Are the laws of electrodynamics fulfilled on the moon? Transformation of physical quantities in relativistic theory. The main consequences arising from the postulates of the theory of relativity

The development of electrodynamics led to new ideas about space and time. According to the classical concepts of space and time, considered unshakable for centuries, movement has no effect on the passage of time (time is absolute), and the linear dimensions of any body do not depend on whether the body is at rest or moving (length is absolute). The old, classical ideas about space and time have been replaced by a new doctrine - Einstein's special theory of relativity.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 was difficult to apply to electromagnetic phenomena. The question arose: do electromagnetic processes occur (interaction of charges and currents, propagation electromagnetic waves and so on) the same in all inertial frames of reference? To answer this question, it is necessary to find out whether the basic laws of electrodynamics change when moving 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 Newton's laws of mechanics, this speed can be equal to 300 million in only one chosen frame of reference. In any other frame of reference, moving in relation 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 moving from one inertial system to another, the laws of electrodynamics should change in the same way as the laws of mechanics. We discovered certain contradictions between electrodynamics and mechanics.
Certain contradictions were discovered between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. The first possibility was to declare untenable the principle of relativity as applied to electromagnetic phenomena. This point of view was shared by the great Dutch physicist, founder of electronic theory, H. Lorentz. According to this theory, the inertial frame of reference, at rest relative to the ether, is a special, preferential system, since electromagnetic phenomena, since the time of Faraday, have been considered as processes in a special, all-pervasive medium that fills all space - the “world ether”. If the speed of light were equal to 300,000 km per second only in the frame of reference in some inertial frame, then it would be possible to detect how this frame moves in relation to the ether. Just as wind arises in a reference system 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 moving from one inertial system to another (in accordance with the usual, classical ideas about space and time). An experiment to detect the “ethereal wind” was carried out 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 interference fringes and measuring the difference in delays of light as it propagated 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 moving. Here the principle of relativity is valid. For example, according to Hertz's theory, when water moves, it completely carries along with it the light propagating in it, since it carries away the ether in which the light propagates. Experience has shown that in reality this is not the case. The third possibility of resolving these difficulties is to abandon the classical concepts of space and time. In this case, both the principle of relativity and Maxwell's laws can be preserved. From this point of view, it turns out that it is the laws of mechanics that need to be changed, and not Maxwell’s laws of electrodynamics. The third possibility turned out to be the only correct one. Consistently developing this 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 constructed the general theory of relativity. It represents the modern theory of gravity. Einstein first introduced the concept of particles of light, they are called photons. In his experiments, he compared the speed of light in the direction of the Earth's movement and in the perpendicular direction. Einstein carried out 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 different seasons. At the same time, it was not possible to detect the movement of the Earth in relation to the ether. It was all like sticking your head out of a car window and not noticing the headwind at 100 km/h. Thus, the idea of ​​the existence of a preferential frame of reference did not stand up to experimental testing. In turn, this meant that no special medium - the “luminiferous ether” - with which such a preferential frame of reference could be associated existed. Now it is easy to reconcile the principle of relativity with Maxwell's electrodynamics. To do this, we need to abandon the classical ideas about space and time, according to which distances and the passage of time do not depend on the reference system.
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 identically in all inertial frames of reference. This means that in all inertial systems the physical laws have the same form. The second postulate: the speed of light in vacuum is the same for all inertial frames of reference. The speed of light has 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. In the relativity of simultaneity lies the solution to the paradox with spherical light signals. Let us describe the situation. Light simultaneously reaches points on a spherical surface with a center at point O only from the point of view of an observer who is at rest relative to the system K (ka). 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 points on the surface of a sphere with a center at O1 (o-1) at different times, and not simultaneously, as it appears to the observer in the K1 (ka-1) system. From this it follows that there is in reality no paradox. 