). [ ]
The easiest way is to visualize the field (when we're talking about, for example, about fundamental fields that do not have an obvious immediate mechanical nature) as a disturbance (deviation from equilibrium, movement) of some (hypothetical or simply imaginary) continuous medium filling all space. For example, as deformation elastic medium, the equations of motion of which coincide with or are close to the field equations of that more abstract field that we want to visualize. Historically, such a medium was called ether, but subsequently the term almost completely fell out of use, and its implied physically meaningful part merged with the very concept of a field. Nevertheless, for a fundamental visual understanding of the concept of a physical field in general terms, such a representation is useful, taking into account the fact that within the framework of modern physics such an approach is usually accepted, by and large, only for illustrative purposes.
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, a generalization of the classical concept of a field variable is also the corresponding operator).
Also field in physics they call physical quantity, considered as depending on place: as a complete set, generally speaking, different meanings this value for all points of some extended continuous body - continuum, describing in its entirety the state or movement of this extended body. Examples of such fields could be:
The dynamics of such fields are also described 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 from the idea electromagnetic field, first realized in a physically concrete and relatively close to modern form Faraday, mathematically consistently realized Maxwell- initially using mechanical model hypothetical continuum - ether, but then went beyond the use of a mechanical model.
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:
There are theories (eg string theory, various others 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.
Historically, among the fundamental fields, the fields responsible for electromagnetic ( electric And magnetic fields then combined into electromagnetic field), And gravitational interaction. 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 in this case- to 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.
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 formalism path integration And Feynman diagrams, the opposite movement also occurred: the fields could be represented to a noticeable extent 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 - as the birth and absorption of each other by particles (also with a superposition of all conceivable variants of it). 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:
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 giving additional features qualitative understanding.
These fields within the standard model are gauge fields. The following types are known:
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, it usually comes down to some kind of reasonable agreement scientific community(whose members are more or less fully aware of what degree of confirmation they 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 to varying degrees thoroughness, and some fields that play an important role in them, in principle, have not yet manifested themselves in the experiment quite definitely, that is, they still look 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 Higgs field, which is important in 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 discovered in the foreseeable future (for example, 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 their checks, allowing you to bypass obvious limitations. Sometimes (as, for example, in many alternative theories of gravity- For example, Dicke's field) such hypothetical fields are introduced, about the strength of manifestation 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 either quite large or arbitrarily small); They are also usually in no hurry to test such theories (since there are many such theories, and each of them has not proven its usefulness in any way, and even formally unfalsifiable), except in cases where one of them does not begin, for some reason, to seem promising for resolving some current difficulties (however, screening out theories on the basis of non-falsifiability - especially due to uncertain constants - is sometimes abandoned here, so how a serious good theory can sometimes be tested in the hope that its effect will be discovered, although there is no guarantee 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 wide class, all at once according to known parameters, without spending special effort on checking 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 GTO), then it is usually not accepted to talk about one or the other as hypothetical (although for the early situation in General Relativity it was possible to 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, first of all, should include tachyon fields. Actually, tachyon fields can rather be called only potentially hypothetical (that is, not reaching the status educated guess), since there are known specific theories in which they play a more or less significant role, for example, and spinor fields.
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
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 the law universal gravity Newton, 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. The sewing machine has a needle and a cutter lathe similar to a plane, an excavator 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 along 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 exposed to it 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.
Field- one of the forms of existence of matter and, perhaps, the most important. The concept of “field” reflects the fact that electric and magnetic forces act at a finite speed over a distance, mutually and continuously generating each other. The field is emitted, propagates at a finite speed in space, and interacts with matter. Faraday formulated the field ideas as new form matter, and put the notes in a sealed envelope, bequeathing it to be opened after his death (this envelope was discovered only in 1938). Faraday used (1840) the idea of the universal conservation and transformation of energy, although the law itself had not yet been discovered.
In his lectures (1845), Faraday spoke not only about the equivalent transformations of energy from one form to another, but also that he had long tried to “discover a direct connection between light and electricity” and that “he succeeded in magnetizing and electrifying a beam of light and illuminating the magnetic force line." He owns a technique for studying the space around a charged body using test bodies, an introduction to the field image power lines. He described his experiments on rotating the plane of polarization of light by a magnetic field. Study of the relationship between electrical and magnetic properties substances led Faraday not only to the discovery of para- and diamagnetism, but also to the establishment of a fundamental idea - the idea of a field. He wrote (1852): “The environment or space surrounding it plays as essential a role as the magnet itself, being part of a real and complete magnetic system.”
