In September 1905 A. Einstein's work "On the Electrodynamics of Moving Bodies" appeared, in which the main provisions of the Special Theory of Relativity (SRT) were outlined. This theory meant a revision of the classical ideas of physics about the properties of space and time. Therefore, this theory in its content can be called the physical doctrine of space and time. . Physical because the properties of space and time in this theory are considered in close connection with the laws of the physical phenomena occurring in them. The term " special” emphasizes the fact that this theory considers phenomena only in inertial frames of reference.
As starting points for the special theory of relativity, Einstein adopted two postulates, or principles:
1) the principle of relativity;
2) the principle of independence of the speed of light from the speed of the light source.
The first postulate is a generalization of Galileo's principle of relativity to any physical processes: all physical phenomena proceed in the same way in all inertial frames of reference. All laws of nature and the equations describing them are invariant, i.e. do not change when moving from one inertial frame of reference to another.
In other words, all inertial frames of reference are equivalent (indistinguishable) in their physical properties. No experience can single out any of them as preferable.
The second postulate states that The speed of light in a vacuum does not depend on the movement of the light source and is the same in all directions.
It means that the speed of light in vacuum is the same in all inertial frames of reference. Thus, the speed of light occupies a special position in nature.
It follows from Einstein's postulates that the speed of light in vacuum is the limit: no signal, no influence of one body on another can propagate at a speed exceeding the speed of light in vacuum. It is the limiting nature of this speed that explains the sameness of the speed of light in all frames of reference. The presence of a limiting speed automatically implies a limitation of the speed of particle movement by the value "c". Otherwise, these particles could carry out the transmission of signals (or interactions between bodies) at a speed exceeding the limit. Thus, according to Einstein's postulates, the value of all possible velocities of movement of bodies and propagation of interactions is limited by the value "c". This rejects the long-range principle of Newtonian mechanics.
Interesting conclusions follow from SRT:
1) LENGTH REDUCTION: the movement of any object affects the measured value of its length.
2) SLOW TIME: With the advent of SRT, the assertion arose that absolute time does not have an absolute meaning, it is only an ideal mathematical representation, because in nature there is no real physical process suitable for measuring absolute time.
The passage of time depends on the speed of the frame of reference. At a sufficiently high speed, close to the speed of light, time slows down, i.e. relativistic time dilation occurs.
Thus, in a rapidly moving system, time flows more slowly than in the laboratory of a stationary observer: if an observer on Earth could follow the clock in a rocket flying at high speed, he would come to the conclusion that they go slower than his own. The time dilation effect means that the occupants of the spacecraft age more slowly. If one of the two twins made a long space trip, then upon returning to Earth, he would find that his twin brother, who remained at home, is much older than him.
In some system, we can only talk about local time. In this regard, time is not an entity that does not depend on matter, it flows at different speeds in different physical conditions. Time is always relative.
3) WEIGHT INCREASE: body mass is also a relative value, depending on the speed of its movement. The greater the speed of a body, the greater its mass becomes.
Einstein also found a connection between mass and energy. He formulates the following law: “the mass of a body is a measure of the energy contained in it: E \u003d mc 2 ". If we substitute m=1 kg and c=300,000 km/s into this formula, then we get a huge energy of 9·10 16 J, which would be enough to burn an electric light bulb for 30 million years. But the amount of energy in the mass of a substance is limited by the speed of light and the amount of mass of the substance.
The world around us has three dimensions. SRT states that time cannot be considered as something taken separately and unchanging. In 1907, the German mathematician Minkowski developed the SRT mathematical apparatus. He suggested that three spatial and one temporal dimensions are closely related. All events in the universe take place in four-dimensional space-time. From a mathematical point of view, SRT is the geometry of the four-dimensional Minkowski space-time.
SRT has been confirmed on extensive material, by many facts and experiments (for example, time dilation is observed during the decay of elementary particles in cosmic rays or in high-energy accelerators) and underlies the theoretical descriptions of all processes occurring at relativistic speeds.
So, the description of physical processes in SRT is essentially connected with the coordinate system. The physical theory does not describe the physical process in itself, but the result of the interaction of the physical process with the means of investigation. Therefore, for the first time in the history of physics, the activity of the subject of cognition, the inseparable interaction of the subject and the object of cognition, was directly manifested.
Special Relativity (SRT)- a physical theory that considers the spatio-temporal properties of physical processes. Regularities of SRT appear at high (comparable to the speed of light) speeds. The laws of classical mechanics do not work in this case. The reason for this is that the transfer of interactions does not occur instantly, but at a finite speed (the speed of light).