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 space civilization. The creation of the theory of relativity showed that this is not so. The idea of ​​absolute time, which flows once and for all at a given pace, completely independent of the structure of matter and its movement, turns out to be incorrect. “A minute is a relative value: if you are on a date with a pretty girl, then it will fly by like an instant, but if you are sitting on a hot stove, then it will seem like an eternity.” This is how Einstein himself tried to explain in simple words his theory of relativity. Indeed, if we assume instantaneous propagation of signals, then the statement that events at two spatially separated points A and B occurred simultaneously will make absolute sense. Any events, for example two lightning strikes, are simultaneous if they occur at the same readings of synchronized clocks. Only by having synchronized clocks at points A and B can one judge whether two events occurred at these points simultaneously or not. To synchronize clocks, it would be more correct to resort to light or electromagnetic signals in general, since the speed of electromagnetic waves in a vacuum is strictly defined, permanent reason. This is exactly the method used when checking watches via radio. Let's take a closer look at one of the simple methods clock synchronization, which does not require any calculations. Let’s say that an astronaut wants to find out whether the clocks A and B (be) installed at opposite ends of the spacecraft are running the same way. To do this, using a source that is located in the middle of the ship and motionless relative to it, the astronaut produces a flash of light. The light reaches both clocks at the same time. If the clock readings are the same at this moment, then the clocks are synchronous. But this will only be true with respect to the reference frame associated with the ship. In the reference system relative to which the ship is moving, the situation is different. The clock on the bow of the ship will move away from where the flash of light from the source occurred, and to reach clock A, the light must travel a distance greater than half the length of the ship. And the clock (be) on the stern is approaching the flash point, and the path of the light signal is less than half the length of the ship. Therefore, an observer located in the system associated with the ship will conclude that the signals reach both clocks simultaneously. Any two events at points A and B (be) 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 due to 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 finite speed of propagation of sound signals. A number of 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 reference frames the dimensions of the body are reduced. Second, time dilation is observed in a moving reference frame.
Since the linear dimensions of a body are reduced in moving reference systems, 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 a vacuum. We will write down the law of addition of velocities for the particular case when the body moves along the axis X1 (x-1) of the reference frame K1 (ka-1), which, in turn, moves with a certain speed ve relative to the reference frame K. Let us denote the speed of the body relative to K through ve1, and the speed of the same body relative to K through ve2. Then the relativistic law of addition of velocities will look like:
When moving, the flow of all physical processes slows down, as well as chemical reactions V human body. It is worth considering the most interesting consequences arising from Einstein's special theory of relativity. The “clock paradox,” also known as the “twin paradox,” is 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 frames of reference. Based on this, a reasoning is built that leads to an apparent contradiction. For clarity, the story of two twin brothers is considered. One of them (hereinafter referred to as the traveler) goes on a space flight, the second (hereinafter referred to as the homebody) remains on Earth. The paradox lies in the following: from the point of view of the couch potato, the clock of the moving traveler has a slow passage of time, therefore, after returning to Earth, it should lag behind the couch potato's clock. Relative to the traveler, the Earth was moving, which means that the couch potato's clock should lag behind. But on the third side , the brothers have equal rights, therefore, after returning, their watches 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 is formed by the gravitational compression of a massive star. If the mass of a certain star is more than 2-3 times the mass of the Sun, then the core of this star contracts and reaches such a density that even light cannot overcome the gravitational force of the surrounding cosmic bodies. Einstein Albert (1879-1955) - great physicist of the 20th century. He created a new theory of space and time - the special theory of relativity. Generalizing this theory for non-inertial reference systems, he developed the general theory of relativity, which is the modern theory of gravity. For the first time he introduced the concept of particles of light - 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 gyromagnetic Einstein-de Haas effect. Since 1933, he worked on problems of cosmology and unified field theory. Thanks to Albert Einstein, science underwent a revision of the understanding of the physical essence of space and time; he built a new theory of gravity to replace Newton’s. Einstein and 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".