Faraday showed that the electromotive force of induction E occurs when magnetic flux changes F(opening, closing, changing current in conductors, approaching or removing a magnet, etc.). Maxwell expressed this fact as follows: E = -dF/dt. According to Faraday, the ability to induce currents manifests itself in a circle around the magnetic resultant. According to Maxwell, an alternating magnetic field is surrounded by a vortex electric field, and the minus sign is associated with Lenz's rule: an induced current arises in such a direction as to prevent the change that generates it. Designation rot - from English. rotor - vortex. In 1846, F. Neumann found that a certain amount of energy must be spent to create an induction current.
In general, the system of equations written by Maxwell in vector form has a compact form:
The electric and magnetic induction vectors (D and B) and the electric and magnetic field strength vectors (E and H) included in these equations are related by the indicated simple relationships with the dielectric constant e and the magnetic permeability of the medium μ. Using this operation means that the magnetic field strength vector rotates around the current density vector j.
According to equation (1), any current causes the appearance of a magnetic field in the surrounding space, direct current - a constant magnetic field. Such a field cannot cause an electric field in the “next” regions, since, according to equation (2), only a changing magnetic field generates a current. Around alternating current an alternating magnetic field is also created, capable of creating in the “next” element of space an electric field of a wave, a continuous wave - the energy of the magnetic field in the void is completely converted into electric energy, and vice versa. Since light travels in the form of transverse waves, two conclusions can be drawn: light is an electromagnetic disturbance; electromagnetic field propagates in space in the form of transverse waves with a speed With= 3 10 8 m/s, depending on the properties of the medium, and therefore “instantaneous long-range action” is impossible. So, in light waves, oscillations are made by the intensity of electric and magnetic fields, and the carrier of the wave is space itself, which is in a state of tension. And due to the displacement current it will create a new magnetic field and so on ad infinitum .
The meaning of equations (3) and (4) is clear - (3) describes Gauss’s electrostatic theorem and generalizes Coulomb’s law, (4) reflects the fact of the absence of magnetic charges. Divergence (from lat. diverge - detect discrepancy) is a measure of the source. If, for example, light rays are not born in glass, but only pass through it, divD = 0. The sun, as a source of light and heat, has a positive divergence, and darkness has a negative one. Therefore the lines of force electric field end on charges whose density is p, and the magnetic ones are closed on themselves and do not end anywhere.
The system of views that formed the basis of Maxwell's equations was called Maxwell's theory of the electromagnetic field. Although these equations have a simple form, the more Maxwell and his followers worked on them, the more profound their meaning was revealed to them. G. Hertz, whose experiments were the first direct proof of the validity of the Faraday-Maxwell theory of the electromagnetic field, wrote about the inexhaustibility of Maxwell’s equations: “You cannot study this amazing theory without at times experiencing the feeling that mathematical formulas live their own life, have their own mind - it seems “that these formulas are smarter than us, smarter even than the author himself, as if they give us more than was originally contained in them.”
The process of field propagation will continue indefinitely in the form of an undamped wave - the energy of the magnetic field in emptiness is completely converted into electric energy, and vice versa. Among the constants included in the equations was the constant c; Maxwell found that its value was exactly equal to the speed of light. It was impossible not to pay attention to this coincidence. So, in light waves, oscillations are made by the intensity of electric and magnetic fields, and the carrier of the wave is space itself, which is in a state of tension.
A light wave is an electromagnetic wave,“running in space and separated from the charges that emitted it,” as Weiskopf put it. He compared Maxwell's discovery in importance to the discovery of Newton's law of gravitation. Newton connected the motion of planets with gravity on Earth and discovered the fundamental laws governing the mechanical movement of masses under the influence of forces. Maxwell connected optics with electricity and derived fundamental laws (Maxwell's equations) governing the behavior of electric and magnetic fields and their interaction with charges and magnets. Newton's works led to the introduction of the concept of the universal law of gravitation, Maxwell's works - the concept of the electromagnetic field and the establishment of the laws of its propagation. If an electromagnetic field can exist independently of a material carrier, then long-range action must give way to short-range action, fields propagating in space at a finite speed. The ideas of displacement current (1861), electromagnetic waves and the electromagnetic nature of light (1865) were so bold and unusual that even the next generation of physicists did not immediately accept Maxwell's theory. In 1888 G. Hertz discovered electromagnetic waves, but such an active opponent of Maxwell’s theory as W. Thomson (Kelvin) could only be convinced by the experiments of P.N. Lebedev, who discovered the existence of light pressure.
