Definition of kinetic energy in the special theory of relativity. Special theory of relativity

First of all, in SRT, as in classical mechanics, it is assumed that space and time are homogeneous, and space is also isotropic. To be more precise (modern approach), inertial frames of reference are actually defined as such frames of reference in which space is homogeneous and isotropic, and time is homogeneous. In fact, the existence of such reference systems is postulated.

Postulate 1 (Einstein's principle of relativity). Any physical phenomenon proceeds in the same way in all inertial frames of reference. It means that the form the dependence of physical laws on space-time coordinates should be the same in all IFRs, that is, the laws are invariant with respect to transitions between IFRs. The principle of relativity establishes the equality of all ISOs.

Taking into account Newton's second law (or the Euler-Lagrange equations in Lagrangian mechanics), it can be argued that if the speed of a certain body in a given IFR is constant (acceleration is zero), then it must be constant in all other IFRs. Sometimes this is taken as the definition of ISO.

Postulate 2 (principle of constancy of the speed of light). The speed of light in a “resting” frame of reference does not depend on the speed of the source.

The principle of the constancy of the speed of light contradicts classical mechanics, and specifically, the law of addition of velocities. When deriving the latter, only the principle of Galileo's relativity and the implicit assumption of the same time in all IFRs are used. Thus, it follows from the validity of the second postulate that time must be relative- not the same in different ISOs. It necessarily follows that "distances" must also be relative. In fact, if light travels a distance between two points in a certain time, and in another system - in another time and, moreover, with the same speed, then it immediately follows that the distance in this system must also differ.

27. Coulomb's law is a law describing the forces of interaction between point electric charges. Modern formulation: The force of interaction of two point charges in vacuum is directed along the straight line connecting these charges, is proportional to their magnitudes and is inversely proportional to the square of the distance between them. It is an attractive force if the signs of the charges are different, and a repulsive force if these signs are the same. Coulomb's law is written as follows:

where is the force with which charge 1 acts on charge 2; is the magnitude of the charges; is the radius vector (a vector directed from charge 1 to charge 2, and equal, in modulus, to the distance between charges -); is the coefficient of proportionality.

Capacity- the internal volume of the vessel, capacity, that is, the maximum volume of liquid placed inside it.

36 . Kirchhoff rules(often, in the literature, they are called not quite correctly Kirchhoff's laws) - relationships that are performed between currents and voltages in sections of any electrical circuit. Kirchhoff's rules allow you to calculate any electrical circuits of direct, alternating and quasi-stationary current. They are of particular importance in electrical engineering because of their versatility, as they are suitable for solving many problems in the theory of electrical circuits and practical calculations of complex electrical circuits. The application of Kirchhoff's rules to a linear electrical circuit makes it possible to obtain a system of linear equations for currents or voltages, and, accordingly, to find the value of currents in all branches of the circuit and all internodal voltages.

To formulate the Kirchhoff rules, the concepts node, branch And circuit electrical circuit. A branch is any two-terminal network included in the circuit, a node is a connection point of three or more branches, a circuit is a closed cycle of branches. Term closed loop means that starting from some node of the chain and once after passing through several branches and nodes, you can return to the original node. The branches and nodes traversed during such a bypass are usually called belonging to this contour. In this case, it must be borne in mind that a branch and a node can belong to several contours at the same time.

In terms of these definitions, Kirchhoff's rules are formulated as follows.

First rule

Kirchhoff's first rule states that the algebraic sum of the currents at each node in any circuit is zero. In this case, the current flowing into the node is considered to be positive, and the current flowing out is negative:

In other words, how much current flows into the node, so much flows out of it. This rule follows from the fundamental law of conservation of charge

After mathematicians created the rules in the space of concepts and numbers, the scientists were sure that all they had to do was to experiment and explain the structure of everything with the help of logical constructions. Within reasonable limits, the laws of mathematics work. But experiments that go beyond everyday concepts and ideas require new principles and laws.

Idea

In the middle of the 19th century, the convenient idea of ​​a universal ether spread everywhere, which suited most scientists and researchers. The mysterious ether became the most widespread model explaining the physical processes known at that time. But many inexplicable facts were gradually added to the mathematical description of the ether hypothesis, which were explained by various additional conditions and assumptions. Gradually, the harmonious theory of the ether acquired "crutches", there were too many of them. New ideas were needed to explain the structure of our world. The postulates of the special theory of relativity met all the requirements - they were brief, consistent and fully confirmed by experiments.

