A field variable can be considered formally in the same way as a spatial coordinate is considered in ordinary quantum mechanics, and a quantum operator of the appropriate name is associated with a 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, unconditionally dominant.

The physical field, therefore, can 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 the potential (scalar, vector, tensor), sometimes by a quantity called the 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 the 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 totality the state or movement of this extended body. Examples of such fields might be:

• temperature (generally speaking, different at different points, as well as at different times) in a certain medium (for example, in a crystal, liquid or gas) - a (scalar) temperature field,
• the speed 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 is also described by differential equations in partial derivatives , and historically, since the 18th century, such fields were the first to be considered in physics.

The modern concept of the 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 - 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 the fields that, according to 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 interacting with each other:

  • fundamental fermionic 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; theory is based on them.

  There are theories (for example, string theory, various other unification theories), in which the role of fundamental fields is occupied by several other, 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 in 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 the 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. Initially, these fields (within the framework of the Newtonian theory of gravitation, electrostatics and magnetostatics) looked for most physicists rather as formal mathematical objects introduced for formal convenience, and not as a full-fledged physical reality, despite attempts at a deeper physical understanding, which, however, remained rather vague or not bearing very significant fruit. But starting with Faraday and Maxwell, the approach to the field (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 more and more clear that matter (particles) has properties that are theoretically inherent 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 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 such). And although this approach is very beautiful, convenient and allows in many ways to return psychologically 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 is in no way "physically" explicable in terms of truly classical particles, it just added to an almost classical "corpuscular" picture, not being its organic element; at the same time, from the field point of view, this superposition has a clear and natural interpretation;
  2. the particle itself, moving along one separate trajectory in the formalism of the path integral, although very similar to the classical one, is still not completely classical: to the usual classical motion along a certain trajectory with a certain momentum and coordinate at each particular moment, even for one the only trajectory - you have to add the concept of a 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 is quite easy to just not think about it) also does not have any organic internal interpretation; and within the framework of the usual field approach, such an interpretation again exists, and it is again organic.

  Thus, we can conclude that the path integration approach 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 proved 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 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 respects providing additional opportunities for qualitative understanding.

  List of fundamental fields

  Fundamental bosonic fields (fields are carriers of fundamental interactions)

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

  • electroweak
    • Electromagnetic field (see also Photon)
    • Field - carrier of weak interaction (see also W- and Z-bosons)
  • Gluon field (see also Gluon)

  Hypothetical fields

  Hypothetical in a broad sense can be considered any theoretical objects (for example, fields) that are described by theories that do not contain internal contradictions, do not explicitly contradict observations and are capable at the same time of giving observable consequences that make it possible to make a choice in favor of these theories compared to 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 terms of their type and mathematical properties, these fields can be completely or almost the same as known non-hypothetical fields, and can differ more or less strongly; in In both cases, their hypotheticality means that they have not yet been observed in reality, have not been discovered experimentally; in relation to some hypothetical fields, the question may be whether they can be observed in principle, and even whether they can exist at all - for example, if the theory in which they are present suddenly turns out to be internally inconsistent).

  The question of what should be considered a criterion that allows one to transfer a certain field from the category of hypothetical to the category of real is rather thin, since the 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 reasonable agreement of the scientific community (whose members are more or less aware of the degree of confirmation in fact).

  Even in theories that are considered 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 definitely in the experiment, that is, so far they look exactly like a hypothesis invented for one or another theoretical purpose, while other fields appearing in the same theory have already been studied well enough to speak of them as a reality).

  An example of such a hypothetical field is the Higgs field, which is important in the Standard Model, the other 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 (so far) have never been observed, and sometimes these theories themselves give such estimates that their hypothetical fields apparently (due to the weakness of their manifestation, which follows from the theory itself) and cannot in principle be discovered in the foreseeable future (for example, a torsion field). Such theories (if they do not contain, besides practically unverifiable, also a sufficient number of more easily verifiable consequences) are not considered as of practical interest, unless some non-trivial new way of testing them emerges, which allows 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 as large as , and arbitrarily small); they are usually not in a hurry to test such theories either (since there are many such theories, and each of them has not proven its usefulness in any way, and is even formally unfalsifiable), except when 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 because of indefinite constants - is sometimes refused here, since a serious good theory can sometimes be tested in the hope that its effect will be found, although there are no guarantees of this; this is especially true when there are few candidate theories at all, or some of them look especially 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 efforts on testing each one separately).

