The development of electrodynamics has 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 moving (absolute length). The old, classical ideas about space and time were replaced by a new teaching - 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 take place (interaction of charges and currents, propagation electromagnetic waves and so on) is 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 in 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 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 only in one chosen frame of reference. In any other frame of reference moving with respect to the first frame with some other speed, the speed of light must already be equal to the difference between these speeds. 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 must change as well as the laws of mechanics. We have 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 invalidate the principle of relativity as applied to electromagnetic phenomena. This point of view was shared by the great Dutch physicist, founder of the electron theory H. Lorenz. According to this theory, the inertial frame of reference, which is at rest relative to the ether, is a special, predominant frame, since electromagnetic phenomena Since the time of Faraday, they have been considered as processes in a special, all-penetrating 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 find out how this frame moves with respect to the ether. Just as in a frame of reference moving relative to air, a wind arises, so when moving relative to the ether of a certain system, an "ethereal 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 during the transition from one inertial frame to another (in accordance with the usual, classical ideas about space and time). An experiment to detect the "ethereal wind" was staged in 1881 by the 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 the delays of light during its propagation along and across the Earth's orbit. 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 drags the light propagating in it, as it drags the ether in which the light propagates. Experience has shown that this is not really the case. The third way to resolve 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 necessary to change the laws of mechanics, and not the laws of Maxwell's electrodynamics. The third possibility turned out to be the only correct one. Consistently developing precisely this theory, Albert Einstein came to new ideas about space and time. He created a new doctrine of space and time, which today is called the special theory of relativity. Generalizing his theory for non-inertial frames of reference, Einstein constructed general theory relativity. She represents modern theory gravity. Einstein first introduced the concept of particles of light, they are called photons. In his experiments, he compared the speeds of light in the direction of the Earth's motion 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 at different times of the year. At the same time, the motion of the Earth with respect to the ether could not be detected. It was all as if you stuck your head out of the car window at a speed of 100 km / h and did not notice the headwind. Thus, the idea of ​​the existence of a predominant frame of reference did not stand experimental verification. In turn, this meant that there is no special medium - "luminiferous ether" - with which such a predominant frame of reference could be associated. Now it is easy to reconcile the principle of relativity with Maxwell's electrodynamics. To do this, it is necessary to abandon the classical ideas about space and time, according to which distances and the passage of time do not depend on the frame of reference.
The theory of relativity under consideration 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 frames of reference. This means that in all inertial frames 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 occupies a special position. As follows from the postulates of the theory of relativity, the speed of light in vacuum is the maximum possible speed transmission of interactions in nature. The solution of the paradox with spherical light signals lies in the relativity of simultaneity Let us describe the situation. Light simultaneously reaches the points of a spherical surface centered at the 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 the observer associated with the K1 (ka-1) system, the light reaches these points at different moments of time. Of course, the opposite is also true: in the K (ka) system, light reaches points on the surface of the sphere centered at O1 (o-1) at different moments of time, and not simultaneously, as it appears to the observer in the K1 (ka-1) system. From this follows 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 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 has shown 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 wrong. “A minute is a relative value: if you have a date with a pretty girl, then it will fly by like an instant, and if you are sitting on a hot stove, then it will seem like an eternity.” So Einstein himself tried to explain in simple words his theory of relativity. Indeed, if one assumes 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, such as two lightning strikes, are simultaneous if they occur at the same synchronized clock readings. Only by placing synchronized clocks at points A and B, it is possible to judge whether any two events occurred at these points simultaneously or not. To synchronize clocks, it would be more correct if they resorted to light or electromagnetic signals in general, since the speed of electromagnetic waves in vacuum is a strictly defined, constant cause. This is the method used when checking watches by radio. Let's take a closer look at one of simple methods clock synchronization, which does not require any calculations. Let's say that the astronaut wants to know whether the ones installed at opposite ends go the same way spaceship clocks A and B (be). To do this, with the help of a source that is located in the middle of the ship and is stationary 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 running synchronously. But this will be so only with respect to the reference system 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 source light flashed, and in order to reach clock A, the light must cover a distance greater than half the length of the ship. And the clock (be) on 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 located in the system connected to the ship will come to the conclusion that the signals reach both clocks at the same time. Any two events at points A and B (be) are simultaneous in the frame of reference associated with the ship, and are not simultaneous in the frame relative to which the ship is moving. But by virtue of the principle of relativity, these systems are absolutely 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 important consequences follow from the postulates of the theory of relativity concerning the properties of space and time. Two relativistic effects are observed. First, in moving frames of reference, the dimensions of the body are reduced. Second, in a moving frame of reference, time dilation is observed.
Since the linear dimensions of the body are reduced in moving frames of reference, this phenomenon leads to the fact that the mass of the body in the moving frame increases accordingly.
It's obvious that classical law 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 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 have the form.
When moving, the course of all physical processes slows down, as well as chemical reactions in the 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 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, an argument is built that leads to an apparent contradiction. For clarity, the story of two twin brothers is considered. One of them (hereinafter the traveler) goes to space flight, the second (hereinafter the homebody) remains on Earth. The paradox lies in the following: from the point of view of a homebody, the clock of a moving traveler has a slow motion of time, so after returning to Earth, it should lag behind the clock of a homebody. Relative to the traveler, the Earth was moving, which means that the clock of the homebody must fall behind. But on the third hand, the brothers are equal, 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. outer space like a black hole. A black hole is formed by the gravitational contraction 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 is compressed and reaches such a density that even light cannot overcome its gravitational forces of the surrounding cosmic bodies. Einstein Albert (1879-1955) - great physicist 20th century Created a new doctrine of space and time - special theory 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 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 in science there was a revision of the understanding of the physical essence of space and time, he built a new theory of gravity to replace the Newtonian. 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.

