, however, rather vague or not bearing too significant fruits. But starting with Faraday and Maxwell, the approach to the field (in this case, the electromagnetic field) as a completely meaningful physical reality began to be applied systematically and very fruitfully, including a significant breakthrough in the mathematical formulation of these ideas.

  On the other hand, as quantum mechanics developed, it became increasingly clear that matter (particles) has properties that are theoretically inherent specifically in fields.

  Current state

  Thus, it turned out that the physical picture of the world can be reduced in its foundation to quantized fields and their interaction.

  To some extent, mainly within the framework of the formalism of integration along trajectories and Feynman diagrams, the opposite movement also occurred: fields can now be significantly represented as almost classical particles (more precisely, as a superposition of an infinite number of almost classical particles moving along all conceivable trajectories) , and the interaction of fields with each other is like the birth and absorption of each other by particles (also with a superposition of all conceivable variants of this). And although this approach is very beautiful, convenient and allows, in many ways, psychologically to return to the idea of ​​a particle having a well-defined trajectory, it, nevertheless, cannot cancel the field view of things and is not even a completely symmetrical alternative to it (and therefore still closer to a beautiful, psychologically and practically convenient, but still just a formal device, than to a completely independent concept). There are two key points here:

  1. the superposition procedure cannot be “physically” explained in any way in terms of truly classical particles; it just added to an almost classical “corpuscular” picture, without being its organic element; at the same time, from a field point of view, this superposition has a clear and natural interpretation;
  2. the particle itself, moving along one separate trajectory in the path integral formalism, although very similar to the classical one, is still not completely classical: to the usual classical movement along a certain trajectory with a certain momentum and coordinate at each specific moment, even for one single trajectory - you have to add the concept of phase (that is, some wave property), which is completely alien to this approach in its pure form, and this moment (although it is really reduced to a minimum and it’s quite easy to just not think about it) also does not have any organic internal interpretation; but within the framework of the usual field approach such an interpretation again exists, and it is again organic.

  Thus, we can conclude that the approach of integration along trajectories is, although very psychologically convenient (after all, say, a point particle with three degrees of freedom is much simpler than the infinite-dimensional field that describes it) and has proven practical productivity, but still only a certain reformulation, albeit a rather radical, field concept, and not its alternative.

  And although in words in this language everything looks very “corpuscular” (for example: “the interaction of charged particles is explained by the exchange of another particle - the carrier of interaction” or “the mutual repulsion of two electrons is due to the exchange of a virtual photon between them”), however, behind this there are such typical field reality, like the propagation of waves, albeit quite well hidden for the sake of creating an effective calculation scheme, and in many ways providing additional opportunities for qualitative understanding.

  List of fundamental fields

  Fundamental bosonic fields (fields that carry fundamental interactions)

  These fields within the standard model are gauge fields. The following types are known:

  • Electroweak
    • Electromagnetic field (see also Photon)
    • The field is the carrier of the weak interaction (see also W- and Z-bosons)
  • Gluon field (see also Gluon)

  Hypothetical fields

  In a broad sense, hypothetical can be considered any theoretical objects (for example, fields) that are described by theories that do not contain internal contradictions, that do not clearly contradict observations, and that at the same time are capable of producing observable consequences that allow one to make a choice in favor of these theories over those which are now accepted. Below we will talk (and this generally corresponds to the usual understanding of the term) mainly about hypotheticality in this narrower and stricter sense, implying the validity and falsifiability of the assumption that we call a hypothesis.

  In theoretical physics, many different hypothetical fields are considered, each of which belongs to a very specific theory (in their type and mathematical properties, these fields can be completely or almost the same as known non-hypothetical fields, and can be more or less very different; in In both cases, their hypothetical nature means that they have not yet been observed in reality, have not been discovered experimentally; in relation to some hypothetical fields, the question may arise as to whether they can be observed in principle, and even whether they can exist at all - for example, if a theory in which they are present suddenly turns out to be internally contradictory).

  The question of what should be considered a criterion that allows one to transfer a certain specific field from the category of hypothetical to the category of real is quite subtle, since confirmation of a particular theory and the reality of certain objects contained in it are often more or less indirect. In this case, the matter usually comes down to some kind of reasonable agreement of the scientific community (whose members are more or less fully aware of what degree of confirmation we are actually talking about).

  Even in theories that are considered to be fairly well confirmed, there is a place for hypothetical fields (here we are talking about the fact that different parts of the theory have been tested with varying degrees of thoroughness, and some fields that play an important role in them in principle have not yet manifested themselves quite clearly in experiment that is, for now they look exactly like a hypothesis invented for certain theoretical purposes, while other fields appearing in the same theory have already been studied well enough to talk about them as reality).

  An example of such a hypothetical field is the Higgs field, which is important in the Standard Model, the remaining fields of which are by no means hypothetical, and the model itself, albeit with inevitable reservations, is considered to describe reality (at least to the extent that reality is known).

  There are many theories containing fields that have (yet) never been observed, and sometimes these theories themselves give such estimates that their hypothetical fields apparently (due to the weakness of their manifestation following from the theory itself) cannot in principle be detected in the foreseeable future (for example, a torsion field). Such theories (if they do not contain, in addition to practically unverifiable ones, a sufficient number of easier-to-verifiable consequences) are not considered to be of practical interest, unless some non-trivial new way of testing them emerges, allowing one to circumvent obvious limitations. Sometimes (as, for example, in many alternative theories of gravity - for example, the Dicke field) such hypothetical fields are introduced, the strength of which the theory itself cannot say anything at all (for example, the coupling constant of this field with others is unknown and can be quite large , and as small as desired); There is also usually no rush to test such theories (since there are many such theories, and each of them has not proven its usefulness in any way, and is not even formally falsifiable), except in cases where one of them does not begin to seem promising for some reason. resolution of some current difficulties (however, screening out theories on the basis of non-falsifiability - especially due to uncertain constants - is sometimes abandoned here, since a serious good theory can sometimes be tested in the hope that its effect will be discovered, although there are no guarantees of this no; this is especially true when there are few candidate theories at all or some of them look particularly fundamentally interesting; also in cases where it is possible to test theories of a wide class all at once according to known parameters, without spending special effort on testing each one separately).

  It should also be noted that it is customary to call hypothetical only those fields that do not have observable manifestations at all (or have them insufficiently, as in the case of the Higgs field). If the existence of a physical field is firmly established by its observable manifestations, and we are only talking about improving its theoretical description (for example, about replacing the Newtonian gravitational field with the field of the metric tensor in General Relativity), then it is usually not accepted to talk about one or the other as hypothetical ( although for the early situation in general relativity one could talk about the hypothetical nature of the tensor nature of the gravitational field).

  In conclusion, let us mention such fields, the type of which is quite unusual, i.e. theoretically quite conceivable, but no fields of similar types have ever been observed in practice (and in some cases, in the early stages of development of their theory, doubts about its consistency may have arisen). These, first of all, include tachyon fields. Actually, tachyon fields can rather be called only potentially hypothetical (that is, not reaching the status educated guess), because known specific theories in which they play a more or less significant role, such as string theory, have not themselves reached the status of being sufficiently confirmed.