In the middle of the 19th century. Maxwell combined electricity and magnetism into a unified field theory. Electric charge is associated with elementary particles, of which the most famous - electron and proton - have the same charge. e, it is a universal constant of nature. In SI = 1.6 10 -19 Cl. Although magnetic charges have not yet been discovered, in theory they are already arising. According to the physicist Dirac, the magnitude of magnetic charges should be a multiple of the electron charge
Further research in the field of the electromagnetic field led to contradictions with the concepts of classical mechanics, which the Dutch physicist X.A. tried to eliminate through mathematical coordination of theories. Lorenz. He introduced coordinate transformations inertial systems, which, unlike the classical Galilean transformations, contained a constant - the speed of light, which communicated with field theory. The time and length scales have changed at speeds close to the speed of light. Physical meaning These Lorentz transformations were explained only by A. Einstein in 1905 in his work “On the Electrodynamics of Moving Bodies,” which formed the basis of the special theory of relativity (STR), or relativistic mechanics.
Natural science not only identifies types of material objects in the Universe, but also reveals the connections between them. The connection between objects in a holistic system is more orderly, more stable than the connection between each element and elements from the external environment. To destroy a system, to isolate one or another element from the system, you need to apply a certain energy to it. This energy has different sizes and depends on the type of interaction between system elements. In the megaworld, these interactions are provided by gravity; in the macroworld, electromagnetic interaction is added to gravity, and it becomes the main one, as stronger. In the microcosm, at the size of an atom, even stronger nuclear interaction appears, ensuring the integrity of atomic nuclei. When moving to elementary particles, the energy of internal bonds, we know that natural substances are chemical compounds of elements built from atoms and collected in the Periodic Table. For some time it was believed that atoms are the elementary building blocks of the universe, but then it was established that the atom represents the “whole Universe” and consists of even more fundamental particles interacting with each other: protons, electrons, neutrons, mesons, etc. The number of particles claiming to be elementary is increasing, but are they really that elementary?
Newtonian mechanics was accepted, but the origin of the forces that cause accelerations was not discussed. Gravitational forces act through emptiness, they are long-range, while electromagnetic forces act through a medium. Currently, all interactions in nature are reduced to four types: gravitational, electromagnetic, strong nuclear and weak nuclear.
Gravity(from lat. gravitas- severity) is historically the first interaction studied. Following Aristotle, they believed that all bodies tend to “their place” (heavy ones - down to the Earth, light ones - up). Physics of the XVII-XVIII centuries. only gravitational interactions were known. According to Newton, two point masses attract each other with a force directed along the straight line connecting them: 
The minus sign indicates that we are dealing with attraction, r- distance between bodies (it is believed that the size of the bodies is much smaller r), t 1 and t 2 - body mass Magnitude G- universal constant that determines the value gravitational forces. If bodies weighing 1 kg are located at a distance of 1 m from each other, then the force of attraction between them is equal to 6.67 10 -11 N. Gravity is universal, all bodies are subject to it, and even the particle itself is the source of gravity. If the value G was greater, the strength would also increase, but G very small and gravitational interaction in the world of subatomic particles it is insignificant, and between macroscopic bodies it is barely noticeable. Cavendish was able to measure the value G, using torsion balances. Versatility is constant G means that anywhere in the Universe and at any moment in time, the force of attraction between bodies weighing 1 kg, separated by a distance of 1 m, will have the same value. Therefore, we can say that the value G determines the structure of gravitating systems. Gravity, or gravitation, is not very significant in the interaction between small particles, but it holds the planets, the entire solar system and galaxies together. We constantly feel gravity in our lives. The law established the long-range nature of the gravitational force and the main property of gravitational interaction - its universality.
Einstein's theory of gravity (GTR) gives different results from Newton's law in strong gravitational fields, in weak ones - both theories coincide. According to GTR, gravity- This is a manifestation of the curvature of space-time. Bodies move along curved trajectories not because gravity acts on them, but because they move in curved space-time. They move “by the shortest path, and gravity is geometry.” The influence of space-time curvature can be detected not only near collapsing objects like neutron stars or black holes. These are, for example, the precession of the orbit of Mercury or the dilation of time on the surface of the Earth (see Fig. 2.3, V). Einstein showed that gravity can be described as the equivalent of accelerated motion.