Michelson's experiments

The last straw that “broke the back” of the ether hypothesis was research in the field of electrodynamics and the Maxwell equations explaining them. When bringing the results of experiments to a mathematical solution, Maxwell used the theory of the ether.

In their experiment, the researchers made two beams going in different directions to be emitted synchronously. Provided that the light moves in the "ether", one beam of light should have traveled more slowly than the other. Despite numerous repetitions of the experiment, the result was the same - the light moved at a constant speed.

Otherwise, it was impossible to explain the fact that, according to the calculations, the speed of light in the hypothetical ether was always the same, regardless of how fast the observer was moving. But in order to explain the results of the research, it was required that the frame of reference be "ideal". And this contradicted Galileo's postulate about the invariance of all inertial frames of reference.

New theory

At the beginning of the 20th century, a whole galaxy of scientists began to develop a theory that would reconcile the results of research on electromagnetic oscillations with the principles of classical mechanics.

When developing a new theory, it was taken into account that:

Movement at near light speeds changes the formula of Newton's second law relating acceleration to force and mass;

The equation for the body's momentum must have a different, more complex formula;

The speed of light remained constant, regardless of the chosen frame of reference.

The efforts of A. Poincare, G. Lorentz and A. Einstein led to the creation of a special theory of relativity, which agreed on all the shortcomings and explained the existing observations.

Basic concepts

The foundations of the special theory of relativity lie in the definitions that this theory operates with.

1. Reference system - a material body that can be taken as the origin of the reference system and the coordinate of time during which the observer will follow the movement of objects.

2. Inertial frame of reference - one that moves uniformly and rectilinearly.

3. Event. Special and general relativity consider an event as a physical process localized in space with a limited duration. The object's coordinates can be given in 3D space as (x, y, z) and a time period t. A standard example of such a process is a flash of light.

The special theory of relativity considers inertial frames of reference, in which the first frame moves near the second one at a constant speed. In this case, the search for object coordinate relations in these inertial systems is a priority for SRT and is included in its main tasks. The special theory of relativity has managed to solve this problem with the help of Lorentz's formulas.

SRT postulates

In developing the theory, Einstein swept aside all the many assumptions that were necessary to support the theory of the ether. Simplicity and mathematical provability - these are the two pillars on which his special theory of relativity rested. Briefly, its premises can be reduced to two postulates that were necessary for the creation of new laws:

1. All physical laws in inertial systems are fulfilled in the same way.
2. The speed of light in vacuum is constant, it does not depend on the location of the observer and his speed.

These postulates of the special theory of relativity made useless the theory of the mythical ether. Instead of this substance, the concept of a four-dimensional space was proposed, linking together time and space. When specifying the location of the body in space, one must also take into account the fourth coordinate - time. This idea seems rather artificial, but it should be noted that the confirmation of this point of view lies within the speed limits commensurate with the speed of light, and in the everyday world the laws of classical physics do their job perfectly. Galileo's principle of relativity is fulfilled for all inertial frames of reference: if the rule F = ma is observed in FR k, then it will be correct in another frame of reference k'. In classical physics, time is a definite quantity, and its value is invariable and does not depend on the motion of the inertial CO.

Transformations in SRT

Briefly, the coordinates of the point and time can be denoted as follows:

x" = x - vt and t" = t.

This formula is given by classical physics. The special theory of relativity offers this formula in a more complicated form.

In this equation, the quantities (x, x’ y, y’ z, z’ t, t’) denote the coordinates of the object and the passage of time in the observed reference frames, v is the speed of the object, and c is the speed of light in vacuum.

The velocities of objects in this case must correspond to a non-standard Galilean

to the formula v= s/t, and to this Lorentz transformation:

As can be seen, at a negligible body velocity, these equations degenerate in everything known equations of classical physics. If we prefer the other extreme and set the speed of the object to be equal to the speed of light, then in this limiting case we still get c. Hence, the special theory of relativity concludes that no body in the observable world can move with a speed exceeding the speed of light.