  It should also be noted that it is customary to call hypothetical only those fields that have no 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, replacing the Newtonian gravitational field with the field of the metric tensor in general relativity), then it is usually not accepted to speak of one or the other as hypothetical ( although for the early situation in general relativity one could speak of the hypothetical nature of the tensor nature of the gravitational field).

  In conclusion, we mention such fields, the very type of which is rather 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 the known concrete theories in which they play a more or less significant role, for example, string theory, have themselves not reached the status of sufficiently confirmed.

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

  one of the main concepts of physics, which arose in the 2nd half. 17th century [although the term "P. f." was introduced into physics much later than English. physicist J.K. Maxwell; in mathematics appearance; the term "field" is associated with the work of the English. mathematician W. R. Hamilton "On Quaternions" (W. R. Hamilton, Lectures on quarternions, Dublin, 1853)]. Since that time, the concept of P. f. repeatedly changed its meaning, retaining, however, at all stages of this change, a close connection with the concept of space, expressed in the use of the concept of P. f. to characterize the spatially continuous distribution of physical. quantities. Representations of modern physics about P. f. unfold along two essentially different lines - classical and quantum. The classical line of development of the concept of P. f. This line begins with Newton's establishment of the law of universal gravitation (1687), which made it possible to calculate the P.f. gravity forces. It continues in the hydrodynamic the works of Euler (50s of the 18th century), who considered the distribution of velocities in a space filled with a moving ideal fluid (velocity field). The greatest merits in the formation of the concept of P. f. belong to English. physicist M. Faraday (30s of the 19th century), who developed in detail the concept of lines of force of P. f. Classic line of development of the concept of P. f. splits into two. The main branch is associated with the study of P. f. electric and magnetic forces (Coulomb's law, 1785), to-rye were considered independent at first, but thanks to the works of dates. physicist H. Oersted (1821), French. physicist A. Ampere (1826) and Faraday (1831), they began to be considered jointly - as components of a single electromagnetic P. f. During this period, the meaning of the concept of P. f. depended on ideas about the nature of the action of forces. In the concept of long-range action, dating back to Newton, the concept of P. f. played help. role, it served only as an abbreviated designation of the region of empty space, in which long-range forces can manifest themselves. Knowing the potential of the P.F., it was possible to calculate at each point in space the force acting on a body placed there, without resorting to the law of interaction of bodies. Bearers of physical attributes. reality (mass, energy, momentum, charge, force) in this concept were bodies interacting at a distance without the help of c.-l. intermediate agents. In the absence of at least one of the interacting bodies, the forces were also absent, i.e. P. f. did not have independence. existence. In the concept of short-range action, originating from Descartes, the interaction was carried out by changing the state of the intermediate medium - the ether, which fills the entire space. The carriers of energy in this concept were not only interactions. bodies, but also the ether surrounding them, so that along with the field of forces it was possible to speak about the field of energy. At the same time, as in mechanical theories explaining the emergence of mechanical forces. displacement and elastic tension of the ether, and in purely electromagnetic theories, which left the ether motionless and not deformable, P. f. was still deprived of independence. existence. Being a characteristic of a change in the state of the ether - a substance that had a primary reality, P. f. had an ontological the status of its attribute, i.e. had only a secondary reality. This change was caused by discrete sources of P. f. - by currents and charges, so that the P. f., inextricably linked with them, in a source-free P. f. broadcast did not exist. The next step in the development of the classic concepts of P. f. associated with the achievements of the theory of free dynamic. electromagnetic P. f. (electromagnetic waves, a special case of which is light), which, being created, can exist regardless of the sources that gave rise to it (Maxwell, 1864; Hertz, 1888). Thanks to this, it became possible to attribute P. f. pulse. However, since the ether continued to perform the function of a material carrier for the dynamic. P. f., the latter was still deprived of independence. existence, so that the impulse P. f. (as well as its energy) was actually a characteristic not of P. f., but of the ether. As a consequence, the expression "energy field" should not be understood in its literal sense, but as a "field of energy". Classic theory of electromagnetic P.f. was completed by the work of A. Einstein on special. Relativity Theory (1905). Depriving the ether of the function to be abs. reference system created the possibility for attributing P. f. independent. existence. Although such a decision was not dictated by necessity, it was nevertheless accepted by the majority of physicists. Having turned from a state of material substance (ether) into independent. material substance, electromagnetic P. f. shared with matter the functions of the carrier of energy, momentum and mass. Energy and momentum continue to be characteristics of motion. [Sometimes the status of a material substance