Special Relativity (SRT) or private theory relativity is the theory of Albert Einstein, published in 1905 in the work "On the electrodynamics of moving bodies" (Albert Einstein - Zur Elektrodynamik bewegter Körper. Annalen der Physik, IV. Folge 17. Seite 891-921. Juni 1905).

It explained the movement between different inertial reference frames or the movement of bodies moving relative to each other at a constant speed. In this case, none of the objects should be taken as a frame of reference, but they should be considered relative to each other. SRT provides only 1 case when 2 bodies do not change the direction of motion and move uniformly.

The laws of special relativity cease to operate when one of the bodies changes the trajectory of movement or increases speed. Here the general theory of relativity (GR) takes place, giving general interpretation movement of objects.

The two postulates on which the theory of relativity is based are:

1. The principle of relativity- According to him, in all existing systems references that move relative to each other with a constant speed and do not change direction, the same laws apply.
2. The principle of the speed of light- The speed of light is the same for all observers and does not depend on the speed of their movement. This is the highest speed, and nothing in nature has a greater speed. The speed of light is 3*10^8 m/s.

Albert Einstein took experimental rather than theoretical data as a basis. This was one of the components of his success. New experimental data served as the basis for creating new theory.

Physicists with mid-nineteenth centuries have been searching for a new mysterious medium called ether. It was assumed that the ether can pass through all objects, but does not participate in their movement. According to beliefs about the ether, by changing the speed of the viewer in relation to the ether, the speed of light also changes.

Einstein, trusting experiments, rejected the notion new environment ether and assumed that the speed of light is always constant and does not depend on any circumstances, such as the speed of the person himself.

Time spans, distances, and their uniformity

The special theory of relativity links time and space. In the Material Universe, there are 3 known in space: right and left, forward and backward, up and down. If we add to them another dimension, called time, then this will form the basis of the space-time continuum.

If you are moving at a slow speed, your observations will not converge with people who are moving faster.

Later, experiments confirmed that space, like time, cannot be perceived in the same way: our perception depends on the speed of the movement of objects.

The connection of energy with mass

Einstein came up with a formula that combined energy with mass. This formula has become widespread in physics, and it is familiar to every student: E=m*s², wherein E-energy; m- body mass, c-speed spread of light.

The mass of a body increases in proportion to the increase in the speed of light. If the speed of light is reached, the mass and energy of the body become dimensionless.

By increasing the mass of an object, it becomes more difficult to achieve an increase in its speed, i.e., for a body with an infinitely huge material mass, infinite energy is needed. But in reality this is impossible to achieve.

Einstein's theory combined two separate positions: the position of mass and the position of energy into one general law. This made it possible to convert energy into material mass and vice versa.

Also in late XIX 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. It was a consequence of the "cascade" scientific discoveries made within an extremely short time historical period covering last years XIX century and the first decades of the XX, many of which did not fit into the idea of ​​ordinary human experience. A prime example can serve as the theory of relativity created by Albert Einstein (1879-1955).

Theory of relativity- physical theory of space-time, that is, a theory that describes the universal space-time properties physical processes. The term was introduced in 1906 by Max Planck to emphasize the role of the principle of relativity.
in special relativity (and, later, general relativity).

AT narrow sense The theory of relativity includes special and general relativity. Special theory of relativity(hereinafter referred to as SRT) refers to processes in the study of which gravitational fields can be neglected; general theory of relativity(hereinafter referred to as GR) is a theory of gravitation that generalizes Newton's.

Special, or private theory of relativity is a theory of the structure of space-time. It was first presented in 1905 by Albert Einstein in his work "On the Electrodynamics of Moving Bodies". The theory describes movement, the laws of mechanics, as well as the space-time relationships that determine them, at any speed of movement,
including those close to the speed of light. Classical Newtonian mechanics
within SRT is an approximation for low velocities.

One of the reasons for Albert Einstein's success is that he put experimental data ahead of theoretical data. When a number of experiments showed results that contradicted the generally accepted theory, many physicists decided that these experiments were erroneous.

Albert Einstein was one of the first who decided to build a new theory based on new experimental data.

At the end of the 19th century, physicists were in search of a mysterious ether - a medium in which, according to generally accepted assumptions, light waves, like acoustic, for the propagation of which air is needed, or another medium - solid, liquid or gaseous. Belief in the existence of the aether led to the belief that the speed of light must vary with the speed of the observer with respect to the aether. Albert Einstein abandoned the concept of aether and suggested that everything physical laws, including the speed of light, remain unchanged regardless of the speed of the observer - as experiments have shown.

