“The laws of electrodynamics and the principle of relativity. Postulates of the theory of relativity. The principle of relativity. Postulates of the theory of relativity Laws of electrodynamics and the principle of relativity summary
The ideas about space and time have changed. According to the classical concepts of space and time, which were considered unshakable for centuries, movement has no effect on the flow of time (time is absolute), and the linear dimensions of any body do not depend on whether the body is at rest or in motion (length is absolute).
Einstein's special theory of relativity is a new doctrine of space and time, replacing the old (classical) concepts.
§ 75 LAWS OF ELECTRODYNAMICS AND THE PRINCIPLE OF RELATIVITY
The principle of relativity in mechanics and electrodynamics. After in the second half of the XIX century. Maxwell formulated the basic laws of electrodynamics, the question arose: does the principle of relativity, which is valid for mechanical phenomena, also apply to electromagnetic phenomena? In other words, do electromagnetic processes (interaction of charges and currents, propagation of electromagnetic waves, etc.) proceed in the same way in all inertial reference frames? Or, perhaps, uniform rectilinear motion, without affecting mechanical phenomena, has some effect on electromagnetic processes?
To answer these questions, it was necessary to find out whether the basic laws of electrodynamics change when passing from one inertial frame of reference to another, or, like Newton's laws, they remain unchanged. Only in the latter case can one discard doubts about the validity of the principle of relativity in relation to electromagnetic processes and consider this principle as a general law of nature.
The laws of electrodynamics are complex, and a rigorous solution to this problem is not easy. However, even simple considerations, it would seem, allow us to find the correct answer. According to the laws of electrodynamics, the speed of propagation of electromagnetic waves in a vacuum is the same in all directions and is equal to c = 3 10 8 m / s. But in accordance with the law of addition of the velocities of Newton's mechanics, the velocity can be equal to the velocity of light only in one selected frame of reference. In any other frame of reference, moving with respect to this selected frame of reference with speed, the speed of light should already be equal to -. This means that if the usual law of addition of velocities is valid, then when passing from one inertial frame of reference to another, the laws of electrodynamics should change so that in this new frame of reference the speed of light is already equal not, but -.
Thus, certain contradictions were revealed between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. They tried to overcome the difficulties that arose in three different ways.
First way: declare the principle of relativity as applied to electromagnetic phenomena untenable. This point of view was shared by the great Dutch physicist, the founder of the electronic theory X. Since the time of Faraday, electromagnetic phenomena have been considered as processes taking place in a special, all-pervading medium that fills all space - the world ether. The inertial frame of reference at rest relative to the ether is, according to Lorentz, a special, predominant frame of reference. In it, Maxwell's laws of electrodynamics are valid and the simplest in form. Only in this frame of reference is the speed of light in vacuum the same in all directions.
Second way: consider Maxwell's equations incorrect and try to change them in such a way that they do not change when passing from one inertial frame of reference to another (in accordance with the usual, classical concepts of space and time). Such an attempt, in particular, was undertaken by G. Hertz. According to Hertz, the ether is completely carried away by moving bodies and therefore electromagnetic phenomena proceed in the same way, regardless of whether the body is at rest or in motion. The principle of relativity remains true.
Finally, the third way: abandon the classical concepts of space and time in order to preserve both the principle of relativity and Maxwell's laws. This is the most revolutionary way, because it means a revision in physics of the most profound, basic concepts. From this point of view, it is not the equations of the electromagnetic field that turn out to be inaccurate, but the laws of Newtonian mechanics, consistent with the old concepts of space and time. It is necessary to change the laws of mechanics, and not the laws of electrodynamics of Maxwell.
The third method turned out to be the only correct one. Consistently developing it, A. Einstein came to new ideas about space and time. The first two ways, as it turned out, are refuted by experiment.
Lorentz's point of view, according to which there should be a selected frame of reference associated with the world ether, which is in absolute rest, was refuted by direct experiments.
If the speed of light were equal to 300,000 to m / s only in the frame of reference connected with the ether, then by measuring the speed of light in an arbitrary inertial frame of reference, one could detect the movement of this frame of reference in relation to the ether and determine the speed of this movement.