is attributed not to P. f., but to energy. Thus, movement (energy) (see F. Engels, Dialectics of Nature, 1964, pp. 45, 78, 168) is transformed from an attribute into a substance. In this case, P. f. still has no independence. existence, but serves as a characteristic of the continuous distribution of energy in space, which again makes the expression "energy field" more correct than "field energy". The direction that attributes the status of a substance to energy is sometimes identified with energetism).] The second branch of the classical. lines of development of the concept of P. f. associated with advances in theory. P.'s research f. forces of gravity (gravitational P. f.). Beginning with Newton and up to the work of Einstein on the general theory of relativity (10s of the 20th century), gravitation was interpreted on the basis of the concept of long-range forces and could not be included in the framework of the concept of short-range action. Based on the fact of equality of inertial and heavy mass, Einstein formulated the relativistic theory of gravity. P. f., in which both gravitational P. f. and geometrical. Holy Islands of space are described by the same value. This allows us to take a new step in the development of the concept of P. f. compared to what was achieved in the classic. relativistic theory of electromagnetism. Specialist. The theory of relativity for the first time revealed the fundamental role of the electromagnetic P. f. in establishing the metric characteristics of space and time, which, as it turned out, depend on the speed of light. But in it the space-time continuum still remained an independent element of the physical. reality, serving only as an arena for the interaction of P. f. and substances. It could be considered as something absolute, because P. f. and matter existed in space-time. In the general theory of relativity, the space-time aspect of reality is fully expressed by gravity. P. f., depending on four coordinate-parameters (three spatial and one temporal). "... It is a property of this field. If we imagine that the field is removed, then there will be no "space", because space does not have an independent existence" (Einstein?., The essence of the theory of relativity, M., 1955 , p. 147). The same is obviously true of time. Availability in classic physics of two types of physical. realities that differ radically in their spatial structure (P. f. and substances), as well as two qualitatively different types of P. f. (electromagnetic and gravitational) gave rise to numerous. attempts to build a consistent unified theory of P. F., in which gravity and electromagnetism, on the one hand, should not be logically dissociated types of P. F., but different aspects of one, unified P. F.; on the other hand, the particles of matter must be treated in it as special regions of the P. f., so that the P. f. and its sources, treated as singular points (singularities) of P. f., would be unities. means of describing the physical reality. However, the lack of success in follow-up and convince. the implementation of such a program gave rise to strong skepticism in relation to it, so that in present. time it has not many supporters. The quantum line of development of the concept of P. f. This line, continuing into the crust. time, arose in connection with the need to interpret the results of experiments on the study of the photoelectric effect. Until the works of L. de Broglie (1924), the idea of ​​light as a stream of spatially discrete particles (photons), introduced by Einstein in 1905 to explain these experiments, seemed incompatible with the classical. the idea of ​​light as a spatially continuous P. f. De Broglie suggested that each particle (and not just the photon) is associated with a wave parametric function. Wave-particle duality has also become an essential feature in nonrelativistic quantum mechanics. However, the ?-field in it is not so straightforwardly ontologized as in de Broglie and E. Schrödinger (1926, 1952) and D. Bohm (1952), who developed his ideas. According to the Copenhagen interpretation of quantum mechanics, shared in present. time by the vast majority of scientists, the ?-field is a so-called. the field of probability (see Microparticles). In relativistic quantum theory in modern. stage of its development, the quantum theory of wave P. f. is unity. way of describing elementary particles and their interactions. Within its framework, the concept of P. f. is undergoing further development. Thanks to the wave properties of any elementary particles and the quantum (corpuscular) properties of all P. f., each P. f. (in the former, classical sense) is at the same time a collective of particles, and each set of particles (in the former, classical sense) is a P. f. Thus, the relativistic quantum theory on a new basis returns to the ontologization of corpuscular-wave dualism, interpreting the Schrödinger?-field as a classical one. P. f. matter (see E. Henley and W. Thirring, Elementary Quantum Field Theory, Moscow, 1963, p. 19). It is important that the ontological equality of particles and P. f. takes place only when taking into account the so-called. v i r t u a l n y x p a s t and c. If, however, only real particles are taken into account, then P. f. turns out to be ontologically more significant, because it has a vacuum state, in which there are no real particles (but there is an indefinite variable number of virtual particles, the existence of which is manifested in fluctuations of the vacuum state of the P.f.). Quite often carry out distinctions between P. f. particles-sources of interaction and P. f. particles-carriers in interactions. This is due to the interpretation of the interaction between source particles as an exchange of virtual quanta of the P.f. , serving as an interaction carrier. With sufficient intensity of interaction (energy serves as a measure of intensity), virtual quanta can turn into real ones, giving