To avoid the compression of the Universe under the influence of self-gravity and ensure its stationarity, he introduced a possible source of gravity with unusual properties, leading to the “pushing” of matter, rather than to its concentration, and the force of repulsion increases with increasing distance. But these properties can only manifest themselves on a very large scale of the Universe. The repulsive force is incredibly small and does not depend on the repulsive mass; it is represented in the form where T - mass of the repelled object; r- its distance from the repelling body; L- constant. Currently there is an upper limit for L= 10 -53 m -2, i.e. for two bodies weighing 1 kg each, located at a distance of 1 m, the force of attraction exceeds cosmic repulsion by at least 10 25 times. If two galaxies with masses of 10 41 kg are located at a distance of 10 million light. years (about 10 22 m), then for them the forces of attraction would be approximately balanced by the forces of repulsion, if the value L really close to the specified upper limit. This quantity has not yet been measured, although it is important for the large-scale structure of the Universe as fundamental.
Electromagnetic interaction, caused by electric and magnetic charges, is carried by photons. The forces of interaction between charges depend in a complex way on the position and movement of the charges. If two charges q 1 and q 2 motionless and concentrated at points at a distance r, then the interaction between them is electrical and is determined by Coulomb’s law: Depending from charge signs q 1 And q 2 the force of electrical interaction directed along the straight line connecting the charges will be a force of attraction or repulsion. Here, the constant that determines the intensity of the electrostatic interaction is denoted; its value is 8.85 10 -12 F/m. Thus, two charges of 1 C each, separated by 1 m, will experience a force of 8.99 10 9 N. An electric charge is always associated with elementary particles. The numerical value of the charge of the most famous among them - the proton and the electron - is the same: this is the universal constant e = 1.6 10 -19 Grade. The charge of a proton is considered positive, and that of an electron is considered negative.
Magnetic forces are generated electric currents- movement of electric charges. There are attempts to unify theories taking into account symmetries, in which the existence of magnetic charges (magnetic monopoles) is predicted, but they have not yet been discovered. Therefore the value e determines the intensity of magnetic interaction. If electric charges moving with acceleration, they emit - give off energy in the form of light, radio waves or x-rays, depending on the frequency range. Almost all information carriers perceived by our senses are of an electromagnetic nature, although they sometimes manifest themselves in complex forms. Electromagnetic interactions determine the structure and behavior of atoms, keep atoms from decay, and are responsible for the connections between molecules, i.e., for chemical and biological phenomena.
Gravity and electromagnetism are long-range forces that extend throughout the Universe.
Strong and weak nuclear forces- short-range and appear only within the size of the atomic nucleus, i.e. in areas of the order of 10 -14 m.
Weak nuclear interaction is responsible for many processes that cause some types of nuclear decays of elementary particles (for example, (3-decay - the transformation of neutrons into protons) with an almost point-like range of action: about 10 -18 m. It has a stronger effect on the transformations of particles than on their movement, therefore its effectiveness is determined by a constant related to the rate of decay - the universal constant connection g(W), determining the rate of processes such as neutron decay. The weak nuclear interaction is carried out by so-called weak bosons, and some subatomic particles can turn into others. The discovery of unstable subnuclear particles revealed that the weak force causes many transformations. Supernovae are one of the few cases of observed weak interaction.
The strong nuclear interaction prevents the decay of atomic nuclei, and without it, the nuclei would disintegrate due to the forces of electrical repulsion of protons. In some cases, the value is introduced to characterize it g(S), similar to an electric charge, but much larger. The strong interaction carried out by gluons drops sharply to zero outside a region with a radius of about 10 -15 m. It binds together the quarks that make up protons, neutrons and other similar particles called hadrons. They say that the interaction of protons and neutrons is a reflection of their internal interactions, but so far the picture of these deep-seated phenomena is hidden from us. It is associated with the energy released by the Sun and stars, transformations in nuclear reactors and the release of energy. Types listed interactions apparently have a different nature. To date, it is not clear whether all interactions in nature are exhausted by them. The strongest is the short-range strong interaction, the electromagnetic interaction is weaker by 2 orders of magnitude, the weak interaction is weaker by 14 orders of magnitude, and the gravitational interaction is weaker by 39 orders of magnitude. In accordance with the magnitude of the interaction forces, they occur over different times. Strong nuclear interactions occur when particles collide at near-light speeds. The reaction time, determined by dividing the radius of action of the forces by the speed of light, gives a value of the order of 10 -23 s. Weak interaction processes occur in 10 -9 s, and gravitational ones - on the order of 10 16 s, or 300 million years.