  Even more exotic (for example, Lorentz-non-invariant - violating the principle of relativity) fields (despite being abstractly theoretically quite conceivable) in modern physics can be classified as standing quite far beyond the scope of a reasoned assumption, that is, strictly speaking, they are not considered even as hypothetical ones.

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  Notes

  1. Scalar, vector, tensor or spinor nature; in any case, this quantity, as a rule, can be reduced to representation by a number or some set of numbers (which, generally speaking, take on different values ​​at different points in space).
  2. Depending on the mathematical form of this quantity, scalar, vector, tensor and spinor fields are distinguished.
  3. A field is defined throughout space if it is a fundamental field. Fields such as the fluid flow velocity field or the crystal deformation field are defined over a region of space filled with the corresponding medium.
  4. In modern presentation, this usually looks like a field on (in) space-time, thus the dependence of the field variable on time is considered almost equally with the dependence on spatial coordinates.
  5. Despite the presence of alternative concepts or reinterpretations more or less distant from its standard version, which, however, cannot yet obtain a decisive advantage over it or even equality with it (without, as a rule, going beyond the rather marginal phenomena of the cutting edge of theoretical physics), nor, as a rule, move too far away from it, leaving it in general still (for now) a central place.
  6. In contrast to the class of physical fields from continuum physics mentioned below, which have a fairly clear nature in themselves and are mentioned later in the article.
  7. For various historical reasons, not the least of which was that the concept of the ether psychologically implied a fairly specific implementation that could give experimentally verifiable consequences, but in reality, physically observable non-trivial consequences of some of these models were not discovered, while the consequences of others directly contradicted experiment, therefore the concept of a physically real ether was gradually recognized as unnecessary, and along with it the term itself fell out of use in physics. Not the least role in this was played by the following reason: at the time of the peak of discussion of the applicability of the concept of ether to the description of the electromagnetic field, “matter”, “particles” were considered objects of a fundamentally different nature, therefore their movement through space filled with ether seemed unthinkable or imaginable with enormous difficulties; Subsequently, this reason essentially ceased to exist due to the fact that matter and particles began to be described as field objects, but by this time the word ether was already almost forgotten as a relevant concept in theoretical physics.
  8. Although in some works of modern theorists the use of the concept of ether is sometimes deeper - see Polyakov A.M. "Gauge Fields and Strings".
  9. By state and movement we can mean the macroscopic position and mechanical movement of elementary volumes of the body, and it can also be dependences on spatial coordinates and changes over time in quantities such as electric current, temperature, concentration of a particular substance, etc.
  10. Matter was, of course, known even earlier, but for a long time it was not at all obvious that the concept of a field could be relevant to the description of matter (which was described primarily “corpuscularly”). Thus, the very concept of a physical field and the corresponding mathematical apparatus were historically developed first in relation to the electromagnetic field and gravity.
  11. Except for cases when even the most vague considerations led to serious discoveries, as they served as a stimulus for experimental research that led to fundamental discoveries, as with Oersted's discovery of the generation of a magnetic field by an electric current.
  12. Peter Galison. Einstein's clocks, Poincaré's maps: empires of time. - 2004. - P. 389. - ISBN 9780393326048.
      See Poincaré’s article “Dynamics of the Electron”, section VIII (A. Poincaré. Selected works, vol. 3. M., Nauka, 1974), report by M. Planck (M. Planck. Selected works. M., Nauka, 1975 .) and the article by Einstein and Laube “On pondemotive forces”, § 3 “Equality of action and reaction” (A. Einstein. Collection of scientific works, vol. 1. M., Science, 1965.) (all for 1908).
  13. Some of the properties of field equations were clarified based on fairly general principles, such as Lorentz invariance and the principle of causality. Thus, the principle of causality and the principle of finiteness of the speed of propagation of interactions require that differential equations describing fundamental fields belong to the hyperbolic type.
  14. These statements are true for fundamental fields of the tachyon type. Macroscopic systems exhibiting the properties of tachyon fields are not unusual; the same can be assumed about certain types of excitations in crystals, etc. (in both cases, the place of the speed of light is taken by another quantity).
  15. This is a description of the situation that currently exists. Of course, they do not mean the fundamental impossibility of the emergence of quite sufficiently motivated theories that include such exotic fields in the future (however, such a possibility should hardly be considered too probable).

  Literature

  • Landau, L. D., Lifshits, E. M. Field theory. - 8th edition, stereotypical. - M.: Fizmatlit, 2001. - 534 p. - (“Theoretical Physics”, Volume II). - ISBN 5-9221-0056-4.
  • Pavlov V. P.// Physical encyclopedia / D. M. Alekseev, A. M. Baldin, A. M. Bonch-Bruevich, A. S. Borovik-Romanov, B. K. Vainshtein, S. V. Vonsovsky, A. V. Gaponov -Grekhov, S. S. Gershtein, I. I. Gurevich, A. A. Gusev, M. A. Elyashevich, M. E. Zhabotinsky, D. N. Zubarev, B. B. Kadomtsev, I. S. Shapiro , D. V. Shirkov; under general ed. A. M. Prokhorova. - M.: Soviet Encyclopedia, 1994. - T. 4. - 704 p. - 40,000 copies.

  An excerpt characterizing the Field (physics)

