In this formulation, theoretical physics does not follow from “experience”, but is an independent method of studying Nature. However, her area of interest is naturally formed taking into account the results of the experiment and observations.
Theoretical physics does not consider questions like “why should mathematics describe nature?” She accepts as a postulate that, for some reason, mathematical description natural phenomena turns out to be extremely effective, and studies the consequences of this postulate. Strictly speaking, theoretical physics studies not the properties of nature itself, but the properties of the proposed mathematical models. In addition, theoretical physics often studies any models “by themselves,” without reference to specific natural phenomena.
Physical theory
The products of theoretical physics are physical theories. Since theoretical physics works specifically with mathematical models, an extremely important requirement is the mathematical consistency of the completed physical theory. The second mandatory property that distinguishes theoretical physics from mathematics, is the ability to obtain predictions within the theory for the behavior of Nature in certain conditions (that is, predictions for experiments) and, in those cases where the result of the experiment is already known, to agree with the experiment.
The above allows us to outline general structure physical theory. It should contain:
- description of the range of phenomena for which a mathematical model is built,
- axioms defining mathematical model,
- axioms matching (at least some) mathematical objects observable, physical objects,
- immediate consequences of mathematical axioms and their equivalents in real world, which are interpreted as predictions of the theory.
From this it becomes clear that statements like “what if the theory of relativity is wrong?” are meaningless. The theory of relativity, how physical theory, meeting the necessary requirements, already true. If it turns out that it does not agree with experiment in some predictions, then it means that it is not applicable to reality in these phenomena. Search required new theory, and it may happen that the theory of relativity turns out to be some kind of limiting case of this new theory. From a theoretical point of view, this is not a disaster. Moreover, it is now suspected that under certain conditions (at energy densities on the order of Planck's) none existing physical theories will not be adequate.
In principle, a situation is possible when for the same range of phenomena there are several different physical theories leading to similar or coinciding predictions. The history of science shows that such a situation is usually temporary: sooner or later, either one theory turns out to be more adequate than another, or it is shown that these theories are equivalent (see the example of quantum mechanics below).
Construction of physical theories
Fundamental physical theories, as a rule, are not derived from already known ones, but are built from scratch. The first step in such a construction is the real “guessing” of which mathematical model should be taken as a basis. It often turns out that to build a theory, a new (and usually more complex) mathematical apparatus is required, unlike that used in theoretical physics elsewhere. This is not a whim, but a necessity: usually new physical theories are built where all previous theories (that is, those based on the “usual” hardware) have shown their inconsistency in describing nature. Sometimes it turns out that the corresponding mathematical apparatus is not available in the arsenal of pure mathematics, and it has to be invented.
Additional, but optional, criteria when constructing a “good” theory can be the concepts
- "mathematical beauty"
- "Occam's razor", as well as the generality of the approach to many systems,
- the ability not only to describe existing data, but also to predict new ones.
- the possibility of reduction into any already well-known theory in any of them general area applicability ( principle of correspondence),
- the opportunity to find out within the theory itself its scope of applicability. So, for example, classical mechanics “does not know” the limits of its applicability, but thermodynamics “knows” the limit within which it should not work.
Examples of fundamentally new physical theories
- Classical mechanics. It was during the construction of classical mechanics that Newton was faced with the need to introduce derivatives and integrals, that is, he created differential and integral calculus.
- General theory of relativity, in the formulation of which it is postulated that empty space also has certain non-trivial geometric properties, and it can be described by methods of differential geometry.
- Quantum mechanics . After classical physics couldn't describe quantum phenomena, attempts were made to reformulate the very approach to describing the evolution of microscopic systems. Schrödinger succeeded in this, who postulated that each particle is associated new object- wave function, as well as Heisenberg, who postulated the existence of a scattering matrix. However, von Neumann found the most successful mathematical model for quantum mechanics (the theory of Hilbert spaces and operators acting in them) and showed that both Schrödinger wave mechanics and Heisenberg matrix mechanics are only variants of this theory, obtained by adding optional words to the theory. Von Neumann's formulation is “better” than the formulations of Schrödinger and Heisenberg, since it discards everything superfluous and unimportant.
- Currently, we are apparently on the verge of creating another fundamentally new theory, M-theory, which would unite all five superstring theories that have been constructed. The existence of M-theory has been suspected for a long time, but it has not yet been possible to formulate it. E. Witten, a leading specialist in this field, expressed the idea that the mathematical apparatus necessary for its construction has not yet been invented.
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Modern physics is an extremely ramified branch of knowledge, and based on certain criteria it is divided into a number of sections. For example, according to the objects of research, physics is distinguished elementary particles, atomic nucleus, atomic physics, molecular physics, physics solids, liquids and gases, plasma physics and physics of cosmic bodies.
Physics can be subdivided according to the processes or forms of motion of matter being studied: mechanical movement; thermal movement; electromagnetic processes; gravitational phenomena; processes caused by strong and weak interactions. The division of physics according to the processes being studied shows that in modern physics they are dealing not with a disparate set of many unrelated or almost unrelated laws, but with a small number of fundamental laws or fundamental physical theories covering vast areas of phenomena. In these theories in the most complete and general form objective processes in nature are reflected.