Einstein Albert (1879-1955)- the great physicist of the XX century. He created a new theory of space and time - the special theory of relativity. Generalizing this theory for non-inertial frames of reference, he developed the general theory of relativity, which is the modern theory of gravitation. He was the first to introduce the concept of light particles - photons. His work on the theory of Brownian motion led to the final victory of the molecular-kinetic theory of the structure of matter.
Just as a wind arises in a frame of reference moving relative to air, when moving relative to the ether (if, of course, ether exists), the "etheric wind" should be detected. An experiment on detecting the "ether wind" was set up in 1881 by the American scientists A. Michelson and E. Morley according to the idea expressed 12 years earlier by Maxwell.
This experiment compared the speed of light in the direction of motion of the Earth and in the perpendicular direction. The measurements were carried out very accurately using a special instrument - a Michelson interferometer. The experiments were carried out at different times of the day and at different times of the year. But a negative result was always obtained: the movement of the Earth in relation to the ether could not be detected.
Thus, the idea of the existence of a predominant frame of reference did not stand up to experimental verification. In turn, this meant that no special medium - "luminiferous ether", with which such a predominant frame of reference could be associated, does not exist.
When Hertz tried to change the laws of Maxwell's electrodynamics, it turned out that the new equations are unable to explain a number of observed facts. So, according to Hertz's theory, moving water should completely entrain the light spreading in it, since it carries away the ether in which the light propagates. Experience has shown that in reality this is not the case.
It turned out to be possible to reconcile the principle of relativity with Maxwell's electrodynamics only by rejecting the classical concepts of space and time, according to which distances and the course of time do not depend on the frame of reference.
Myakishev G. Ya., Physics. Grade 11: textbook. for general education. institutions: basic and profile. levels / G. Ya. Myakishev, BV Bukhovtsev, VM Charugin; ed. V.I. Nikolaeva, N.A. Parfentieva. - 17th ed., Rev. and add. - M.: Education, 2008 .-- 399 s: ill.
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After in the second half of the XIX century. Maxwell formulated the basic laws of electrodynamics, the question arose whether the principle of relativity, which is valid for mechanical phenomena, also applies to electromagnetic phenomena. In other words, do electromagnetic processes (interaction of charges and currents, propagation of electromagnetic waves, etc.) proceed in the same way in all inertial reference frames? Or, perhaps, a uniform rectilinear motion, without affecting mechanical phenomena, has some effect on electromagnetic processes?
To answer this question, it was necessary to find out whether the basic laws of electrodynamics (Maxwell's equations) change when passing from one inertial system to another, or, like Newton's laws, they remain unchanged. Only in the latter case can one discard doubts about the validity of the principle of relativity in relation to electromagnetic processes and consider this principle as a general law of nature.
The values of coordinates and time in two inertial reference systems are related to each other by Galileo's transformations. Galileo's transformations express classical ideas about space and time. Newton's equations are invariant under Galileo's transformations, and this fact just expresses the principle of relativity in mechanics.
The laws of electrodynamics are complex, and it is not easy to find out whether these laws are invariant with respect to Galileo's transformations or not. However, even simple considerations allow us to find the answer. In Maxwell's electrodynamics, the speed of propagation of electromagnetic waves in vacuum is the same in all directions and is equal to with= 3⋅10 10 cm / s. But, on the other hand, in accordance with the law of addition of velocities arising from Galileo's transformations, the velocity can be equal to c in only one selected frame of reference. In any other frame of reference moving with respect to this chosen frame with the speed \ (\ vec (\ upsilon), \) the speed of light must be \ (\ vec (c) - \ vec (\ upsilon) \). This means that if the usual law of addition of velocities is valid, then when passing from one inertial system to another, the laws of electrodynamics should change so that in this new frame of reference the speed of light is not \ (\ vec (c) \), but \ (\ vec (c) - \ vec (\ upsilon). \)
Thus, certain contradictions were revealed between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. The difficulties encountered could be attempted in three different ways.
The first possibility was to declare invalid the principle of relativity as applied to electromagnetic phenomena. The great Dutch physicist and founder of the electronic theory H. Lorentz took this point of view. Since the time of Faraday, electromagnetic phenomena have been considered as processes in a special, all-pervading medium that fills all space - the "world ether". The inertial reference frame at rest relative to the ether is, according to Lorentz, a special preferential system. In it, Maxwell's laws of electrodynamics are valid and have the simplest form. Only in this frame of reference is the speed of light in vacuum the same in all directions.