  “Dear birthday girl with the children,” she said in her loud, thick voice, suppressing all other sounds. “What, you old sinner,” she turned to the count, who was kissing her hand, “tea, are you bored in Moscow?” Is there anywhere to run the dogs? What should we do, father, this is how these birds will grow up...” She pointed to the girls. - Whether you want it or not, you have to look for suitors.
  - Well, what, my Cossack? (Marya Dmitrievna called Natasha a Cossack) - she said, caressing Natasha with her hand, who approached her hand without fear and cheerfully. – I know that the potion is a girl, but I love her.
  She took out pear-shaped yakhon earrings from her huge reticule and, giving them to Natasha, who was beaming and blushing for her birthday, immediately turned away from her and turned to Pierre.
  - Eh, eh! kind! “Come here,” she said in a feignedly quiet and thin voice. - Come on, my dear...
  And she menacingly rolled up her sleeves even higher.
  Pierre approached, naively looking at her through his glasses.
  - Come, come, my dear! I was the only one who told your father the truth when he had a chance, but God commands it to you.
  She paused. Everyone was silent, waiting for what would happen, and feeling that there was only a preface.
  - Good, nothing to say! good boy!... The father is lying on his bed, and he is amusing himself, putting the policeman on a bear. It's a shame, father, it's a shame! It would be better to go to war.
  She turned away and offered her hand to the count, who could hardly restrain himself from laughing.
  - Well, come to the table, I have tea, is it time? - said Marya Dmitrievna.
  The count walked ahead with Marya Dmitrievna; then the countess, who was led by a hussar colonel, the right person with whom Nikolai was supposed to catch up with the regiment. Anna Mikhailovna - with Shinshin. Berg shook hands with Vera. A smiling Julie Karagina went with Nikolai to the table. Behind them came other couples, stretching across the entire hall, and behind them, one by one, were children, tutors and governesses. The waiters began to stir, the chairs rattled, music began to play in the choir, and the guests took their seats. The sounds of the count's home music were replaced by the sounds of knives and forks, the chatter of guests, and the quiet steps of waiters.
  At one end of the table the Countess sat at the head. On the right is Marya Dmitrievna, on the left is Anna Mikhailovna and other guests. At the other end sat the count, on the left the hussar colonel, on the right Shinshin and other male guests. On one side of the long table are older young people: Vera next to Berg, Pierre next to Boris; on the other hand - children, tutors and governesses. From behind the crystal, bottles and vases of fruit, the Count looked at his wife and her tall cap with blue ribbons and diligently poured wine for his neighbors, not forgetting himself. The countess also, from behind the pineapples, not forgetting her duties as a housewife, cast significant glances at her husband, whose bald head and face, it seemed to her, were more sharply different from his gray hair in their redness. There was a steady babble on the ladies' end; in the men's room, voices were heard louder and louder, especially the hussar colonel, who ate and drank so much, blushing more and more, that the count was already setting him up as an example to the other guests. Berg, with a gentle smile, spoke to Vera that love is not an earthly, but a heavenly feeling. Boris named his new friend Pierre the guests at the table and exchanged glances with Natasha, who was sitting opposite him. Pierre spoke little, looked at new faces and ate a lot. Starting from two soups, from which he chose a la tortue, [turtle,] and kulebyaki and to hazel grouse, he did not miss a single dish and not a single wine, which the butler mysteriously stuck out in a bottle wrapped in a napkin from behind his neighbor’s shoulder, saying or “drey Madeira", or "Hungarian", or "Rhine wine". He placed the first of the four crystal glasses with the count's monogram that stood in front of each device, and drank with pleasure, looking at the guests with an increasingly pleasant expression. Natasha, sitting opposite him, looked at Boris the way thirteen-year-old girls look at a boy with whom they had just kissed for the first time and with whom they are in love. This same look of hers sometimes turned to Pierre, and under the gaze of this funny, lively girl he wanted to laugh himself, not knowing why.
  Nikolai sat far from Sonya, next to Julie Karagina, and again with the same involuntary smile he spoke to her. Sonya smiled grandly, but apparently was tormented by jealousy: she turned pale, then blushed and listened with all her might to what Nikolai and Julie were saying to each other. The governess looked around restlessly, as if preparing to fight back if anyone decided to offend the children. The German tutor tried to memorize all kinds of dishes, desserts and wines in order to describe everything in detail in a letter to his family in Germany, and was very offended by the fact that the butler, with a bottle wrapped in a napkin, carried him around. The German frowned, tried to show that he did not want to receive this wine, but was offended because no one wanted to understand that he needed the wine not to quench his thirst, not out of greed, but out of conscientious curiosity.

  At the male end of the table the conversation became more and more animated. The colonel said that the manifesto declaring war had already been published in St. Petersburg and that the copy that he himself had seen had now been delivered by courier to the commander-in-chief.
  - And why is it difficult for us to fight Bonaparte? - said Shinshin. – II a deja rabattu le caquet a l "Autriche. Je crins, que cette fois ce ne soit notre tour. [He has already knocked down the arrogance of Austria. I am afraid that our turn would not come now.]
  The colonel was a stocky, tall and sanguine German, obviously a servant and a patriot. He was offended by Shinshin's words.
  “And then, we are a good sovereign,” he said, pronouncing e instead of e and ъ instead of ь. “Then that the emperor knows this. He said in his manifesto that he can look indifferently at the dangers threatening Russia, and that the safety of the empire, its dignity and the sanctity of its alliances,” he said, for some reason especially emphasizing the word “unions”, as if this was the whole essence of the matter.
  And with his characteristic infallible, official memory, he repeated the opening words of the manifesto... “and the desire, the sole and indispensable goal of the sovereign: to establish peace in Europe on solid foundations - they decided to now send part of the army abroad and make new efforts to achieve this intention “.
  “That’s why, we are a good sovereign,” he concluded, edifyingly drinking a glass of wine and looking back at the count for encouragement.
  – Connaissez vous le proverbe: [You know the proverb:] “Erema, Erema, you should sit at home, sharpen your spindles,” said Shinshin, wincing and smiling. – Cela nous convient a merveille. [This comes in handy for us.] Why Suvorov - they chopped him up, a plate couture, [on his head,] and where are our Suvorovs now? Je vous demande un peu, [I ask you,] - he said, constantly jumping from Russian to French.
  “We must fight until the last drop of blood,” said the colonel, hitting the table, “and die for our emperor, and then everything will be fine.” And to argue as much as possible (he especially drew out his voice on the word “possible”), as little as possible,” he finished, again turning to the count. “That’s how we judge the old hussars, that’s all.” How do you judge, young man and young hussar? - he added, turning to Nikolai, who, having heard that it was about war, left his interlocutor and looked with all his eyes and listened with all his ears to the colonel.
  “I completely agree with you,” answered Nikolai, all flushed, spinning the plate and rearranging the glasses with such a decisive and desperate look, as if at the moment he was exposed to great danger, “I am convinced that the Russians must die or win,” he said. feeling the same way as others, after the word had already been said, that it was too enthusiastic and pompous for the present occasion and therefore awkward.
  “C"est bien beau ce que vous venez de dire, [Wonderful! What you said is wonderful],” said Julie, who was sitting next to him, sighing. Sonya trembled all over and blushed to the ears, behind the ears and to the neck and shoulders, in While Nikolai was speaking, Pierre listened to the colonel's speeches and nodded his head approvingly.
  “That’s nice,” he said.
  “A real hussar, young man,” shouted the colonel, hitting the table again.
  -What are you making noise about there? – Marya Dmitrievna’s bass voice was suddenly heard across the table. -Why are you knocking on the table? - she turned to the hussar, - who are you getting excited about? right, you think that the French are in front of you?
  “I’m telling the truth,” said the hussar, smiling.
  “Everything about the war,” the count shouted across the table. - After all, my son is coming, Marya Dmitrievna, my son is coming.
  - And I have four sons in the army, but I don’t bother. Everything is God’s will: you will die lying on the stove, and in battle God will have mercy,” Marya Dmitrievna’s thick voice sounded without any effort from the other end of the table.
  - This is true.
  And the conversation focused again - the ladies at their end of the table, the men at his.
  “But you won’t ask,” said the little brother to Natasha, “but you won’t ask!”
  “I’ll ask,” Natasha answered.
  Her face suddenly flushed, expressing desperate and cheerful determination. She stood up, inviting Pierre, who was sitting opposite her, to listen, and turned to her mother:
  - Mother! – her childish, chesty voice sounded across the table.
  - What do you want? – the countess asked in fear, but, seeing from her daughter’s face that it was a prank, she sternly waved her hand, making a threatening and negative gesture with her head.
  The conversation died down.
  - Mother! what kind of cake will it be? – Natasha’s voice sounded even more decisively, without breaking down.
  The Countess wanted to frown, but could not. Marya Dmitrievna shook her thick finger.
  “Cossack,” she said threateningly.
  Most of the guests looked at the elders, not knowing how to take this trick.
  - Here I am! - said the countess.
  - Mother! what kind of cake will there be? - Natasha shouted now boldly and capriciously cheerfully, confident in advance that her prank would be well received.
  Sonya and fat Petya were hiding from laughter.
  “That’s why I asked,” Natasha whispered to her little brother and Pierre, whom she looked at again.
  “Ice cream, but they won’t give it to you,” said Marya Dmitrievna.
  Natasha saw that there was nothing to be afraid of, and therefore she was not afraid of Marya Dmitrievna.
  - Marya Dmitrievna? what ice cream! I don't like cream.
  - Carrot.
  - No, which one? Marya Dmitrievna, which one? – she almost shouted. - I want to know!
  Marya Dmitrievna and the Countess laughed, and all the guests followed them. Everyone laughed not at Marya Dmitrievna’s answer, but at the incomprehensible courage and dexterity of this girl, who knew how and dared to treat Marya Dmitrievna like that.
  Natasha fell behind only when she was told that there would be pineapple. Champagne was served before the ice cream. The music started playing again, the count kissed the countess, and the guests stood up and congratulated the countess, clinking glasses across the table with the count, the children, and each other. Waiters ran in again, chairs rattled, and in the same order, but with redder faces, the guests returned to the drawing room and the count's office.