Physical theory is one of the elements of the system methodological knowledge, This complete system physical knowledge, which fully describes a certain range of phenomena and is one of the structural elements of the physical picture of the world.
Fundamental theories of dynamic type include: classical Newtonian mechanics, mechanics continuum, thermodynamics, Maxwell's macroscopic electrodynamics, theory of gravitation. TO statistical theories include: classical statistical mechanics (or more generally - statistical physics), quantum mechanics, quantum statistics, quantum electrodynamics and relativistic quantum theories of other fields.
The school physics course is structured around four fundamental physical theories: classical mechanics, molecular kinetic theory, electrodynamics, quantum theory. Theoretical core school course Physics embodies the four indicated fundamental theories, specially adapted for the school course. This makes it possible to identify general directions in a physics course in the form of educational and methodological lines and then form all the material around these lines. Such generalization educational material allows students to develop adequate ideas about the structure modern physics, as well as the implementation of a theoretical method of teaching.
Generalization of educational material is aimed at ensuring high-quality assimilation of the knowledge system, which is scientific base general polytechnic education, to ensure efficiency educational process and deep and integral perception of a certain field of knowledge; on the formation and development of a creative, scientific and theoretical way of thinking.
Based on the work of V.F. Efimenko, V.V. Multanovsky identified the following structural elements physical theory: foundation, core, consequences and interpretations.
Generalization at the level of physical theory in a school physics course unfolds in accordance with the stages of the cycle scientific knowledge, differing from generalizations at the level of concept and law in volume: the materials of an entire section of the course should be grouped around the core of the theory. The use of generalizations at the level of theory would solve the issue of generalization of knowledge. However, the use of generalizations in a school course at the level of fundamental theories encounters a number of difficulties. They consist mainly of inconsistency mathematical knowledge students of the complex mathematical apparatus used in physical theories. It follows that for a school course, physical theory should be specially constructed as educational system knowledge that has a structure theoretical generalization in accordance with the laws of knowledge, solving a limited but sufficient circle by elementary means specific tasks. At the same time, the basic concepts, ideas, models of material objects and their interactions must correspond modern level science and provide qualitative explanations for a wide range of physical phenomena.
It should be noted that generalizations in different sections of a high school physics course are not equivalent. If classical mechanics presented in the classical form of theoretical generalization, then in the section “ Molecular physics» generalizations are not all-encompassing. There are no theoretical nuclei identified in school “Electrodynamics”, “Oscillations and Waves”, “Quantum Physics”.
This means that the structure of classical mechanics and molecular kinetic theory can be most fully considered within the framework of a school physics course. Fully expand the structure, for example, like this fundamental theory How classical electrodynamics is not possible (in particular, due to the student’s insufficient mathematical skills). When studying physics in high school The fundamental physical theory “classical mechanics” has the following components:
| CLASSICAL MECHANICS | |||
| Base | Core | Consequences | Interpretation |
| Empirical basis: observation of phenomena (movement of bodies, free fall, pendulum swing...) Models: mat. point, absolute solid body System of concepts: x, l, s, v, a, m, F, p… Kinematic equations of motion | Laws: Newton's laws, abs. TV bodies, the law of universal gravitation. Conservation laws: ZSE, ZSI, ZSMI Principles: long-range action, independence of the action of forces, Galilean relativity. Postulates: homogeneity and isotropy of space, homogeneity of time. Fund. physical constants: gravitational constant | Explanation various types motion Solution of straight line and inverse problem mechanics Application of laws in technology (space, airplanes, transport...) Prediction: Discovery of the planets Neptune and Pluto. | Interpretation of basic concepts and laws. Limits of applicability of the theory: macroscopic bodies v << c |
When studying physics, it is important to note that there are diverse connections between physical theories that occur at different levels. They manifest themselves primarily in the fact that there are concepts common to all theories (speed, mass, momentum, etc.), general laws (the law of conservation of energy-momentum). Connections between theories are also carried out at the level of general physical principles, which currently have the status of methodological general scientific principles. These include the principles of correspondence, complementarity, symmetry and causation.
V.N.Guskov
Accepted abbreviations:
CBN is the concept of direct proximity action.
FO - a physical object (any physical formation: field, particle, atom, etc.).
From the general picture of the subject’s worldview, a number of ideas related to physical nature can be identified. Expressed in the form of a series of agreed upon provisions, they will represent one or another worldview concept.
Any fundamental physical theory has such a philosophical conceptual basis.
Therefore, whether we like it or not, physics as a theoretical science begins not with mathematical formulas, but with the identification of the most general laws of the physical world.
Any physical theory is built on the basis of the conscious or intuitive ideas of its creators about the general structure of the physical world.
The worldview positions of the authors of physical theory are decisive in the formation of their views on the specifics of specific physical phenomena and the structure of the FO. All experimental data are also perceived and explained from these positions.
The problem is that there is no connection between the conceptuality of the philosophical foundations of physics and their regularity, strict correspondence with physical reality. Philosophical concepts can be (despite all their external scientificity) very far from physical reality. (It is for this reason that physicists try to stay away from philosophical verbiage).
Nevertheless, nature has general fundamental laws, and relying on them is the primary task of theoretical physics.
Conceptual in Newtonian mechanics were the provisions on the existence of physical corpuscles (indivisible particles), bodies consisting of them and emptiness filling the space between them. The instantaneity of action between distant bodies through emptiness was also affirmed.