Goal: to form students’ understanding of 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 basic concepts, reveal the content of the main provisions of SRT, introduce the conclusions of SRT and the experimental facts that confirm them.

Equipment: computer, projector, presentation.

During the classes.

I. Organizational moment.

II. Analysis of test work.

III. Learning new material.

At the end of the 19th century, the basic principles of electrodynamics were formulated. A question arose about the validity of Galileo's principle of relativity in relation to electromagnetic phenomena. Do electromagnetic phenomena occur in the same way in different inertial systems: how do electromagnetic waves propagate, how do charges and currents interact when moving from one inertial system to another?

Inertial is a reference system relative to which free bodies move at a constant speed. Does uniform rectilinear motion have an effect on electromagnetic processes (does it not affect mechanical phenomena)? When moving from one inertial frame to another, do the laws of electrodynamics change or do Newton's laws remain constant?

For example, according to the laws of addition of velocities in mechanics, the speed can be equal to c = 3·10 8 m/s in only one reference system. In another frame of reference, which itself moves with speed V, the speed of light should be equal to с̄-V̄. 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. To resolve the contradictions that arose, three different methods were proposed.

First way was to abandon the principle of relativity as applied to electromagnetic phenomena. This possibility was supported by the founder of electronic theory, H. Lorenz (Dutch). Then it was believed that electromagnetic phenomena occur in the “world ether” - this is an all-pervasive medium that fills the entire world space. The inertial reference system was considered by Lorentz as a system at rest relative to the ether. In this system, the laws of electrodynamics are strictly observed and in this reference system 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 moving 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 abandon traditional ideas about space and time. Maxwell's equations and the principle of relativity were preserved, but the most obvious, most basic ideas 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 second attempts to correct the contradictions that arose between electrodynamics and mechanics, leaving the principle of relativity unchanged. Developing the third way to solve the problem, A. Einstein proved that ideas about 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 away light, since it will carry away the ether in which the light propagates. The experiments of American scientists A. Michelson and E. Morley proved that no medium like the “luminiferous ether” exists. It turned out to be possible to combine Maxwell's electrodynamics and the principle of relativity by abandoning traditional ideas about space and time, i.e. Neither the distance nor the passage of time depend on the reference system.

Special theory of relativity (STR; also private theory relativity) is a theory that describes motion, the laws of mechanics and space-time relations at arbitrary speeds of movement less than the speed of light in a vacuum, including those close to the speed of light. Within the framework of special relativity, classical Newtonian mechanics is a low-velocity approximation. A generalization of STR for gravitational fields is called general relativity.

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 speeds at which such effects become significant are called relativistic speeds.

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 Michelson's experiment. His results were unexpected for the classical physics of his time: the independence of the speed of light from 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 change. Newton's second law, relating force and acceleration, must be modified for bodies with velocities close to the speed of light. In addition, the expression for the momentum and kinetic energy of the body has a more complex dependence on speed than in the nonrelativistic case. The special theory of relativity has received numerous experimental confirmations and is a correct theory in its field of applicability.

The fundamental nature of the special theory of relativity for physical theories built on its basis has now led to the fact that the term “special theory of relativity” itself is practically not used in modern scientific articles; they usually only talk about 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 represents 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 reference system, and a method for measuring time. Usually a distinction is 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 (IRS)) - this is a system in relation to which an object not subject to external influences, moves uniformly and rectilinearly.

Event is any physical process that can be localized in space, and at the same time having a very short duration. In other words, the event is completely characterized by coordinates (x, y, z) and 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." The time and coordinates of some event measured relative to the system S are denoted as (t, x, y, z) , and the coordinates and time of the same event, measured relative to the system S" 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. One of the problems of SRT is to search for relations connecting (t", x", y", z") and (t, x, y, z), which are called Lorentz transformations.

Usually two inertial systems S and S are considered." The time and coordinates of some 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 are designated 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. One of the problems of SRT is to search for relations connecting (t", x", y", z") and (t, 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 identically in all inertial frames of reference).

This means that in all inertial systems the physical laws (not just mechanical ones) have the same form. Thus, the principle of relativity of classical mechanics is generalized to all processes of nature, including electromagnetic ones. This generalized principle is called Einstein's principle of relativity.

2 principle of relativity.

The speed of light in a vacuum does not depend on the speed of movement of the light source or observer and is the same in all inertial frames of reference.

The speed of light occupies a special position in the SRT. This is the maximum speed of transmission of interactions and signals from one point in space to another.