The “inverse square law,” according to which point gravitational masses or electric charges act on each other, follows, as P. Ehrenfest showed, from the three-dimensionality of space (1917). In space P measurements, point particles would interact according to the inverse power law ( n- 1). For n = 3, the inverse square law is valid, since 3 - 1 = 2. And with u = 4, which corresponds to the inverse cube law, the planets would move in spirals and quickly fall into the Sun. In atoms with more than three dimensions there would also be no stable orbits, i.e. there would be no chemical processes and no life. Kant also pointed out the connection between the three-dimensionality of space and the law of gravity.
In addition, it can be shown that the propagation of waves in their pure form is impossible in space with an even number of dimensions - distortions appear that disrupt the structure (information) carried by the wave. An example of this is the propagation of a wave over a rubber coating (over a surface of dimension P= 2). In 1955, mathematician H. J. Withrow concluded that since living organisms require the transmission and processing of information, higher forms of life cannot exist in even-dimensional spaces. This conclusion applies to the forms of life and laws of nature known to us and does not exclude the existence of other worlds, of a different nature.
From Newton and P. Laplace, the consideration of mechanics as universal has been preserved physical theory. In the 19th century this place was taken by the mechanical picture of the world, including mechanics, thermodynamics and the kinetic theory of matter, the elastic theory of light and electromagnetism. The discovery of the electron stimulated a revision of ideas. At the end of the century, H. Lorentz built his electron theory to cover all natural phenomena, but did not achieve this. Problems associated with charge discreteness and field continuity, and problems in the theory of radiation (“ultraviolet catastrophe”) led to the creation of a quantum field picture of the world and quantum mechanics. After the creation of SRT, it was expected that the electromagnetic picture of the world, combining the theory of relativity, Maxwell’s theory and mechanics, could provide a universal coverage of the natural world, but this illusion was soon dispelled.
Many theorists have tried to cover gravitation and electromagnetism with unified equations. Under the influence of Einstein, who introduced four-dimensional space-time, multidimensional field theories were built in attempts to reduce phenomena to geometric properties space.
The unification was carried out on the basis of the established independence of the speed of light for different observers moving in empty space in the absence of external forces. Einstein depicted world line object on a plane, where the spatial axis is directed horizontally and the temporal axis is directed vertically. Then the vertical line is the world line of an object that is at rest in a given frame of reference, and the inclined line is the world line of an object moving at a constant speed. A curved world line corresponds to an object moving with acceleration. Any point on this plane corresponds to a position in a given place at a given time and is called event. In this case, gravity is no longer a force acting on the passive background of space and time, but represents a distortion of space-time itself. After all, the gravitational field is the “curvature” of space-time.
To establish a connection between reference systems moving relative to each other, it is necessary to measure spatial intervals in the same units as time ones. The multiplier for such a recalculation can be speed of light, relating distance to the time it takes light to travel this distance. In such a system, 1 m is equal to 3.33 not (1 not = 10 -9 s). Then the world line of the photon will pass at an angle of 45°, and of any material object - at a smaller angle (since its speed is always less speed Sveta). Since the spatial axis corresponds to three Cartesian axes, the world lines of material bodies will be located inside the cone described by the photon world line. Observation results solar eclipse 1919 brought worldwide fame to Einstein. The displacements of stars, which can be seen in the vicinity of the Sun only during an eclipse, coincided with the predictions of Einstein's theory of gravity. So his geometric approach to the construction of the theory of gravity was confirmed by impressive experiments.
In the same 1919, when general relativity appeared, T. Kaluza, a private associate professor at the University of Königsberg, sent Einstein his work, where he proposed fifth Dimension. Trying to find the fundamental principle of all interactions (at that time two were known - gravity and electromagnetism), Kaluza showed that they can be derived uniformly in five-dimensional general relativity. The size of the fifth dimension did not matter for the success of the unification and, perhaps, it is so small that it cannot be detected. Only after two years of correspondence with Einstein was the article published. Swedish physicist O. Klein proposed a modification of the fundamental equation of quantum mechanics with five variables instead of four (1926). He “collapsed” the dimensions of space that we cannot perceive to a very small size (giving the example of a carelessly thrown irrigation hose, which from a distance seems like a winding line, but up close each point turns out to be a circle). The dimensions of these peculiar loops are 10–20 times smaller than the size of an atomic nucleus. Therefore, the fifth dimension is not observable, but it is possible.