Thanks to the instantaneity of long-range action, the simultaneity of actions in interaction was ensured, which made it possible to see a single physical process in the interaction.
The theoretical “viability” of the concept of instantaneous action at a distance is connected with this. This view of interaction allowed the successful development of not only classical mechanics, but also other areas of physical science, including the emerging theory of electromagnetism.
This the purely formal unity of actions in interaction is reflected in Newton’s third law. The formalism of this law consists in the absence of explanations reasons for unity actions. He simply stated the fact of the observed simultaneity of actions.
In fact, of course, the instantaneousness of actions had no direct relation to the objective interdependence of actions in interaction inherent in them by nature. In fact, no action simply can occur without a strictly corresponding reaction.
This circumstance does not allow you to arbitrarily separate actions from each other, to see in them separate, independent physical relationships, and especially phenomena. However, there were no clear ideas about the interdependence of actions at that time, and the observed simultaneity of actions was explained by the instantaneity of long-range action through emptiness.
In the course of further historical development, a change occurred in the conceptual basis of physical theory. The concept of long-range action through emptiness has been replaced by the concept of long-range action through the material environment (intermediary).
In modern physics it wrong called the concept of short-range action.
The basis for the emergence of a new concept was Faraday’s assumption about the existence of field matter filling, as previously believed, empty space. This hypothesis was later confirmed in Hertz's experiments. Maxwell, performing a mathematical formulation of Faraday's field hypothesis, came to the conclusion that the speed of propagation of physical processes in the field environment is finite.
All this put an end to the concept of instantaneous long-range action through emptiness. It should be noted, however, that in these progressive views of physical nature no objective reasons
to reject the simultaneity of actions in interaction.
On the contrary(!), if we think logically, then the fact of the materiality of space should lead to the conclusion about immediate (direct) contact of bodies previously separated by emptiness.
The materialization of physical space allows us to see physical bodies in bodies that were previously strictly delimited from each other. systems, which include fields as missing, previously unnoticed and therefore supposedly absent, elements.
But the opposite happened - the fields, or rather the processes occurring in them, were perceived as intermediaries between objects. In material processes perceived as actions the void that previously separated the bodies has materialized, becoming insurmountable barrier for their direct interaction.
As a result, along with the “soap foam” of instant long-range action, the “child” was thrown out - a formally correct understanding of the interaction process.
The affirmation of the material mediation of action has led to the emergence of many problems. Let's pay attention to some of them.
1. The field as an intermediary (carrier of action) cannot be an element of the physical system: body + field.
Having recognized the field as a full-fledged element of the system, it is necessary to recognize that the system directly interacts with surrounding objects, as a result of which mediation will disappear.
2. If the material field is a “carrier” of action, then the entire matter must be divided into two types. On matter, which itself is actually can't act, but can perceive the impact- these are all material formations. And on the matter that transfers the action and has a direct(!) effect, but cannot perceive opposition- these are the fields.
This is exactly how the mechanism of interaction between electrically charged bodies is explained - the field of each of them acts on another body, but the fields themselves do not interact with each other, although it seems exist in the same space.
3. Newton’s law of interaction stops “working.” Actions turn out to be unrelated to each other, their coincidence in time and space is random and unpredictable.
As a result interaction as a full-fledged physical phenomenon disappears from the theory
. (Just from theory(!), in physical nature it has been and remains the main element of any physical relationship).
As noted above, the fact of the finite speed of propagation of physical processes is used as the main argument against instantaneous long-range action, and at the same time against the reality of full interaction. However, in reality this argument doesn't work against interaction.
Action and reaction in interaction“simultaneous” not because the speed of their “propagation” is instantaneous, but because they are not only unthinkable without each other, but also really cannot be implemented on one's own .
Any action can arise only when there is a reaction and it disappears along with it
. If we talk about some sequence in the onset of “events”: action - reaction, then it absolutely absent.
And the point is not that they begin and end at the same time, but that they represent one objectively indivisible whole (event)
, where time (as well as space) is one for them.
Therefore, the idea of a possible sequential development of events such as: the emergence of an action – its spread – implementation – the emergence of counteraction, etc. not true. And the fact that a FO can, for example, emit a photon, which only after a certain period of time reaches another object and comes into contact with it, in this context does not mean anything, since this process is not an action.
Action is inextricably linked not only with reaction, but also with the active object, manifestation of content which it is.
Therefore, if we claim that at some point in space-time a specific object performs an action, then, consequently, his content and he himself(!) are there. Otherwise it can not be!
There is a space-time zone directly connected with both interacting objects, in which the “mystery” of interaction occurs, expressed in the transformation of interacting parties
. This area is shared and cannot be removed from them.
That. It is impossible to identify the consistent development of a specific process (such as the emission of a photon - its movement in material space - absorption or reflection by another object) with a single action.
This process may involve many sequential interactions, but not actions.
To see it as a single action is only possible abstracting from its specific content. Naturally, such an abstract “action” is not a reflection of a real physical phenomenon and cannot be identified with it.
In fact action is a side of an objectively indivisible single process of interaction and it, as a physical phenomenon, does not exist in nature.