rise to the existence of the so-called. free P. f. Free parametric functions that describe the state of particles before and after interaction are not observable, because observation in quantum mechanics is inseparable from interaction. The latter, with t. sp. quantum theory P. f., is nothing but the transformation of one determinate. P.'s state f. (collection of particles) into another. P.'s interaction f. usually interpreted on the basis of the concept of absorption and emission of particles. These particles can be both real and virtual. For virtual particles, the energy and momentum obey the conservation laws only up to the indeterminacy of the relation, therefore, at small distances, an exchange of a very large number of virtual particles can occur. This leads to the fact that, in the presence of interactions, the simple connection between particles and P. f. noted above is lost. Interacting particles (as well as one real particle interacting with vacuum in the absence of others, as well as with its own PF, of which it itself is a source) are surrounded by a cloud of virtual particles. Strictly speaking, a real particle can no longer be compared with one separate unit. P. f. Dr. In other words, her image includes, to one degree or another, P. f. all other elementary particles. Main difficulties of modern quantum theory of P. f. consist in the absence of methods for the exact solution of the equations of interacting P. f. In quantum electrodynamics (the theory of the interaction of electromagnetic and electron-positron P. f.), the approximate solution of such equations is facilitated by the smallness of the interaction force, which makes it possible to use a simplified model of interaction (perturbation theory). In the theory of strong interactions, where the quantum theory of P. f. represents only a scheme, so far not a single problem has been solved rigorously without the assumption of the smallness of the interaction. Necessity of attraction of all P. f. (including the gravitational one, to which the quantum approach is also applicable) for an accurate description of the interactions of elementary particles gave rise to the desire to build a unified quantum theory. P. f., which would not take from experience the entire spectrum of masses and spins of elementary particles, but would receive it automatically. The most well-known attempt in this direction belongs to Heisenberg (the theory of a single non-linear spipor P. f. - "forematter"), which, however, has not yet brought tangible physical. results. The difficulties mentioned in the quantum theory of P. f. brought to life the idea of ​​replacing attempts to solve equations for operators of P. f. the construction of such a system of equations, which would be based only on the general properties of the scattering matrix (S-matrix), directly linking the state of the free P. f. before and after the interaction and would not pretend to a detailed spatio-temporal description of the processes of interaction. On this path to present. time, some scientists put forward radical demands to completely abandon the use of the concept of P. f. This is done on the basis of the assumption that the concept of the space-time continuum has no physical. meaning in modern microphysics and in its status is similar to the concept of ether in physics of the 19th century. (See G. F. Chew, The dubious role of space-time continuum in microscopic physics, in Science Progress, 1963, v. 51, No 204, p. 529). At the same time, the rejection of the use of spatiotemporal concepts (and, with it, the concept of P. F.) in microphysics, of course, in no way means a rejection of their use in macrophysics (see ibid., E. I. Zimmerman, The macroscopio nature of space-time, in "American Journal of Physics", 1962, v. 30, p. 97). However, most scientists still consider it necessary to use the concept of P. f. (and along with it, of course, the spatio-temporal representation) as ontological. bases for describing the interaction of elementary particles. On this path in the theory of P. f. in particular, an interesting idea arises about the existence in nature of the so-called. compensating and x P. f., each of which is responsible for the preservation of one or another fundamental physical. quantities in interactions. Methodological complex. problems arising from the modern ideas about P. f., is extremely versatile. It involves the problem of interpreting a highly abstract mathematical modern apparatus. theories of P. f. (in particular, this includes the question of the ontological status of virtual particles) and the problem of methods for describing the interaction (Hamiltonian formalism or the S-matrix?). The last problem is similar to the old problem of expressing motion in the logic of concepts, fixed in the aporias of Zeno of Elea: how to describe the interaction - through its results (S-matrix) or through its space-time flow (Hamiltonian formalism). This also includes the problem of the adequacy of the description of interaction on the basis of sep. ideas about P. f. and about its source, set by Pauli back in the 30s. Discussions on all these and many other methodological issues. problems of the theory of P. f. ongoing and far from complete. Lit.: Maxwell D.K., Izbr. op. on the theory of the electromagnetic field, trans. [from English], M., 1954; Einstein?., Infeld L., The evolution of physics, trans. from English, 2nd ed., M., 1956; Ovchinnikov? ?., The concept of mass and energy in their historical. development and philosophy. meaning, M., 1957, p. 177; Markov. ?., Hyperons and K-mesons, Moscow, 1958; his own, O modern. form of atomism, "VF", 1960, No 3, 4; Shteinman R. Ya., Space and time, M., 1962, p. 68, 143; Kuznetsov B.G., Development of physical. ideas from Galileo to Einstein in the light of modern. sciences, M., 1963, ch. 2, 3, 4; Whittaker?., The history of the theories of aether and electricity. The classical theories, L.–, 1951.