The consequences of the theory created on the basis of these principles were confirmed by endless experimental tests. STR made it possible to resolve all the problems of “pre-Einstein” physics and explain the “contradictory” results of experiments in the field of electrodynamics and optics known at that time. Subsequently, STR was supported by experimental data obtained from studying the movement of fast particles in accelerators, atomic processes, nuclear reactions, etc.

Example. The postulates of SRT are in clear contradiction with classical ideas. Let's consider the following thought experiment: at the moment of time t = 0, when the coordinate axes of two inertial systems K and K" coincide, a short-term flash of light occurred at the common origin of coordinates. During time t, the systems will move relative to each other by a distance υt, and the spherical wave front will each system will have a radius ct, since the systems are equal and in each of them the speed of light is equal to c. From the point of view of an observer in system K, the center of the sphere is at point O, and from the point of view of an observer in system K" it will be at point O ". Consequently, the center of the spherical front is simultaneously located at two different points!

Explanation of contradictions.

The reason for the misunderstanding that arises lies not in the contradiction between the two principles of SRT, 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 the same way in both systems: t = t". Consequently, Einstein’s postulates are in conflict not with each other, but with the Galilean transformation formulas. Therefore, to replace the Galilean transformations, SRT proposed other transformation formulas when transitioning from one inertial system to another - the so-called Lorentz transformations, which at motion speeds close to the speed of light allow us to explain all relativistic effects, and at low speeds (υ

IV. Reinforcing the material learned

1. Solving which problem led to new ideas about space and time.

2. Three ways to solve this problem.

3. Which method turned out to be fair?

4. Which of the following statements correspond to the postulates of the theory of relativity: 1 - all processes of nature proceed identically in any inertial frame of reference; 2 - the speed of light in vacuum is the same in all reference systems; 3 - all processes of nature are relative and proceed differently in different frames of reference?

A. Only 1 B. Only 2 IN. 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 is (the same).

VI. Homework: §75.76.

« Physics - 11th grade"

Laws of electrodynamics and the principle of relativity

According to the classical concepts of space and time, considered unshakable for centuries, movement has no effect on the passage of time (time is absolute), and the linear dimensions of any body do not depend on whether the body is at rest or moving (length is absolute).

Einstein's special theory of relativity is a new doctrine of space and time, which replaced the old (classical) ideas.

The principle of relativity in mechanics and electrodynamics

After in the second half of the 19th 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 (the interaction of charges and currents, the propagation of electromagnetic waves, etc.) proceed the same way in all inertial frames of reference? 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 moving from one inertial frame of reference to another, or, like Newton's laws, they remain unchanged. Only in the latter case can we cast aside 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 an easy task. However, simple considerations would seem to 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 s = 3 10 8 m/s. But in accordance with the law of addition of velocities of Newtonian mechanics, the speed can be equal to the speed of light only in one selected frame of reference. In any other frame of reference, moving with respect to this chosen frame of reference with speed , the speed of light must already be equal to - . This means that if the usual law of addition of velocities is valid, then when moving from one inertial frame of reference to another, the laws of electrodynamics must change so that in this new frame of reference the speed of light is no longer equal to , but - .

Thus, certain contradictions were discovered 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 invalid as applied to electromagnetic phenomena. This point of view was shared by the great Dutch physicist, founder of electronic theory, X. Lorentz. Since the time of Faraday, electromagnetic phenomena have been considered as processes occurring in a special, all-pervasive 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, preferential frame of reference. In it, Maxwell's laws of electrodynamics are valid and most simple in form. Only in this reference frame 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 moving from one inertial reference system to another (in accordance with the usual, classical concepts of space and time). Such an attempt, in particular, was made by G. Hertz. According to Hertz, the ether is completely entrained by moving bodies and therefore electromagnetic phenomena proceed in the same way regardless of whether the body is at rest or moving. The principle of relativity remains valid.

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 path, because it means a revision of the deepest, most basic concepts in physics. From this point of view, it is not the equations that turn out to be inaccurate electromagnetic field, and Newton's laws of mechanics, consistent with old ideas about space and time. It is the laws of mechanics that need to be changed, not Maxwell's laws of electrodynamics.