Conclusion - in the formation of the fundamental concept of modern theoretical physics (the concept of indirect action) the lack of serious philosophical analysis, the necessity of which was pointed out by the far-sighted Maxwell.
The question arises: can a physical theory formed on the basis of an internally contradictory concept that does not reflect reality to the maximum extent possible be correct? The answer is obvious - no.
Consequences for theoretical physics of such an unprofessional approach to the formation of a fundamental concept catastrophic. In her constructions, she moves further and further away from reality, gradually plunging into the world pure abstractions.
Now let's turn to the concept of direct proximity action (NDA), which is outlined in one of the first articles on this site.
It is also ideological and can be used as a basis for the formation of a physical theory. How is it different from the concepts discussed above and how is it similar to them?
According to the author, it is devoid of a number of significant shortcomings of its predecessors and at the same time relies on everything rational that was in them.
From the concept of instantaneous action at a distance, she uses the proposition about the equality and simultaneity of actions in interaction, and from the concept of indirect action the proposition about the materiality of physical space.
On the other hand, the KNB refused to recognize emptiness as a physical factor existing along with matter and the idea of action as an independent physical process.
In the NSC, the provision on equality and simultaneity of actions in interaction and the provision on the materiality of physical space were further developed.
It's already in there not an action, but interaction is considered as an elementary act of any physical process
. Reveals the transformative essence of physical interaction.
This point of view on the nature of physical interaction is not “made up”, but arose as the only possible option for explaining the mechanism of movement of physical objects in material space.
It turned out that the opposing parties in interaction (which are the content of interacting objects) transform each other “in their own image and likeness.”
As a result of interaction between the Federal District as if change their content. And if the entire content of an object undergoes transformation, then it is accordingly completely moved to the adjacent area of material space.
In turn, understanding interaction as a transformative process entailed a change in ideas about what FO actually is.
It turned out that if we take into account the transformative nature of physical interaction, then it is impossible to imagine the FO as some kind of substance education associated once and for all with concrete matter. What does it mean?
This means that the movement of the FO in material space is the process of moving a certain states of matter in matter
, and not matter itself as such.
Accordingly all attributes inherent in the FO(such as mass, energy, momentum, etc.) also do not move in space, but appear (and disappear) again and again at each adjacent point of material space in the course of transformative interactions.
It only remains to add that, according to the CBN, the absolute materiality of the physical world presupposes not just the materiality of physical space, but something more, which ensures the actual transition of the concept of “space” from the category of defining (fundamental) concepts to the category of derivatives.
Spatiality becomes just qualitative indicator of matter(its property). Therefore it is more correct to see not matter(as a kind of geometric volume filler) in space, A spatial matter.
Accordingly, all geometric indicators now characterize not some abstract space that exists in itself, but namely matter with the property of spatiality.
Everything new in the idea of physical nature associated with the transformative process of interaction is perhaps the most difficult element of CBN to understand.
Without sufficient awareness of the transformative essence of physical interaction and all accompanying components, it is impossible to understand CBN as the basis of a holistic theory.
This is not the full version of the NSC.
Some of its “minor” provisions are omitted, and the logical sequence in the presentation of the material is not always observed.
Also not mentioned is one of the possible consequences of CBN - the semiquantum hypothesis. (We will probably use it to explain the mechanism of electromagnetic phenomena and the structures of the FOs involved in them).
For more complete information, please refer to the first articles on the site.
Why is this article placed in the section on electromagnetic phenomena as an introductory one?
Yes, because without a clear (at least in general terms) idea of the content of CBN and its role in the formation of new views on the nature of seemingly well-studied electromagnetic phenomena, it is impossible to understand the logic of the author’s reasoning.
Our goal is to show how the physical world can really be structured in its specific manifestations, if we base our knowledge on CBN.
POST-NON-CLASSICAL UNITY OF PHYSICS
A.S. Kravets
According to A.B. Migdal, “the history of natural science is the history of attempts to explain homogeneous phenomena by common causes.” The desire for such unity is by no means limited to ideological needs in explaining the world: in physics it has always played an important constructive role in the formation of new theories. Thus, G. Galileo, who eliminated the qualitative difference between the laws of Heaven and Earth, proclaimed and implemented a program of searching for unified fundamental physical principles with the help of which any mechanical phenomenon can be explained. His work was continued by I. Newton, who created the great theory that became the banner of classical physics.
In the works of L. Euler, P. Lagrange, W. Hamilton, B. Jacobi, classical mechanics became a truly universal theory, capable of explaining all mechanical phenomena on the basis of a minimum number of initial postulates. Ultimately, the successes of classical mechanics were so great that most scientists began to believe that the ideal of the unity of all science had already been achieved; it was only necessary to extend the principles of mechanics to all sections of natural science, and perhaps even to social science (J.-P. Laplace). Unity was thus understood as the reducibility of all physical phenomena (and not only physical ones) to one single ideal theory.