The second possibility is to consider the Maxwell equations themselves incorrect and try to change them in such a way that they do not change when passing from one inertial system to another (in accordance with the usual, classical concepts of space and time). Such an attempt, in particular, was undertaken by G. Hertz. According to Hertz, the ether is completely carried away by moving bodies, and therefore the electromagnetic phenomena playing out in the ether proceed in the same way, regardless of whether the body is at rest or in motion. The principle of relativity is true.
Finally, the third possibility of resolving these difficulties is to reject the classical concepts of space and time in order to preserve both the principle of relativity and Maxwell's equations. This is the most revolutionary path, for it means a revision of the deepest, most basic concepts in physics. From this point of view, it is not the equations of the electromagnetic field that are inaccurate, but the laws of Newtonian mechanics, consistent with the old concepts of space and time, expressed by Galileo's transformations. It is necessary to change the laws of mechanics, and not the laws of electrodynamics of Maxwell.
The third option turned out to be the only correct one. Consistently developing it, Einstein came to new ideas about space and time. The first two ways, as it turned out, are refuted by experiment.
When Hertz tried to change the laws of Maxwell's electrodynamics, it turned out that the new equations were not able to explain a number of observed facts. So, according to the theory of Hertz, the moving water should completely entrain the light spreading in it, since it carries away the ether in which the light propagates. Experience has shown that in reality this is not the case.
Lorentz's point of view, according to which there should be a selected frame of reference associated with the world ether, which is in absolute rest, was also refuted by direct experiments.
Literature
Myakishev G.Ya. Physics: Optics. The quantum physics. 11th grade: Textbook. for in-depth study of physics. - M .: Bustard, 2002 .-- S. 189-191.
The principle of relativity and Newton's laws
Galileo's principle of relativity organically entered the classical mechanics created by I. Newton. It is based on three "axioms" - three famous Newton's laws. Already the first of them, which says: "Every body continues to be held in its state of rest or uniform and rectilinear motion, as long as and since it is not forced by the applied forces to change this state," speaks of the relativity of motion and simultaneously indicates the existence of reference systems (they were called inertial), in which bodies that do not experience external influences move "by inertia" without accelerating or decelerating. It is these inertial systems that are meant when formulating the other two Newton's laws. During the transition from one inertial system to another, many quantities that characterize the motion of bodies, for example, their speed or the shape of the trajectory of motion, change, but the laws of motion, that is, the relations connecting these quantities, remain constant.
Galileo transformations
To describe mechanical movements, that is, the change in the position of bodies in space, Newton clearly formulated the concept of space and time. Space was thought of as a kind of "background" against which the movement of material points unfolds. Their position can be determined, for example, using the Cartesian coordinates x, y, z, depending on the time t. When passing from one inertial reference system K to another K ", moving relative to the first along the x-axis with a speed v, the coordinates are transformed: x" = x - vt, y "= y, z" = z, and the time remains unchanged: t "= t. Thus, it is assumed that time is absolute. These formulas are called Galileo transformations.
According to Newton, space acts as a kind of coordinate grid, which is not affected by matter and its movement. Time in such a "geometrical" picture of the world is, as it were, counted by some absolute clock, the course of which nothing can accelerate or slow down.
The principle of relativity in electrodynamics
For more than three hundred years, Galileo's principle of relativity was attributed only to mechanics, although in the first quarter of the 19th century, primarily due to the works of M. Faraday, the theory of the electromagnetic field arose, which was then further developed and mathematically formulated in the works of J.K. Maxwell. But the transfer of the principle of relativity to electrodynamics seemed impossible, since it was believed that all space was filled with a special medium - ether, in which the tensions were interpreted as the strengths of the electric and magnetic fields. At the same time, the ether did not affect the mechanical movements of bodies, so in mechanics it "was not felt", but the movement relative to the ether ("etheric wind") should have affected the electromagnetic processes. As a result, the experimenter in a closed cabin, by observing such processes, could, it seemed, determine whether his cabin was in motion (absolute!), Or whether it was at rest. In particular, scientists believed that the "etheric wind" should influence the propagation of light. Attempts to discover the "etheric wind", however, were unsuccessful, and the concept of mechanical ether was rejected, due to which the principle of relativity was reborn, as it were, but already as a universal one, valid not only in mechanics, but also in electrodynamics, and other areas of physics.
