Einstein's theory of relativity from a philosophical point of view. Philosophical conclusions from the theory of relativity. The problem of determining Einstein's philosophical views

To see the significance of Einstein's theory of relativity for the evolution of physical thought, one should first dwell on the most general concepts of the relativity of the position and movement of bodies and the homogeneity of space and time. In Einschiein's theory, the homogeneity and isotropy of space-time is involved. Let's imagine a material particle lost in an infinite, absolutely empty space. What do the words “spatial position” of the particle mean in this case? Does these words correspond to any real property of the particle? If there were other bodies in space, we could determine the position of a given particle in relation to them, but if space is empty, the position of a given particle turns out to be a meaningless concept. Spatial position has a physical meaning only in the case when there are other bodies in space that serve as bodies of reference. If we take different bodies as reference bodies, we will come to different definitions of the spatial position of a given particle. We can associate a certain reference system with any body, for example a system of rectangular coordinates. Such systems are equal: in whatever reference system we determine the position of the points that make up a given body, the dimensions and shape of the body will be the same, and by measuring the distances between points, we will not find a criterion to distinguish one reference system from another . We can place the origin of coordinates at any point in space, we can then transfer this origin to any other point, or rotate the axes, or do both - the shape and dimensions of the body with such a transfer and rotation will not change, since the distance between any two fixed points of this body. The invariance of this distance during the transition from one reference system to another is called invariance with respect to the specified transition. We say that the distances between points of the body are invariant when moving from one rectangular coordinate system to another, with a different origin and a different direction of the axes. The distances between points of the body serve as invariants of such coordinate transformations. The invariance of distances between points relative to the translation of the origin of coordinates expresses the homogeneity of space, the equality of all its points relative to the origin of coordinates. If the points of space are equal, then we cannot determine the spatial position of the body in an absolute way, we cannot find a privileged frame of reference. When we talk about body position, i.e. about the coordinates of its points, then it is necessary to indicate the reference system. “Spatial position” in this sense is a relative concept - a set of quantities that change when moving from one coordinate system to another system, in contrast to the distances between points, which do not change during the specified transition. The homogeneity of space is further expressed in the fact that a free body, moving from one place to another, maintains the same speed and, accordingly, retains the momentum it has acquired. We explain each change in speed and, accordingly, momentum not by the fact that the body has moved in space, but by the interaction of bodies. We attribute the change in the momentum of a given body to a certain force field in which the body in question finds itself. We also know the homogeneity of time. It is expressed in the conservation of energy. If over time the influence experienced by a given body from other bodies does not change, in other words, if other bodies act in an unchanged way on a given body, then its energy is conserved. We attribute the change in the energy of a body due to changes in time of the forces acting on it, and not due to time itself. Time itself does not change the energy of the system, and in this sense, all moments are equal. We cannot find a privileged moment in time, just as we cannot find a point in space that differs from other points in the behavior of the particle that hits that point. Since all instants are equal, we can count time from any instant, declaring it the initial one. Considering the course of events, we are convinced that they proceed in an unchanged manner, regardless of the choice of the starting moment, the beginning of the countdown. We could say that time is relative in the sense that when moving from one time reference point to another, the description of events remains valid and does not require revision. However, the relativity of time is usually understood as something else. In the simple and obvious sense of the independence of the flow of events from the choice of the initial moment, the relativity of time could not become the basis of a new theory, not at all obvious, overturning the usual idea of time.

By the relativity of time we will understand the dependence of the flow of time on the choice of a spatial reference system. Accordingly, absolute time is time that does not depend on the choice of spatial coordinate system, flowing uniformly on all reference systems moving one relative to another - a sequence of moments occurring simultaneously at all points in space. In classical physics, there was an idea of the flow of time, which does not depend on the real movements of the body - about time that flows throughout the Universe with the same speed. What real process underlies such a concept of absolute time, of an instant simultaneously occurring at distant points in space? Let us recall the conditions for identifying time at different points

space. The time of an event that occurred at point a 41 0 and the time of an event that occurred at point a 42 0 can be identified if the events are connected by the instantaneous impact of one event on another. Let there be a rigid body at point a 41 0, connected by an absolutely rigid, completely non-deformable rod to a body located at point a 42 0. The push received by the body at point a 41 0 is instantly, with infinite speed, transmitted through the rod to the body at point 4 0a 42 0. Both bodies will move at the same instant. But the whole point is that in nature there are no absolutely rigid rods, there are no instantaneous actions of one body on another. The interactions of bodies are transmitted at a finite speed, never exceeding the speed of light. In the rod connecting the bodies, when pushed, a deformation occurs, which propagates at a finite speed from one end of the rod to the other, just as a light signal travels at a finite speed from the light source to the screen. In nature, there are no instantaneous physical processes that connect events that occurred at points in space that are distant from one another. The concept of "same point in time" has an absolute meaning. So far we are not faced with slow movements of bodies and can attribute infinite speed to a light signal, a push transmitted through a solid rod, or any other interaction of moving bodies. In the world of fast movements, in comparison with which the propagation of light and the interaction between bodies can no longer be attributed to infinitely greater speed. In this world, the concept of simultaneity has a relative meaning, and we must abandon the usual image of a single time flowing throughout the Universe - a sequence of the same, simultaneous moments at different points in space. Classical physics proceeds from a similar image. She admits that the same thing instantly occurs everywhere - on Earth, on the Sun, on Sirius, on extragalactic nebulae so far away from us that their light takes billions of years to reach us. If the interactions of bodies (for example, the gravitational forces connecting all bodies of nature) propagated instantly, with infinite speed, we could talk about the coincidence of the moment when one body begins to influence another, and the moment when a second body, distant from the first, experiences this influence . Let us call the effect of a body on another body distant from it a signal. Instantaneous signal transmission is the basis for identifying moments that occur at distant points in space. This identification can be thought of as clock synchronization. The task is often to ensure that the clocks at point a 41 and at point a 42 show the same time. If instantaneous signals exist, this task is not difficult. The clock could be synchronized by radio, by a light signal, by a cannon shot, by a mechanical impulse (for example, placing the clock hands in a 41 and in a 42 on one long absolutely rigid shaft), if the radio receiver, light, sound and mechanical stresses were in shaft were transmitted at an infinitely high speed. In this case we could talk about purely spatial connections in nature, about processes occurring in a zero period of time. Accordingly, three-dimensional geometry would have real physical prototypes. In this case, we could consider space outside of time, and such a view would give an accurate idea of reality. Temporal instantaneous signals serve as a direct physical equivalent of three-dimensional geometry. We see that three-dimensional geometry finds a direct prototype in classical mechanics, which includes the idea of the infinite speed of signals, the instantaneous propagation of interactions between distant bodies. Classical mechanics admits that there are real physical processes that can be described with absolute accuracy by instant photography. Instant photography, stereoscopic of course, is like a three-dimensional spatial section of the space-time world, it is a four-dimensional world of events, taken at the same moment. Infinitely fast interaction is a process that can be described within the framework of an instantaneous time picture of the world. But the theory of the field as a real physical medium excludes instantaneous Newtonian long-range action and instantaneous propagation of signals through an intermediate medium. Not only sound, but also light and radio signals have a finite speed. The speed of light is the maximum speed of signals. What is the physical meaning of simultaneity in this case? What corresponds to the sequence of moments that are the same for the entire Universe? What corresponds to the concept of a single time, flowing uniformly throughout the world? We can find some physical meaning for the concept of simultaneity and thus give an independent reality to the purely spatial aspect of existence, on the one hand, and absolute time, on the other, even in the case when all interactions propagate at a finite speed. But the condition for this is the existence of a generally motionless world ether and the ability to determine the speeds of moving bodies in an absolute manner, relating them to the ether as a single privileged body of reference. Let's imagine a ship with screens at the bow and stern. A lantern is lit in the center of the ship at equal distances from both screens. The light of the lantern simultaneously reaches the screens, and the moments when this happens can be identified. The light falls on the screen located at the bow of the ship at the same instant as on the screen located at the stern. Thus, we find a physical prototype of simultaneity. Synchronization with the help of light signals simultaneously arriving at two points from a source located at an equal distance from them is possible if the light source and these two points are at rest in the world ether, i.e. when the ship is motionless in relation to the ether. Synchronization is also possible when the ship is moving on the air. In this case, the light will reach the screen at the bow of the ship a little later, and the screen at the stern a little earlier. But, knowing the speed of the ship relative to the ether, we can determine the advance of the beam going to the screen on the stern and the delay of the beam going to the screen on the bow, and, taking into account the indicated advance and delay, synchronize the clocks installed on the stern and on the bow of the ship. We can further synchronize the clocks on two ships moving relative to the ether at different but constant speeds known to us. But for this it is also necessary that the speed of the ships relative to the ether has a certain meaning and a certain meaning. Two cases are possible here. If the ship, when moving, completely carries along the ether located between the lantern and the screens, then there will be no delay in the beam going to the screen on the bow of the ship. When the ether is completely entrained, the ship does not shift relative to the ether located above its deck, and the speed of light relative to the ship will not depend on the movement of the ship. However, we will be able to register the movement of the ship using optical effects. The speed of light will not change relative to the ship, but it will change relative to the shore. Let the ship move along the embankment: on the embankment there are two screens a 41 and a 42, and the distance between them is equal to the distance between the screens on the ship. When the screens on the moving ship are opposite the screens on the embankment, a lantern is lit in the center of the ship. If the ship carries the ether with it, then the light of the lantern will simultaneously reach the screen at the stern and the screen at the bow, but in this case the light will reach the screens on the motionless embankment at different moments. In one direction, the speed of the ship relative to the embankment will be added to the speed of light, and in the other direction, the speed of the ship will need to be subtracted from the speed of light. This result - different speeds of light relative to the shore - will happen if the ship is carried away by the ether. If the ship does not carry the ether, then the light will move at the same speed relative to the shore and at different speeds relative to the ship. Thus, the change in the speed of light will be the result of the ship's movement in both cases. If the ship moves, dragging the ether, then the speed relative to the shore changes; if the ship does not carry away the ether, then the speed of light relative to the ship itself changes. In the mid-19th century, optical experimentation and measurement techniques made it possible to detect very small differences in the speed of light. It turned out to be possible to check whether moving bodies entrain the ether or not. In 1851, Fizeau (1819 - 1896) proved that bodies do not completely entrain the ether. The speed of light relative to stationary bodies does not change when light passes through moving media. Fizeau passed a beam of light through a stationary tube through which water flowed. Essentially, the water played the role of a ship, and the tube - a motionless shore. The result of Fizeau's experiment led to a picture of the motion of bodies in a motionless ether without dragging the ether. The speed of this movement can be determined by the delay of the beam catching up with the body (for example, the beam directed towards the screen at the bow of a moving ship), compared to the beam going towards the body (for example, compared to the flashlight beam directed towards the screen at the stern). Thus, it was possible, as it seemed then, to distinguish a body motionless relative to the ether from a body moving in the ether. In the first, the speed of light is the same in all directions, in the second it does not change depending on the direction of the beam. There is an absolute difference between rest and motion; they differ from each other in the nature of optical processes in resting and moving media. This point of view made it possible to talk about the absolute simultaneity of events and the possibility of absolute synchronization of clocks. Light signals reach points located at the same distance from a stationary source at the same instant. If the light source and screens move relative to the ether. Then we can determine and take into account the delay of the light signal caused by this movement. And consider as one and the same instant 1) the moment of light hitting the front screen, corrected for retardation, and 2) the moment light hits the rear screen, corrected for advance. The difference in the speed of light propagation will indicate the movement of the light source and screens in relation to the ether - the absolute body of reference. The experiment, which was supposed to show the change in the speed of light in moving bodies and, accordingly, the absolute nature of the movement of these bodies, was carried out in 1881 by Michelson (1852 -1931). Subsequently, it was repeated more than once. Essentially, Michelson's experiment corresponded to comparing the speed of signals traveling to screens at the stern and at the bow of a moving ship. But the Earth itself was used as a ship, moving in space at a speed of about 30 km/sec. Further, we compared not the speed of the beam catching up with the body and the beam going towards the body, but the speed of light propagation in the longitudinal and transverse directions. In the instrument used in Michelson's experiment, the so-called interferometer, one beam went in the direction of the Earth's movement - in the longitudinal arm of the interferometer, and the other beam - in the transverse arm. The difference in the speeds of these rays was supposed to demonstrate the dependence of the speed of light in the device on the movement of the Earth. The results of Michelson's experiment were negative. On the surface of the Earth, light travels at the same speed in all directions. This conclusion seemed extremely paradoxical. It was supposed to lead to a fundamental rejection of the classical rule of adding velocities. The speed of light is the same in all bodies moving uniformly and rectilinearly in relation to each other. Light passes at a constant speed of approximately 300,000 km/sec, past a stationary body, past a body moving towards the light, past a body that the light is catching up with. Light is a traveler who walks along the railway track, between the tracks, at the same speed relative to an oncoming train, relative to a train going in the same direction, relative to the railway track itself, relative to an airplane flying over it, etc.. Or a passenger who moves along the carriage of a speeding train at the same speed relative to the carriage and relative to the Earth. In order to abandon the classical principles that seemed completely obvious and indisputable, it took brilliant strength and courage of physical thought. Immediate predecessor. Einstein came very close to the theory of relativity, but they could not take the decisive step, they could not admit that light, not in appearance, but in reality, propagates at the same speed relative to bodies that are displaced one relative to another.