Soviet scientists G.A. contributed to the development of the five-dimensional theory. Mandel and V.A. Fok. They showed that the trajectory of a charged particle in five-dimensional space can be strictly described as a geodesic line (from the Greek. geodaisia- land division), or the shortest path between two points on the surface, i.e. the fifth dimension can be physically real. It was not detected due to the Heisenberg uncertainty relation, which represents each particle in the form of a wave packet occupying a region in space, the size of which depends on the energy of the particle (the higher the energy, the smaller the volume of the region). If the fifth dimension is folded into a small circle, then in order to detect it, the particles illuminating it must have high energy. Accelerators produce beams of particles that provide a resolution of 10 -18 m. Therefore, if a circle in the fifth dimension has smaller dimensions, it cannot yet be detected.
Soviet professor Yu.B. Rumer, in his five-dimensional theory, showed that the fifth dimension can be given meaning actions. Attempts immediately appeared to visualize this five-dimensional space, like the earlier four-dimensional space-time introduced by Einstein. One of these attempts is the hypothesis of the existence of “parallel” worlds. It was not difficult to imagine a four-dimensional image of a ball: it is a set of its images at each time point - a “pipe” of balls that stretches from the past to the future. And a five-dimensional ball is already a field, a plane of absolutely identical worlds. In all worlds that have from three to five dimensions, even one cause, even if random, can give rise to several consequences. Six-dimensional The universe built by the outstanding Soviet aircraft designer L.R. Bartini, includes three spatial dimensions and three temporal ones. For Bartini, the length of time is duration, the width is the number of options, the height is the speed of time in each of the possible worlds.
Quantum gravity theory was supposed to connect GTR and quantum mechanics. In a Universe subject to the laws of quantum gravity, the curvature of space-time and its structure must fluctuate; the quantum world is never at rest. And the concepts of past and future, the sequence of events in such a world should also be different. These changes have not yet been detected, since quantum effects appear on extremely small scales.
In the 50s XX century R. Feynman, Y. Schwinger and S. Tomogawa independently created quantum electrodynamics, connecting quantum mechanics with relativistic concepts and explaining many effects obtained in the study of atoms and their radiation. The theory of weak interactions was then developed and it was shown that electromagnetism could be unified mathematically only with the weak force. One of its authors, Pakistani theoretical physicist A. Salam, wrote: “The secret of Einstein’s achievement is that he realized the fundamental importance of charge in gravitational interaction. And until we understand the nature of charges in electromagnetic, weak and strong interactions as deeply as Einstein did for gravity, there is little hope for success in final unification... We would not only like to continue Einstein's attempts in which he failed to succeed , but also include other charges in this program.”
Interest in multidimensional theories was revived, and the works of Einstein, Bergman, Kaluza, Rumer, and Jordan began to be turned again. The works of Soviet physicists (L.D. Landau, I.Ya. Pomeranchuk, E.S. Fradkin) show that at distances of 10 -33 cm, irremovable contradictions appear in quantum electrodynamics (divergences, anomalies, all charges become zero). Many scientists worked on ideas for creating a unified theory. S. Weinberg, A. Salam and S. Glashow showed that electromagnetism and the weak nuclear force can be considered a manifestation of a certain “electroweak” force and that the true carriers of the strong force are quarks. The theory created - quantum chromodynamics- built protons and neutrons from quarks and formed the so-called standard model of elementary particles.
Planck also noted the fundamental role of quantities composed of three constants that define the basic theories - STR (speed of light c), quantum mechanics (Planck's constant h) and Newton's theory of gravity (gravitational constant G). From their combination you can get three quantities (Planckian) With
dimensions of mass, time and length
5 10 93 g/cm 3 . The Planck length coincides with the critical distance at which quantum electrodynamics becomes meaningless. Now the geometry has been determined only at distances of more than 10 - 16 cm, which are 17 orders of magnitude greater than Planck's! The unification of interactions is necessary to eliminate divergences and anomalies in the theory - the problem was the definition of particles as points and their distortion of space-time. And they began to look for it with the help of ideas of higher symmetries. These ideas received a “second wind” in the 80s. XX century in grand unification theories of GUT and supergravity. GUT is a theory that allows us to unify all interactions except gravitational ones. If we manage to combine gravitational interaction with it, we will get the Theory of Everything That Exists (TVS). Then the world will be described uniformly. The search for such a “superpower” continues.