Lorentz transformations
Just as Newton's equations are the mathematical formulation of the laws of mechanics, Maxwell's equations are a quantitative representation of the laws of electrodynamics. The form of these equations must also remain unchanged when passing from one inertial reference system to another. To satisfy this condition, it is necessary to replace Galileo's transformations with other ones: x "= g (x-vt); y" = y; z "= z; t" = g (t-vx / c 2), where g = (1-v 2 / c 2) -1/2, and c is the speed of light in vacuum. The last transformations established by H. Lorentz in 1895 and bearing his name are the basis of the special (or particular) theory of relativity. At vc, they turn into Galileo transformations, but if v is close to c, then significant differences from the space-time picture, which is commonly called nonrelativistic, appear. First of all, the inconsistency of the usual intuitive ideas about time is revealed, it turns out that events that occur simultaneously in one frame of reference cease to be simultaneous in another. The law of transformation of speeds also changes.
Conversion of physical quantities in relativistic theory
In the relativistic theory, spatial distances and time intervals do not remain unchanged when passing from one frame of reference to another, moving relative to the first with a speed v. The lengths are shortened (in the direction of movement) by 1 / g times, and the intervals of time are "stretched" by the same number of times. The relativity of simultaneity is the main fundamentally new feature of the modern special theory of relativity.
The development of electrodynamics led to new ideas about space and time. According to the classical concepts of space and time, which were considered unshakable for centuries, movement has no effect on the flow of time (time is absolute), and the linear dimensions of any body do not depend on whether the body is at rest or in motion (length is absolute). The old, classical concepts of space and time were replaced by a new doctrine - Einstein's special theory of relativity.
After Maxwell formulated the basic laws of electrodynamics in the second half of the 19th century, scientists realized that Galileo's principle of relativity is difficult to apply to electromagnetic phenomena. The question arose: do electromagnetic processes (interaction of charges and currents, propagation of electromagnetic waves, and so on) proceed in the same way in all inertial reference frames? To answer this question, it is necessary to find out whether the basic laws of electrodynamics change during the transition from one inertial system to another, or, like Newton's laws, they remain unchanged. The laws of electrodynamics are complex. According to them, the speed of propagation of electromagnetic waves in a vacuum is the same in all directions and is equal to 300 million meters per second. But, on the other hand, according to the laws of Newtonian mechanics, this speed can be equal to 300 million in only one selected frame of reference. In any other frame of reference moving with respect to the first frame with some other speed, the speed of light should already be equal to the difference of these speeds. This means that if the usual law of addition of velocities is valid, then when passing from one inertial system to another, the laws of electrodynamics should change as well as the laws of mechanics. We found certain contradictions between electrodynamics and mechanics.
Certain contradictions were found between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. The first possibility was to declare invalid the principle of relativity as applied to electromagnetic phenomena. This point of view was shared by the great Dutch physicist, founder of the electronic theory H. Lorentz. According to this theory, the inertial reference frame at rest relative to the ether is a special, predominant system, since electromagnetic phenomena since the time of Faraday have been considered as processes in a special, all-pervading medium that fills all space - "world ether". If the speed of light were equal to 300,000 km per second only in the frame of reference in some inertial system, then it would be possible to find out how this system moves in relation to the ether. Just as a wind arises in a frame of reference moving relative to air, so when moving relative to the ether of a certain system, an "etheric wind" should be detected. If, of course, the ether exists. The second possibility is to consider Maxwell's equations incorrect and try to change them in such a way that they do not change when passing from one inertial system to another (in accordance with the usual, classical concepts of space and time). An experiment to detect the "ether wind" was set up in 1881 by American scientists A. Michelson and E. Morley. This idea was expressed by Maxwell 12 years earlier. It consisted in observing the displacement of the interference fringes and measuring the difference in the delays of light during its propagation along and across the Earth's orbital motion. Such an attempt was made even earlier by Heinrich Hertz. According to his assumption, the ether is completely carried away by moving bodies, and therefore electromagnetic phenomena proceed in the same way, regardless of whether the body is at rest or in motion. Here the principle of relativity is true. For example, according to Hertz's theory, when water moves, it completely carries away the light spreading in it, since it carries away the ether in which the light spreads. Experience has shown that in reality this is not the case. The third possibility of resolving these difficulties is to reject the classical concepts of space and time. At the same time, both the principle of relativity and Maxwell's laws can be preserved. From this point of view, it turns out that it is necessary to change the laws of mechanics, and not the laws of electrodynamics of Maxwell. The third option turned out to be the only correct one. Consistently developing this particular theory, Albert Einstein came to new ideas about space and time. He created a new theory of space and time, which today is called the special theory of relativity. Generalizing his theory for non-inertial frames of reference, Einstein built the general theory of relativity. It represents the modern theory of gravitation. Einstein was the first to introduce the concept of light particles, they are called photons. In his experiments, he compared the speed of light in the direction of motion of the Earth and in the perpendicular direction. Einstein made measurements very accurately using a special interferometer device developed by Michelson