The emergence of non-classical physics (special relativity and quantum mechanics) dealt a crushing blow to these unitarist ambitions. The shock from the formation of unconventional theories, radically diverging from classical attitudes, was so great that many researchers began to talk about the ruins of old principles. It took science considerable time to comprehend the qualitative specificity of non-classical physics and its irreducibility to classical ideals. The idea of the unity of physics seemed to be noticeably shaken. Physicists began to give preference to the idea of diversity over the idea of unity. Physics was divided into various subject areas: the region of motion with low speeds was opposed to motion with high (relativistic) speeds, the field was opposed to matter, the microworld was opposed to the macroworld, etc. It is with the establishment of non-classical physics that comes the conviction that true development in science occurs only through cardinal revolutionary revolutions, and a new physical theory must be an alternative to the old one. One of the brilliant founders of new physics, N. Bohr, even spoke in the spirit that a new theory in physics should be so unconventional as to seem quite “crazy.” True, N. Bohr himself, during the development of quantum mechanics, took several important steps to establish a connection between quantum theory and classical physics. He masterfully applied the principle of dualism and the principle of correspondence. The first principle made it possible to build a bridge between field and matter, wave and corpuscular properties, combining them in a quantum mechanical approach, which made it possible to find limiting connections between new and old theories. And yet the conviction in the qualitative diversity of physics, in the fundamental irreducibility of theories, was universal.
But the mole of history dug diligently. Gradually, physics entered a new stage of its development, which can be called post-nonclassical. The idea of this stage was introduced into the methodology of science by V.S. Stepin. “In the historical development of science,” he writes, “starting from the 17th century, three types of scientific rationality arose and, accordingly, three major stages in the evolution of science, replacing each other within the framework of the development of technogenic civilization: 1) classical science (in its two states: pre-disciplinary and disciplinary organized science); 2) non-classical science; 3) post-non-classical science. There are peculiar overlaps between these stages, and the emergence of each new stage did not discard previous achievements, but only outlined the scope of their action, their applicability to certain types of problems. The field of tasks itself expanded sharply at each new stage due to the development of new tools and methods.” The characteristic features of the post-nonclassical stage in physics, which unfolded mainly in the last third of the 20th century, have yet to be comprehended by methodologists, but it is already clear that it has significantly changed our ideas about the unity of physics. This stage dialectically overcomes the thesis of the classical period about the unitary unity of physics and the antithesis of the non-classical period about its qualitative diversity, leading to the conclusion “about unity in diversity.”
The process of integration of physical theories began immediately after the development of new fundamental theories (special theory of relativity and quantum mechanics) and unfolded at two levels of development of physical theories. First, in-depth work continued to build bridges between classical and quantum physics. Basically, this process was carried out at a very abstract level of generalization of mathematical formalisms. As a result, it became obvious that, despite all the qualitative differences in the specific physical meanings and interpretations of the basic formulas of classical and quantum mechanics, they have much in common (after all, both are mechanics after all). The mathematical invariant here is the generalized mathematical formalism of P. Lagrange, which is modified accordingly in each theory (the generalized coordinates of the classical theory correspond to Hermitian operators in the non-classical theory). General group-theoretic laws were also found, to which both theories are subject.
Secondly, the search for new theories by synthesizing existing theories began. The maximum task that physicists set for themselves was the goal of creating a general field theory. The precedent for the search for such a general theory was set by A. Einstein when developing the general theory of gravitation (gravity), in which he tried to build a bridge from gravity to electrodynamics. However, an attempt to quantize such fields encountered insoluble mathematical difficulties due to the appearing infinities. The first significant breakthrough was achieved in the development of quantum electrodynamics, which was a kind of synthesis of electrodynamics, quantum mechanics and the special theory of relativity. However, quantum electrodynamics was solvable, i.e. led to consistently calculated results, only for special exceptional cases of fields that do not interact with particles: it well described the state of the field with the lowest, unexcited energy of the physical vacuum. An attempt to take into account excited levels and the interaction of the electromagnetic field with the electron-positron field led to the same divergences.
The second breakthrough was achieved towards explaining strong interactions. Quantum chromodynamics was created, which was largely built by analogy with quantum electrodynamics. Quantum chromodynamics introduced the idea of fundamental subparticles - quarks, from which complex particles - multiplets - are built. The construction of quantum chromodynamics suggested two fundamental ideas that subsequently formed the basis of a program for unifying various types of physical interactions. The first idea made it possible to introduce the concept of an effective charge depending on the interaction distance (the idea of asymptotic freedom). The second was that any objective theory must be invariant with respect to gauge transformations, i.e. must be a theory of gauge fields of a special type - the so-called non-Abelian gauge fields.
In the 70s, progress was made towards unifying weak and electromagnetic interactions into one theory of electroweak interaction. The “democratic” principle of unification was based on the construction of two multiplets. One of them corresponded to the group-theoretical properties of leptons (electrons, muons, neutrons and corresponding antiparticles), the other united intermediate vector particles (photons and W-mesons) that carry the interaction between leptons. It was in the construction of a unified theory of electroweak interactions that the guiding principle for the synthesis of various interactions was found - the principle of local symmetry.
Global symmetries are usually understood as internal symmetries of interactions that do not depend on position in space and time. The use of global symmetries has proven to be particularly effective in the theory of quark interaction (“eight-fold path”). Local symmetry leaves the characteristic functions of the fields identical during continuous transition from point to point. The principle of local symmetry has built a bridge between dynamic symmetries and space and time. The physical consequences of local symmetry are the existence of massless particles that serve as carriers of interaction, and the conservation of the particle’s charge, which characterizes the strength of interaction with this carrier.