  The Boston tables were moved apart, the parties were drawn up, and the Count's guests settled in two living rooms, a sofa room and a library.
  The Count, fanning out his cards, could hardly resist the habit of an afternoon nap and laughed at everything. The youth, incited by the countess, gathered around the clavichord and harp. Julie was the first, at the request of everyone, to play a piece with variations on the harp and, together with other girls, began to ask Natasha and Nikolai, known for their musicality, to sing something. Natasha, who was addressed as a big girl, was apparently very proud of this, but at the same time she was timid.
  - What are we going to sing? – she asked.
  “The key,” answered Nikolai.
  - Well, let's hurry up. Boris, come here,” Natasha said. - Where is Sonya?
  She looked around and, seeing that her friend was not in the room, ran after her.
  Running into Sonya’s room and not finding her friend there, Natasha ran into the nursery - and Sonya was not there. Natasha realized that Sonya was in the corridor on the chest. The chest in the corridor was the place of sorrows of the younger female generation of the Rostov house. Indeed, Sonya in her airy pink dress, crushing it, lay face down on her nanny’s dirty striped feather bed, on the chest and, covering her face with her fingers, cried bitterly, shaking her bare shoulders. Natasha's face, animated, with a birthday all day, suddenly changed: her eyes stopped, then her wide neck shuddered, the corners of her lips drooped.
  - Sonya! what are you?... What, what's wrong with you? Wow wow!…
  And Natasha, opening her big mouth and becoming completely stupid, began to roar like a child, not knowing the reason and only because Sonya was crying. Sonya wanted to raise her head, wanted to answer, but she couldn’t and hid even more. Natasha cried, sitting down on the blue feather bed and hugging her friend. Having gathered her strength, Sonya stood up, began to wipe away her tears and tell the story.
  - Nikolenka is leaving in a week, his... paper... came out... he told me himself... Yes, I still wouldn’t cry... (she showed the piece of paper she was holding in her hand: it was poetry written by Nikolai) I still wouldn’t cry, but you didn’t you can... no one can understand... what kind of soul he has.
  And she again began to cry because his soul was so good.
  “You feel good... I don’t envy you... I love you, and Boris too,” she said, gathering a little strength, “he’s cute... there are no obstacles for you.” And Nikolai is my cousin... I need... the metropolitan himself... and that’s impossible. And then, if mamma... (Sonya considered the countess and called her mother), she will say that I am ruining Nikolai’s career, I have no heart, that I am ungrateful, but really... for God’s sake... (she crossed herself) I love her so much too , and all of you, only Vera... For what? What did I do to her? I am so grateful to you that I would be glad to sacrifice everything, but I have nothing...
  Sonya could no longer speak and again hid her head in her hands and the feather bed. Natasha began to calm down, but her face showed that she understood the importance of her friend’s grief.
  - Sonya! - she said suddenly, as if she had guessed the real reason for her cousin’s grief. – That’s right, Vera talked to you after lunch? Yes?
  – Yes, Nikolai himself wrote these poems, and I copied others; She found them on my table and said that she would show them to mamma, and also said that I was ungrateful, that mamma would never allow him to marry me, and he would marry Julie. You see how he is with her all day... Natasha! For what?…
  And again she cried more bitterly than before. Natasha lifted her up, hugged her and, smiling through her tears, began to calm her down.
  - Sonya, don’t believe her, darling, don’t believe her. Do you remember how all three of us talked with Nikolenka in the sofa room; remember after dinner? After all, we decided everything how it would be. I don’t remember how, but you remember how everything was good and everything was possible. Uncle Shinshin’s brother is married to a cousin, and we are second cousins. And Boris said that this is very possible. You know, I told him everything. And he is so smart and so good,” Natasha said... “You, Sonya, don’t cry, my dear darling, Sonya.” - And she kissed her, laughing. - Faith is evil, God bless her! But everything will be fine, and she won’t tell mamma; Nikolenka will say it himself, and he didn’t even think about Julie.
  And she kissed her on the head. Sonya stood up, and the kitten perked up, his eyes sparkled, and he seemed ready to wave his tail, jump on his soft paws and play with the ball again, as was proper for him.
  - You think? Right? By God? – she said, quickly straightening her dress and hair.
  - Really, by God! – Natasha answered, straightening a stray strand of coarse hair under her friend’s braid.
  And they both laughed.
  - Well, let's go sing "The Key."
  - Let's go to.
  “You know, this fat Pierre who was sitting opposite me is so funny!” – Natasha suddenly said, stopping. - I'm having a lot of fun!
  And Natasha ran down the corridor.
  Sonya, shaking off the fluff and hiding the poems in her bosom, to her neck with protruding chest bones, with light, cheerful steps, with a flushed face, ran after Natasha along the corridor to the sofa. At the request of the guests, the young people sang the “Key” quartet, which everyone really liked; then Nikolai sang the song he had learned again.
  On a pleasant night, in the moonlight,
  Imagine yourself happily
  That there is still someone in the world,
  Who thinks about you too!
  As she, with her beautiful hand,
  Walking along the golden harp,
  With its passionate harmony
  Calling to itself, calling you!
  Another day or two, and heaven will come...
  But ah! your friend won't live!
  And he had not yet finished singing the last words when the young people in the hall were preparing to dance and the musicians in the choir began to knock their feet and cough.