  Materialization of spirits and distribution of elephants.
  Entrance tickets from 50 k. to 2 p.
  I. Ilf, E Petrov

  What are fundamental interactions and fundamental fields? Why can fundamental fields be considered one of the constituents of matter?

  Lesson-lecture

  The fact that the field is a special kind of matter can be read in many physics textbooks and even in the encyclopedic dictionary. But explanations for this statement are not always found. Therefore, the meaning of what has been said is often misunderstood. Let's try to understand this and "materialize the field." Note that the above statement does not apply to any fields, but only to fundamental ones. What are fundamental fields?

  Fundamental interactions and fundamental fields. While studying physics, you got acquainted with various forces - the force of elasticity, the force of friction, the force of gravity. Each of these forces characterizes some interaction between bodies. As you know, the development of science has shown that all macroscopic bodies consist of atoms and molecules (more precisely, of nuclei and electrons). It follows from the atomic-molecular model that some of the interactions between macroscopic bodies can be represented as the result of interaction between atoms and molecules or, with even greater depth into the structure of matter, as a result of the interaction between nuclei and electrons that make up macroscopic bodies.

  In particular, such forces as the force of elasticity and the force of friction are the result of forces acting between electrons and nuclei. But it was not possible to reduce gravitational interactions and electromagnetic interactions to some other interactions, although such attempts were made.

  To characterize interactions that are not reducible to other interactions, they began to use the concept fundamental which means "basic".

  As mentioned in the previous paragraph, the fundamental gravitational and electromagnetic interactions can be considered _ on the basis of interaction with the field. The fields corresponding to fundamental interactions began to be called fundamental fields.

  The fundamental interactions are gravitational and electromagnetic interactions.

  The development of science has shown that gravitational and electromagnetic interactions are not the only fundamental interactions. Four fundamental interactions have been discovered so far. We learn about two other fundamental interactions when studying the microworld.

  Electromagnetic and gravitational fields are fundamental fields that cannot be reduced to the motion of any particles.