SRT explained how to interpret motions between different inertial frames of reference - simply put, objects that move with constant speed in relation to each other. Einstein explained that when two objects are moving at a constant speed, one should consider their motion relative to each other, instead of taking one of them as an absolute frame of reference. So if two astronauts are flying on two spaceships and want to compare their observations, the only thing they need to know is their speed relative to each other.

Special relativity considers only one special case (hence the name), when the motion is straight and uniform.

Based on the impossibility of detecting absolute motion, Albert Einstein concluded that all inertial systems reference. 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 (states the same thing, but not for all laws of nature, but only for laws classical mechanics, leaving open question about the applicability of the principle of relativity to optics and electrodynamics) to any physical. 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 drawn inside a closed ISO, it is impossible to establish whether it is at rest or moving uniformly and in a straight line. Thus, all ISOs are completely equal, and physical laws are invariant with respect to the choice of ISOs (i.e., the equations expressing these laws have the same shape 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 source and receiver of light. It is the same in all directions and in all inertial frames of reference. The speed of light in a vacuum - the limiting speed in nature - this is one of the most important physical constants, the so-called world constants.

The most important consequence of SRT was the famous Einstein's formula on the relationship between mass and energy E \u003d mc 2 (where C is the speed of light), which showed the unity of space and time, expressed in a joint change in their characteristics depending on the concentration of masses and their movement and confirmed by data modern physics. Time and space were no longer considered independently of each other, and the idea of ​​a space-time four-dimensional continuum arose.

According to the theory of the great physicist, when the speed of a material body increases, approaching the speed of light, its mass also increases. Those. the faster an object moves, the heavier it becomes. In the case of reaching the speed of light, the mass of the body, as well as its energy, become infinite. The heavier the body, the more difficult it is to increase its speed; an infinite amount of energy is required to accelerate a body with infinite mass, so it is impossible for material objects to reach the speed of light.

In the theory of relativity, "two laws - the law of conservation of mass and conservation of energy - have lost their independent friend justice from each other and turned out to be united into a single law, which can be called the law of conservation of energy or mass. Thanks to fundamental connection between these two concepts, matter can be turned into energy, and vice versa - energy into matter.

General theory relativity- The theory of gravity published by Einstein in 1916, which he worked on for 10 years. Is an further development special theory of relativity. If the material body accelerates or turns to the side, the SRT laws no longer apply. Then GR comes into force, which explains the motions of material bodies in the general case.

The general theory of relativity postulates that gravitational effects are caused not by the force interaction of bodies and fields, but by the deformation of the very space-time in which they are located. This deformation is associated, in particular, with the presence of mass-energy.

General Relativity is currently the most successful theory of gravity, well supported by observations. General relativity has generalized SRT to accelerated ones, i.e. non-inertial systems. The basic principles of general relativity are as follows:

- limiting the applicability of the principle of constancy of the speed of light to areas where gravitational forces can be neglected(where gravity is strong, the speed of light slows down);

- extension of the principle of relativity to all moving systems(and not just inertial ones).

In general relativity, or the theory of gravitation, he also proceeds from the experimental fact of the equivalence of inertial and gravitational masses, or the equivalence of inertial and gravitational fields.

The equivalence principle plays important role in science. We can always calculate directly the action of the forces of inertia on any physical system, and this gives us the opportunity to know the action of the gravitational field, abstracting from its inhomogeneity, which is often very insignificant.

From GR, a series was obtained important findings:

1. The properties of space-time depend on the moving matter.

2. A beam of light, which has an inert, and, consequently, gravitational mass, must be bent in the gravitational field.

3. The frequency of light under the influence of the gravitational field should shift towards lower values.

Long time experimental evidence OT was not enough. The agreement between theory and experiment is quite good, but the purity of the experiments is violated by various complex side effects. However, the effect of space-time curvature can be detected even in moderate gravitational fields. Very sensitive clocks, for example, can detect time dilation on the Earth's surface. In order to expand the experimental base of general relativity, in the second half of the 20th century, new experiments were carried out: the equivalence of the inertial and gravitational masses was tested (including by laser ranging of the Moon);
with the help of radar, the movement of the perihelion of Mercury was clarified; measured gravitational deflection radio waves by the Sun, planetary radar was carried out solar system; the influence of the gravitational field of the Sun on radio communications with spacecraft that were sent to the distant planets of the solar system was evaluated, etc. All of them, one way or another, confirmed the predictions obtained on the basis of general relativity.