The third method turned out to be correct. Consistently developing it, A. Einstein came to new ideas about space and time. The first two ways, as it turns out, are refuted by experiment.

Lorentz's point of view, according to which there must be a chosen frame of reference associated with the world ether, which is at absolute rest, was refuted by direct experiments.

If the speed of light were equal to 300,000 km/s only in the reference frame associated with the ether, then by measuring the speed of light in an arbitrary inertial reference frame, it would be possible to detect the movement of this reference system relative to the ether and determine the speed of this movement. Just as wind arises in a frame of reference moving relative to air, when moving relative to the ether (if, of course, the ether exists), an “etheric wind” should be detected. The experiment to detect the “ethereal wind” was carried out in 1881 by American scientists A. Michelson and E. Morl and based on an idea expressed 12 years earlier by Maxwell.

This experiment compared the speed of light in the direction of the Earth's motion and in the perpendicular direction. The measurements were carried out very accurately using a special device - a Michelson interferometer. The experiments were carried out at different times of the day and different seasons. But it always worked out negative result: the movement of the Earth in relation to the ether could not be detected.

Thus, the idea of ​​the existence of a preferential frame of reference did not stand up to experimental testing. In turn, this meant that no special medium, the “luminiferous ether,” with which such a preferential frame of reference could be associated, existed.

When Hertz tried to change Maxwell's laws of electrodynamics, it turned out that the new equations were unable to explain a number of observed facts. Thus, according to Hertz’s theory, moving water should completely entrain the light propagating in it, since it entrains the ether in which the light propagates. Experience has shown that in reality this is not the case.

So,
It turned out to be possible to reconcile the principle of relativity with Maxwell's electrodynamics only by abandoning the classical concepts of space and time, according to which distances and the passage of time do not depend on the reference system.

Postulates of the theory of relativity

The theory of relativity is based on two postulates.

What is a postulate?

Postulate in physical theory plays the same role as an axiom in mathematics.
This is a basic proposition that cannot be logically proven.
In physics, a postulate is the result of a generalization of experimental facts.

1.
All processes in nature proceed identically in all inertial frames of reference.

This means that in all inertial frames of reference the physical laws have the same form.
Thus, the principle of relativity of classical mechanics applies to all processes in nature, including electromagnetic ones.

2.
The speed of light in vacuum is the same in all inertial frames of reference and does not depend on either the speed of the source or the speed of the receiver of the light signal.

The speed of light thus occupies a special position.
Moreover, 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.

In order to formulate the postulates of the theory of relativity, great scientific courage was needed, since they contradicted the classical ideas about space and time.

In fact, let us assume that at the moment of time when the origin of coordinates of the inertial reference systems TO And K 1, moving relative to each other at a speed , coincide, a short-term flash of light occurs at the origin of coordinates.
During t the reference systems will shift relative to each other by a distance υt, and the spherical wave surface will have a radius υt.
Reference systems TO And K 1 are equal, and the speed of light is the same in both frames of reference.

Therefore, from the point of view of the observer associated with the reference frame TO, the center of the sphere will be at the point ABOUT, and from the point of view of the observer associated with the reference system K 1, - at the point O 1.

But the same spherical surface cannot have centers at points O and O 1.
This obvious contradiction follows from reasoning based on the postulates of the theory of relativity.

So,
there is a contradiction with classical ideas about space and time, which are unfair at high speeds of movement.
However, the theory of relativity itself does not contain contradictions and is absolutely logical.

Abstract on the subject of Concepts of Modern Natural Science

Theory of relativity

The development of electrodynamics led to a revision of ideas about space and time. According to the classical concepts of space and time, considered unshakable for centuries, movement has no effect on the passage of time (time is absolute), and the linear dimensions of any body do not depend on whether the body is at rest or moving (length is absolute).

Einstein's special theory of relativity is a new theory of space and time that replaced the old (classical) ideas.

Laws of electrodynamics and the principle of relativity

After the creation of electrodynamics, doubts arose about the validity of Galileo's principle of relativity as applied to electromagnetic phenomena.