The idea of local symmetry was supplemented by the second fundamentally important idea of spontaneous symmetry breaking. Roughly speaking, if the first idea made it possible to find the group-theoretic unity of two types of interactions, then the second made it possible to explain the differences that arise between them under certain physical conditions. Spontaneous symmetry breaking associated with a special state of the field (formation of a Bose condensate) should have led to the appearance of actually observable particle masses, charges and separation of interactions. To provide a theoretical explanation for these complex processes, the Higgs theory was developed.
Finally, one cannot help but mention the serious progress in the old problem of renormalization of masses and charges (the fight against divergences). On the path of unifying interactions, this problem turned out to be easier to cope with. Ultimately, a general theory of renormalizations was developed - the theory of renormalization group transformations, which revealed the dependence of the interaction constant on the interaction radius.
All these streams of development of theoretical thought led to a new unification - a unified theory of electroweak and strong interactions - usually called the Great Unification. This theory, which essentially incorporates all the main results of elementary particle physics, is based on the synthesis of new physical principles (the principle of gauge fields, the principle of local symmetry together with the idea of spontaneously broken symmetry) and the new status of renormalization group transformations. Modern physics has opened up great prospects for a new decisive step in the synthesis of interactions. Ahead is the unification of gravity with other types of interactions (super unification). “Uniting all interactions into a superunification,” writes A.B. Migdal, “in principle, would mean the ability to explain all physical phenomena from a single point of view. In this sense, the future theory is called the Theory of Everything.”
The program for the unification of physics stimulated methodological interest in the analysis of relationships between physical theories, called intertheoretical. Currently, five types of intertheoretical relations are known.
Generalization is the process of generalizing physical theories, as a result of which it is possible to describe a class of physical phenomena in a more uniform way compared to previous formulations (variants) of the theory. Generalization of physical theories always presupposes a change in mathematical formalism, which not only expands the scope of the theory, but also allows us to identify new patterns and discover a more “subtle” structure of physical reality.
Reduction, which, as a specific relationship between theories, is the subject of long-standing methodological debate. In a broad philosophical sense, reduction is understood as the possibility of reducing (or deducing) the laws (properties) of a complex object to the laws (properties) of its constituent elements. It is in this regard that the most heated philosophical discussions about the relationships between biology and physics, chemistry and physics take place. However, the question of reducing physical theories is narrower and more specific. In this specific meaning, reduction appears as a logical relationship between two theories, one of which is the ideological and conceptual basis for deriving the other. Then we can say that the first theory is a basic (fundamental) theory, and the second is a reducible (phenomenological) theory.
Asymptotic relations are essential for understanding the continuity in the development of physical theories. The essence of these relations is that they express the limiting transitions of theories into each other. The term “asymptotic” (limit) indicates the special non-deductive nature of the connection between physical theories. Asymptotic relations cannot be reduced either to generalizations (generalizations) or to reduction. Asymptotic transitions are most clearly manifested in the connections between fundamental theories relating to different levels of physical reality.
Equivalent relations offer equality of theoretical descriptions of the same objective reality. The equivalence relation conceals a deep dialectical contradiction in the connections between theory and empiricism, which in antinomic form can be expressed as “difference of the identical” or “identity of the different.” This hidden dialectic of equivalent descriptions leads to very ambiguous assessments of their role in scientific knowledge. Absolutization of differences actually leads to denial of the very possibility of equivalence of theoretical descriptions. The absolutization of identity leads to the other extreme: to the recognition of their conventionality, the possibility of a purely conditional choice of physical theories.
Translation is a heuristic and very common technique for transferring ideas, methods, models from one theory to another. A special case of translation is the use of analogies.
Finally, synthesis, which is a heuristic form of combining different theories, their original principles or formalisms, resulting in a new theory. Synthesis cannot be reduced to a mechanical unification of theories, but is always based on new constructive ideas that make it possible to combine already known principles and formalisms in a single approach. A classic example of synthesis is the creation of quantum electrodynamics. Modern unifying theories also arose along the paths of synthesis, although during their creation the relations of generalization and translation of physical ideas were also actively used.
The presence of intertheoretical relations suggests that there is no impassable gap between different physical theories, that physics is not a conglomerate of theories, but, on the contrary, is a developing theoretical system. Each theory occupies a very specific place in this system and is connected with other theories through intertheoretical relationships. Its ideas, to a greater or lesser extent, can be borrowed from other theories (translation); a physical theory can be a generalization or specification of another theory, be one of the equivalent descriptions, be a reduction or an asymptotic approximation, or arise as a result of the synthesis of several theories. Thus, the system of physical theories has a very complex structure. This structure reveals a “subtle” dialectic of unity and difference; it manifests itself differently at different levels of the physical description of reality. In the work of N.P. Konopleva, four such levels are identified: 1) fundamental general principles; 2) mathematical apparatus; 3) theoretical models; 4) experiment. The transition from the first level to the fourth corresponds to the concretization of physical statements, and vice versa, when ascending from empirical descriptions to fundamental principles, the abstractness and generality of statements increases. This scheme should apparently be clarified, since even more general than the fundamental principles will be statements of a metatheoretical nature, i.e. general laws of the structure of physical theories, models of physical theories, etc.