  Pierre was sitting in the living room, where Shinshin, as if with a visitor from abroad, began a political conversation with him that was boring for Pierre, to which others joined. When the music started playing, Natasha entered the living room and, going straight to Pierre, laughing and blushing, said:
  - Mom told me to ask you to dance.
  “I’m afraid of confusing the figures,” said Pierre, “but if you want to be my teacher...”
  And he offered his thick hand, lowering it low, to the thin girl.
  While the couples were settling down and the musicians were lining up, Pierre sat down with his little lady. Natasha was completely happy; she danced with a big one, with someone who came from abroad. She sat in front of everyone and talked to him like a big girl. She had a fan in her hand, which one young lady had given her to hold. And, assuming the most secular pose (God knows where and when she learned this), she, fanning herself and smiling through the fan, spoke to her gentleman.
  - What is it, what is it? Look, look,” said the old countess, passing through the hall and pointing at Natasha.
  Natasha blushed and laughed.
  - Well, what about you, mom? Well, what kind of hunt are you looking for? What's surprising here?

  In the middle of the third eco-session, the chairs in the living room, where the count and Marya Dmitrievna were playing, began to move, and most of the honored guests and old people, stretching after a long sitting and putting wallets and purses in their pockets, walked out the doors of the hall. Marya Dmitrievna walked ahead with the count - both with cheerful faces. The Count, with playful politeness, like a ballet, offered his rounded hand to Marya Dmitrievna. He straightened up, and his face lit up with a particularly brave, sly smile, and as soon as the last figure of the ecosaise was danced, he clapped his hands to the musicians and shouted to the choir, addressing the first violin:
  - Semyon! Do you know Danila Kupor?
  This was the count's favorite dance, danced by him in his youth. (Danilo Kupor was actually one figure of the Angles.)
  “Look at dad,” Natasha shouted to the whole hall (completely forgetting that she was dancing with a big one), bending her curly head to her knees and bursting into her ringing laughter throughout the hall.
  Indeed, everyone in the hall looked with a smile of joy at the cheerful old man, who, next to his dignified lady, Marya Dmitrievna, who was taller than him, rounded his arms, shaking them in time, straightened his shoulders, twisted his legs, slightly stamping his feet, and with a more and more blooming smile on his round face, he prepared the audience for what was to come. As soon as the cheerful, defiant sounds of Danila Kupor, similar to a cheerful chatterbox, were heard, all the doors of the hall were suddenly filled with men's faces on one side and women's smiling faces of servants on the other, who came out to look at the merry master.
  - Father is ours! Eagle! – the nanny said loudly from one door.
  The count danced well and knew it, but his lady did not know how and did not want to dance well. Her huge body stood upright with her powerful arms hanging down (she handed the reticule to the Countess); only her stern but beautiful face danced. What was expressed in the count's entire round figure, in Marya Dmitrievna was expressed only in an increasingly smiling face and a twitching nose. But if the count, becoming more and more dissatisfied, captivated the audience with the surprise of deft twists and light jumps of his soft legs, Marya Dmitrievna, with the slightest zeal in moving her shoulders or rounding her arms in turns and stamping, made no less an impression on merit, which everyone appreciated her obesity and ever-present severity. The dance became more and more animated. The counterparts could not attract attention to themselves for a minute and did not even try to do so. Everything was occupied by the count and Marya Dmitrievna. Natasha pulled the sleeves and dresses of all those present, who were already keeping their eyes on the dancers, and demanded that they look at daddy. During the intervals of the dance, the Count took a deep breath, waved and shouted to the musicians to play quickly. Quicker, quicker and quicker, faster and faster and faster, the count unfolded, now on tiptoes, now on heels, rushing around Marya Dmitrievna and, finally, turning his lady to her place, made the last step, raising his soft leg up from behind, bending his sweaty head with a smiling face and roundly waving his right hand amid the roar of applause and laughter, especially from Natasha. Both dancers stopped, panting heavily and wiping themselves with cambric handkerchiefs.
  “This is how they danced in our time, ma chere,” said the count.
  - Oh yes Danila Kupor! - Marya Dmitrievna said, letting out the spirit heavily and for a long time, rolling up her sleeves.

  While the Rostovs were dancing the sixth anglaise in the hall to the sounds of tired musicians out of tune, and tired waiters and cooks were preparing dinner, the sixth blow struck Count Bezukhy. The doctors declared that there was no hope of recovery; the patient was given silent confession and communion; They were making preparations for the unction, and in the house there was the bustle and anxiety of expectation, common at such moments. Outside the house, behind the gates, undertakers crowded, hiding from the approaching carriages, awaiting a rich order for the count's funeral. The Commander-in-Chief of Moscow, who constantly sent adjutants to inquire about the Count’s position, that evening himself came to say goodbye to the famous Catherine’s nobleman, Count Bezukhim.
  The magnificent reception room was full. Everyone stood up respectfully when the commander-in-chief, having been alone with the patient for about half an hour, came out of there, slightly returning the bows and trying as quickly as possible to pass by the gazes of doctors, clergy and relatives fixed on him. Prince Vasily, who had lost weight and turned pale during these days, saw off the commander-in-chief and quietly repeated something to him several times.
  Having seen off the commander-in-chief, Prince Vasily sat down alone on a chair in the hall, crossing his legs high, resting his elbow on his knee and closing his eyes with his hand. After sitting like this for some time, he stood up and with unusually hasty steps, looking around with frightened eyes, walked through the long corridor to the back half of the house, to the eldest princess.
  Those in the dimly lit room spoke in an uneven whisper to each other and fell silent each time and, with eyes full of question and expectation, looked back at the door that led to the dying man’s chambers and made a faint sound when someone came out of it or entered it.
  “The human limit,” said the old man, a clergyman, to the lady who sat down next to him and naively listened to him, “the limit has been set, but you cannot pass it.”
  “I’m wondering if it’s too late to perform unction?” - adding the spiritual title, the lady asked, as if she had no opinion of her own on this matter.
  “It’s a great sacrament, mother,” answered the clergyman, running his hand over his bald spot, along which ran several strands of combed, half-gray hair.
  -Who is this? was the commander in chief himself? - they asked at the other end of the room. - How youthful!...
  - And the seventh decade! What, they say, the count won’t find out? Did you want to perform unction?
  “I knew one thing: I had taken unction seven times.”
  The second princess just left the patient’s room with tear-stained eyes and sat down next to Doctor Lorrain, who was sitting in a graceful pose under the portrait of Catherine, leaning his elbows on the table.
  “Tres beau,” said the doctor, answering a question about the weather, “tres beau, princesse, et puis, a Moscou on se croit a la campagne.” [beautiful weather, princess, and then Moscow looks so much like a village.]
  “N"est ce pas? [Isn’t that right?],” said the princess, sighing. “So can he drink?”
  Lorren thought about it.
  – Did he take the medicine?
  - Yes.
  The doctor looked at the breget.
  – Take a glass of boiled water and put in une pincee (with his thin fingers he showed what une pincee means) de cremortartari... [a pinch of cremortartar...]
  “Listen, I didn’t drink,” the German doctor said to the adjutant, “so that after the third blow there was nothing left.”
  – What a fresh man he was! - said the adjutant. – And who will this wealth go to? – he added in a whisper.
  “There will be a okotnik,” the German answered, smiling.
  Everyone looked back at the door: it creaked, and the second princess, having made the drink shown by Lorren, took it to the sick man. The German doctor approached Lorrain.