Lorentz (1853-1928) put forward a theory that preserves the motionless ether and the classical rule for adding velocities and at the same time is compatible with the results of Michelson's experiments. Lorenz suggested that all bodies experience longitudinal contraction when moving; they reduce their extent along the direction of movement. If all bodies reduce their longitudinal dimensions, then such a reduction cannot be detected by direct measurement. Thus, Lorentz considers the constancy of the speed of light discovered by Michelson as a purely phenomenological result of the mutual compensation of two effects of motion: a decrease in the speed of light and a reduction in the distance it travels. From this point of view, the classical rule for adding velocities remains unshakable. The absolute nature of the movement is preserved - a change in the speed of light exists; therefore, movement can be attributed not to other bodies equal to the ether, but to the universal body of reference - the motionless ether. The contraction is absolute in nature - there is a true length of the rod at rest relative to the ether, in other words, a rod at rest in the absolute sense. In 1905, Albert Einstein (1879-1955) published the article “On the Electrodynamics of Moving Bodies.” For Einstein, absolute motion does not hide from the observer, but simply does not exist. If motion relative to the ether does not cause any effects in moving bodies, then it is physically a meaningless concept. Thus, from the physical picture of the world the concept of a single time covering the entire Universe is eliminated. Here Einstein approached the most fundamental problems of science - the problems of space, time and their connection with each other. If there is no world ether, then it is impossible to attribute immobility to a certain body and on this basis consider it the beginning of a motionless, in an absolute sense, privileged coordinate system. Then we cannot talk about the absolute simultaneity of events, we cannot say that two events that are simultaneous in one coordinate system will be simultaneous in any other coordinate system.

The ideas expressed by Einstein in 1905 attracted the interest of very wide circles in the coming years. People felt that a theory that so boldly encroached on traditional ideas about space and time could not but lead, in its development and application, to very profound industrial, technical and cultural shifts. Of course, only now has the path become clear from abstract reasoning about space and time to the idea of colossal reserves of energy hidden in the depths of matter and waiting to be released in order to change the face of production technology and culture. Until the middle of our century, in all areas of technology, only such insignificant changes in the rest energy and rest mass of bodies were used. Now practically applied reactions have appeared, in which the main body of rest energy contained in a substance is expended or replenished. In modern physics, there is an idea of the complete transition of rest energy into motion energy, i.e. about the transformation of a particle with a rest mass into a particle with zero rest mass and a very large energy of motion and mass of motion. Such transitions are observed in nature. The practical application of such processes is still a long way off. Now processes are used that release the internal energy of atomic nuclei. Nuclear power proved to be the decisive experimental and practical proof of Einstein's theory of relativity.

In 1907-1908 Herman Minkovsky (1864 - 1908) gave the theory of relativity a very harmonious and important geometric form for subsequent generalization. In the article “The Principle of Relativity” (1907) and in the report “Space and Time” (1908), Einstein’s theory was formulated in the form of a doctrine of invariants of four-dimensional Euclidean geometry. When a geometric figure moves in space, the coordinates of the points change, but the distances between them remain unchanged. In itself, the four-dimensional representation of particle motion can be easily grasped; it seems almost obvious and, in fact, familiar. Everyone knows that real events are determined by four numbers: three spatial coordinates and the time elapsed before the event from the beginning of chronology, or from the beginning of the year, or from the beginning of the day. matter space natural science

In 1908, Minkowski presented the theory of relativity in the form of four-dimensional geometry. He called the presence of a particle at a point defined by four coordinates an “event”, since an event in mechanics should be understood as something defined in space and time - the presence of a particle at a certain spatial point at a certain moment. Further, he called the totality of events - the spatio-temporal diversity - “the world”, since the real world unfolds in space and time. A line depicting the movement of a particle, i.e. Minkowski called a four-dimensional line, each point of which is determined by four coordinates, a “world line.”

The homogeneity of space-time means that in nature there are no distinguished space-time world points. There is no event that would be the absolute beginning of a four-dimensional, space-time frame of reference. In the light of the ideas presented by Einstein in 1905, the four-dimensional distance between world points, i.e. the space-time interval will not change when these points are moved together along the world line. This means that the spatio-temporal connection of two events does not depend on which world point is chosen as the origin, and that any world point can play the role of such an origin. Thus, the idea of homogeneity is the core idea of science in the 17th-20th centuries. It is consistently generalized, transferred from space to time, and further, to space-time.

In 1911-1916. Einstein created the general theory of relativity. The theory, created in 1905, is called the special theory of relativity, since it is valid only for a special case, rectilinear and uniform motion.

For many years, Einstein had the idea of subordinating accelerated motion to the principle of relativity and creating a general theory of relativity, which would consider not only inertial, but also all kinds of motion. The force of inertia acts uniformly on all objects. There is a force that also acts uniformly on all bodies. This is the force of gravity.

Einstein called the principle of equivalence the statement about the equivalence of the force of gravity acting on a system and the force of inertia that manifests itself during accelerated motion. This principle allows us to consider accelerated motion as relative. In fact, the manifestations of accelerated motion (forces of inertia) are no different from the forces of gravity in a stationary system. This means that there is no internal criterion for motion, and motion can only be judged in relation to external bodies. Movement, including accelerated movement of body A, consists of changing the distance from some body of reference B, and we can with the same right say that B moves relative to A.