The principle of relativity in mechanics and electrodynamics . After Maxwell formulated the basic laws of electrodynamics in the second half of the 19th century, the question arose whether the principle of relativity also applies to electromagnetic phenomena. In other words, do electromagnetic processes (interaction of charges and currents, propagation of electromagnetic waves, etc.) proceed the same way in all inertial frames of reference? Or, perhaps, 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 change when moving from one inertial system to another or, like Newton’s laws, they remain unchanged. Only in the latter case can we cast aside 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 an easy task. However, simple considerations would seem to 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, on the other hand, in accordance with the law of addition of velocities of Newton’s mechanics, the speed can be equal to c only in one selected frame of reference. In any other frame of reference moving with respect to this chosen frame with speed v, the speed of light should already be equal c ─ v. This means that if the usual law of addition of velocities is valid, then when moving from one inertial frame to another, the laws of electrodynamics should change so that in this new frame of reference the speed of light is no longer equal to With, A c ─ v.

Thus, certain contradictions were discovered 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.

The first possibility was to declare untenable the principle of relativity as applied to electromagnetic phenomena. This position was defended by the great Dutch physicist, founder of electronic theory, H. Lorentz. Since the time of Faraday, electromagnetic phenomena have been considered as processes in a special, all-pervasive medium that filled all space, the “world ether.” The inertial frame of reference, 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 reference frame is the speed of light in vacuum the same in all directions.

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 moving from one inertial system to another (in accordance with the usual, classical ideas about space and time). Such an attempt, in particular, was made by G. Hertz. According to Hertz, the ether is completely entrained by moving bodies, and therefore electromagnetic phenomena proceed in the same way, regardless of whether the body is at rest or moving. The principle of relativity is correct.

Finally, the third possibility of resolving these difficulties is to 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 path, because 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 turn out to be inaccurate, but Newton’s laws of mechanics, consistent with the old ideas about space and time. It is the laws of mechanics that need to be changed, not Maxwell's laws of electrodynamics.

The third possibility 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 turns out, are refuted by experiment.

When Hertz tried to change Maxwell's laws of electrodynamics, it turned out that the new equations were not able to explain a number of observed facts. Thus, according to Hertz’s theory, moving water should completely carry away the light propagating in it, because it carries away the ether in which light travels. Experience has shown that in reality this is not the case.

Lorentz's point of view, according to which there must be a chosen frame of reference associated with the world ether, which is at absolute rest, was also refuted by direct experiments.

If the speed of light were equal to 300,000 km/s only in the reference frame associated with the ether, then by measuring the speed of light in an arbitrary inertial frame, it would be possible to detect the movement of this system in relation to the ether and determine the speed of this movement. Just as wind arises in a frame of reference moving relative to air, when moving relative to the ether (if, of course, the ether exists), an “etheric wind” should be detected. An experiment to detect the “ethereal wind” was carried out in 1881 by American scientists A. Michelson and E. Morley, based on an idea expressed 12 years earlier by Maxwell.

This experiment compared the speed of light in the direction of the Earth's motion and in the perpendicular direction. The measurements were carried out very accurately using a special device - a Michelson interferometer. The experiments were carried out at different times of the day and different seasons. But the result was always negative: the movement of the Earth in relation to the ether could not be detected.

Thus, the idea of ​​the existence of a preferential frame of reference did not stand up to experimental testing. In turn, this meant that no special medium—the “luminiferous ether”—with which such a preferential frame of reference could be associated existed.

It turned out to be possible to reconcile the principle of relativity with Maxwell's electrodynamics only by abandoning the classical concepts of space and time, according to which distances and the passage of time do not depend on the reference system.

Postulates of the theory of relativity

The theory of relativity is based on two postulates.

To explain the negative results of the experiment of Michelson and other experiments, which were supposed to detect the movement of the Earth relative to the ether, various hypotheses were introduced. With the help of these hypotheses, they tried to explain why it was not possible to detect a preferential frame of reference (it was believed that such a system supposedly exists in reality).

Einstein approached the problem in a completely different way: there is no point in inventing various hypotheses to explain the negative results of all attempts to discover the difference between inertial systems. The law of nature is the complete equality of all inertial reference systems in relation to not only mechanical, but also electromagnetic processes. There is no difference between the state of rest and uniform motion in a straight line.