Consequences of SRT

Upon further consideration of the Lorentz transformations, it becomes clear that non-standard things begin to happen with standard objects. The consequences of special relativity are the change in the length of an object and the flow of time. If the length of the segment in one reference system is equal to l, then observations from another OS will give the following value:

Thus, it turns out that an observer from the second frame of reference will see a segment shorter than the first one.

Amazing transformation touched such a value as time. The equation for the t coordinate will look like this:

As you can see, time in the second frame of reference flows more slowly than in the first. Naturally, both of these equations will give results only at speeds comparable to the speed of light.

Einstein was the first to derive the time dilation formula. He also offered to unravel the so-called "twin paradox". According to the condition of this task, there are twin brothers, one of whom remained on Earth, and the second flew on a rocket into space. According to the formula written above, the brothers will age differently, as time passes more slowly for a traveling brother. This paradox has a solution if we take into account that the homebody brother was in the inertial frame of reference all the time, and the fidget twin traveled in a non-inertial frame of reference, which moved with acceleration.

Mass change

Another consequence of SRT is the change in the mass of the observed object in different FRs. Since all physical laws operate equally in all inertial frames of reference, the fundamental conservation laws of momentum, energy, and angular momentum must be respected. But since the speed for an observer in a stationary CO is greater than in a moving one, then, according to the law of conservation of momentum, the mass of the object must change by:

In the first frame of reference, the object must have a larger body mass than in the second.

Taking the speed of the body equal to the speed of light, we get an unexpected conclusion - the mass of the object reaches an infinite value. Of course, any material body in the observable universe has its own finite mass. The equation only says that no physical object can move at the speed of light.

Mass-to-energy ratio

When the speed of the object is much less than the speed of light, the equation for the mass can be reduced to the form:

The expression m 0 c is a certain property of the object, which depends only on its mass. This quantity is called rest energy. The sum of the energies of rest and motion can be written as follows:

mc 2 = m 0 c + E kin.

It follows from this that the total energy of an object can be expressed by the formula:

The simplicity and elegance of the formula of the energy of the body gave completeness,

where E is the total energy of the body.

The simplicity and elegance of Einstein's famous formula completed the special theory of relativity, making it internally consistent and not requiring many assumptions. Thus, the researchers explained many contradictions and gave impetus to the study of new natural phenomena.

Definition 1

SRT (special relativity) is the modern physical theory of space and time.

The theory of relativity, together with such a science as quantum mechanics, is the theoretical basis for the development of modern physics and technology. SRT is also called the relativistic theory; the phenomena, the specifics of which this theory considers, are called relativistic effects. The creator of the theory of relativity is Albert Einstein.

Classical Newtonian mechanics gives an excellent description of the motion of macrobodies, which move at low speeds (v< < c) . Нерелятивистская физика принимала как очевидность существование единого мирового времени t, which is the same for all reference systems. The basis of classical mechanics is the mechanical principle of relativity.

Definition 2

Mechanical principle of relativity(also called Galileo's principle of relativity): the laws of dynamics are the same for all inertial frames of reference.

Allegorically, one can also call the laws of dynamics invariant or unchanged with respect to Galileo's transformations, which make it possible to calculate the coordinates of a moving body in one inertial frame (K) for given coordinates of this body in another inertial frame (K "). In particular, when the system K" moves at velocity v along the positive direction of the axis x systems K(Fig. 4 . 1 . 1), Galilean transformations look like this:

x = x " + v t , y = y " , z = z " , t = t " .

In this case, initially there is an assumption about the coincidence of the coordinate axes of both systems at the initial moment.

Figure 4. one . one . Two inertial frames of referenceKAnd K" .

The consequence of the Galileo transformations is the classical law of the transformation of velocities when moving from one frame of reference to another:

v x = v x " + v , v y = v y " , v z = v z "

The body in all inertial systems has the same accelerations:

a x = a x " , a y = a y " , a z = a z " or a → = a " →

From what has been said, we can conclude that the equation of motion, which is one of the foundations of classical mechanics (Newton's second law), m a → = F → retains its form when moving from one inertial frame to another.

By the end of the 19th century, there was already a certain baggage of experimental facts that clearly contradicted the laws of classical mechanics. The application of Newtonian mechanics to explain the propagation of light caused great difficulty. At a certain moment, an assumption was formed that light propagates in a special medium - ether; this assumption was refuted by many experiments. In 1881, the American physicist A. Michelson (in 1887 he was joined by the physicist E. Morley) began to attempt to detect the motion of the Earth relative to the ether (“ether wind”) using interference experience. A simplified diagram of the Michelson–Morley experiment is shown in Fig. 4 . one . 2.