Classical mechanics is a special case of SRT at low speeds. The phenomena described by SRT and contradicting the laws of classical physics are called relativistic. According to SRT, the simultaneity of events, distances and time intervals are relative.
In any inertial frame of reference under the same conditions, all mechanical phenomena proceed in the same way (Galileo's principle of relativity). In classical mechanics, the measurement of time and distances in two frames of reference and the comparison of these quantities are considered obvious. This is not the case in STO.
Events are simultaneous if they occur at the same synchronized clock readings. Two events that are simultaneous in one inertial frame of reference are not simultaneous in another inertial frame of reference.
In 1905, Einstein created the special theory of relativity (SRT). At the heart of it theory of relativity there are two postulates:
- Any physical phenomena in all inertial frames of reference under the same conditions proceed in the same way (Einstein's principle of relativity).
- The speed of light in vacuum in all inertial frames of reference is the same and does not depend on the speed of the source and receiver of light (principle of constancy of the speed of light).
The first postulate extends the principle of relativity to all phenomena, including electromagnetic ones. The problem of the applicability of the principle of relativity arose with the discovery of electromagnetic waves and the electromagnetic nature of light. The constancy of the speed of light leads to a discrepancy with the law of addition of velocities of classical mechanics. According to Einstein, there should not be a change in the nature of the interaction when the reference frame is changed. Einstein's first postulate follows directly from the Michelson-Morley experiment, which proved the absence of an absolute frame of reference in nature. In this experiment, the speed of light was measured depending on the speed of the light receiver. From the results of this experiment, Einstein's second postulate about the constancy of the speed of light in vacuum follows, which conflicts with the first postulate, if we extend to electromagnetic phenomena not only the principle of Galileo's relativity, but also the rule of addition of velocities. Consequently, Galileo's transformations for coordinates and time, as well as his rule for adding velocities to electromagnetic phenomena, are inapplicable.
Consequences from the postulates of SRT
If we compare distances and clock readings in different reference systems using light signals, then we can show that the distance between two points and the duration of the time interval between two events depend on the choice of the reference system.
Relativity of distances:
where \(I_0 \) is the length of the body in the frame of reference relative to which the body is at rest, \(l \) is the length of the body in the frame of reference relative to which the body is moving, \(v \) is the speed of the body.
This means that the linear size of a reference moving relative to the inertial frame decreases in the direction of motion.
Relativity of time intervals:
where \(\tau_0 \) is the time interval between two events occurring at the same point of the inertial frame of reference, \(\tau \) is the time interval between the same events in a moving \(v \) reference system.
This means that clocks moving relative to an inertial reference frame run slower than stationary clocks and show a shorter time interval between events (time dilation).
The law of addition of speeds in SRT is written like this:
where \(v \) is the speed of the body relative to the fixed frame of reference, \(v' \) is the speed of the body relative to the moving frame of reference, \(u \) c \) is the speed of light.
At speeds much lower than the speed of light, the relativistic law of addition of velocities becomes classical, and the length of the body and the time interval become the same in the stationary and moving frames of reference (correspondence principle).
To describe the processes in the microworld, the classical law of addition is inapplicable, while the relativistic law of addition of velocities works.
total energy
Total energy \(E \) of the body in a state of motion is called the relativistic energy of the body:
The total energy, mass and momentum of a body are related to each other - they cannot change independently.
The law of proportionality of mass and energy is one of the most important conclusions of SRT. Mass and energy are different properties of matter. The mass of a body characterizes its inertia, as well as the ability of the body to enter into gravitational interaction with other bodies.
Important!
The most important property of energy is its ability to transform from one form to another in equivalent quantities during various physical processes - this is the content of the law of conservation of energy. The proportionality of mass and energy is an expression of the inner essence of matter.
Rest energy
The body has the lowest energy \(E_0 \) in the frame of reference relative to which it is at rest. This energy is called rest energy:
The rest energy is the internal energy of the body.
In SRT, the mass of a system of interacting bodies is not equal to the sum of the masses of the bodies included in the system. The difference between the sum of the masses of free bodies and the mass of a system of interacting bodies is called mass defect– \(\Delta m\) . The mass defect is positive if the bodies are attracted to each other. The change in the system's own energy, i.e., for any interactions of these bodies inside it, is equal to the product of the mass defect and the square of the speed of light in vacuum:
Experimental confirmation of the connection between mass and energy was obtained by comparing the energy released during radioactive decay with the difference in the masses of the initial nucleus and the final products.
This statement has a variety of practical applications, including the use of nuclear energy. If the mass of a particle or a system of particles decreases by \(\Delta m \) , then energy must be released \(\Delta E=\Delta m\cdot c^2 \).