The principle of relativity is the main postulate of Einstein's theory. It can be formulated like this: all processes of nature proceed identically in all inertial frames of reference.

This means that in all inertial systems the physical laws have the same form. Thus, the principle of relativity of classical mechanics is generalized to all processes in nature, including electromagnetic ones. But the theory of relativity is based not only on the principle of relativity. There is also a second postulate: the speed of light in vacuum is the same for all inertial frames of reference. It does not depend either on the speed of the source or on the speed of the receiver of the light signal.

The speed of light thus occupies a special position. Moreover, 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 interaction in nature.

In order to decide to formulate the postulates of the theory of relativity, a great scientific thought was needed, because they contradicted classical ideas about space and time.

In fact, let us assume that at the moment of time when the origin of coordinates of the inertial reference systems TO And TO 1 , moving relative to each other at a speed v, coincide, a short-term flash of light occurs at the origin. During t the systems will move relative to each other by a distance vt, and the spherical wave surface will have a radius ct:

a contradiction with classical ideas about space and time, which are no longer fair at high speeds.

The relativity of simultaneity

Until the beginning of the 20th century, no one doubted that time is absolute. Two events that are simultaneous for the inhabitants of the Earth are simultaneous for the inhabitants of any space civilization. The creation of the theory of relativity showed that this is not so.

The reason for the failure of classical ideas about space and time is the incorrect assumption about the possibility of instantaneous transmission of interactions and signals from one point in space to another. The existence of the ultimate finite speed of transmission of interactions necessitates a profound change in the usual concepts of space and time, based on everyday experience. The idea of ​​absolute time, which flows once and for all at a given pace, completely independent of matter and its movement, turns out to be incorrect.

If we assume instantaneous propagation of signals, then the statement that events at two spatially separated points A And IN happened at the same time would make absolute sense. Can be placed at points A And IN clock and synchronize them using instantaneous signals. If such a signal is sent from A, for example, at 0 hours 45 minutes and at the same moment in time according to the clock B he arrived at point B, then the clocks show the same time, i.e. go in sync. If there is no such coincidence, then the clocks can be synchronized by moving forward those clocks that show the shorter time at the moment the signal is sent.

Any events, for example, two lightning strikes, are simultaneous if they occur at the same readings of synchronized clocks.

Only by placing it at points A And IN synchronized clocks, one can judge whether two events occurred at these points simultaneously or not. But how can you synchronize clocks located at some distance from each other if the speed of signal propagation is not infinite?

To synchronize clocks, it is natural to resort to light or even an electromagnetic signal, because the speed of electromagnetic waves in a vacuum is a strictly defined, constant value.

Let's take a closer look at a simple clock synchronization method that does not require any calculations. Let's say that an astronaut wants to know whether the clocks are ticking at the same time. A And IN, installed at opposite ends of the spacecraft.

moves, the position is different. The clock on the bow of the ship moves away from the place where the flash of light from the source occurred (the point with the coordinate OS), and to reach the clock A, the light must travel a distance greater than half the length of the ship.

The simultaneity of events is relative. We are not able to visualize this, to “feel” it, due to the fact that the speed of light is much greater than the speeds at which we move.

The main consequences arising from the postulates of the theory of relativity.

A number of important consequences concerning the properties of space and time follow from the postulates of the theory of relativity.

Relativity of distances . Distance is not an absolute value, but depends on the speed of movement of the body relative to a given reference system.

Let us denote by l o rod length with reference system TO, relative to which the rod is at rest. Then the length l of this rod in the reference system TO 1 , relative to which the rod moves at a speed determined by the formula:

As can be seen from this formula, l l 0 . This is the relativistic reduction in the size of a body in moving frames of reference (relativistic effects are those observed at speeds of motion close to the speed of light).

Relativity of time intervals . Let the time interval between two events occurring at the same point in the inertial system TO, equal to τ 0. These events, for example, could be two beats of a metronome counting down the seconds.

Then the interval τ between these same events in the reference system TO 1, moving relative to the system TO is expressed like this:

It is obvious that τ > τ o . This is the relativistic effect of time dilation in moving frames of reference.