  As soon as we moved on to the physical foundations of the concept of modern natural science, then, as you probably noticed, in physics there are a number of seemingly simple but fundamental concepts, which, however, are not so - easy to understand right away. These include space, time, which are constantly discussed in our course, and now another fundamental concept - field. In the mechanics of discrete objects, the mechanics of Galileo, Newton, Descartes, Laplace, Lagrange, Hamilton and other mechanics of physical classicism, we would agree that the forces of interaction between discrete objects cause changes in the parameters of their motion (speed, momentum, angular momentum), change their energy, do work, etc. And this, in general, was clear and understandable. However, with the study of the nature of electricity and magnetism, an understanding arose that electric charges can interact with each other without direct contact. In this case, we seem to be moving from the concept of short-range action to non-contact long-range action. This led to the concept of field.

  The formal definition of this concept is as follows: a physical field is a special form of matter that connects particles (objects) of matter into unified systems and transmits the action of some particles to others at a finite speed. True, as we have already noted, such definitions are too general and do not always determine the deep and concrete practical essence of the concept. Physicists had difficulty abandoning the idea of ​​physical contact interaction of bodies and introduced models such as electric and magnetic “fluid” to explain various phenomena; to propagate vibrations, they used the idea of ​​mechanical vibrations of particles of the medium - models of ether, optical fluids , caloric, phlogiston in thermal phenomena, describing them also from a mechanical point of view, and even biologists introduced “vital force” to explain processes in living organisms. All this is nothing more than attempts to describe the transmission of action through a material (“mechanical”) medium.

  However, the work of Faraday (experimentally), Maxwell (theoretically) and many other scientists showed that electromagnetic fields exist (including in vacuum) and it is they that transmit electromagnetic oscillations. It turned out that visible light is the same electromagnetic vibrations in a certain range of vibration frequencies. It was found that electromagnetic waves are divided into several types on the vibration scale: radio waves (103 - 10-4), light waves (10-4 - 10-9 m), IR (5 × 10-4 - 8 × 10-7 m), UV (4 ×10-7 - 10-9 m), X-ray radiation (2 ×10-9 - 6 ×10-12 m), γ-radiation (< 6 ×10-12 м).

  So what is a field? It is best to use some kind of abstract representation, and in this abstraction, again, there is nothing unusual or incomprehensible: as we will see later, the same abstractions are used in constructing the physics of the microworld and the physics of the Universe. The easiest way to say that a field is any physical quantity that takes on different values ​​at different points in space. For example, temperature is a field (scalar in this case), which can be described as T = T(x, y, z), or, if it varies over time, T = T (x, y, z , t). There may be pressure fields, including atmospheric air, a field of distribution of people on Earth or different nations among the population, distribution of weapons on Earth, different songs, animals, whatever. There may also be vector fields, such as, for example, the velocity field of a flowing fluid. We already know that speed (x, y, z, t) is a vector. Therefore, we write down the speed of fluid movement at any point in space at moment t in the form (x, y, z, t). Electromagnetic fields can be represented similarly. In particular, the electric field is vector, since the Coulomb force between charges is naturally a vector:

  (1.3.1)
  Much ingenuity has gone into helping people visualize the behavior of fields. And it turned out that the most correct point of view is the most abstract one: you just need to consider the field as a mathematical function of the coordinates and time of some parameter that describes a phenomenon or effect.

  However, we can also assume a clear, simple model of the vector field and its description. You can build a mental picture of the field by drawing vectors at many points in space that determine some characteristic of the process of interaction or movement (for a fluid flow, this is the velocity vector of a moving flow of particles; electrical phenomena can be considered as a model as a charged liquid with its own field strength vector, etc.). Note that the method of determining the parameters of motion through coordinates and momentum in classical mechanics is the Lagrange method, and the determination through velocity vectors and flows is the Euler method. Such a model representation is easy to remember from a school physics course. These are, for example, electric field lines (Fig.). By the density of these lines (more precisely, tangents to them), we can judge the intensity of the fluid flow. The number of these lines per unit area located perpendicular to the lines of force will be proportional to the electric field strength E. Although the picture of the lines of force introduced by Faraday in 1852 is very visual, it should be understood that this is only a conventional picture, a simple physical model ( and therefore abstract), since, of course, there are no lines or threads in nature that extend in space and are capable of influencing other bodies. Lines of force do not actually exist; they only facilitate the consideration of processes associated with fields of forces.

  You can go further in this physical model: determine how much liquid flows in or flows out of a certain volume around a selected point in the field of velocities or intensities. This is due to the understandable idea of ​​the presence in a certain volume of sources of liquid and its drains. Such ideas lead us to the widely used concepts of vector field analysis: flow and circulation. Despite some abstraction, in fact they are visual, have a clear physical meaning and are quite simple. By flow we mean the total amount of liquid flowing out per unit time through some imaginary surface near a point we have chosen. Mathematically it is written like this:

  (1.3.2)
  those. this quantity (flow Фv) is equal to the total product (integral) of the velocity on the surface ds through which the liquid flows.

  The concept of circulation is also associated with the concept of flow. One may ask: does our liquid circulate, does it come through the surface of the selected volume? The physical meaning of circulation is that it determines the measure of movement (i.e., again related to speed) of a fluid through a closed loop (line L, as opposed to flow through surface S). This can also be written down mathematically: circulation along L

  (1.3.3)
  Of course, you can say that these concepts of flow and circulation are still too abstract. Yes, this is true, but it is still better to use abstract representations if they ultimately give the correct results. It’s a pity, of course, that they are an abstraction, but nothing can be done for now.

  However, it turns out that using these two concepts of flow and circulation, one can arrive at Maxwell's famous four equations, which describe almost all the laws of electricity and magnetism through the representation of fields. There, however, two more concepts are used: divergence - divergence (for example, of the same flow in space), describing the measure of the source, and rotor - vortex. But we won’t need them for a qualitative consideration of Maxwell’s equations. Naturally, we will not cite them, much less remember them, in our course. Moreover, from these equations it follows that the electric and magnetic fields are related to each other, forming a single electromagnetic field in which electromagnetic waves propagate at a speed equal to the speed of light c = 3 × 108 m/s. From here, by the way, the conclusion was made about the electromagnetic nature of light.