The kinetic energy of a body (particle) is equal to:
Important!
In classical mechanics, the rest energy is zero.
Relativistic momentum
relativistic momentum body is called a physical quantity equal to:
where \(E \) is the relativistic energy of the body.
For a body with mass \ (m \) , you can use the formula:
In experiments to study the interactions of elementary particles moving at speeds close to the speed of light, the prediction of the theory of relativity about the conservation of relativistic momentum in any interactions was confirmed.
Important!
The law of conservation of relativistic momentum is a fundamental law of nature.
The classical law of conservation of momentum is a particular case of the universal law of conservation of relativistic momentum.
The total energy \(E \) of a relativistic particle, the rest energy \(E_0 \) and the momentum \(p \) are related by:
It follows from it that for particles with a rest mass equal to zero, \(E_0 \) = 0 and \(E=pc \) .
You sit facing the direction of the starship and look at the light bulb, which is located in its bow. The light from the light bulb, not paying attention to its movement, moves relative to the stars at a speed of C = 300,000 km/s. You are moving towards the light at a speed , therefore, relative to you, the light must have a speed
You measure this speed, compare it with the known value of C and come to the conclusion that you are moving at a speed of 50,000 km / s, so electromagnetic phenomena seem to distinguish between rest and uniform rectilinear motion. That is, a paradox is obtained: on the one hand, the speed of light of 300,000 km / s should not depend on whether the light source is moving or at rest, on the other hand, according to the classical law of addition of velocities, it should depend on the choice of reference frame.
Different solutions were offered, one of the opinions, which Lorentz was a supporter, said: inertial reference frames, equal in mechanical phenomena, are not equal in the laws of electrodynamics.
That is, in electrodynamics there is a certain privileged, main, absolute frame of reference, which scientists associated with the so-called ether.
American scientists Michelson and Morley tried to verify the validity of the presence of a reference system associated with the ether, and the presence of this ether itself. They checked whether there is a so-called absolute frame of reference associated with the ether, and all other frames of reference moving relative to it, that is, the so-called ethereal wind, which could influence the magnitude of the speed of light. And, as you have just seen, there is no ethereal wind. The physics of that time faced an insoluble paradox: what is true - classical mechanics, Maxwell's electrodynamics, or something else.
At the time of the publication of his work, Albert Einstein was not a recognized world scientist, the ideas that he expressed seemed so revolutionary that at first they had practically no supporters. Nevertheless, a huge number of experiments and measurements that were carried out after that showed the validity of the point of view of Albert Einstein.
Let us formulate again the problems that the physics of that time faced and talk about the solutions proposed by Einstein.
It is not possible to detect a privileged reference system associated with the motionless world ether.
Does this mean that it does not exist at all, that privileged absolute frame of reference does not exist? Albert Einstein extended the operation of Galileo's principle in mechanics to the whole of physics, and this is how Einstein's principle of relativity came about: any physical phenomenon under the same initial conditions proceeds in the same way in any inertial frame of reference.
That is, not any mechanical phenomenon, but any physical phenomenon.
The next difficulty: electrodynamics contradicts mechanics in that Maxwell's equations are not invariant under Galilean transformations, that is, this is exactly the difficulty associated with the speed of light.
Maybe Maxwell is wrong? Nothing of the kind, Maxwell's electrodynamics is quite fair. Does this mean that all other areas of physics are unfair, the transformations of Galileo that connect these parts of physics are incorrect? After all, the classical law of speed addition follows from them, which we use when solving problems, such as: a train travels at a speed of 40 km/h, and a passenger walks along the car at a speed of 5 km/h, and relative to an observer on the ground, this passenger will move with speed of 45 km/h (Fig. 2).
Rice. 2. An example of the classical addition of speeds ()
Einstein actually declares: since Galileo's transformations are unfair, then this law of addition of velocities is also unfair. A complete demolition of the foundations, an absolutely obvious life example, an absolutely obvious life law turns out to be unfair, what is the problem here? The problem is deep within those foundations of classical mechanics that were laid down by Newton. It turns out that the main problem of classical mechanics is that it is assumed that all interactions within the framework of mechanics propagate instantaneously. Consider, for example, the gravitational attraction of bodies.