and now bearing his name. The experiments were carried out at different times of the day and at different times of the year. At the same time, the movement of the Earth in relation to the ether could not be detected. All of this was as if, sticking your head out of the car window, at a speed of 100 km / h, you would not notice the headwind. Thus, the idea of the existence of a predominant frame of reference did not stand up to experimental verification. In turn, this meant that no special medium - "luminiferous ether" - with which such a predominant frame of reference could be associated, does not exist. Now you can easily reconcile the principle of relativity with Maxwell's electrodynamics. For this, it is necessary to abandon the classical concepts of space and time, according to which distances and the course of time do not depend on the frame of reference.
The theory of relativity we are considering is based on two postulates. The principle of relativity is the first and main postulate of Einstein's theory. It can be formulated as follows: all processes of nature proceed in the same way in all inertial reference frames. This means that in all inertial systems, physical laws have the same form. The second postulate: the speed of light in a vacuum is the same for all inertial reference frames. The speed of light occupies a special position. As follows from the postulates of the theory of relativity, the speed of light in a vacuum is the maximum possible speed of transmission of interactions in nature. The relativity of simultaneity is the solution to the paradox with spherical light signals. Let's describe the situation. Light simultaneously reaches points on a spherical surface centered at point O only from the point of view of an observer at rest with respect to the K (ka) system. From the point of view of an observer associated with the K1 (ka-1) system, light reaches these points at different times. Of course, the opposite is also true: in the K (ka) system, light reaches the points on the surface of the sphere centered at O1 (o-1) at different times, and not simultaneously, as it seems to the observer in the K1 (ka-1) system. Hence the conclusion that there is no paradox in reality. Until the beginning of the 20th century, no one doubted that time is absolute. That is, when two events, simultaneous for the inhabitants of the Earth, are simultaneous for the inhabitants of any cosmic civilization. The creation of the theory of relativity has shown that this is not the case. The idea of absolute time, which flows once and for all at a given pace, completely independently of the structure of matter and its motion, turns out to be wrong. "A minute is a relative value: if you have a date with a pretty girl, then she will fly by like an instant, and if you are sitting on a hot stove, it will seem like an eternity." So Einstein himself tried to explain his theory of relativity in simple words. Indeed, if we assume the instantaneous propagation of signals, then the statement that events at two spatially separated points A and B occurred simultaneously will have absolute meaning. Any events, for example two lightning strikes, are simultaneous if they occur with the same readings of the synchronized clock. Only by placing synchronized clocks at points A and B, it is possible to judge whether any two events occurred at these points at the same time or not. For clock synchronization, it will be more correct if they resort to light or electromagnetic signals in general, since the speed of electromagnetic waves in a vacuum is a strictly defined, constant cause. This is the method used when checking the clock on the radio. Let's take a closer look at one of the simple clock synchronization methods that does not require any calculations. Let us suppose that the astronaut wants to know whether the clocks A and B (be) set on opposite ends of the spacecraft are running the same way. For this, with the help of a source, which is located in the middle of the spacecraft and is motionless relative to it, the astronaut produces a flash of light. The light reaches both clocks at the same time. If the clock readings at this moment are the same, then the clock runs synchronously. But this will be so only with respect to the frame of reference associated with the ship. In the frame of reference, relative to which the ship is moving, the situation is different. The clock on the bow of the ship will move away from the place where the flash of the source light occurred, and in order to reach the clock A, the light must travel a distance greater than half the length of the ship. And the clock (bh) at the stern is approaching the place of the flash, and the path of the light signal is less than half the length of the ship. Therefore, an observer in the system associated with the ship will conclude that the signals reach both clocks at the same time. Any two events at points A and B (bs) are simultaneous in the frame of reference associated with the ship, and not simultaneous in the frame relative to which the ship is moving. But by virtue of the principle of relativity, these systems are completely equal. None of these systems can be preferred. Therefore, we must come to the conclusion that the simultaneity of spatially separated events is relative. The reason for the relativity of simultaneity is, as we see, the finiteness of the speed of propagation of sound signals. A number of the most important consequences concerning the properties of space and time follow from the postulates of the theory of relativity. Two relativistic effects are observed. First, in moving frames of reference, the dimensions of the body are reduced. Second, time dilation is observed in a moving frame of reference.