In the second half of the 19th century, D. Maxwell formulated the basic laws of electrodynamics. At the same time, doubts arose about the validity of Galileo's mechanical principle of relativity as applied to electromagnetic phenomena. Let us recall the essence of the mechanical principle of relativity.
If frames of reference move uniformly and rectilinearly relative to each other, and Newton's laws of dynamics are valid in one of them, then these frames are inertial. In all inertial frames of reference, the laws of classical dynamics have the same form (invariant); this is the essence of the mechanical principle of relativity or Galileo's principle of relativity.
To prove this principle, consider two frames of reference: the inertial frame To(with coordinates x, y, z), which we will conditionally consider to be fixed and moving system K"(with coordinates x", y", z") moving relative to To evenly and straight with speed u= const. Let us assume that at the initial moment of time t= 0 start O and O" both coordinate systems are the same. Location of coordinate systems at an arbitrary point in time t has the form shown in Fig. 5.1. Speed u directed along a straight line OO", and the radius vector drawn from the point O exactly O", is equal to r 0 =ut.
Coordinates of an arbitrary material point A in fixed and moving reference systems are determined by radius-vectors r and r", and

In projections onto the coordinate axes, the vector equation (5.1) is written in the form called Galilean transformations:

(5.2)

In the particular case when the system K" moving at a speed v along the positive direction of the axis x systems K, Galilean coordinate transformations have the following form:

In classical mechanics, it is assumed that the course of time does not depend on relative motion reference systems. Therefore, the system of equations (5.2) is supplemented by one more relation:

(5.3)

Relations (5.2) – (5.3) are valid only in the case u . At speeds comparable to the speed of light, Galilean transformations are replaced by more general Lorentz transformations.
Let us differentiate equation (5.1) with respect to time and taking into account that u= const, we find the relationship between the velocities and accelerations of the point BUT with respect to both frames of reference:

where
(5.4)

As well as

(5.5)

If on a point BUT other bodies do not act, then a= 0 and according to (5.5) a"= 0, i.e. mobile system K" is inertial - an isolated material point either moves uniformly and rectilinearly relative to it, or is at rest.
From expression (5.5) it follows that

those. Newton's equations (dynamic equations) for a material point are the same in all inertial frames of reference or are invariant with respect to Galilean transformations. This result is often formulated as follows: the uniform and rectilinear motion of the system as a whole does not affect the course of the mechanical processes occurring in it.
Classical Newtonian mechanics reliably describes the motion of macroscopic bodies moving at speeds much less than the speed of light. At the end of the XIX century. it was found that the conclusions of classical mechanics contradict some experimental data. In particular, when studying the motion of fast charged particles, it turned out that their motion does not obey Newton's laws. Further difficulties arose when trying to apply classical mechanics to explain the propagation of light. According to the laws of electrodynamics, the speed of propagation of electromagnetic waves in vacuum is the same in all directions and is approximately equal to with\u003d 3 * 10 8 m / s. But in accordance with the laws of classical physics, the speed of light can be equal to with only in one chosen frame of reference. In any other frame of reference moving relative to the chosen frame with a speed v, it should already equal with-v, or with+v. This means that if the law of addition of velocities of classical mechanics is valid (formula (5.4)), then when passing from one inertial frame to another, the laws of electrodynamics must change, since the speed of light must change. Thus, contradictions were revealed between Newton's electrodynamics and mechanics, the laws of which are consistent with Galileo's principle of relativity. Various methods have been proposed to overcome the difficulties that have arisen:

1. Accept the failure of the principle of relativity in relation to electromagnetic phenomena. Since the time of Faraday, electromagnetic phenomena have been considered as processes in a special, all-penetrating medium that fills all space - broadcast. According to H. Lorentz, an inertial frame of reference, at rest relative to the ether, is a special frame in which Maxwell's laws of electrodynamics are valid. Only in this frame of reference is the speed of light in vacuum the same in all directions.
2. Consider Maxwell's equations of electrodynamics as erroneous and try to change them in such a way that they do not change during the transition from one inertial frame to another (in accordance with the classical concepts of space and time). Such an attempt, in particular, was made by G. Hertz, who believed that the ether is completely carried away by moving bodies, so electromagnetic phenomena proceed in the same way, regardless of whether the body is at rest or moving. The principle of relativity is correct.
3. Abandon classical concepts of space and time in order to preserve both the principle of relativity and Maxwell's laws. From this point of view, it is not the equations electromagnetic field, but the laws of Newtonian mechanics, consistent with the old ideas about space and time. Thus, it is necessary to change the laws of classical mechanics, and not the laws of Maxwell's electrodynamics.

Let us recall how space and time were treated in classical physics. Space was considered as an infinite empty extension containing all bodies and independent of matter. Time was seen as the absolute factor in the uniform flow of duration in which everything comes and goes. At the same time, time does not depend on any processes in the world.
The development of natural science has refuted these ideas. There is no absolute space and time. The universe is filled with matter in the form of matter and field, and space acts as a universal property of matter. Time is always associated with the movement and development of matter. Thus, space- this is a form of being of matter, which expresses its extension and structure; time- this is a form of existence of matter, characterizing the duration of the existence of all objects, fields and the sequence of events.
The main properties of space and time are: a) the unity and inseparable connection of matter, space and time; b) absolute continuity and relative discontinuity of space and time. Continuity is manifested in the spread of material fields in the space of all bodies and systems, in the endless succession of length elements when a body moves between two points. The discontinuity of space is relative and manifests itself in the separate existence of material objects and systems, each of which has certain dimensions and boundaries. The discontinuity of time is characterized only by the time of existence of qualitative states of matter, each of which arises and disappears, passing into other forms; c) time has duration, unidirectionality, irreversibility.
Consistently developing new, different from the classical, ideas about space and time, A. Einstein at the beginning of the 20th century. created special relativity(HUNDRED). Within the framework of this theory, it was possible to reconcile the principle of relativity with Maxwell's electrodynamics. Wherein new theory did not cancel the old (Newtonian mechanics), but included it as a special, limiting case.

At the end of the 19th century, experimental data were obtained that could not be explained from the standpoint of Newtonian physics. In particular, if the light source and receiver move towards each other uniformly and rectilinearly, then their Newtonian velocities must add up. However, the American physicist Michelson and others, conducting experiments with a sensitive interferometer, showed that the speeds of light in vacuum do not depend on the speed of the source and receiver and are the same in all inertial frames of reference. Einstein came to the conclusion that constancy of the speed of light is a fundamental law of nature. This conclusion was put by Einstein at the basis of his special theory of relativity (see section 2.5). The invariance of the Maxwell equations (see section 3.5) under the Lorentz transformations was also proved, while they are not invariant under the Galilean transformations (see 2.4). It followed from Einstein's theory that electromagnetic interactions (for example, charges) are transmitted in vacuum at a speed limited by the speed of light, through a field (the concept of short-range action) in all frames of reference.

Separation of the electromagnetic field into electric and magnetic field relatively - in nature there is a single electromagnetic field. Light also has an electromagnetic nature (Fig. 3.27).

Regularities were explained on the basis of the special theory of relativity Doppler effect for electromagnetic waves. When the light source moves away from the observer at a speed V, there is a change in frequency (or wavelength by Δλ) in the radiation spectrum of the source with a radiation wavelength λ ( redshift):

The Doppler effect has found application in radar to measure the speed V and distance to a moving object, in astrophysics - to measure the receding velocities of galaxies, etc.

The change in the apparent position of stars in the celestial sphere due to the finiteness of the speed of light is called aberrations of light.