  Long range and close range. We already know that the interaction between particles (charged and uncharged) can be described using fields, but it is also possible not to introduce the concept of a field. The concept, according to which the interaction between particles is described directly, without introducing the concept of a field, is called the concept of long-range interaction. This name means that the particles interact at a far distance. On the contrary, the second concept, according to which the interaction is carried out through the medium of the field (gravitational and electromagnetic), is called the concept of close action. The meaning of the concept of short-range action lies in the fact that a particle interacts with a field that exists near it, although this field itself can be created by particles that are very far away (Fig. 13).

  Rice. 13. Illustration of interaction based on the concept of long-range action (a) and the concept of short-range action (b. c)

  In the first case (see Fig. 13, a), the charge q is affected by the force F from the charge Q, located at a distance r. In the second case, the charge Q creates a field E(x, y, z) in the space around it. In particular, at a point with coordinates x 0, y 0, z 0, where the charge q is located, a field E (x 0, y 0, z 0) is created (see Fig. 13, b). This field, and not directly the charge Q, interacts with the charge q (see Fig. 13, c).

  Historically, knowledge about nature has developed in such a way that the concept of short-range action, proposed in the 30s. XIX century, by the English physicist M. Faraday, was perceived only as a convenient description.

  The situation fundamentally changed after the discovery of electromagnetic waves propagating at a finite speed - the speed of light. It followed from the theory of electromagnetic waves that any change in the electromagnetic field propagates through space also at the speed of light. Referring to the example shown in Figure 13, we can say that if the charge Q starts moving at some point in time, then the charge q will “feel” a change in the force acting on it not at the same time, but after a time r / s ( c is the speed of light), that is, the time required for an electromagnetic wave to travel from charge Q to charge q.

  The finiteness of the propagation of electromagnetic waves leads to the fact that the description of electromagnetic interaction based on the concept of long-range action becomes inconvenient.

  To understand this, consider the following example. In 1054, a bright star appeared in the sky, the light of which was observed even during the day for several weeks. Then the star died out, and at present, in the region of the celestial sphere where the star was located, a faintly luminous formation is noted, which was called the Crab Nebula. In accordance with modern ideas about the evolution of stars, an outburst of a star occurred, during which its radiation power increased billions of times, after which the star disintegrated. In place of a brightly luminous star, a practically non-radiating neutron star and an expanding cloud of faintly luminous gas were formed.

  From the point of view of the concept of short-range action, the observation of the light of a star is reduced to the following. The charges on the star created a field that reached the Earth in the form of a wave and affected the electrons in the retina of the observer's eye. At the same time, the wave reached the Earth for hundreds of years. People watched the flash of a star when the star itself was no longer there. If we try to describe this observation on the basis of the concept of long-range action, then we have to assume that the charges in the retina of the eye do not interact with the charges of the star, but with those that were once on the star, which no longer exists. Note that during the formation of a neutron star, many charges disappear, since neutrons are formed from electrons and protons - neutral particles that practically do not participate in electromagnetic interaction. Agree that a description based on interaction with what once was, but does not exist at the present time, is “not very convenient”.

  Another reason to recognize the field as material is related to the fact that an electromagnetic wave transfers energy and momentum through space (for more details, see § 57). If the field is not considered material, then it should be recognized that energy and momentum are not associated with something material and are themselves transferred through space.

  The theory of relativity, formulated in 1905 by Albert Einstein, is based on the postulate that there are no interactions (including fundamental ones) propagating faster than light.

  We began this paragraph with the "materialization of spirits." Physicists are witty people, and the concept of "spirits" is already used in modern field theory. It can be said that these spirits have not yet materialized, that is, they are not observed in experience. But the science of fundamental fields has not yet been completed.

  The finiteness of the propagation of fundamental fields and their connection with energy and momentum (the transfer of energy and momentum by these fields) lead to the recognition of these fields as one of the constituents of matter. Matter, thus, is represented by particles (substance) and fundamental fields.

  • What is the meaning of the concepts of "fundamental fields" and "fundamental interactions"?
  • Give examples of fields that are not fundamental.
  • Think and give examples of non-fundamental interactions.