Einstein identified gravity, which bends the world lines of moving bodies, with the curvature of space-time. This idea will always be an example of the courage and depth of physical thought and at the same time an example of the new nature of scientific thinking, which finds real physical equivalents of Euclidean and non-Euclidean geometric relationships. A body left to its own devices moves in a straight line in three-dimensional space. It moves in a straight line in the four-dimensional space-time world, since on the space-time graph, each shift along the time axis (each increment in time) is accompanied by the same increment in the spatial distance traveled. Thus, movements by inertia correspond to straight world lines, i.e. straight lines of four-dimensional space-time. accelerated movements correspond to the curved world lines of the four-dimensional space-time world. Gravity imparts the same acceleration to bodies. It imparts the same acceleration to light. Consequently, gravity bends world lines. If straight lines drawn on a plane suddenly turned out to be curved, and acquired the same curvature, we would assume that the plane was curved, became a curved surface, for example, the surface of a ball. Perhaps gravity, uniformly bending world lines, means that space-time at a given world point (at a given spatial point and at a given moment in time) has acquired a certain curvature. A change in gravitational forces, a change in the intensity and direction of gravity, can then be considered as a change in the curvature of space-time. The curvature of the line requires no explanation. The curvature of the surface is also quite a visual representation. We know that on a curved surface, for example the surface of the globe, the theorems of Euclidean geometry on the plane cease to be valid. Instead of straight lines, other geodesic lines become the shortest lines, for example, in the case of the surface of a ball of a great circle arc: to travel the shortest route from north to south, you need to move along the arc of the meridian. On a geodesic line, which replaces a straight line, many different perpendiculars can be lowered from one point, for example, from a pole to the equator. We cannot visualize the curvature of three-dimensional space. But we can call curvature the deviation of the three-dimensional world from Euclidean geometry. We can do the same with a four-dimensional manifold. Let us repeat the starting points of the general theory of relativity. At every point located in the field of gravitational forces of any large mass, for example the Sun, all bodies fall with the same acceleration, and not only bodies, but light also acquires acceleration, and the same acceleration depends on the mass of the Sun. In four-dimensional geometry, such acceleration can be represented as a space-time world. According to the general theory of relativity, the presence of heavy masses bends the space-time world, and this curvature is expressed in gravity, changing the paths and speeds of bodies and light rays. In 1919, astronomical observations confirmed Einstein's theory of gravity - general relativity. The rays of stars are bent as they pass by the Sun, and their deviations from the straight path turned out to be the same as those calculated theoretically by Einstein. The curvature of spacetime changes depending on the distribution of heavy masses. If you set out on a journey through the Universe without changing direction, i.e. following the geodetic lines of the surrounding space, we will meet on the way four-dimensional hillocks - the gravitational fields of planets, mountains - the gravitational fields of stars, large ridges - the gravitational fields of galaxies. Traveling in this way across the surface of the Earth, we, in addition to hills and mountains, know about the curvature earth's surface in general and are confident that, continuing the journey in the same direction, for example along the equator, we will return to the place from which we left. When traveling in the Universe, we also encounter the general curvature of space, which relates to the gravitational fields of planets, stars and galaxies, just as the curvature of the Earth relates to the relief of its surface. If not only space, but also time were curved, we would return, as a result of space travel, to the original spatial path and to the original spatial position. This is impossible. Einstein suggested that only space is curved.

In 1922, A.A. Friedman (1888-1925) put forward a hypothesis about the change in the radius of the general curvature of space over time. Some astronomical observations confirm this hypothesis; the distances between galaxies increase over time, and the galaxies move apart. However, cosmological concepts associated with the general theory of relativity are still very far from the certainty and uniqueness that is characteristic of the special theory of relativity.

ABSTRACT

Philosophical aspects of the theory of relativity

Einstein

Gorinov D.A.

Perm 1998
Introduction.

IN late XIX At the beginning of the 20th century, a number of major discoveries were made, which began a revolution in physics. It led to a revision of almost all classical theories in physics. Perhaps one of the largest in importance and which played the most important role in the development of modern physics, along with quantum theory, was A. Einstein’s theory of relativity.

The creation of the theory of relativity made it possible to revise traditional views and ideas about the material world. Such a revision of existing views was necessary, since many problems had accumulated in physics that could not be solved with the help of existing theories.

One of these problems was the question of the limiting speed of light propagation, which was excluded from the point of view of the then dominant principle of Galileo’s relativity, which was based on Galileo’s transformations. Along with this, there were many experimental facts in favor of the idea of the constancy and limit of the speed of light (the universal constant). An example here is the experiment of Michelson and Morley, carried out in 1887, which showed that the speed of light in a vacuum does not depend on the movement of light sources and is the same in all inertial frames of reference. As well as the observations of the Danish astronomer Ole Roemer, who determined back in 1675. based on the delay of eclipses of Jupiter's satellites, the final value of the speed of light.

Another significant problem that arose in physics was related to ideas about space and time. The ideas about them that existed in physics were based on the laws of classical mechanics, since in physics the dominant view was that every phenomenon has, ultimately, a mechanistic nature, since Galileo’s principle of relativity seemed universal, relating to any laws, and not just the laws of mechanics . From Galileo's principle, based on Galileo's transformations, it followed that space does not depend on time and, conversely, time does not depend on space.

Space and time were thought of as given forms independent of each other; all the discoveries made in physics fit into them. But such a correspondence between the provisions of physics and the concept of space and time existed only until the laws of electrodynamics, expressed in Maxwell’s equations, were formulated, since it turned out that Maxwell’s equations are not invariant under Galilean transformations.

Shortly before the creation of the theory of relativity, Lorentz found transformations under which Maxwell's equations remained invariant. In these transformations, unlike Galileo’s transformations, time in different reference systems was not the same, but the most important thing was that from these transformations it no longer followed that space and time were independent of each other, since time was involved in the transformation of coordinates, and when converting time - coordinates. And as a consequence of this, the question arose - what to do? There were two solutions, the first was to assume that Maxwell's electrodynamics was erroneous, or the second was to assume that classical mechanics with its transformations and Galileo's principle of relativity is approximate and cannot describe all physical phenomena.

Thus, at this stage in physics, contradictions appeared between the classical principle of relativity and the position of the universal constant, as well as between classical mechanics and electrodynamics. There have been many attempts to give other formulations to the laws of electrodynamics, but they have not been successful. All this played the role of prerequisites for the creation of the theory of relativity.

Einstein's work, along with enormous significance in physics, is also of great philosophical meaning. The obviousness of this follows from the fact that the theory of relativity is associated with such concepts as matter, space, time and motion, and they are one of the fundamental philosophical concepts. Dialectical materialism found argumentation for its ideas about space and time in Einstein's theory. In dialectical materialism, a general definition of space and time is given as forms of existence of matter, and therefore, they are inextricably linked with matter, inseparable from it. “From the standpoint of scientific materialism, which is based on the data of special sciences, space and time are not independent realities independent of matter, but internal forms of its existence.” Such an inextricable connection between space and time and moving matter was successfully demonstrated by Einstein’s theory of relativity.

There were also attempts to use the theory of relativity by idealists as proof that they were right. For example, the American physicist and philosopher F. Frank said that the physics of the twentieth century, especially the theory of relativity and quantum mechanics, stopped the movement of philosophical thought towards materialism, based on the dominance of the mechanical picture of the world in the last century. Frank said that “in the theory of relativity, the law of conservation of matter no longer applies; matter can be transformed into intangible entities, into energy.”

However, all idealistic interpretations of the theory of relativity are based on distorted conclusions. An example of this is that sometimes idealists replace the philosophical content of the concepts “absolute” and “relative” with physical ones. They argue that since the coordinates of a particle and its speed will always remain purely relative values (in the physical sense), that is, they will never turn even approximately into absolute values and therefore, supposedly, will never be able to reflect the absolute truth (in the philosophical sense) . In reality, coordinates and speed, despite the fact that they do not have an absolute character (in the physical sense), are an approximation to the absolute truth.

The theory of relativity establishes the relative nature of space and time (in the physical sense), and idealists interpret this as its denial of the objective nature of space and time. Idealists try to use the relative nature of the simultaneity and sequence of two events resulting from the relativity of time to deny the necessary nature of the causal relationship. In the dialectical-materialist understanding, both the classical ideas about space and time and the theory of relativity are relative truths that include only elements of absolute truth.

Until the middle of the 19th century, the concept of matter in physics was identical to the concept of substance. Until this time, physics knew matter only as a substance that could have three states. This idea of matter took place due to the fact that “the objects of study of classical physics were only moving material bodies in the form of matter; besides matter, natural science did not know other types and states of matter (electromagnetic processes were attributed either to material matter or to its properties) ". For this reason, the mechanical properties of matter were recognized as universal properties of the world as a whole. Einstein mentioned this in his works, writing that “for a physicist of the early nineteenth century, the reality of our external world consisted of particles between which simple forces, depending only on distance."

Ideas about matter began to change only with the advent of a new concept introduced by the English physicist M. Faraday - field. Faraday, having discovered electromagnetic induction in 1831 and discovered the connection between electricity and magnetism, became the founder of the doctrine of the electromagnetic field and thereby gave impetus to the evolution of ideas about electromagnetic phenomena, and therefore to the evolution of the concept of matter. Faraday first introduced such concepts as electric and magnetic fields, expressed the idea of the existence of electromagnetic waves and thereby opened a new page in physics. Subsequently, Maxwell supplemented and developed Faraday's ideas, as a result of which the theory of the electromagnetic field appeared.

For a certain time, the fallacy of identifying matter with substance did not make itself felt, at least obviously, although substance did not cover all known objects of nature, not to mention social phenomena. However, it was of fundamental importance that matter in the form of a field could not be explained with the help of mechanical images and ideas, and that this area of \u200b\u200bnature, to which electromagnetic fields belong, was increasingly beginning to manifest itself.