Now it becomes clear that the degree of similarity (commonality) and differences between physical theories depends on the level of abstraction of the analysis of these theories, i.e. theories may coincide in fundamental principles, but differ in mathematical formalism, models, etc.; they can be based on the same mathematical formalism, but differ in other levels of specification of physical statements. Of course, there is a well-known difference between classical and quantum theories. However, if we limit ourselves to a comparative analysis of their mathematical formalism, we will see a lot in common here. Indeed, the Lagrangian formalism, which embodies classical theories, can be extrapolated into the field of quantum theories through appropriate generalization. Moreover, this difference is smoothed out at the level of fundamental general principles, for example, symmetry and invariance.
At the level of mathematical formalisms, one can see the difference between dynamic and group theoretical theories. The former describe the interaction between objects, formulate equations of motion in differential or integral form, the latter act as a theory of invariants of physical quantities, they formulate the corresponding group-theoretic transformations of physical quantities, the rules for finding invariants of the theory. However, at the metatheoretical level it turns out that each dynamic theory can be compared with a corresponding group and thus at this level the alternative opposition of these classes of theories is eliminated. Consequently, what at one level of analysis of a theory appears as specific, qualitatively original, at another level, more abstract, appears as unified and general.
This situation can be explained with an analogy. So, for example, vegetarians and meat-eaters are usually considered as antipodes, but from a more general point of view they are all identical as people who consume food.
Apparently, there still remains a deep fundamental difference (at the level of mathematical formalisms) between probabilistic-statistical and strictly deterministic theories. However, in the light of recent research on the theory of strange attractors, this alternative seems to be shaken, because it was possible to show that strictly dynamic systems (strictly determined) can behave in exactly the same way as probabilistic systems.
The most general building blocks of physical science are its fundamental principles. These include the principle of causality (due to the sequential transmission of physical interaction from point to point, i.e. short-range action), extremal principles, as well as the principles of symmetry and invariance. The last class of principles plays a particularly important role in the construction of physical theories. E. Wigner calls them superprinciples. Indeed, if a physical law establishes a certain identity (uniformity) in a class of phenomena, then the principle of invariance already establishes uniformity in a class of physical laws, i.e. some of their identity in relation to mathematical transformations (translations, shifts, rotations, etc. in physical space and time). “It is the transition from one level to another, higher one,” writes E. Wigner, “from phenomena to the laws of nature, from the laws of nature to symmetry, or the principles of invariance, that represents what I call the hierarchy of our knowledge about the world around us.” .
In recent decades, a “silent” revolution has occurred in physics, associated with some revaluation of the principles of symmetry. It was usually believed that the main thing for constructing a physical theory was the preservation of the symmetry of physical characteristics. But it turned out that the violation of symmetry types is of no less heuristic importance. The discovery of the phenomenon of broken symmetry led to a significant breakthrough in the development of elementary particle physics.
The formalism of the Lagrangian and Hamiltonian types has no less generality than the fundamental physical principles. Together with the addition of some extreme principles, it is applicable to describe a wide class of physical objects (particles, currents, fields, etc.).
If we go down to a more specific level of theoretical descriptions in physics, here we find isolated, qualitatively different fundamental theories. The concept of a fundamental theory usually includes two characteristics: firstly, a fundamental theory is not deducible and cannot be reduced to another theory, and has an independent status; secondly, it is universal, which means its applicability to describe a wide class of phenomena that are by no means of the same type and are not isomorphic with each other.
Fundamental theories include classical mechanics, statistical mechanics, classical electrodynamics, special relativity, and quantum mechanics. Based on these fundamental theories, their hybrids and derivative forms can arise through synthesis: relativistic classical mechanics, relativistic electrodynamics, quantum electrodynamics, the unified theory of electroweak and strong interactions, etc. Thus, we can talk about the existence of elementary (initial) and synthetic (derivative) fundamental theories.
Fundamental theories are related to physical reality using specially selected theoretical models. Each fundamental theory is surrounded by a number of particular theories that specify the fundamental description scheme in relation to a certain class of models. Fundamental theory tends to develop not only in terms of specification (giving rise to a family of particular theories), but also in terms of further generalization. In this case, the fundamental physical theory begins to approach the mathematical theory in its form. This is how Lagrange’s analytical mechanics, the Dirac operator formulation of quantum mechanics, the theory of gauge fields, etc. arise.
Along with fundamental and particular theories in physics, auxiliary theories are also needed to solve those mathematical problems and transformations that arise in the course of the development of physical theories. Auxiliary theories include renormalization theories, perturbation theory, self-consistent field method (Hartree-Fock method), etc.
Thus, a rather complex network of connections between physical theories is revealed. The supporting structure of the entire edifice of physics is represented by fundamental principles and universal mathematical formalisms; the entire edifice rests on elementary fundamental theories, over which derivative fundamental, particular theories, and hybrid forms rise. Between the floors of the building there are many “stairs”, “passages”, “supporting structures”, etc.
The identification of general patterns in the structure and development of physical theories allows us to raise the question of the possibility of a general formalized approach to the construction of physical theories. And such approaches already exist in modern theoretical physics. The initial subject of their research is a variety of physical theories; therefore, they are, in principle, metatheoretical and represent the upper level in the development of physics.