3.7. Quasi-stationary magnetic field

The displacement current is fundamentally different from the conduction current - it is not related to the movement of charges. It is only due to change over time. electric field(see 3.5). Even in a vacuum, a change in the electric field leads to the occurrence of a magnetic field in the surrounding space. It is on this basis that the displacement current is identical to the conduction current, and this makes it possible to conventionally call it "current".

The displacement current j cm occurs not only in vacuum or dielectrics, but also in conductors when an alternating current of conduction j pr passes through them. However, it is small compared to j pr (in view of this, they are neglected).

In massive conductors placed in an alternating magnetic field, induced currents can be induced in accordance with the law (3.70). These currents are eddy currents in the volume of conductors and are known as Foucault currents.

Foucault currents create their own magnetic field, which, in accordance with Lenz's rule (see 3.73), prevent a change in the magnetic flux that caused them. High-frequency Foucault currents lead to heating of conductors, which allows them to be used for melting metals in induction furnaces, in microwave ovens for heating conductive products, in physiotherapy (the human body is a conductor), etc. In other cases, to reduce heat losses in electrical machines and transformers, the resistance to Foucault currents is increased, making their cores not solid, but from thin plates isolated from each other.

In circuits with alternating electric current, the electrical resistance of conductors increases with increasing frequency of the current. This is explained by the fact that the current density distribution over the conductor cross section becomes non-uniform, taking into account the Foucault currents: the current density increases near the surface (the so-called skin effect). This also allows you to make conductors hollow (tubular). The skin-effect is the basis for the methods of high-frequency hardening of the surface of parts.

The strength of the alternating current is at the same time unequal in different parts of the conductor. This is due to the finite speed of propagation along the conductor of a changing electromagnetic field. However, if we take into account the low speed of charge carriers in comparison with the speed of field propagation, then the currents can be considered quasi-stationary as well as the magnetic fields they excite.

Alternating currents are obtained using generators. When the circuit rotates in a uniform magnetic field with angular velocity through the area bounded by the contour, periodically changes magnetic flux(see 3.67).

where Ф 0 is the maximum value of the flow through the area S of the contour.

The electromotive force arising from this (see 3.70) will be
change sinusoidally. ε 0 \u003d ωF 0 is the amplitude of the EMF. If the circuit is closed, then alternating current will flow in it:

.

In general, any conductor, in addition to ohmic resistance R, has inductance L and capacitance C. They provide additional resistance to the current due to the appearance of self-induction EMF (see 3.73) and the inertia of recharging the capacitance. Then the amplitude value of the alternating current:

(3.90)

Value
has the character of impedance ( impedance). It depends on the values ​​of R, L, C and frequency . When  satisfying the condition:

,

the impedance has a minimum value equal to R, and the amplitude of the alternating current reaches its maximum value:

Frequency
- is called resonant. R L \u003d L and
- called inductive and capacitive resistances in an alternating current circuit.

Alternating electric current has great practical application. It can be transmitted with low losses over long distances and, with the help of transformers, its strength and voltage can be varied over a wide range.

To characterize action alternating current in comparison with direct current, the concept is introduced effective values ​​of current and voltage. The effective value of the current strength is the value of I associated with the amplitude of I 0 as follows:

likewise the tension
. They determine the power of the alternating current. You can also give another definition: I D: the effective value of the AC strength is equal to the DC strength that releases the same amount of heat in the circuit as the AC.

Changed 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 moving (absolute length).

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

§ 75 LAWS OF ELECTRODYNAMICS AND THE PRINCIPLE OF RELATIVITY

The principle of relativity in mechanics and electrodynamics. After 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 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 one cast aside doubts about the validity of the principle of relativity as applied 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, already simple considerations, it would seem, make it possible to find the correct answer. According to the laws of electrodynamics, the speed of propagation of electromagnetic waves in 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 velocities of Newtonian mechanics, the speed can be equal to the speed of light only in one chosen frame of reference. In any other frame of reference moving with respect to this chosen frame of reference with the 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 already equal to not , but - .

Thus, certain contradictions were revealed between electrodynamics and Newtonian mechanics, the laws of which are consistent with the principle of relativity. The difficulties encountered were overcome 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, founder of the electron theory X. . Since the time of Faraday, electromagnetic phenomena have been considered as processes taking place in a special, all-penetrating medium that fills all space - the world ether. The inertial frame of reference, which is 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 during the transition from one inertial frame of reference 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 carried away 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.

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, which are consistent with the old ideas about space and time. It is necessary to change the laws of mechanics, and not the laws of Maxwell's electrodynamics.