The discovery of electric and magnetic fields became one of the fundamental discoveries of physics. It greatly influenced further development science, as well as philosophical ideas about the world. For some time, electromagnetic fields could not be scientifically substantiated or a coherent theory could be built around them. Scientists have put forward many hypotheses in an attempt to explain the nature of electromagnetic fields. This is how B. Franklin explained electrical phenomena by the presence of a special material substance consisting of very small particles. Euler tried to explain electromagnetic phenomena through the ether; he said that light in relation to the ether is the same as sound in relation to air. During this period, the corpuscular theory of light became popular, according to which light phenomena were explained by the emission of particles by luminous bodies. There have been attempts to explain electrical and magnetic phenomena by the existence of certain material substances corresponding to these phenomena. “They were assigned to various substantial spheres. Even in early XIX V. magnetic and electrical processes were explained by the presence of magnetic and electrical fluids, respectively.”

ABSTRACT

Philosophical aspects of the theory of relativity

Einstein

Gorinov D.A.

Perm 1998
Introduction.

At the end of the 19th and beginning of the 20th centuries, a number of major discoveries were made, which began a revolution in physics. It led to a revision of almost all classical theories in physics. Perhaps one of the largest in importance and which played the most important role in the development of modern physics, along with quantum theory, was A. Einstein’s theory of relativity.

Einstein's work, along with its enormous significance in physics, also has great philosophical significance. The obviousness of this follows from the fact that the theory of relativity is associated with such concepts as matter, space, time and motion, and they are one of the fundamental philosophical concepts. Dialectical materialism found argumentation for its ideas about space and time in Einstein's theory. In dialectical materialism, a general definition of space and time is given as forms of existence of matter, and therefore, they are inextricably linked with matter, inseparable from it. “From the standpoint of scientific materialism, which is based on the data of special sciences, space and time are not independent realities independent of matter, but internal forms of its existence.” Such an inextricable connection between space and time and moving matter was successfully demonstrated by Einstein’s theory of relativity.

Until the middle of the 19th century, the concept of matter in physics was identical to the concept of substance. Until this time, physics knew matter only as a substance that could have three states. This idea of matter took place due to the fact that “the objects of study of classical physics were only moving material bodies in the form of matter; besides matter, natural science did not know other types and states of matter (electromagnetic processes were attributed either to material matter or to its properties) ". For this reason, the mechanical properties of matter were recognized as universal properties of the world as a whole. Einstein mentioned this in his works, writing that “for the physicist of the early nineteenth century, the reality of our external world consisted of particles between which simple forces act, depending only on distance.”

The discovery of electric and magnetic fields became one of the fundamental discoveries of physics. It greatly influenced the further development of science, as well as philosophical ideas about the world. For some time, electromagnetic fields could not be scientifically substantiated or a coherent theory could be built around them. Scientists have put forward many hypotheses in an attempt to explain the nature of electromagnetic fields. This is how B. Franklin explained electrical phenomena by the presence of a special material substance consisting of very small particles. Euler tried to explain electromagnetic phenomena through the ether; he said that light in relation to the ether is the same as sound in relation to air. During this period, the corpuscular theory of light became popular, according to which light phenomena were explained by the emission of particles by luminous bodies. There have been attempts to explain electrical and magnetic phenomena by the existence of certain material substances corresponding to these phenomena. “They were assigned to various substantial spheres. Even at the beginning of the 19th century. magnetic and electrical processes were explained by the presence of magnetic and electrical fluids, respectively.”

Phenomena associated with electricity, magnetism and light have been known for a long time and scientists, studying them, tried to explain these phenomena separately, but since 1820. such an approach became impossible, since the work carried out by Ampere and Ørsted could not be ignored. In 1820 Oersted and Ampere made discoveries, as a result of which the connection between electricity and magnetism became clear. Ampere discovered that if a current is passed through a conductor located next to a magnet, then forces from the magnet’s field begin to act on this conductor. Oersted observed another effect: the influence of an electric current flowing through a conductor on a magnetic needle located next to the conductor. From this it could be concluded that the change electric field accompanied by the appearance of a magnetic field. Einstein noted the special significance of the discoveries made: “The change in the electric field produced by the movement of a charge is always accompanied by a magnetic field - a conclusion based on Oersted’s experiment, but it contains something more. It contains the recognition that the connection between the electric field, which changes over time, and the magnetic field is very significant."

On the basis of experimental data accumulated by Oersted, Ampere, Faraday and other scientists, Maxwell created a holistic theory of electromagnetism. Later, his research led to the conclusion that light and electromagnetic waves have the same nature. Along with this, it was discovered that the electric and magnetic field has such a property as energy. Einstein wrote about this: “Being at first only an auxiliary model, the field becomes more and more real. The attribution of energy to the field is a further step in development, in which the concept of the field becomes more and more essential, and the substantial concepts characteristic of the mechanistic point of view become increasingly secondary." Maxwell also showed that an electromagnetic field, once created, can exist independently, regardless of its source. However, he did not isolate the field into a separate form of matter, which would be different from matter.

Further development of the theory of electromagnetism by a number of scientists, including G.A. Lorenz, shook the usual picture of the world. Thus, in Lorentz’s electronic theory, in contrast to Maxwell’s electrodynamics, the charge generating the electromagnetic field was no longer formally represented; electrons began to play the role of charge carrier and field source for Lorentz. But a new obstacle arose on the path to clarifying the connection between the electromagnetic field and matter. Matter, in accordance with classical ideas, was thought of as a discrete material formation, and the field was represented as a continuous medium. The properties of matter and field were considered incompatible. The first person to bridge this gap separating matter and field was M. Planck. He came to the conclusion that the processes of emission and absorption of fields by matter occur discretely, in quanta with energy E=h n. As a result of this, ideas about field and matter changed and led to the fact that the obstacle to recognizing the field as a form of matter was removed. Einstein went further, he suggested that electromagnetic radiation not only is it emitted and absorbed in portions, but it is distributed discretely. He said that free radiation is a flow of quanta. Einstein associated the quantum of light, by analogy with matter, with momentum - the magnitude of which was expressed in terms of energy E/c=h n /c(the existence of an impulse was proven in experiments conducted by the Russian scientist P. N. Lebedev in experiments on measuring the pressure of light on solids and gases). Here Einstein showed the compatibility of the properties of matter and field, since the left side of the above relationship reflects corpuscular properties, and the right side reflects wave properties.

Thus, approaching the turn of the 19th century, a lot of facts had accumulated regarding the concepts of field and matter. Many scientists began to consider field and matter as two forms of existence of matter; based on this, as well as a number of other considerations, the need arose to combine mechanics and electrodynamics. “However, it turned out to be impossible to simply attach the laws of electrodynamics to Newton’s laws of motion and declare them to be a unified system describing mechanical and electromagnetic phenomena in any inertial frame of reference.” The impossibility of such a unification of the two theories resulted from the fact that these theories, as mentioned earlier, are based on different principles; this was expressed in the fact that the laws of electrodynamics, unlike the laws of classical mechanics, are non-covariant with respect to Galilean transformations.

In order to build a unified system that would include both mechanics and electrodynamics, there were two most obvious ways. The first was to change Maxwell's equations, that is, the laws of electrodynamics, so that they began to satisfy Galileo's transformations. The second path was associated with classical mechanics and required its revision and, in particular, the introduction of other transformations instead of Galileo’s transformations, which would ensure the covariance of both the laws of mechanics and the laws of electrodynamics.

The second path turned out to be correct, which Einstein followed, creating the special theory of relativity, which finally established new ideas about matter in their own right.

Subsequently, knowledge about matter was supplemented and expanded, and the integration of the mechanical and wave properties of matter became more pronounced. This can be shown by the example of a theory that was presented in 1924 by Louis de Broglie. In it, de Broglie suggested that not only waves have corpuscular properties, but also particles of matter, in turn, have wave properties. So de Broglie associated a moving particle with a wave characteristic - wavelength l = h/p, Where p- momentum of the particle. Based on these ideas, E. Schrödinger created quantum mechanics, where the motion of a particle is described using wave equations. And these theories, which showed the presence of wave properties in matter, were confirmed experimentally - for example, it was discovered when microparticles passed through crystal lattice It is possible to observe phenomena that were previously thought to be inherent only to light, these are diffraction and interference.

And also a quantum field theory was developed, which is based on the concept of a quantum field - special kind matter, it is in the particle state and in the field state. An elementary particle in this theory is represented as an excited state of a quantum field. A field is the same special type of matter that is characteristic of particles, but only in an unexcited state. In practice, it has been shown that if the energy of a quantum of the electromagnetic field exceeds the intrinsic energy of the electron and positron, which, as we know from the theory of relativity, is equal to mc 2 and if such a quantum collides with a nucleus, then as a result of the interaction of the electromagnetic quantum and the nucleus, an electron-positron pair will appear. There is also a reverse process: when an electron and a positron collide, annihilation occurs - instead of two particles, two g-quanta appear. Such mutual transformations of the field into matter and back of matter into the field indicate the existence of a close connection between the material and field forms of matter, which was taken as the basis for the creation of many theories, including the theory of relativity.

As you can see, after publication in 1905. The special theory of relativity made many discoveries related to particular studies of matter, but all these discoveries relied on the general idea of matter, which was first given in the works of Einstein in the form of a holistic and consistent picture.