If one of the bodies is moved to the side, then, according to the law of universal gravitation, the second body will feel this fact instantly, as soon as the distance from it to the first body changes, that is, the interaction is transmitted at an infinite speed. In reality, the interaction mechanism is as follows: changing the position of the first body changes the gravitational field around it. This change in the field begins to run at some speed to all points in space, and when it reaches the point where the second body is located, the interaction of the first and second bodies changes accordingly. That is, the rate of propagation of interaction has some finite value. But if interactions are transmitted at some finite speed, then in nature there must be some maximum allowable speed for the propagation of these interactions, the maximum speed with which the interaction can be transmitted. This is stated by the second postulate, which assigns the exclusive role of the speed of light, the principle of invariance of the speed of light: in each inertial frame of reference, light moves in vacuum with the same speed. The value of this speed does not depend on whether the light source is at rest or moving.
Thus, we will not be able to carry out the example described above with a light bulb in a spaceship in reality, this will contradict this postulate of Einstein's theory. The speed of light relative to the observer in the starship will be equal to C, and not C + V, as we said before, and the observer will not be able to notice the fact that the starship is moving. The classical law of addition of velocities in relation to the speed of light does not work, oddly enough for us, but the speed of light for an observer on Earth and for an astronaut will be exactly the same and equal to 300,000 km/s. It is this position that underlies the theory of relativity and has been quite successfully proved by a huge number of experiments.
The mechanics that was built on the basis of these two postulates is called relativistic mechanics (from the English relativity - “relativity”). It may seem that relativistic mechanics cancels Newton's classical mechanics, since it is based on other postulates, but the fact is that Newton's classical mechanics is a special case of Einstein's relativistic mechanics, which manifests itself at speeds much lower than the speed of light. In the world around us, we live at such speeds, the speeds that we encounter are much less than the speed of light. Therefore, classical Newtonian mechanics is enough to describe our life.
For small speeds, much less than the speed of light, we quite successfully use classical mechanics, but if we work with speeds close to the speed of light, or we want great accuracy in describing phenomena, we must use the special theory of relativity, that is, relativistic mechanics.
Bibliography
- Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemozina, 2012.
- Gendenstein L.E., Dick Yu.I. Physics grade 10. - M.: Mnemosyne, 2014.
- Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.
- Pppa.ru ().
- Sfiz.ru ().
- eduspb.com().
Homework
- Define Einstein's principle of relativity.
- Define Galileo's principle of relativity.
- Define Einstein's principle of invariance.
O Basic concepts
Galileo's principle of relativity
The principle of relativity (Einstein's first postulate): the laws of nature are invariant under the change of reference frame
Light speed invariance (Einstein's second postulate)
Einstein's postulates as a manifestation of the symmetries of space and time
Basic relativistic effects (consequences from Einstein's postulates).
Correspondence of SRT and classical mechanics: their predictions coincide at low speeds (much less than the speed of light)
& Summary
The principle of relativity is a fundamental physical principle. Distinguish:
Principle of relativity of classical mechanics-postulate of G. Galileo, according to which in any inertial reference frames all mechanical phenomena proceed in the same way under the same conditions. The laws of mechanics are the same in all inertial frames of reference.
The principle of relativity of relativistic mechanics - A. Einstein's postulate, according to which in any inertial reference frames all physical phenomena proceed in the same way. Those. all laws of nature are the same in all inertial frames of reference.
Inertial frame of reference(ISO) - a frame of reference in which the law of inertia is valid: a body that is not affected by external forces is at rest or uniform rectilinear motion.
Any frame of reference moving uniformly and rectilinearly relative to the IFR is also an IFR. According to the principle of relativity, all IFRs are equal, and all the laws of physics act in them in the same way.
The assumption of the existence of at least two IFRs in an isotropic space leads to the conclusion that there is an infinite set of such systems moving relative to each other at constant velocities.
If the velocities of the relative motion of the IFR can take on any values, the connection between the coordinates and times of any "event" in different IFRs is carried out by Galilean transformations.
If the speeds of the relative motion of the IFR cannot exceed a certain final speed "c", the connection between the coordinates and time moments of any "event" in different IFRs is carried out by Lorentz transformations. Postulating the linearity of these transformations, one obtains the constancy of the speed "c" in all inertial frames of reference.
The father of the principle of relativity is considered Galileo Galilei, who drew attention to the fact that being in a closed physical system, it is impossible to determine whether this system is at rest or moves uniformly. In the days of Galileo, people dealt mainly with purely mechanical phenomena. Galileo's ideas were developed in Newton's mechanics. However, with the development of electrodynamics, it turned out that the laws of electromagnetism and the laws of mechanics (in particular, the mechanical formulation of the principle of relativity) do not agree well with each other. These contradictions led to Einstein's creation of the special theory of relativity. After that, the generalized principle of relativity began to be called "Einstein's principle of relativity", and its mechanical formulation - "Galileo's principle of relativity".