Since in moving frames of reference the linear dimensions of the body are reduced, this phenomenon leads to the fact that the mass of the body in the moving frame increases accordingly.
Obviously, the classical law of addition of velocities cannot be valid, since it contradicts the statement about the constancy of the speed of light in vacuum. We will write down the law of addition of velocities for the particular case when the body moves along the X1 (x-1) axis of the K1 (ka-1) frame of reference, which, in turn, moves with a certain velocity ve relative to the frame of reference K. We denote the body's velocity relative to K through be1, and the speed of the same body relative to K through be2. Then the relativistic law of addition of velocities will have the form.
When moving, the course of all physical processes, as well as chemical reactions in the human body, slows down. It is worth considering the most interesting consequences arising from Einstein's special theory of relativity. "The clock paradox", also known as the "twins paradox" - a thought experiment with the help of which they try to "prove" the inconsistency of the special theory of relativity. According to the special theory of relativity, from the point of view of "stationary" observers, all processes in moving objects slow down. But on the other hand , the same principle of relativity declares the equality of all inertial reference systems. On the basis of this reasoning is built, leading to an apparent contradiction. For clarity, the story of two twin brothers is considered. One of them (hereinafter the traveler) goes into space flight, the second (hereinafter homebody) remains The paradox is as follows: from the point of view of a couch potato, the clock of a moving traveler has a slow time course, therefore, after returning to Earth, they should lag behind the clocks of a couch potato. , brothers are equal, therefore , after returning, their watch should show the same time. The postulates of Einstein's theory of relativity also easily explain such an interesting phenomenon of outer space as a black hole. A black hole forms when a massive star is gravitationally compressed. If the mass of a star is more than 2-3 times the mass of the Sun, then the core of this star shrinks and reaches such a density that even light cannot overcome the forces of gravity of the surrounding cosmic bodies. Einstein Albert (1879-1955) - the great physicist of the XX century. He created a new theory of space and time - the special theory of relativity. Generalizing this theory for non-inertial frames of reference, he developed the general theory of relativity, which is the modern theory of gravitation. He was the first to introduce the concept of light particles - photons. His work on the theory of Brownian motion led to the final victory of the molecular-kinetic theory of the structure of matter. He predicted "quantum teleportation" and the Einstein-de Haas gyromagnetic effect. Since 1933 he worked on problems of cosmology and unified field theory. Thanks to Albert Einstein, science revised the understanding of the physical essence of space and time, he built a new theory of gravity to replace the Newtonian one. Einstein, along with Planck, laid the foundations of quantum theory. All these concepts have been repeatedly confirmed by experiments and form the foundation of modern physics.
Topic: “The laws of electrodynamics and the principle of relativity. Postulates of the theory of relativity ”.
Purpose: to form an idea of students about how the concepts of space and time have changed under the influence of the provisions of Einstein's special theory of relativity. To acquaint students with the special theory of relativity, introduce the basic concepts, reveal the content of the main provisions of the SRT, acquaint them with the conclusions of the SRT and the experimental facts that confirm them.
Equipment: computer, projector, presentation.
During the classes.
I. Organizational moment.
II. Analysis of the test work.
III. Learning new material.
At the end of the 19th century, the main provisions of electrodynamics were formulated. A question arose as to the validity of Galileo's principle of relativity as applied to electromagnetic phenomena. In different inertial systems, do electromagnetic phenomena proceed in the same way: how do electromagnetic waves propagate, how do charges and currents interact when passing from one inertial system to another?