Space and time

The problem of space and time, like the problem of matter, is directly related to physical science and philosophy. In dialectical materialism, a general definition of space and time is given as forms of the existence of matter. “From the standpoint of scientific materialism, which is based on data from particular sciences, space and time are not independent realities independent of matter, but internal forms of its existence,” and therefore, they are inextricably linked with matter, inseparable from it. This idea of space and time also exists in modern physics, but during the period of the dominance of classical mechanics it was not so - space was divorced from matter, was not connected with it, and was not its property. This position of space relative to matter followed from the teachings of Newton, he wrote that “absolute space, by its very essence, regardless of anything external, always remains the same and motionless. The relative is its measure or some limited moving part, which is determined by our senses by its position relative to certain bodies and which in everyday life is accepted as motionless space... Place is the part of space occupied by a body, and in relation to space it can be either absolute , or relative."

Time also seemed separate from matter and did not depend on any ongoing phenomena. Newton divided time, as well as space, into absolute and relative, the absolute existed objectively, this “true mathematical time, in itself and its very essence, without any relation to anything external, flows uniformly and is otherwise called duration.” Relative time was only apparent, comprehended only through the senses, a subjective perception of time.

Space and time were considered independent not only from phenomena occurring in the material world, but also from each other. This is a substantial concept in this concept, as mentioned earlier, space and time are independent in relation to moving matter and do not depend on each other, subject only to their own laws.

Along with the substantial concept, another concept of space and time existed and developed - the relational one. This concept was mainly adhered to by idealist philosophers; in materialism, such a concept was the exception rather than the rule. According to this concept, space and time are not something independent, but are derived from a more fundamental essence. The roots of the relational concept go back centuries to Plato and Aristotle. According to Plato, time was created by God; in Aristotle, this concept was further developed. He wavered between materialism and idealism and therefore recognized two interpretations of time. According to one of them (idealistic), time was presented as the result of the action of the soul, the other materialist was that time was presented as the result of objective movement, but the main thing in his ideas about time was that time was not an independent substance.

During the dominance in physics of ideas about the space and time of data in Newton's theory, the relational concept prevailed in philosophy. Thus, Leibniz, based on his ideas about matter, which were broader than Newton’s, developed it quite fully. Leibniz represented matter as a spiritual substance, but it was valuable that in defining matter he did not limit himself only to its material form; he also included light and magnetic phenomena as matter. Leibniz rejected the existence of emptiness and said that matter exists everywhere. Based on this, he rejected Newton’s concept of space as absolute, and therefore rejected the idea that space is something independent. According to Leibniz, it would be impossible to consider space and time outside of things, since they were properties of matter. “Matter, he believed, plays a determining role in the space-time structure. However, this idea of Leibniz about time and space was not confirmed in contemporary science and therefore was not accepted by his contemporaries.”

Leibniz was not the only one who opposed Newton; among the materialists one can single out John Toland; he, like Leibniz, rejected the absolutization of space and time; in his opinion, it would be impossible to think of space and time without matter. For Toland, there was no absolute space distinct from matter, which would be the container of material bodies; There is no absolute time, isolated from material processes. Space and time are properties of the material world.

The decisive step towards the development of a materialistic doctrine of space, based on a deeper understanding of the properties of matter, was made by N. I. Lobachevsky in 1826. Until this time, Euclid's geometry was considered true and unshakable, it said that space can only be rectilinear. Almost all scientists relied on Euclidean geometry, since its provisions were perfectly confirmed in practice. Newton was no exception in creating his mechanics.

Lobachevsky was the first to attempt to question the inviolability of Euclid’s teaching, “he developed the first version of the geometry of curvilinear space, in which more than one straight line parallel to a given one can be drawn through a point on a plane, the sum of the angles of a triangle is less than 2d, and so on; By introducing the postulate about the parallelism of straight lines, Lobachevsky obtained an internally non-contradictory theory.”

Lobachevsky's geometry was the first of many similar theories developed later, examples being Riemann's spherical geometry and Gaussian geometry. Thus, it became clear that Euclidean geometry is not an absolute truth, and that under certain circumstances other geometries other than Euclidean may exist.

“The successes of the natural sciences, which led to the discovery of matter in a field state, mathematical knowledge, which discovered non-Euclidean geometries, as well as the achievements of philosophical materialism were the foundation on which the dialectical-materialist doctrine of the attributes of matter arose. This doctrine absorbed the entire body of accumulated natural science and philosophical knowledge, based on a new idea of matter.” In dialectical materialism, the categories of space and time are recognized as reflecting the external world, they reflect the general properties and relationships of material objects and therefore have a general character - no material formation is conceivable outside of time and space.

All these provisions of dialectical materialism were a consequence of the analysis of philosophical and natural science knowledge. Dialectical materialism combines all the positive knowledge accumulated by humanity over all the millennia of its existence. A theory appeared in philosophy that brought man closer to understanding the world around him, which gave an answer to the main question - what is matter? In physics until 1905. such a theory did not exist, there were many facts and guesses, but all the theories put forward contained only fragments of the truth, many emerging theories contradicted each other. This state of affairs existed until Einstein published his works.

The endless ladder of knowledge

The creation of the theory of relativity was a natural result of processing the physical knowledge accumulated by mankind. The theory of relativity became the next stage in the development of physical science, incorporating the positive aspects of the theories that preceded it. Thus, Einstein in his works, while denying the absolutism of Newtonian mechanics, did not completely discard it; he gave it its rightful place in the structure of physical knowledge, believing that the theoretical conclusions of mechanics are suitable only for a certain range of phenomena. The situation was similar with other theories that Einstein relied on; he asserted the continuity of physical theories, saying that “the special theory of relativity is the result of adapting the foundations of physics to Maxwell-Lorentz electrodynamics. From previous physics it borrows the assumption of the validity of Euclidean geometry for the laws of spatial arrangement absolutely solids, inertial system and the law of inertia. The special theory of relativity accepts the law of equivalence of all inertial systems from the point of view of formulating the laws of nature as valid for all physics (special principle of relativity). From Maxwell-Lorentz electrodynamics, this theory borrows the law of constancy of the speed of light in a vacuum (the principle of constancy of the speed of light).”

At the same time, Einstein understood that the special theory of relativity (STR) was also not an unshakable monolith of physics. “One can only conclude,” Einstein wrote, “that the special theory of relativity cannot claim unlimited applicability; its results are applicable only as long as the influence of the gravitational field on physical phenomena (for example, light) can be ignored.” STR was just another approximation of a physical theory, operating within a certain framework, which was the gravitational field. The logical development of the special theory was the general theory of relativity; it broke the “gravitational fetters” and became head and shoulders above the special theory. However, the general theory of relativity did not refute the special theory, as Einstein’s opponents tried to imagine; on this occasion, he wrote in his works: “For an infinitesimal region, coordinates can always be chosen in such a way that the gravitational field will be absent in it. Then we can assume that in such an infinitesimal region the special theory of relativity holds. Thus, the general theory of relativity is connected with the special theory of relativity, and the results of the latter are transferred to the former.”

The theory of relativity made it possible to make a huge step forward in describing the world around us, uniting the previously separate concepts of matter, motion, space and time. She gave answers to many questions that remained unresolved for centuries, made a number of predictions that were later confirmed, one of such predictions was the assumption made by Einstein about the curvature of the trajectory of a light beam near the Sun. But at the same time, new problems arose for scientists. What is behind the phenomenon of singularity, what happens to giant stars when they “die”, what gravitational collapse actually is, how the universe was born - it will be possible to solve these and many other questions only by climbing one more step up the endless ladder knowledge.

Orlov V.V. Fundamentals of Philosophy (Part One)

Newton I. Mathematical principles of natural philosophy.

D. P. Gribanov Philosophical foundations of the theory of relativity M. 1982, p. 143

V.V. Orlov Fundamentals of Philosophy, part one, p. 173

Gribanov D.P. Philosophical foundations of the theory of relativity. M. 1982, p. 147

Einstein A. Collection scientific works, M., 1967, vol. 2, p. 122

Einstein A. Collection of scientific works, M., 1967, vol. 1, p. 568

Einstein A. Collection of scientific works, M., 1967, vol. 1, p. 423

INTRODUCTION 3
1. MATTER, SPACE, TIME 4
2. REASONS FOR THE ARISE OF RELATIVITY THEORIES
EINSTEIN 9
3. A. EINSTEIN’S THEORY OF RELATIVITY 13
CONCLUSION 19
REFERENCES 20

INTRODUCTION

Achievements modern science indicate the preference of a relational approach to understanding space and time. In this regard, first of all, it is necessary to highlight the achievements of physics of the 20th century. The creation of the theory of relativity was a significant step in understanding the nature of space and time, which allows us to deepen, clarify, and concretize philosophical ideas about space and time.
Albert Einstein, theoretical physicist, one of the founders of modern physics, was born in Germany, lived in Switzerland since 1893, in Germany since 1914, emigrated to the USA in 1933. His creation of the theory of relativity became the most fundamental discovery of the 20th century, which had a huge impact on the entire picture of the world,
According to modern researchers, the theory of relativity has eliminated universal time and left only local time, which is determined by the intensity of gravitational fields and the speed of movement of material objects. Einstein formulated fundamentally new and methodologically important provisions that helped to better understand the features of space and time in various spheres of objective reality.