If v c, then in the formulas we can neglect the quantity v 2 / c 2 . Then l ≈ lo and τ ≈ τ o , i.e. the relativistic reduction in the size of bodies and the slowdown of time in a moving frame of reference can be ignored.

Relativistic law of addition of velocities . The new law of addition of velocities corresponds to the new relativistic ideas about space and time. 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 a vacuum.

If the train is moving at a speed v and a light wave propagates in the carriage in the direction of movement of the train, then its speed relative to the Earth should again be equal to With, but not v + c. The new law for adding speeds should lead to the required result.

If and, then the fraction in the denominator can be neglected, and instead of this garbage on the left we get the classical law of addition of velocities: v 2 = v 1 +v. At v 1 =c speed v 2 is also equal c, as required by the second postulate of the theory of relativity. Really,

A remarkable property of the relativistic law of addition of velocities is that at any velocities v electrodynamics And principle relativity. Postulates of the special theory of relativity...

After the creation of electrodynamics, doubts arose about the validity of Galileo's principle of relativity as applied to electromagnetic phenomena.

After in the second half of the 19th 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 (the interaction of charges and currents, the propagation of electromagnetic waves, etc.) proceed the same way in all inertial frames of reference? Or, perhaps, 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 moving from one inertial system to another, or, like Newton's laws, they remain unchanged. Only in the latter case can we cast aside 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 Galilean transformations. Galileo's transformations express classical ideas about space and time. Newton's equations are invariant under Galilean transformations, and this fact expresses the principle of relativity in mechanics.

The laws of electrodynamics are complex, and finding out whether these laws are invariant under Galilean transformations or not is not an easy task. However, simple considerations already 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, resulting from Galileo’s transformations, the velocity can be equal to c only in one selected reference frame. In any other frame of reference moving with respect to this chosen frame with speed \(\vec(\upsilon ),\) the speed of light must be equal to \(\vec(c)-\vec(\upsilon )\). This means that if the usual law of addition of velocities is valid, then when moving from one inertial frame to another, the laws of electrodynamics should change so that in this new frame of reference the speed of light is not equal to \(\vec(c)\), but \(\ vec(c)-\vec(\upsilon).\)

Thus, certain contradictions were discovered between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. The difficulties that arose could be overcome in three different ways.

The first possibility was to declare untenable the principle of relativity as applied to electromagnetic phenomena. The great Dutch physicist, founder of electronic theory, H. Lorentz, came to this point of view. Since the time of Faraday, electromagnetic phenomena have been considered as processes in a special, all-pervasive 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 preferential system. In it, Maxwell's laws of electrodynamics are valid and have the most simple form. Only in this reference frame is the speed of light in vacuum the same in all directions.

The second possibility is to consider Maxwell’s equations themselves incorrect and try to change them in such a way that they do not change when moving from one inertial system to another (in accordance with the usual, classical concepts of space and time). Such an attempt, in particular, was made by G. Hertz. According to Hertz, the ether is completely carried away by moving bodies, and therefore electromagnetic phenomena occurring in the ether proceed in the same way, regardless of whether the body is at rest or moving. The principle of relativity is correct.

Finally, the third possibility of resolving these difficulties is to abandon 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, because it means revising the deepest, most basic ideas in physics. From this point of view, it is not the equations of the electromagnetic field that turn out to be inaccurate, but Newton’s laws of mechanics, consistent with the old ideas about space and time, expressed by Galileo’s transformations. It is the laws of mechanics that need to be changed, not Maxwell's laws of electrodynamics.

The third possibility 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 turns out, are refuted by experiment.

When Hertz tried to change Maxwell's laws of electrodynamics, it turned out that the new equations were not able to explain a number of observed facts. Thus, according to Hertz’s theory, moving water should completely entrain the light propagating in it, since it entrains 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 must be a chosen frame of reference associated with the world ether, which is at absolute rest, was also refuted by direct experiments.

Literature

Myakishev G.Ya. Physics: Optics. The quantum physics. 11th grade: Educational. for in-depth study of physics. - M.: Bustard, 2002. - P. 189-191.