Figure 4. one . 2. A simplified scheme of the Michelson–Morley interference experiment. v → is the orbital velocity of the Earth.

During the experiment, one of the arms of the Michelson interferometer was set parallel to the direction of the Earth's orbital velocity (v = 30 km/s), after which the instrument was rotated by 90°. In this case, the second arm was oriented in the direction of the orbital velocity. The calculations made made it clear that in the case of the existence of a fixed ether, when the device was turned, the interference fringes would have shifted by a distance proportional to v c 2 .

The Michelson-Morley experiment, subsequently repeated many times, gave an unambiguous negative result. As a result of the analysis of the results of the Michelson-Morley experiment, as well as some other experiments, it became possible to assert the fallacy of the concept of the ether as a medium in which light waves propagate. That is, there is no chosen (absolute) frame of reference for light. The motion of the Earth in orbit does not affect the optical phenomena on Earth.

Maxwell's theory had a significant influence on the development of ideas about space and time. At the beginning of the 20th century, this theory was generally accepted. Maxwell's theory predicted electromagnetic waves that propagated at a finite speed, and this hypothesis was put into practice in 1895, when A. S. Popov invented the radio. But Maxwell's theory also says that the speed of propagation of electromagnetic waves in any inertial frame of reference has the same value, equal to the speed of light in vacuum.

This statement means that the equations that describe the propagation of electromagnetic waves are non-invariant under the Galilean transformations. When an electromagnetic wave (particularly light) propagates in a frame of reference K"(Fig. 4 . 1 . 1) in the positive direction of the axis x", in system K light should, in accordance with Galileo's kinematics, propagate at a speed c + v, and not c.

Thus, on the border of the 19th and 20th centuries, a serious crisis arose in the development of physics. A. Einstein found a way out, refusing, as often happens in the case of the greatest discoveries, from the classical vision. In this case, it was about classical ideas about space and time. The most important step here was a different view of the concept of absolute time, which was used in classical physics. Habitual ideas, which seemed logical and obvious, in fact showed their inconsistency. Many concepts and quantities, which in non-relativistic physics were considered absolute or not dependent on the frame of reference, in the theory of relativity turned out to be transferred to the category of relative ones.

The basis of the special theory of relativity are the principles or postulates that Einstein formulated in 1905.

Definition 3

SRT principles:

1. The principle of relativity: all laws of nature are invariant with respect to the transition from one inertial frame of reference to another. This principle means the unity of the form of physical laws (not only mechanical ones) in all inertial systems.
   Those. the principle of relativity of classical mechanics is generalized for all processes of nature, in particular, electromagnetic ones. This generalized principle is called Einstein's principle of relativity.
2. The principle of constancy of the speed of light: The speed of light in vacuum does not depend on the speed with which the light source or the observer is moving, and is the same in all inertial frames of reference. The speed of light in the theory of relativity is in a special position. The speed of light is the maximum speed with which interactions and signals are transmitted from one point in space to another.

These principles must be regarded as a generalization of the entire set of experimental facts. The conclusions and consequences of the theory based on these principles have been confirmed in the course of a huge number of experimental tests. The special theory of relativity made it possible to find answers to all the questions of “pre-Einsteinian” physics and to explain the contradictory results of experiments already available at that time in the field of electrodynamics and optics. Subsequently, the theory of relativity was reinforced in the form of experimental data, which were obtained in the process of studying the motion of fast particles in accelerators, atomic processes, nuclear reactions, etc.

The postulates of the theory of relativity clearly contradict classical ideas. Let's carry out the following mental experiment: at the moment of time t = 0 , at which there is a coincidence of the coordinate axes of two inertial systems KAnd K " , a short flash of light occurred at the common origin. During the time t systems will be displaced relative to each other by a distance v t , and the spherical wave front in each system will have a radius c t(Fig. 4 . 1 . 3), since the systems are equal, and in each of them the speed of light is equal to c.

Figure 4. one . 3 . Seeming contradiction of SRT postulates.

From the position of an observer in the system K the center of the sphere is at the point O, and from the position of the observer in the system K "the center is located in Oh". Thus, it turns out that the center of the spherical front is simultaneously located at two different points!