1. MATTER, SPACE, TIME

If we say that matter means the external world that exists independently of our consciousness, then many will agree with this approach. It also correlates with ideas at the level of common sense. And unlike some philosophers, who thought it frivolous to reason at the level of everyday thinking, materialists accept this “natural attitude” as the basis of their theoretical constructions.
But, agreeing with such a preliminary understanding of matter, taking it for granted, people do not experience a sense of surprise and admiration for its deep meaning, the wealth of methodological possibilities that open up in its content. A short historical analysis of previous concepts of matter and understanding of the essence of this category will help us evaluate its significance.
The limitations of 18th century materialism. in the understanding of matter was expressed primarily in the absolutization of achieved scientific knowledge, attempts to “endow” matter with physical characteristics. Thus, in the works of P. Holbach, along with the most general understanding of matter as a world perceived through the senses, it is said that matter has such absolute properties as mass, inertia, impenetrability, and the ability to have a figure.
This means that the main principle of materiality was the materiality, the physicality of the objects surrounding a person. However, with this approach, beyond the limits of materiality were such physical phenomena as electricity and magnetic field, which clearly did not have the ability to have a figure.
There was also an understanding of matter as a substance, which is especially characteristic of the philosophy of B. Spinoza. "Substance is not the world, surrounding a person, but something behind this world, determining its existence." Substance has attributes such as extension and thought. At the same time, it remained unclear how a single, eternal, unchanging substance is connected with the world of changing things. This gave rise to ironic metaphors, comparing a substance with a hanger on which various properties are hung, leaving it unchanged.
The limitations of the understanding of matter in both of its variants were clearly revealed in the 19th century. Usually the main reason that necessitated the transition to a new understanding of matter as a philosophical category is the crisis of the methodological foundations of physics on turn of the 19th century and 20th centuries
As is known, the most significant achievement of the philosophy of Marxism was the discovery of a materialist understanding of history. Social existence, according to this theory, determines social consciousness. However economic relations only ultimately determine the functioning and development of society; social consciousness and ideology are relatively independent and also influence social development. This is how Marxist theory differs from “economic determinism.”
In Marxist theory, the boundaries of materiality seem to be expanded, which includes not only the objects themselves with their materiality and physicality, but also properties and relationships (not only fire, but also the property of heat, not only people themselves, but also their production relations, etc.). d.). This is precisely the contribution of Marxism to the understanding of matter, which has not yet been sufficiently studied.
Understanding matter as an objective reality that exists independently of man and is not identical to the totality of his sensations contributed to overcoming the contemplative nature of previous philosophy. This is caused by the analysis of the role of practice in the process of cognition, which allows us to identify new objects and their properties, included at this stage of historical development in objective reality.
The peculiarity of this understanding of matter is that not only bodily objects are recognized as material, but also the properties and relationships of these objects. Cost is material because it is the amount of socially necessary labor spent on producing a product. Recognition of the materiality of production relations served as the basis for a materialistic understanding of history and the study of objective laws of the functioning and development of society.
One can try to find certain boundaries for the application of such categories as “being” and “matter”. Firstly, being is a broader category, since it covers not only objective, but also subjective reality. Secondly, being and matter can be used to distinguish between what exists and what exists (appears). Then the existing can be presented as an objective reality, realized by a person in the process of his activity.
In the modern methodology of scientific knowledge, such concepts as “physical reality”, “biological reality”, “social reality” occupy an important place. We are talking about objective reality, which becomes accessible to a person in a certain sphere of his activity and at a certain stage of historical development.
Philosophical understanding of the world usually begins with the distinction between the material and the ideal. But for a more complete description of the objects being studied, other categories are needed. Among them, the categories of “movement” and “rest” occupy an important place.
Marxist philosophy, relying on the best traditions of previous thinkers, recognizes that the whole world is in a state of continuous movement, which is inherent in material objects and does not require the intervention of divine forces or a first impulse for its existence. Movement is understood as a philosophical category to denote any change, from simple movement to thinking. The world is not a collection of finished things, but a collection of processes.
The basis of the social form of movement is the purposeful activity of people, and above all, according to Marx, “the method of producing material goods.” Man acts as an object and subject of history. Ultimately, history is the activity of people pursuing their interests.
Space and time as independent categories already appear in the philosophy of the Ancient East, where they are considered along with such principles as fire, water, earth (Sankhya). Aristotle's nine main categories are time, place, and position. In the philosophy of Ancient Greece, the basic concepts of space and time begin to take shape: substantial and relational. The first considers space and time as independent entities, the principles of the world; the second - as a way of existence of material objects. This understanding of space and time finds its most vivid expression in the philosophy of Aristotle and Lucretius Cara.
In modern philosophy, the basis of the substantial concept was I. Newton’s provisions on absolute space and time. He argued that absolute space in its essence, regardless of anything external, always remains the same and motionless. Absolute time was considered as pure duration. The basis for such statements was the experience of classical physics and mathematical research (in particular, Euclid’s geometry).