  Maxwell's equations are a mathematical description of the experimental laws of electricity and magnetism, previously established by many scientists (Amper, Oersted, Bio-Savart, Lenz and others), and in many ways by Faraday, about whom they said that he does not have time to write down what he discovers. It should be noted that Faraday formulated the ideas of the field as a new form of existence of matter, not only at a qualitative, but also at a quantitative level. It is curious that he sealed his scientific notes in an envelope, asking him to open it after his death. This was done, however, only in 1938. Therefore, it is fair to consider the theory of the electromagnetic field to be the Faraday-Maxwell theory. Paying tribute to Faraday’s merits, the founder of electrochemistry and president of the Royal Society of London, G. Davy, for whom Faraday initially worked as a laboratory assistant, wrote: “Although I have made a number of scientific discoveries, the most remarkable thing is that I discovered Faraday.”

  We will not touch here on numerous phenomena related to electricity and magnetism (there are sections in physics for this), but we note that both the phenomena of electro- and magnetostatics, and the dynamics of charged particles in the classical representation are well described by the equations Maxwell. Since all bodies in the micro- and macrocosm are charged in one way or another, the Faraday-Maxwell theory acquires a truly universal character. Within its framework, the movement and interaction of charged particles in the presence of magnetic and electric fields are described and explained. The physical meaning of Maxwell's four equations consists of the following provisions.

  1. Coulomb’s law, which determines the forces of interaction between charges q1 and q2

  (1.3.4)
  reflects the effect of the electric field on these charges

  (1.3.5)
  where is the electric field strength, and is the Coulomb force. From here you can get other characteristics of the interaction of charged particles (bodies): field potential, voltage, current, field energy, etc.

  2. Electric lines of force begin on some charges (conventionally considered to be positive) and end on others - negative, i.e. they are discontinuous and coincide (this is their model meaning) with the direction of the electric field strength vectors - they are simply tangent to the lines of force. Magnetic forces are closed on themselves, have neither beginning nor end, i.e. continuous. This is proof of the absence of magnetic charges.

  3. Any electric current creates a magnetic field, and this magnetic field can be created either by a constant (then there will be a constant magnetic field) and alternating electric current, or by an alternating electric field (alternating magnetic field).

  4. An alternating magnetic field due to the phenomenon of electromagnetic induction by Faraday creates an electric field. Thus, alternating electric and magnetic fields create each other and influence each other. That is why they talk about a single electromagnetic field.

  Maxwell's equations include a constant c, which coincides with amazing accuracy with the speed of light, from which it was concluded that light is a transverse wave in an alternating electromagnetic field. Moreover, this process of wave propagation in space and time continues indefinitely, since the energy of the electric field transforms into the energy of the magnetic field and vice versa. In electromagnetic light waves, the intensity vectors of the electric and magnetic fields oscillate mutually perpendicularly (hence it follows that light is transverse waves), and space itself acts as the carrier of the wave, which is thereby tense. However, the speed of propagation of waves (not only light) depends on the properties of the medium. Therefore, if gravitational interaction occurs “instantaneously”, i.e. is long-range, then the electrical interaction will be short-range in this sense, since the propagation of waves in space occurs at a finite speed. Typical examples are the attenuation and dispersion of light in various media.

  Thus, Maxwell's equations connect light phenomena with electric and magnetic ones and thereby give fundamental importance to the Faraday-Muswell theory. Let us note once again that the electromagnetic field exists everywhere in the Universe, including in different media. Maxwell's equations play the same role in electromagnetism as Newton's equations do in mechanics, and form the basis of the electromagnetic picture of the world.

  20 years after the creation of the Faraday-Maxwell theory in 1887, Hertz experimentally confirmed the presence of electromagnetic radiation in the wavelength range from 10 to 100 m using a spark discharge and recording a signal in a circuit several meters from the spark gap. Having measured the radiation parameters (wavelength and frequency), he found that the speed of wave propagation coincides with the speed of light. Subsequently, other frequency ranges of electromagnetic radiation were studied and developed. It was found that it is possible to obtain waves of any frequency, provided that an appropriate radiation source is available. Electromagnetic waves up to 1012 Hz (from radio waves to microwaves) can be obtained by electronic methods; infrared, light, ultraviolet and x-ray waves can be obtained by atomic radiation (frequency range from 1012 to 1020 Hz). Gamma radiation with an oscillation frequency above 1020 Hz is emitted by atomic nuclei. Thus, it was established that the nature of all electromagnetic radiation is the same and they all differ only in their frequencies.

  Electromagnetic radiation (like any other field) has energy and momentum. And this energy can be extracted by creating conditions under which the field sets bodies in motion. In relation to the determination of the energy of an electromagnetic wave, it is convenient to expand the concept of flow (in this case energy) mentioned by us to the representation of energy flow density, introduced for the first time by the Russian physicist Umov, who, by the way, was also involved in more general issues of natural science, in particular communications living in nature with energy. Energy flux density is the amount of electromagnetic energy passing through a unit area perpendicular to the direction of wave propagation per unit time. Physically, this means that the change in energy within a volume of space is determined by its flow, i.e. Umov vector:

  (1.3.6)
  where c is the speed of light.
  Since for a plane wave E = B and the energy is divided equally between the waves of the electric and magnetic fields, we can write (1.3.6) in the form

  (1.3.7)
  As for the momentum of a light wave, it is easier to obtain it from Einstein’s famous formula E = mc2, obtained by him in the theory of relativity, which also includes the speed of light c as the speed of propagation of an electromagnetic wave, therefore the use of Einstein’s formula here is physically justified . We will deal with the problems of the theory of relativity further in Chapter 1.4. Here we note that the formula E = mc2 reflects not only the relationship between energy E and mass m, but also the law of conservation of total energy in any physical process, and not separately the conservation of mass and energy.

  Then, taking into account that the energy E corresponds to the mass m, the impulse of the electromagnetic wave, i.e. product of mass and speed (1.2.6), taking into account the speed of the electromagnetic wave with

  (1.3.8)
  This distribution is presented for clarity, since, strictly speaking, formula (1.3.8) is incorrect to obtain from Einstein’s relation, since it has been experimentally established that the mass of a photon as a quantum of light is equal to zero.

  From the standpoint of modern natural science, it is the Sun, through electromagnetic radiation, that provides the conditions for life on Earth, and we can quantitatively determine this energy and impulse by physical laws. By the way, if there is a pulse of light, then the light must exert pressure on the surface of the Earth. Why don't we feel it? The answer is simple and lies in the given formula (1.3.8), since the value of c is a huge number. Nevertheless, the pressure of light was discovered experimentally in very subtle experiments by the Russian physicist P. Lebedev, and in the Universe it is confirmed by the presence and position of cometary tails arising under the influence of a pulse of electromagnetic light radiation. Another example confirming that the field has energy is the transmission of signals from space stations or from the Moon to Earth. Although these signals travel at the speed of light c, but with a finite time due to large distances (from the Moon the signal travels 1.3 s, from the Sun itself - 7 s). Question: Where is the radiation energy between the transmitter on the space station and the receiver on Earth? In accordance with the law of conservation, it must be somewhere! And it really is contained in this way precisely in the electromagnetic field.