Theories of supergravity use multidimensional constructions inherent in the geometric approach when constructing general relativity. You can build a world from different numbers dimensions (they use 11- and 26-dimensional models), but 11-dimensional ones are the most interesting and beautiful from a mathematical point of view: 7 is the minimum number of hidden dimensions of space-time, which allow the inclusion of three non-gravitational forces in the theory, and 4 are ordinary dimensions of space -time. The four known interactions are treated as geometric structures having more than five dimensions.
Superstring theory has been developed since the mid-80s. XX century along with supergravity. This theory began to be developed by the English scientist M. Green and the American scientist J. Schwartz. Instead of a point, they associated particles with a one-dimensional string placed in a multidimensional space. This theory, by replacing point particles with tiny energy loops, eliminated the absurdities that arise in the calculations. Cosmic strings - these are exotic invisible formations generated by the theory of elementary particles. This theory reflects the hierarchical understanding of the world - the possibility that there is no final basis for physical reality, but only a sequence of smaller and smaller particles. There are very massive particles, and about a thousand particles without mass. Each string having a Planck size (10 -33 cm) can have infinitely many types (or modes) of vibrations. Just as the vibration of the strings of a violin generates various sounds, the vibration of these strings can generate all forces and particles. Superstrings allow us to understand chirality (from the Greek. cheir- hand), while supergravity cannot explain the difference between left and right - it contains equal parts of particles of each direction. Superstring theory, like supergravity, is not associated with experience, but with the elimination of anomalies and divergences, which is more characteristic of mathematics.
American physicist E. Witten concluded that superstring theory is the main hope for the future of physics; it not only takes into account the possibility of gravity, but also asserts its existence, and gravity is a consequence of superstring theory. Its technology, borrowed from topology and quantum field theory, allows the discovery of deep symmetries between high-dimensional entangled knots. The dimension corresponding to the relatively consistent theory was fixed, it is equal to 506.
Using superstring theory, it is possible to explain the “ragged” distribution of matter in the Universe. Superstrings are threads left over from the matter of the newly born Universe. They are incredibly mobile and dense, bending the space around them, forming balls and loops, and massive loops could create a gravitational attraction strong enough to give birth to elementary particles, galaxies and clusters of galaxies. By 1986, many papers on cosmic strings had been published, although they themselves had not yet been discovered. It is believed that superstrings can be found by the curvature of space they cause, acting as a gravitational lens, or by the gravitational waves they emit. The evolution of superstrings is played out on computers, and pictures appear on the display screen that correspond to those observed in space - filaments, layers and giant voids are also formed there, in which there are practically no galaxies.
This extraordinary convergence of cosmology and particle physics in the last 30 years has made it possible to understand the essence of the processes of the birth of space-time and matter in a short interval from 10 -43 to 10 -35 s after the primary singularity, called Big Bang. The number of dimensions 10 (supergravity) or 506 (superstring theory) is not final; more complex geometric images may appear, but many additional dimensions are not directly detectable. The true geometry of the Universe probably does not have three spatial dimensions, which is typical only for our Metagalaxy - the observable part of the Universe.
And all of them, except three, at the time of the Big Bang (10-15 billion years ago) curled up to Planck sizes. On long distances(up to the size of the Metagalaxy 10 28 cm) the geometry is Euclidean and three-dimensional, and on Planck ones it is non-Euclidean and multidimensional. It is believed that the Theories of Everything That Exist (TEC) currently being developed should combine descriptions of all fundamental interactions between particles.
The coincidence of the subject of research changed the established methodology of the sciences. Astronomy was considered an observational science, and accelerators were considered a tool in particle physics. Now they began to make assumptions about the properties of particles and their interactions in cosmology, and it became possible for the current generation of scientists to test them. Thus, it follows from cosmology that the number of fundamental particles should be small. This prediction related to the analysis of the processes of primary fusion of nucleons, when the age of the Universe was about 1 s, and it was made at a time when it seemed that achieving greater powers at accelerators would lead to an increase in the number of elementary particles. If there were many particles, the Universe would be different now.