2. REASONS FOR THE ARISE OF EINSTEIN’S THEORIES OF RELATIVITY

How did Einstein’s private (special) theory of relativity arise, which narrowed the study of a global phenomenon to limited, partial relativity, to the relativity of some basic concepts, to the particular principle of relativity? Why did it even arise and fall on the fertile soil of public perception?
It is impossible not to notice the objective reasons for the appearance of works on the theory of relativity. They are due to the “warmed up, revolutionary” political state of society and the spontaneously, dynamically developing natural science of the second half of the 19th - early 20th centuries. At that time, science, in many of its spheres, systematically rejected, one after another, many stereotypes - the then generally accepted standards of ideas, which left its mark on the methodological nihilism of the theory of relativity as a whole.
To a large extent, the emergence of the theory of relativity was influenced by the now authoritative philosophy of Immanuel Kant, the doctrine of infinity, finally recognized by that time, as well as some mathematical works, for example, the non-Euclidean geometries of Lobachevsky (1792-1856) and Riemann (1826-1866), ideas about time of Minkowski and Poincaré. The above reasons and, as a consequence, the emerging theories of Einstein’s relativity are united by a general lack of methodology of cognition; they are united by the fact that they are not contradictory, but uniquely interpret (or do not interpret at all) the basic concepts that systematically form their theories and do not apply general scientific principles of cognition. Why did they dare to do this? Because these concepts and principles were, due to the natural immaturity of science, methodologically not defined by their predecessors. And the use of technologies for “processing concepts of knowledge” that were rapidly developing by that time (methods of logic, mathematics, physics, etc.) made it possible to obtain very original final conclusions at the output.
The ancient Greek scientist Ptolemy, and then Immanuel Kant, postulated the dependence of reality on knowledge itself. An object, according to Kant, exists as such only in the forms of activity of the subject. Until now, the methodology of knowledge applies the principle of Kant and Ptolemy: “What I see is the essence.” The parable of the four blind wise men who felt an elephant comes to mind. Moreover, each felt the elephant especially in certain places: one only the leg, the other only the stomach, the third the trunk, the fourth the tail. And then they argued in discord about the “truth” and “truthfulness” of the elephant’s appearance that they knew. In fact, in the approach to knowledge of Kant and Ptolemy: “What I see is the essence,” precisely this subjective approach to knowledge is implemented and the possibility of objective knowledge is rejected in comparison with generally accepted standards - the principles of knowledge.
The concept of infinity has not yet been defined in the general scientific concept. This is a non-relative concept that is not cognizable in principle in magnitude and does not have a standard, and therefore a relative comparative magnitude.
For this reason, Minkowski defined his own vision of the concept of “time”. When constructing his “metric spaces,” he introduced a concept synonymous with the concept of time - “the plane of the world manifesting process,” which “runs” at the speed of light from any arbitrarily chosen “origin of coordinates.” The basic concept of time was “adjusted” to the existing geometric technical process of cognition. And modern scientists are now intensively looking for ways and means of traveling in space-time.
The symbiosis of the theories of Minkowski and Riemann gave rise to a four-dimensional abstract interpretation of space-time, which has very limited practical applicability. For example, it cannot be used to model real physical, changing objects of nature, as functions of their changing properties (parameters).
Space-time is an interpretation of the space of events emptied of dimension, having only properties: spatial coordinates of the places of occurrence and moments in time of the occurrence of events. The properties of space and time are disproportionate to each other, because from a change in one, the other does not change cause-and-effect, does not depend. The result is a space of events devoid of physical essence - nature (dimension).
Einstein considered the principle of relativity that he formulated, supposedly not contradicting the principle of relativity of Galileo, to be the basis of the special theory of relativity. The absence of methodologically formed concepts of “time” and “simultaneity” in Einstein’s scientific arsenal, taking into account the adoption of the postulate of the global constancy of the speed of light, allowed Einstein to “achieve” in the special theory of relativity the simultaneity of events at different points in space using signals sent from one source to two objects light signals synchronizing the clocks of these objects, forming the same time scale.
According to Einstein, by forming time on the clocks of these objects and then giving the objects different speeds, he, using the Lorentz transformation, mathematically strictly substantiates that time flows differently in objects moving at different speeds. Which in itself is not only mathematically but also physically obvious. The clocks in the case of such a method of knowing “time”, with such synchronization, will run differently, because the time scale ceases to be a single reference for both clocks “running away” differently from the light synchronization pulses of the time scales of objects. And if the scale standards are different, then the ratio of any duration of any process at the facility to different duration standards will be different. Systems of knowledge of time are not inertial. If you “run away” from synchronizing pulses “flying” at the speed of light, then such a clock on the object will stop altogether. Einstein went much further in his generalizations and conclusions. He “dramatically revolutionary” claims that the lengths of objects will change and biological processes (for example, aging in the “twin paradox”) will proceed differently in objects (twins) that move relative to each other and relative to the light source at different speeds. In fact, Einstein, as it were, “theoretically substantiated” the principle of cognition: “The magnitude of the properties of a cognizable object (for example, properties characterizing aging, or the duration of processes on an object, or its length) causally depends on the “ruler”, on the way in which this value is measured ( will be known)".
3. A. EINSTEIN'S THEORY OF RELATIVITY
The most fundamental discovery of the 20th century, which had a huge impact on the entire picture of the world, was the creation of the theory of relativity.
In 1905, a young and unknown theoretical physicist Albert Einstein (1879-1955) published an article in a special physics journal under the discreet title “On the electrodynamics of moving bodies.” This article outlined the so-called special theory of relativity.
Essentially, this was a new concept of space and time, and new mechanics were developed accordingly. Old, classical physics was quite consistent with practice that dealt with macrobodies moving at not very high speeds. And only studies of electromagnetic waves, fields and other types of matter associated with them forced a new look at the laws of classical mechanics.
Michelson's experiments and Lorentz's theoretical works served as the basis for a new vision of the world of physical phenomena. This concerns, first of all, space and time, the fundamental concepts that determine the construction of the entire picture of the world. Einstein showed that the abstractions of absolute space and absolute time introduced by Newton should be abandoned and replaced by others. First of all, it should be noted that the characteristics of space and time will appear differently in systems that are stationary and moving relative to each other.
So, if you measure a rocket on Earth and establish that its length is, for example, 40 meters, and then from Earth determine the size of the same rocket, but moving at high speed relative to the Earth, it turns out that the result will be less than 40 meters. And if you measure the time flowing on Earth and on a rocket, it turns out that the clock readings will be different. On a rocket moving at high speed, time, in relation to earthly time, will flow more slowly, and the slower the higher the rocket’s speed, the closer it approaches the speed of light. This entails certain relationships that, from our usual practical point of view, are paradoxical.
This is the so-called twin paradox. Let's imagine twin brothers, one of whom becomes an astronaut and goes on a long space journey, the other remains on Earth. Time passes. The spaceship is returning. And between the brothers there is something like this conversation: “Hello,” says the one who remained on Earth, “I’m glad to see you, but why haven’t you changed almost at all, why are you so young, because thirty years have passed since the moment you flew away.” “Hello,” the astronaut replies, “and I’m glad to see you, but why are you so old, I’ve only been flying for five years.” So, according to the earth's clock, thirty years have passed, but according to the astronauts' clocks, only five. This means that time does not flow the same throughout the Universe; its changes depend on the interaction of moving systems. This is one of the main conclusions of the theory of relativity.
This is a completely unexpected conclusion for common sense. It turns out that a rocket that had a certain fixed length at the start should become shorter when moving at a speed close to the speed of light. At the same time, in the same rocket, the clock, the cosmonaut’s pulse, his brain rhythms, and the metabolism in the cells of his body would slow down, that is, time in such a rocket would flow slower than the time of the observer who remained at the launch site. This, of course, contradicts our everyday ideas, which were formed in the experience of relatively low speeds and are therefore insufficient for understanding processes that unfold at near-light speeds.
The theory of relativity has revealed another significant aspect of the space-time relations of the material world. She revealed a deep connection between space and time, showing that in nature there is a single space-time, and separately space and time act as its unique projections, into which it is split in different ways depending on the nature of the movement of bodies.
The abstracting ability of human thinking separates space and time, placing them separately from each other. But to describe and understand the world, their compatibility is necessary, which is easy to establish by analyzing even situations of everyday life. In fact, to describe an event, it is not enough to determine only the place where it occurred; it is also important to indicate the time when it occurred.
Before the creation of the theory of relativity, it was believed that the objectivity of a space-time description is guaranteed only when, during the transition from one reference system to another, separate spatial and separate time intervals are preserved. The theory of relativity generalized this position. Depending on the nature of the movement of reference systems relative to each other, various splittings of a single space-time occur into separate spatial and separate time intervals, but they occur in such a way that a change in one, as it were, compensates for a change in the other. If, for example, the spatial interval has decreased, then the time interval has increased by the same amount, and vice versa.
It turns out that the splitting into space and time, which occurs differently at different speeds of movement, is carried out in such a way that the space-time interval, that is, the joint space-time (the distance between two nearby points of space and time), is always preserved, or, to put it scientific language, remains invariant. The objectivity of a spatio-temporal event does not depend on from which frame of reference and at what speed the observer characterizes it while moving. The spatial and temporal properties of objects separately turn out to be variable when the speed of movement of the objects changes, but the space-time intervals remain invariant. Thus, the special theory of relativity revealed the internal connection between space and time as forms of the existence of matter. On the other hand, since the very change in spatial and time intervals depends on the nature of the body’s movement, it turned out that space and time are determined by the states of moving matter. They are such as moving matter is.
Thus, philosophical conclusions from the special theory of relativity testify in favor of a relational consideration of space and time: although space and time are objective, their properties depend on the nature of the movement of matter and are associated with moving matter.
The ideas of the special theory of relativity were further developed and specified in the general theory of relativity, which was created by Einstein in 1916. In this theory, it was shown that the geometry of space-time is determined by the nature of the gravitational field, which, in turn, is determined by the relative position of the gravitating masses. Near large gravitating masses, space curvature occurs (its deviation from the Euclidean metric) and time slows down. If we specify the geometry of space-time, then the nature of the gravitational field is automatically given, and vice versa: if a certain nature of the gravitational field, the location of gravitating masses relative to each other, is given, then the nature of space-time is automatically given. Here space, time, matter and movement are organically fused with each other.
The peculiarity of the theory of relativity created by Einstein is that it studies the movement of objects at speeds approaching the speed of light (300,000 km per second).
Special relativity states that as the speed of an object approaches the speed of light, “time intervals slow down and the length of the object shortens.”
General relativity states that near strong gravitational fields, time slows down and space bends. In a strong gravitational field, the shortest distance between points will no longer be a straight line, but a geophysical curve corresponding to the curvature of gravitational field lines. In such a space, the sum of the angles of a triangle will be greater or less than 180°, which is described by the non-Euclidean geometries of N. Lobachevsky and B. Riemann. The bending of a light beam in the gravitational field of the Sun was tested by English scientists already in 1919 during a solar eclipse.
If in the special theory of relativity the connection between space and time with material factors was expressed only depending on their movement while abstracting from the influence of gravity, then in the general theory of relativity their determination by the structure and nature of material objects (matter and electromagnetic field) was revealed. It turned out that gravity affects electromagnetic radiation. In gravity, a connecting thread between cosmic objects was found, the basis of order in the Cosmos, made general conclusion about the structure of the world as a spherical formation.
Einstein's theory cannot be seen as a refutation of Newton's theory. There is continuity between them. The principles of classical mechanics retain their significance in relativistic mechanics within the limits of low speeds. Therefore, some researchers (for example, Louis de Broglie) argue that the theory of relativity in a certain sense can be considered as the crown of classical physics.

CONCLUSION

The special theory of relativity, the construction of which was completed by A. Einstein in 1905, proved that in the real physical world, spatial and time intervals change when moving from one reference system to another.
A reference system in physics is an image of a real physical laboratory, equipped with a clock and rulers, that is, instruments with which one can measure the spatial and temporal characteristics of bodies. Old physics believed that if frames of reference move uniformly and rectilinearly relative to each other (such motion is called inertial), then spatial intervals (the distance between two nearby points) and time intervals (the duration between two events) do not change.
The theory of relativity refuted these ideas, or rather, showed their limited applicability. It turned out that only when the speeds of movement are small in relation to the speed of light, we can approximately assume that the sizes of bodies and the passage of time remain the same, but when we are talking about movements with speeds close to the speed of light, then a change in spatial and time intervals becomes noticeable. With an increase in the relative speed of movement of the reference system, spatial intervals are reduced and time intervals are stretched.

BIBLIOGRAPHY

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a physical theory, the main meaning of which is the statement: in the physical world everything happens due to the structure of space and changes in its curvature. There are special and general theories of relativity.

The particular theory formulated by A. Einstein in 1905 is based on two postulates: 1. All laws of physics have the same form in all inertial reporting systems. 2. In all physical systems, the speed of light is constant.

Developing this theory, in 1918 G. K4inkovsky showed that the properties of our Universe should be described by a vector in four-dimensional space-time. In 1916, Einstein took the next step and published the general theory of relativity (GR) - essentially a theory of gravity. The cause of gravity, according to this theory, is the curvature of space near massive bodies. Tensor analysis and general Riemannian geometry are used as a mathematical apparatus in general relativity.

A number of important consequences follow from the theory of relativity. Firstly, the law of equivalence of mass and energy. Secondly, the rejection of hypotheses about the world ether and absolute space and time. Thirdly, the equivalence of gravitational and inertial masses. The theory of relativity has found numerous experimental confirmations and is used in cosmology, particle physics, nuclear engineering, etc.