The reason for such a misunderstanding is not a contradiction between the two postulates of the theory of relativity, but the assumption of the fact that the position of the fronts of spherical waves for both systems is related to the same moment in time. Such an assumption is contained in the Galilean transformation formulas, according to which time flows in the same way in both systems: t \u003d t ". Thus, Einstein's principles do not contradict each other, but the Galilean transformation formulas, and in this case, the theory of relativity wrote down to replace the Galilean transformations other formulas for the transformation during the transition from one inertial frame to another, called Lorentz transformations Lorentz transformations at speeds close to the speed of light make it possible to explain all relativistic effects, and at low speeds (υ< < c) переходят в формулы преобразования Галилея. Итак, новая теория (специальная теория относительности или СТО) не отвергает прежнюю классическую механику Ньютона, а лишь уточняет пределы ее применения. Эта взаимосвязь между прежней и новой, более общей теорией, частью которой является прежняя в качестве предельного случая, получила название принципа соответствия.

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A natural skeptical question: "What are the limits of applicability of Galileo's transformations?" arose before mankind by the end of the 19th - beginning of the 20th centuries. It arose in connection with the study of the paradoxical properties of the ether - a hypothetical absolutely elastic medium in which light propagates without attenuation, as in an absolutely solid medium.

Doubts about the infinite applicability of Galileo's transformations, at least in terms of the law of addition of velocities, arose when analyzing the results of the Michelson-Morley experiments to determine the speed of the "ethereal wind" from a comparison of the speed of light emitted by a source moving along the direction of the Earth's movement in orbit and the speed of light along a direction perpendicular to the tangent to the orbit. The measurements were made on an extremely precise instrument, the Michelson interferometer. The earth was wittily chosen as an object moving at a linear speed of 30 km/sec, practically unattainable by modern technology for massive objects.

Michelson's experiment, first staged in 1881, and giving a negative answer, was set fundamentally: a plate up to 0.5 m thick, on which mirrors were mounted, was made of granite, which expands slightly with heating, and floated in mercury for deformation-free rotation. The primary accuracy of the experiment made it possible to detect the "ethereal wind" at a speed of 10 km/s. Later, it was repeated many times, the accuracy was increased to the possibility of detecting wind at a speed of 30 m/s. But the answer was consistently zero.

Galileo's transformations were not confirmed when observing motions at high speeds. For example, there were no disturbances in the rhythm of the periodic motion of binary stars, while the direction of the speed of their motion changes on the forward and backward circulation paths. The speed of light, therefore, turned out to be independent of the motion of the source.

From the time of the experiments by Michelson and Morley in 1881 until 1905 - before the development of the foundations of SRT - numerous attempts were made to develop hypotheses in which the results of the key experiment would be explained. And at the same time, everyone tried to preserve the ether, modifying only its properties.

The most famous are the curious attempts of the Irish physicist George Fitzgerald and the Dutch physicist Hendrik Lorentz. The first proposed the idea of ​​reducing the length of the body in the direction of movement, the greater, the higher the speed of movement. Lorentz suggested the possibility of a local flow of time ("local time") in a moving system, according to laws that differ from those in a stationary system. Lorentz proposed to modify Galileo's coordinate transformations.

Einstein's postulates in special relativity

The decisive contribution to the creation of the special and then the general theory of relativity was made by Albert Einstein. In 1905, in the journal "Annalen fur physicist" 26-year-old, unknown employee of the Swiss patent office Albert Einstein published a small 3-page article "On the electrodynamics of moving media." According to historians of physics, he did not hear about the results of the Michelson-Morley experiments.

Einstein's concept allows one to reject the existence of the ether and build a theory now called the special theory of relativity (SRT) and confirmed by all experiments known today.

SRT is based on two postulates.

"The principle of the constancy of the speed of light".

The speed of light does not depend on the speed of the light source, is the same in all inertial coordinate systems, and is equal to c=3 in vacuum 10 8 m/s.

Later, in the general theory of relativity (GR), published in 1916, it was stated that the speed of light remains unchanged in non-inertial coordinate systems.

Special principle of relativity.

The laws of nature are the same (invariant, covariant) in all inertial coordinate systems.