Inertial is a frame of reference relative to which free bodies move at a constant speed. Does uniform rectilinear motion have an effect on electromagnetic processes (it does not affect mechanical phenomena)? When passing from one inertial system to another, do the laws of electrodynamics change, or how do Newton's laws remain constant?
For example, according to the laws of addition of velocities in mechanics, the velocity can be equal to c = 3 · 10 8 m / s only in one frame of reference. In another frame of reference, which itself moves with the speed Ѵ, the speed of light should be equal to c̄-̄. But according to the laws of electrodynamics, the speed of electromagnetic waves in vacuum in different directions is equal to c = 3 10 8 m / s
Contradictions arose between electrodynamics and Newtonian mechanics. In order to resolve the contradictions that have arisen, three different methods have been put forward.
The first way was to abandon the principle of relativity as applied to electromagnetic phenomena. This possibility was supported by the founder of the electronic theory H. Lorentz (Dutch). Then it was believed that electromagnetic phenomena take place in the "world ether" - this is an all-pervading medium that fills the entire world space. The inertial frame of reference was considered by Lorentz as a frame at rest with respect to the ether. In this system, the laws of electrodynamics are strictly fulfilled and in this frame of reference the speed of light in vacuum is the same in all directions.
Second way was to declare Maxwell's equations incorrect. G. Hertz tried to rewrite them in such a way that they did not change when passing from one inertial system to another, i.e. like the laws of mechanics. Hertz believed that the ether moves together with moving bodies and therefore electromagnetic processes occur in the same way regardless of the movement or rest of the bodies. That is, G. Hertz retained the principle of relativity. The third way was to reject traditional ideas about space and time. Maxwell's equations and the principle of relativity were retained, but the most obvious, most basic concepts of classical mechanics had to be abandoned. This method of resolving contradictions turned out to be correct in the end. The experiment refuted both the first and the second attempts to correct the contradictions between electrodynamics and mechanics, leaving the principle of relativity unchanged. Developing the third way to solve the problem, A. Einstein proved that the concepts of space and time were outdated and replaced them with new ones. Maxwell's equations, corrected by Hertz, could not explain the observed phenomena. Experience has shown that the medium cannot carry the light along with it, since it will carry away the ether in which the light propagates. The experiments of the American scientists A. Michelson and E. Morley proved that no medium of the "luminiferous ether" type exists. It turned out to be possible to combine Maxwell's electrodynamics and the principle of relativity by rejecting the traditional concepts of space and time, i.e. neither distance nor the passage of time depend on the frame of reference.
Special theory of relativity (SRT; also special theory of relativity) is a theory that describes motion, the laws of mechanics and space-time relations at arbitrary speeds of motion, less than the speed of light in a vacuum, including those close to the speed of light. Within the framework of the special theory of relativity, the classical mechanics of Newton is the approximation of low speeds. Generalization of SRT for gravitational fields is called general theory of relativity.
The deviations in the course of physical processes from the predictions of classical mechanics described by the special theory of relativity are called relativistic effects, and the velocities at which such effects become significant are called relativistic velocities.
The special theory of relativity was developed at the beginning of the 20th century through the efforts of G.A. Lorentz, A. Poincaré, A. Einstein and other scientists. The experimental basis for the creation of SRT was the Michelson experiment. His results were unexpected for the classical physics of his time: the independence of the speed of light from the direction (isotropy) and the orbital motion of the Earth around the Sun. An attempt to interpret this result at the beginning of the 20th century resulted in a revision of classical concepts, and led to the creation of the special theory of relativity.
When moving at near-light speeds, the laws of dynamics are modified. Newton's second law, linking force and acceleration, must be modified at the speeds of bodies close to the speed of light. In addition, the expression for the momentum and kinetic energy of a body has a more complex dependence on velocity than in the nonrelativistic case. The special theory of relativity has received numerous experimental confirmations and is the correct theory in its field of applicability.
The fundamental nature of the special theory of relativity for physical theories built on its basis has led to the fact that the term "special theory of relativity" is practically not used in modern scientific articles, usually they speak only of the relativistic invariance of a separate theory.
The special theory of relativity, like any other physical theory, can be formulated on the basis of basic concepts and postulates (axioms) plus the rules of correspondence to its physical objects.