  Note also that energy transfer in space can only occur in alternating electromagnetic fields when the particle speed changes. With a constant electric current, a constant magnetic field is created, which acts on a charged particle perpendicular to the direction of its movement. This is the so-called Lorentz force, which “twists” the particle. Therefore, a constant magnetic field does not do any work (δA = dFdr) and, therefore, there is no transfer of energy from charges moving in the conductor to particles outside the conductor in the space around through a constant magnetic field. In the case of an alternating magnetic field caused by an alternating electric field, charges in a conductor experience acceleration along the direction of movement and energy can be transferred to particles located in space near the conductor. Therefore, only charges moving with acceleration can transfer energy through the alternating electromagnetic field they create.

  Returning to the general concept of a field as a certain distribution of corresponding quantities or parameters in space and time, we can assume that such a concept is applied to many phenomena not only in nature, but also in the economy or society when using the corresponding physical models. It is only necessary to make sure in each case whether the selected physical quantity or its analogue exhibits such properties that its description using a field model would be useful. Note that the continuity of the quantities describing the field is one of the main parameters of the field and allows the use of the corresponding mathematical apparatus, including the one briefly mentioned above.

  In this sense, it is quite justified to talk about the gravitational field, where the vector of the gravitational force changes continuously, and about other fields (for example, the information field, the field of the market economy, the force fields of works of art, etc.), where forces unknown to us or substances. Having rightfully extended his laws of dynamics to celestial mechanics, Newton established the law of universal gravitation

  (1.3.9)
  according to which the force acting between two masses m1 and m2 is inversely proportional to the square of the distance R between them, G is the gravitational interaction constant. If, by analogy with the electromagnetic field, we introduce the vector of the gravitational field strength, then we can go from (1.3.9) directly to the gravitational field.

  Formula (1.3.9) can be understood as follows: mass m1 creates certain conditions in space to which mass m2 reacts, and as a result experiences a force directed towards m1. These conditions are the gravitational field, the source of which is the mass m1. In order not to write down the force depending on m2 each time, we divide both sides of equation (1.3.9) by m2, considering it as the mass of the test body, i.e. that on which we act (it is assumed that the test mass does not introduce disturbances into the gravitational field). Then

  (1.3.10)
  Essentially, now the right-hand side of (1.3.10) depends only on the distance between the masses m1 and m2, but does not depend on the mass m2 and determines the gravitational field at any point in space distant from the source of gravity m1 at a distance R regardless to whether there is mass m2 there or not. Therefore, we can once again rewrite (1.3.10) so that the mass of the source of the gravitational field has a determining value. Let us denote the right-hand side of (1.3.10) by g:

  (1.3.11)
  where M = m1.
  Since F is a vector, then, naturally, g is also a vector. It is called the gravitational field strength vector and gives a complete description of this field of mass M at any point in space. Since the value of g determines the force acting on a unit of mass, then in its physical meaning and dimension it is acceleration. Therefore, the equation of classical dynamics (1.2.5) coincides in form with the forces acting in the gravitational field

  (1.3.12)
  The concept of lines of force can also be applied to the gravitational field, where the magnitude of the acting forces is judged by their thickness (density). The gravitational force lines of a spherical mass are straight, directed towards the center of a sphere of mass M as a source of gravity, and according to (1.3.10) the interaction forces decrease with distance from M according to the law of inverse proportionality to the square of the distance R. Thus, in Unlike the lines of force of the electric field, which begin on the positive and end on the negative, in the gravitational field there are no specific points where they begin, but at the same time they extend to infinity.

  By analogy with the electric potential (the potential energy of a unit charge located in an electric field), we can introduce the gravitational potential

  (1.3.13)
  The physical meaning of (1.3.13) is that Fgr is the potential energy per unit mass. The introduction of electric and gravitational field potentials, which, in contrast to vector magnitudes of intensities, are scalar quantities, simplifies quantitative calculations. Note that the principle of superposition is applicable to all field parameters, which consists in the independence of the action of forces (intensities, potentials) and the possibility of calculating the resulting parameter (both vector and scalar) by the corresponding addition.

  Despite the similarity of the basic laws of electric (1.3.4) and gravitational (1.3.9) fields and the methodologies for introducing and using the parameters that describe them, it has not yet been possible to explain their essence on the basis of their general nature. Although such attempts, starting from Einstein and until recently, are constantly being made with the goal of creating a unified field theory. Naturally, this would simplify our understanding of the physical world and allow us to describe it uniformly. We will discuss some of these attempts in Chapter 1.6.

  It is believed that gravitational and electric fields act independently and can coexist at any point in space simultaneously without affecting each other. The total force acting on a test particle with charge q and mass m can be expressed by the vector sum u. It makes no sense to sum the vectors, since they have different dimensions. The introduction in classical electrodynamics of the concept of an electromagnetic field with the transfer of interaction and energy through the propagation of waves through space made it possible to move away from the mechanical representation of the ether. In the old concept, the concept of ether as a certain medium that explains the transfer of contact action of forces was refuted both experimentally by Michelson’s experiments in measuring the speed of light, and, mainly, by Einstein’s theory of relativity. It turned out to be possible to describe physical interactions through fields, which is why the characteristics common to different types of fields that we talked about here were formulated. True, it should be noted that now the idea of ​​ether is partly being revived by some scientists on the basis of the concept of physical vacuum.

  So, after the mechanical picture, a new electromagnetic picture of the world was formed by that time. It can be considered as intermediate in relation to modern natural science. Let us note some general characteristics of this paradigm. Since it includes not only ideas about fields, but also new data that had appeared by that time about electrons, photons, the nuclear model of the atom, the laws of the chemical structure of substances and the arrangement of elements in the periodic table of Mendeleev and a number of other results on ways of understanding nature, then, of course, this concept also included the ideas of quantum mechanics and the theory of relativity, which will be discussed further.

  The main thing in this representation is the ability to describe a large number of phenomena based on the concept of field. It was established, in contrast to the mechanical picture, that matter exists not only in the form of a substance, but also a field. Electromagnetic interaction based on wave concepts quite confidently describes not only electric and magnetic fields, but also optical, chemical, thermal and mechanical phenomena. The methodology of field representation of matter can also be used to understand fields of a different nature. Attempts have been made to link the corpuscular nature of micro-objects with the wave nature of processes. It was found that the “carrier” of the interaction of the electromagnetic field is the photon, which already obeys the laws of quantum mechanics. Attempts are being made to find the graviton as a carrier of the gravitational field.

  However, despite significant progress in understanding the world around us, the electromagnetic picture is not free from shortcomings. Thus, it does not consider probabilistic approaches, essentially probabilistic patterns are not recognized as fundamental, Newton’s deterministic approach to the description of individual particles and the strict unambiguity of cause-and-effect relationships are preserved (which is now disputed by synergetics) , nuclear interactions and their fields are explained not only by electromagnetic interactions between charged particles. In general, this situation is understandable and explainable, since every insight into the nature of things deepens our understanding and requires the creation of new adequate physical models.