Einstein later wrote:

“In all inertial coordinate systems, the laws of nature are in agreement. Physical reality is possessed not by a point in space and not by a moment in time when something happened, but only by the event itself. There is no absolute (independent of the reference space) relation in space, and there is no absolute relation in time, but there is an absolute (independent of the reference space) relationship in space and time" ( emphasized by Einstein).

Later, Einstein asserted the validity of this postulate for all frames of reference, including non-inertial ones.

The mathematical apparatus of SRT uses a four-dimensional xyzt space-time continuum (Minkowski space) and Lorentz coordinate transformations as a mathematical reflection of facts objectively existing in the material world.

The assumption that the speed of light is absolute leads to a number of consequences that are unusual and not observed under the conditions of Newtonian mechanics. One of the consequences of the constancy of the speed of light is the rejection of the absolute character of time, which was grafted into Newton's mechanics. We must now admit that time flows differently in different frames of reference - events that are simultaneous in one system will turn out to be non-simultaneous in another.

Consider two inertial frames of reference K And K", moving relative to each other. Let in a dark room moving with the system K", the lamp flashes. Since the speed of light in the system K"is equal (as in any reference system) c, then the light reaches both opposite walls of the room at the same time. Not that will happen from the point of view of the observer in the system K. The speed of light in the system K is also equal to c, but since the walls of the room move with respect to the system K, then the observer in the system K will find that the light touches one of the walls before the other, i.e. in system K these events are non-simultaneous.

Thus, in Einstein's mechanics relative Not only space properties, but also time properties.

Introduction

2. Einstein's general theory of relativity

Conclusion

List of sources used

Introduction

Even at the end of the 19th century, most scientists were inclined to the point of view that the physical picture of the world was basically built and would remain unshakable in the future - only the details had to be clarified. But in the first decades of the twentieth century, physical views changed radically. This was the result of a "cascade" of scientific discoveries made during an extremely short historical period, spanning the last years of the 19th century and the first decades of the 20th, many of which did not fit at all into the representation of ordinary human experience. A striking example is the theory of relativity created by Albert Einstein (1879-1955).

For the first time, the principle of relativity was established by Galileo, but it received its final formulation only in Newtonian mechanics.

The principle of relativity means that in all inertial systems all mechanical processes occur in the same way.

When the mechanistic picture of the world dominated in natural science, the principle of relativity was not subjected to any doubt. The situation changed dramatically when physicists came to grips with the study of electrical, magnetic, and optical phenomena. For physicists, the insufficiency of classical mechanics for describing natural phenomena has become obvious. The question arose: is the principle of relativity also valid for electromagnetic phenomena?

Describing the course of his reasoning, Albert Einstein points out two arguments that testified in favor of the universality of the principle of relativity:

This principle is fulfilled with great precision in mechanics, and therefore it can be hoped that it will turn out to be correct in electrodynamics as well.

If inertial systems are not equivalent for describing natural phenomena, then it is reasonable to assume that the laws of nature are most simply described in only one inertial system.

For example, consider the movement of the Earth around the Sun at a speed of 30 kilometers per second. If the principle of relativity were not fulfilled in this case, then the laws of motion of bodies would depend on the direction and spatial orientation of the Earth. Nothing like that, ie. physical inequality of different directions was not found. However, here appears the apparent incompatibility of the principle of relativity with the well-established principle of the constancy of the speed of light in a vacuum (300,000 km/s).

A dilemma arises: the rejection of either the principle of the constancy of the speed of light, or the principle of relativity. The first principle is so precisely and unambiguously established that it would be manifestly unjustified to reject it; no less difficulties arise when the principle of relativity is denied in the field of electromagnetic processes. In fact, as Einstein showed:

"The law of the propagation of light and the principle of relativity are compatible."

The apparent contradiction between the principle of relativity and the law of the constancy of the speed of light arises because classical mechanics, according to Einstein, relied on “two unjustified hypotheses”: the time interval between two events does not depend on the state of motion of the reference body and the spatial distance between two points of a rigid body does not depends on the state of motion of the reference body. During the development of his theory, he had to abandon: the Galilean transformations and accept the Lorentz transformations; from the Newtonian concept of absolute space and the definition of the motion of a body relative to this absolute space.

Each movement of the body occurs relative to a certain reference body, and therefore all physical processes and laws must be formulated in relation to a precisely specified reference system or coordinates. Therefore, there is no absolute distance, length, or extent, just as there can be no absolute time.