Frame of reference is a certain material body, chosen as the beginning of this system, a method for determining the position of objects relative to the beginning of the frame of reference and a method for measuring time. A distinction is usually made between reference systems and coordinate systems. Adding a time measurement procedure to a coordinate system "turns" it into a reference system.
Inertial reference system (ISO) - this is such a system, relative to which the object, not subject to external influences, moves uniformly and rectilinearly.
Event is called any physical process that can be localized in space, and with a very short duration. In other words, the event is fully characterized by the coordinates (x, y, z) and the moment of time t.
Examples of events are: a flash of light, the position of a material point at a given time, etc. Usually, two inertial systems S and S are considered. "Time and coordinates of an event, measured relative to the S system, are denoted as (t, x, y, z) , and the coordinates and time of the same event, measured relative to the S "system, as (t", x ", y", z "). It is convenient to assume that the coordinate axes of the systems are parallel to each other and the system S "moves along the x-axis of the system S with a speed v. x, y, z), which are called Lorentz transformations.
Usually two inertial systems S and S are considered. "The time and coordinates of an event measured relative to the S system are denoted as (t, x, y, z), and the coordinates and time of the same event, measured relative to the S system, as (t" , x ", y", z "). It is convenient to assume that the coordinate axes of the systems are parallel to each other and the system S "moves along the x-axis of the system S with speed v. x, y, z), which are called Lorentz transformations.
1 principle of relativity.
All laws of nature are invariant with respect to the transition from one inertial frame of reference to another (they proceed in the same way in all inertial frames of reference).
This means that in all inertial systems, physical laws (not only mechanical) have the same form. Thus, the principle of relativity of classical mechanics is generalized to all processes of nature, including electromagnetic. This generalized principle is called Einstein's principle of relativity.
2 the principle of relativity.
The speed of light in a vacuum does not depend on the speed of movement of the light source or the observer and is the same in all inertial reference frames.
The speed of light in SRT occupies a special position. This is the maximum rate of transmission of interactions and signals from one point in space to another.
The consequences of a theory based on these principles have been confirmed by endless experimental tests. SRT allowed solving all the problems of "pre-Einstein" physics and explaining the "contradictory" results of experiments known by that time in the field of electrodynamics and optics. Subsequently, SRT was supported by experimental data obtained in the study of the motion of fast particles in accelerators, atomic processes, nuclear reactions, etc.
Example. SRT postulates are in clear contradiction with classical concepts. Consider such a thought experiment: at time t = 0, when the coordinate axes of the two inertial systems K and K "coincide, a short flash of light occurred at the common origin of coordinates. During time t, the systems will shift relative to each other by a distance υt, and the spherical wave front at each system will have a radius ct, since the systems are equal and in each of them the speed of light is c. From the point of view of an observer in frame K, the center of the sphere is at point O, and from the point of view of an observer in frame K "it will be at point O ". Consequently, the center of the spherical front is simultaneously located at two different points!
Explanation of the contradictions.
The reason for the resulting misunderstanding lies not in the contradiction between the two principles of STR, but in the assumption that the position of the fronts of spherical waves for both systems refers to the same moment in time. This assumption is contained in the Galilean transformation formulas, according to which time flows in both systems in the same way: t = t ". Consequently, Einstein's postulates are in contradiction not with each other, but with the Galilean transformation formulas. Therefore, to replace the Galilean transformations, SRT proposed other transformation formulas during the transition from one inertial system to another - the so-called Lorentz transformations, which, at speeds of motion close to the speed of light, can explain all relativistic effects, and at low speeds (υ
IV. Consolidation of the studied material
1. The solution to which problem led to new ideas about space and time.
2. Three ways to solve this problem.
3. Which method was fair?
4. Which of the following statements correspond to the postulates of the theory of relativity: 1 - all processes of nature proceed in the same way in any inertial frame of reference; 2 - the speed of light in vacuum is the same in all reference frames; 3 - all processes of nature are relative and do not proceed in different frames of reference in the same way?
A... Only 1 B. Only 2 V. Only 3 G. 1 and 2 D. 1 and 3
5. From Maxwell's equations it follows that the speed of propagation of light waves in vacuum in all directions (the same).
6. Is it possible to establish by any mechanical experiments whether the inertial frame of reference is at rest or is it moving straight and uniformly?
V. Lesson summary
Vi. Homework: §75.76.