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 chosen frame of reference associated with the world ether, which is in absolute rest, was refuted by direct experiments.

If the speed of light was equal to 300,000 km/s only in the frame of reference associated with the ether, then by measuring the speed of light in an arbitrary inertial frame of reference, it would be possible to detect the movement of this frame of reference with respect to the ether and determine the speed of this movement.

Einstein Albert (1879-1955)- the great physicist of the XX century. Created a new doctrine 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. 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.

Just as a wind arises in a frame of reference moving relative to air, when moving relative to the ether (if, of course, the ether exists), an "ether wind" should be detected. An experiment to detect the "ethereal wind" was staged in 1881 by the American scientists A. Michelson and E. Morley on the basis of an idea expressed 12 years earlier by Maxwell.

In this experiment, the speed of light was compared in the direction of the Earth's motion and in the perpendicular direction. The measurements were carried out very accurately with the help of a special device - the 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 motion of the Earth with respect to the ether could not be detected.

Thus, the idea of ​​the existence of a predominant frame of reference did not stand experimental verification. In turn, this meant that there was no special medium - "luminiferous ether", with which such a predominant frame of reference could be associated.

When Hertz tried to change the laws of Maxwell's 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 must completely entrain the light propagating in it, since it entrains the ether, in which the light propagates. Experience has shown that this is not really the case.

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 frame of reference.

Myakishev G. Ya., Physics. Grade 11: textbook. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; ed. V. I. Nikolaev, N. A. Parfenteva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

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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" - Newton's three famous laws. Already the first of them, which reads: “Every body continues to be held in its state of rest or uniform and rectilinear motion until and since it is not forced by the applied forces to change this state”, speaks of the relativity of motion and at the same time indicates the existence of frames of reference (they were called inertial), in which bodies that do not experience external influences move “by inertia”, without accelerating and without slowing down. It is precisely such inertial systems that are meant when formulating the other two Newton's laws. During the transition from one inertial frame to another, many quantities that characterize the movement of bodies change, for example, their speeds or the shape of the trajectory of movement, but the laws of motion, that is, the relationships connecting these quantities, remain constant.

Galilean transformations

To describe mechanical movements, that is, a change in the position of bodies in space, Newton clearly formulated ideas about space and time. Space was conceived as a kind of "background" against which the movement of material points unfolds. Their position can be determined, for example, using Cartesian coordinates x, y, z depending on time t. When moving from one inertial reference frame K to another K ", moving relative to the first one along the x axis with a speed v, the coordinates are transformed: x" \u003d x - vt, y "= y, z" \u003d z, and the time remains unchanged: t" = t. Thus, it is assumed that the time is absolute. These formulas are called Galilean 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 "geometric" picture of the world is, as it were, counted by some absolute clock, the course of which can neither be accelerated nor slowed down.

The principle of relativity in electrodynamics

Galileo's principle of relativity was attributed only to mechanics for more than three hundred years, although in the first quarter of the 19th century, primarily thanks 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, the tension in which was interpreted as the strength of the electric and magnetic fields. At the same time, the ether did not affect the mechanical movements of bodies, so that in mechanics it was “not felt”, but on electromagnetic processes movement relative to the ether (“ethereal wind”) should have had an effect. As a result, an experimenter in a closed cabin could, by observing such processes, seem to be able to determine whether his cabin was in motion (absolute!), or whether it was at rest. In particular, scientists believed that the "ethereal wind" should influence the propagation of light. Attempts to discover the "ether wind", however, were unsuccessful, and the concept of a mechanical ether was rejected, thanks 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

Similar to mathematical formulation The laws of mechanics are Newton's equations, Maxwell's equations are a quantitative representation of the laws of electrodynamics. The form of these equations must also remain unchanged during the transition from one inertial frame of reference to another. To satisfy this condition, it is necessary to replace the Galileo transformations with others: x"= g(x-vt); y"= y; z "= z; t" \u003d g (t-vx / c 2), where g \u003d (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 private) theory of relativity. At vc they turn into Galilean transformations, but if v is close to c, then there are significant differences from the space-time picture, which is usually called non-relativistic. First of all, the failure 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 speed conversion also changes.

Transformation of physical quantities in relativistic theory

In the relativistic theory, spatial distances and time intervals do not remain unchanged during the transition from one frame of reference to another, moving relative to the first with a speed v. The lengths are reduced (in the direction of motion) by 1/g times, and the time intervals are "stretched" by the same number of times. The relativity of simultaneity is the main fundamentally new feature of the modern private theory of relativity.