New concepts and principles of the theory of relativity significantly changed the physical and general scientific ideas about space, time and motion, which dominated science for more than two hundred years.

All of the above justifies the relevance of the chosen topic.

The purpose of this work is a comprehensive study and analysis of the creation of special and general theories of relativity by Albert Einstein.

The work consists of an introduction, two parts, a conclusion and a list of references. The total amount of work is 16 pages.

1. Einstein's special theory of relativity

In 1905, Albert Einstein, proceeding from the impossibility of detecting absolute motion, concluded that all inertial frames of reference are equal. He formulated two important postulates that formed the basis of a new theory of space and time, called the Special Theory of Relativity (SRT):

1. Einstein's principle of relativity - this principle was a generalization of Galileo's principle of relativity to any physical phenomena. It says: all physical processes under the same conditions in inertial reference systems (ISF) proceed in the same way. This means that no physical experiments carried out inside a closed ISO can determine whether it is at rest or moving uniformly and rectilinearly. Thus, all IFRs are completely equal, and physical laws are invariant with respect to the choice of IFR (ie, the equations expressing these laws have the same form in all inertial frames of reference).

2. The principle of constancy of the speed of light - the speed of light in vacuum is constant and does not depend on the movement of the light source and receiver. It is the same in all directions and in all inertial frames of reference. The speed of light in vacuum - the limiting speed in nature - is one of the most important physical constants, the so-called world constants.

A deep analysis of these postulates shows that they contradict the concepts of space and time accepted in Newton's mechanics and reflected in Galileo's transformations. Indeed, according to principle 1, all laws of nature, including the laws of mechanics and electrodynamics, must be invariant with respect to the same transformations of coordinates and time, carried out during the transition from one frame of reference to another. Newton's equations satisfy this requirement, but Maxwell's equations of electrodynamics do not, i.e. turn out to be invariant. This circumstance led Einstein to the conclusion that Newton's equations needed to be refined, as a result of which both the equations of mechanics and the equations of electrodynamics would turn out to be invariant with respect to the same transformations. The necessary modification of the laws of mechanics was carried out by Einstein. As a result, a mechanics emerged that is consistent with Einstein's principle of relativity - relativistic mechanics.

The creator of the theory of relativity formulated the generalized principle of relativity, which now extends to electromagnetic phenomena, including the motion of light. This principle states that no physical experiments (mechanical, electromagnetic, etc.) carried out within a given frame of reference can distinguish between the states of rest and uniform rectilinear motion. The classical addition of velocities is not applicable to the propagation of electromagnetic waves, light. For all physical processes, the speed of light has the property of infinite speed. In order to tell a body a speed equal to the speed of light, an infinite amount of energy is required, and that is why it is physically impossible for any body to reach this speed. This result was confirmed by measurements that were carried out on electrons. The kinetic energy of a point mass grows faster than the square of its speed, and becomes infinite for a speed equal to the speed of light.

The speed of light is the limiting speed of propagation of material influences. It cannot add up at any speed and for all inertial systems it turns out to be constant. All moving bodies on Earth in relation to the speed of light have a speed equal to zero. Indeed, the speed of sound is only 340 m/s. It is stillness compared to the speed of light.

From these two principles - the constancy of the speed of light and the extended principle of relativity of Galileo - mathematically follow all the provisions of the special theory of relativity. If the speed of light is constant for all inertial frames, and they are all equal, then the physical quantities of the body length, time interval, mass for different frames of reference will be different. So, the length of a body in a moving system will be the smallest in relation to a resting one. According to the formula:

where /" is the length of a body in a moving system with a speed V with respect to a stationary system; / is the length of a body in a resting system.

For a period of time, the duration of a process, the opposite is true. Time will, as it were, stretch, flow more slowly in a moving system in relation to a stationary one, in which this process will be faster. According to the formula:

Recall that the effects of the special theory of relativity will be detected at velocities close to the speed of light. At speeds much less than the speed of light, the SRT formulas turn into the formulas of classical mechanics.

Fig.1. Einstein Train Experiment

Einstein tried to visually show how the flow of time slows down in a moving system in relation to a stationary one. Imagine a railway platform, past which a train passes at a speed close to the speed of light (Fig. 1).