One of the interesting approaches developed by Yu.I. Kulakov was called the theory of physical structures. This theory abstracts from the primary (and in principle indefinable, according to the author) concepts and models of physical theories (such as wave, particle, current, etc.) and focuses on the relationships that exist between physical objects. Distraction from the “internal” nature of a physical object, presenting it as a “black box” is the price that must be paid in order to reveal the structural unity of physical theories. The main task of the theory of physical structures is to find a general symmetry in the relationships of the corresponding sets of objects, called phenomenological symmetry. The initial set of analysis is an empirical matrix, the elements of which are obtained from measurements of two classes of objects. A restriction is imposed on the ratios of matrix elements, which is expressed in the existence of some functional dependence, the type of which does not depend on the choice of measured objects from the original classes. This is the principle of phenomenological symmetry. Limitation of a specific type of functional dependence (its equality to zero) leads to the formulation of a physical law.
Thus, through the analysis of the type of phenomenological symmetry, we come to the discovery of the fundamental laws of physics, and physics as a whole will be represented by various physical structures.
The analyzed theory is not applicable to all branches of physics and has a number of fundamental objections from the point of view of its real feasibility. However, its value lies in the fact that it opens up a new, unconventional way of constructing physical theories “from above” and emphasizes the deep structural unity of physics.
Another metatheoretical approach, developed by G.A. Zaitsev, is based on the ideas of unifying geometric theories set out in the “Erlangen Program”. This approach is called the general theory of physical theories, the main and defining characteristic of which is proposed to be the corresponding fundamental group.
In the general theory of physical theories, a set of physical theories are selected that have common invariant-group properties and at the same time differ in some group parameter. Fundamental groups (representing these theories) must be connected by passage to the limit. The limiting parameters of the group (for example, the speed of light c) and the method of passing to the limit will determine the corresponding physical theory.
However, the group-theoretic approach to the construction of physical theories is clearly insufficient; it does not make it possible to distinguish some essential features of fundamentally different theories. For example, the same Galilean group represents both non-relativistic classical mechanics and non-relativistic quantum mechanics. Therefore, the further stage in the development of the general theory of physical theories is associated with the synthesis of group-theoretic and algebraic representations, i.e. with the algebraization of the general theory of physical theories.
Fundamental in the algebraic approach is the concept of algebra of observables, which is defined by a system of algebraic operations and identity relations on the set of observables (generalized coordinates and momenta for non-classical theories, Hermitian operators for quantum theories).
Lie algebras and Lie groups act as the mathematical apparatus of the algebraic scheme of the general theory of physical theories. The general structure of a particular physical theory, determined by passage to the limit, is specified by the properties of the algebra of observables, and the fundamental group characterizes the invariant properties of dynamic equations and with its help the interpretation of individual observables is clarified.
The possibilities of the algebraic theory of physical theories, of course, should not be assessed as the discovery of a universal algorithm for constructing physical theories. This approach also has a number of fundamental difficulties, but it certainly makes it possible to see what previously went unnoticed - the systemic unity of physics, the deep connection of the formalisms of fundamental physical theories.
Until now, physics has developed in a traditional way, which can be called “Babylonian”: from individual facts and dependencies to the construction of physical theories that historically looked like unrelated or even opposite to each other. The second way, which can be called “Greek,” initially starts from some general abstract mathematical properties of many physical theories. The first path involves an ascent from the particular to the general, the second - the creation of a universal constructive scheme of physical theories and from it - a descent (through concretization and interpretation) to individual physical theories. The first path has given us everything we have in physics; the second path has so far only illuminated what has already been achieved with new light. It is possible that the difficulties on the “Greek” path will turn out to be even deeper than those that we encountered on the “Babylonian” path, however, the heuristic value of the developed metatheoretical approaches lies primarily in the fact that they allow us to identify the internal unity of physical theories and present physics as system of physical theories.
Any new physical theory has, in a sense, potential foundations in an already existing system of physical theories. Analysis of a complex network of physical theories allows one to make certain predictions about the structure of a possible new theory, similar to how Mendeleev's periodic system made it possible to predict chemical elements that had not yet been discovered empirically. The connections between new theories and existing ones can be characterized as intertheoretical relationships, i.e. arising on the path of synthesis, generalization, asymptotic approximation of existing theories. In the light of the above, it becomes more clear that modern physics has not followed the path of inventing a “crazy” theory predicted by N. Bohr, but along the path of unifying and generalizing known theories.
The new post-nonclassical unity of physics can be characterized as a systemic unity, and physics as a whole can be considered as a system of physical theories. In its organization, it strongly resembles biological systems, for example, biogeocynoses. Indeed, there are their own kinds and families of theories, the relationship between the genotype (abstract formalism) and the phenotype (its specific embodiments and interpretations) that is characteristic of the structure of theories. The new theory inherits some features of the parent theories and arises along the way of their “crossing”. The system as a whole is constantly evolving, giving rise to new “types” of physical theories. An essential feature of a system of physical theories is its high adaptability to physical reality. It is thanks to this adaptability, the roots of which are nourished by the activity of the human mind, that a relatively limited network of theories is able to fish out the necessary information from the endless ocean of objective reality. The “cunning of the mind” becomes sufficient to understand the infinite complexity of the world around us.
Literature
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