A. Einstein showed that the principle of relativity can be preserved if the fundamental concepts of space and time, which have not been questioned for centuries, are radically revised. Einstein's work became part of the educational system of a brilliant new generation of physicists that grew up in the 1920s. Subsequent years did not reveal any weaknesses in the private theory of relativity.
However, Einstein was haunted by the fact, previously noted by Newton, that the whole idea of the relativity of motion collapses if acceleration is introduced; in this case, inertia forces come into play, which are absent in uniform and rectilinear motion. Ten years after the creation of the private theory of relativity, Einstein proposed a new, highly original theory, in which the hypothesis of curved space plays the main role and which gives a unified picture of the phenomena of inertia and gravity. In this theory, the principle of relativity is preserved, but presented in a much more general form, and Einstein was able to show that his general theory of relativity, with minor changes, includes most of Newton's theory of gravity, one of which explains a known anomaly in the motion of Mercury.
For more than 50 years after the appearance of the general theory of relativity in physics, it was not given much importance. The fact is that calculations based on the general theory of relativity give almost the same answers as calculations within the framework of Newton's theory, and the mathematical apparatus of the general theory of relativity is much more complicated. It was worthwhile to carry out long and laborious calculations only in order to understand the phenomena that are possible in gravitational fields of unheard-of high intensity. But in the 1960s, with the advent of the era of spaceflight, astronomers began to realize that the universe is much more diverse than it was first imagined, and that there may be such compact high-density objects as neutron stars and black holes in which the gravitational field is really reaches an unusually high intensity. At the same time, the development of computer technology partly removed the burden of tedious calculations from the shoulders of the scientist. As a result, the general theory of relativity began to attract the attention of numerous researchers, and rapid progress began in this area. New exact solutions of Einstein's equations were obtained and new ways of interpreting their unusual properties were found. The theory of black holes was developed in more detail. The applications of this theory, bordering on fantasy, indicate that the topology of our universe is much more complex than one might think, and that there may be other universes separated from ours by gigantic distances and connected to it by narrow bridges of curved space. It is possible, of course, that this assumption will turn out to be wrong, but one thing is clear: the theory and phenomenology of gravity is a mathematical and physical wonderland that we have barely begun to explore.
The two fundamental principles of SRT are:
Einstein's first postulate(principle of relativity): the laws of nature are invariant with respect to a change in the reference system (all laws of nature are the same in all coordinate systems moving rectilinearly and uniformly relative to each other. In other words, no experiments can distinguish a moving frame of reference from a resting one. For example, the sensations experienced by a person in a stationary car at an intersection, when the car closest to him begins to move slowly, the person has the illusion that his car is rolling back.)
Einstein's second postulate:light speed invariance(principle of constancy of the speed of light: the speed of light in vacuum is the same in all frames of reference moving rectilinearly and uniformly relative to each other (c=const=3 10 8 m/s). The speed of light in a vacuum does not depend on the movement or rest of the light source. The speed of light is the maximum possible speed of propagation of material objects).
Correspondence of SRT and classical mechanics: their predictions agree at low speeds (much less than the speed of light).
Einstein abandoned Newton's concepts of space and time.
Space without matter, as a pure receptacle, does not exist, and the geometry (curvature) of the world, and the slowing down of the flow of time are determined by the distribution and movement of matter.
Basic relativistic effects(consequences from Einstein's postulates):
timerelatively, i.e. the speed of the clock is determined by the speed of the clock itself relative to the observer.
space is relatively, i.e. the distance between points in space depends on the speed of the observer.
relativity of simultaneity (if for a stationary observer two events are simultaneous, then for an observer who moves, this is not so)
distance relativity ( relativistic length contraction: in a moving reference frame, spatial scales are shortened along the direction of motion)
relativity of time intervals ( relativistic time dilation: in a moving reference frame, time passes more slowly). This effect is manifested, for example, in the need to adjust the clocks on Earth's satellites.
invariance of the space-time interval between events (the interval between two events has the same value in one frame of reference as in another)
invariance of cause-and-effect relationships
unity of space-time (space and time represent a single four-dimensional reality - we see the world always as space-time.)
mass-energy equivalence
Thus ,in Einstein's theory, space and time are relative- the results of measuring length and time depend on whether the observer is moving or not.
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 accuracy 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 arises the seeming 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 established so precisely and unambiguously that it would be clearly unjustified to refuse 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 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, based on 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 IRF can determine whether it is at rest or moving uniformly and rectilinearly. Thus, all IFRs are absolutely 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 Galileo's extended principle of relativity - all the provisions of the special theory of relativity follow mathematically. 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).