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specialist. (STR) and general (GTR) theories of relativity were developed by A. Einstein in 1905 and 1916, respectively. General relativity is based on two postulates (principles): 1) Einstein’s principle of relativity (all physical processes in inertial systems proceed exactly the same); 2) The principle of constancy of the speed of light (the speed of light in all inertial systems is the same in all directions and does not depend on the movement of the source and receiver of light. The speed of light in a vacuum is the maximum speed that exists in nature). A number of consequences follow from these postulates: the mass of a body increases with the speed of its movement; time flows differently in different systems; time and space are interconnected and form a four-dimensional world (its properties do not depend on matter), mass and energy are related by the formula E = mc2, a new formula for adding velocities (instead of Galileo’s formula), etc. In General Relativity, the principle of relativity was extended to all systems. This followed from the equivalence of inertial and gravitational masses, and GTR became the general theory of gravitation. The principle of the constancy of the speed of light was limited to areas where gravitational forces can be neglected. A number of conclusions followed from GTR: 1) The properties of spacetime depend on the movement of matter. Material bodies bend space-time, thereby creating gravitational fields. 2) A ray of light, having inertial, and therefore gravitational mass, must bend in the gravitational field. 3) The frequency of light must change as a result of the gravitational field. STO and OTO along with quantum mechanics lie at the basis of modern physics. F.M.Dyagilev

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physical theory, in the development of which it is necessary to distinguish 3 stages. 1) The principle of relativity of classical mechanics (Galileo, Newton) states: in all uniformly and rectilinearly moving systems, mechanical processes proceed in exactly the same way as in those at rest. Consequently, the rectilinear uniform motion of the corresponding system cannot be determined or established without the help of bodies located outside the system. So, for example, if you throw a ball vertically upward in a straight-line and uniformly moving railway carriage, it will again fall down perpendicularly, just as if the carriage was standing. On the contrary, to an observer standing on a railway embankment, the trajectory appears as a parabola. Based on the shape of the parabola observed from the outside and recorded (photographed), it is possible to determine the speed of the train in relation to the location of the observer. The situation is similar with the movement of celestial bodies in the Universe. Attempts (Fizeau in 1849, Michelson in 1881, V. Wien and others) using electromagnetic (optical) means to create an absolute system of relations in world space (something similar to a resting “ether” as an absolute, motionless space - Newton) ended unsuccessfully. 2) In Einstein’s special theory of relativity (1905), a new concept of time was created for physics. Time is no longer determined through the rotation of the Earth, but through the propagation of light (300,000 km/s). This time is so closely related to spatial dimensions that together they form space, which has four dimensions. Having become a coordinate, time loses its absolute character and becomes only a “relative” value in a system of connections. A concept of spatial time was found that corresponds to all physical facts. 3) The general theory of relativity (Einstein, 1916) establishes that gravity and acceleration are equivalent, that in accordance with the world of Minkowski (1908), the three-dimensional coordinate system of classical physics is supplemented by time as the fourth coordinate (see Continuum). It expands observation, including consideration of uniformly accelerated and rotating systems, which requires complex mathematical apparatus; the geometry necessary for this is first determined thanks to this physical theory of relativity (see Metageometry). The theory of relativity resolves problems that arise from observing the propagation of electromagnetic and optical phenomena, especially the propagation of light in moving systems. The results of observations interpreted using the theory of relativity deviate from the results of observations of classical mechanics and electrodynamics only where high speeds and enormous distances are involved.

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physical theory of space and time, formulated by Einstein in 1905 (special theory) and in 1916 (general theory). It comes from the so-called. the classical principle of relativity of Galileo - Newton, according to which mechanical processes occur uniformly in inertial reference systems, moving one relative to the other rectilinearly and uniformly. The development of optics and electrodynamics led to the conclusion that this principle is applicable to the propagation of light, i.e., electromagnetic waves (independence of the speed of light from the motion of the system) and to the abandonment of the concept of absolute time, absolute simultaneity and absolute space. According to special theory, the passage of time depends on the movement of the system, and time intervals (and spatial scales) change so that the speed of light is constant in any reference system and does not change depending on its movement. From these premises, a large number of physical conclusions were derived, which are usually called “relativistic,” that is, based on O. t. Among them, the law of the relationship between mass and energy acquired particular importance, according to which the mass of a body is proportional to its energy and which is widely used in modern times. nuclear physics. Developing and generalizing special O. t., Einstein came to general O. t., which in its basic form. content is a new theory of gravity. It is based on the assumption that four-dimensional space-time, in which gravitational forces act, obeys the relations of non-Euclidean geometry. On a plane, these relations can be visually represented as ordinary Euclidean relations on surfaces with curvature. Einstein considered the deviation of geometric relationships in four-dimensional space-time from Euclidean ones as a curvature of space-time. He identified such curvature with the action of gravitational forces. A similar assumption was confirmed in 1919 by astronomical observations, which showed that the ray of a star, as a prototype of a straight line, is bent near the Sun under the influence of gravitational forces. General optical theory has not yet acquired the character of a complete and indisputable physical concept that the special theory has. The philosophical conclusions of philosophical theory confirm and enrich the ideas of dialectical materialism. O. t. showed an inextricable connection between space and time (it is expressed in the unified concept of the space-time interval), as well as between material movement, on the one hand, and its space-time forms of existence, on the other. Determination of spatiotemporal properties depending on features material movement(“slowdown” of time, “curvature” of space) revealed the limitations of classical physics’ ideas about absolute space and time, the illegality of their isolation from moving matter. Ottomans acted as a rational generalization of classical mechanics and the extension of the principles of mechanics to the area of motion of bodies with velocities approaching the speed of light. The idealistic and positivist trends of bourgeois philosophy, replacing the concept of a reference system with the “position of the observer,” tried to use optical theory to affirm the subjective nature of science and the dependence of physical processes on observation. However, theoretical theory, or relativistic mechanics, should not be confused with philosophical relativism, which denies the objectivity of scientific knowledge. O. t. is a more adequate (adequacy) reflection of reality than classical mechanics.

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the theory of space and time, according to which they only relate. "sides" of a single form of existence of matter - space-time. There are private (or special) and general O. t. (GTO). General gravity is a theory of space-time that explains universal gravitation through its structure (therefore it is also called the theory of gravitation). Prerequisites of O.T. The doctrine of spaces. forms and relationships developed in ancient times and was mathematically formalized in the form of Euclidean geometry. Physics accepted it in its finished form. Time became part of the general laws of mechanics formulated by Galileo and Newton. Classic performances physicists about space and time reflected primarily general laws relative position and motion of rigid bodies. In particular, the idea of absolute, identically flowing time everywhere suited them well. According to Newton's second law, in principle there are no restrictions on the speed that can be given to a body. Therefore, coordination in time by transmitting influences (“signals”) is established with any accuracy (one can, in principle, compare times in different bodies with any accuracy), from which it follows that time flows the same everywhere (the widespread opinion is that this requires instantaneous, t i.e. with infinite speed, signal transmission, erroneously). The laws of mechanics of Galileo - Newton are formulated for the so-called. inertial reference systems. In Newtonian mechanics, Galileo's principle of relativity is fulfilled, according to which the laws of mechanics. phenomena are the same in relation to all inertial systems. In general, for a certain class of phenomena? and for a certain class of systems S? the principle of relativity is fulfilled, or, in other words, these systems are equal in relation to these phenomena, if the laws of the phenomena? are the same in systems S, i.e. when in two systems S?, S" for phenomena??, ?" of the same type, identical (relative to these systems) conditions are realized, then these phenomena will flow relative to these systems in exactly the same way. Math. the expression of the laws of these phenomena in these systems is one and the same, i.e. it is invariant (unchanging) with respect to the transition from one system to another, expressed by the corresponding transformation of coordinates and other quantities. After Maxwell in the 60s. 19th century formulated the basic laws of electromagnetic phenomena, the problem arose of identifying the laws of electrodynamics of moving bodies in relation to any inertial frame of reference. The experiments led to results that were contrary to what was “to be expected.” A particularly important role was played by Michelson's experiment (1881–87), which did not reveal the expected dependence of the speed of light on the direction of its propagation in relation to the direction of the Earth's motion. Math. an expression of the contradiction was given by Lorentz (1904), showing that Maxwell's equations are invariant with respect to transformations (the so-called Lorentz transformations) different from the Galilean transformations, with respect to which the laws of Newtonian mechanics are invariant. The resolution of the contradiction was carried out by Einstein in his work “On the Electrodynamics of Moving Bodies” (A. Einstein, Zur Elektrodynamik bewegter Körper, 1905) by constructing a new theory of space and time – partial theory of theory and, accordingly, a new mechanics – “relativistic” , in contrast to Newtonian - classical. A. Poincaré arrived at essentially the same results independently. Particular O. t. Einstein based his theory on the following. provisions (which are given in a slightly amended formulation): I. There are inertial reference systems. II. The geometry of space is Euclidean. III. The principle of relativity: all inertial systems are equal in relation to all physics. phenomena. IV. Law of constancy of the speed of light: relative to all inertial systems, light propagates at the same speed c. The first three provisions are borrowed from the classic. theories, only the principle of relativity is understood in a general way; the fourth is a generalization of experimental data (Michelson's experiment and others) and is quite consistent with the theory of electromagnetism. From position II, IV it follows purely mathematically that for any inertial systems S, S? coordinates x, y, z, x?, y?, z and times t, t? are related by the Lorentz transformation. In particular, if the coordinate axes x, x? in systems S and S? are parallel and the x axis is directed along the movement of S? relative to S, then (with an appropriate choice of scales) the differences in coordinates and time in the systems S and S? for any two events - instantaneous point phenomena P1, ?2 are related by the formulas: where? - speed S? relative to S. The following follows from these relations. conclusions: (1) Systems can move relative to each other at a speed less than the speed of light (since at ??c the formulas become meaningless). (2) Two events that are simultaneous in S (t12=0), but occurring at points with different coordinates x (x12?0), are not simultaneous in S? (t?12?0). Moreover, the event P1, preceding P2 with respect to system S, can follow it with respect to S?. Namely, if t12>0, but less than?/c2 x12, then t?12