So, special theory relativity is based on the postulates of the constancy of the speed of light and the sameness of the laws of nature in all physical systems, and the main results to which it comes are as follows: the relativity of the properties of space-time; relativity of mass and energy; equivalence of heavy and inertial masses.

The most significant result of the general theory of relativity from a philosophical point of view is the establishment of the dependence of the space-time properties of the surrounding world on the location and movement of gravitating masses. It is due to the influence of bodies
with in large numbers light paths are bent. Consequently, the gravitational field created by such bodies ultimately determines the space-time properties of the world.

The special theory of relativity abstracts from the action of gravitational fields and therefore its conclusions are applicable only for small areas of space-time. The cardinal difference between the general theory of relativity and the fundamental ones preceding it physical theories in the rejection of a number of old concepts and the formulation of new ones. It is worth saying that the general theory of relativity has made a real revolution in cosmology. Based on it, there various models Universe.

About the teachings of Albert Einstein, which testifies to the relativity of everything that happens in this mortal world, does not know unless the lazy. For almost a hundred years, disputes have been going on not only in the world of science, but also in the world of practicing physicists. Einstein's theory of relativity, described in simple words quite accessible, and is not a secret to the uninitiated.

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A few general questions

Taking into account the peculiarities of the theoretical teachings of the great Albert, his postulates can be ambiguously regarded by a wide variety of currents of theoretical physicists, quite high scientific schools, as well as adherents of the irrational current of the physical and mathematical school.

Back at the beginning of the last century, when there was a surge of scientific thought and against the background of social change certain scientific trends began to emerge, the theory of relativity of everything in which a person lives appeared. No matter how our contemporaries evaluate this situation, all in real world really not static Einstein's special theory of relativity:

• Times are changing, the views and mental opinion of society on certain problems in the social plan are changing;
• Social foundations and worldview regarding the doctrine of probability in various government systems and at special conditions development of society changed over time and under the influence of other objective mechanisms.
• How did society's views on problems develop? social development, the same was the attitude and opinions about Einstein's theories about time.

Important! Einstein's theory of gravity was the basis for systemic disputes among the most reputable scientists, both at the beginning of its development and during its completion. They talked about her, numerous disputes took place, she became the topic of conversation in the most high-ranking salons in different countries.

Scientists discussed it, it was the subject of conversation. There was even such a hypothesis that the doctrine is accessible for understanding only to three people from the scientific world. When the time came to explain the postulates, the priests of the most mysterious of the sciences, Euclidean mathematics, began. Then an attempt was made to build its digital model and the same mathematically verified consequences of its action on world space, the author of the hypothesis admitted that it became very difficult to understand even what he created. So what is general theory of relativity, what explores and what applied application she found in the modern world?

History and roots of the theory

Today, in the vast majority of cases, the achievements of the great Einstein are briefly called the complete denial of what was originally an unshakable constant. It was this discovery that made it possible to refute what is known to all schoolchildren as a physical binomial.

Most of the world's population, one way or another, attentively and thoughtfully or superficially, even once, turned to the pages of the great book - the Bible.

It is in it that you can read about what has become a true confirmation essence of the doctrine- what a young American scientist worked on at the beginning of the last century. The facts of levitation and other fairly common things in Old Testament history once became miracles in modern times. Ether is a space in which a person lived a completely different life. The features of life on the air were studied by many world celebrities in the field natural sciences. And Einstein's theory of gravity confirmed that the ancient book- this is true.

The works of Hendrik Lorentz and Henri Poincaré made it possible to experimentally discover certain features of the ether. First of all, it is the creation of mathematical models peace. The basis was a practical confirmation that when material particles move in the ethereal space, they contract relative to the direction of movement.

The works of these great scientists made it possible to create the foundation for the main postulates of the doctrine. Exactly given fact gives permanent material to assert that the works of the Nobel laureate and Albert's relativistic theory were and still are plagiarism. Many scientists today argue that many postulates were accepted much earlier, for example:

• The concept of conditional simultaneity of events;
• Principles of the constant binomial hypothesis and criteria for the speed of light.

What to do to understand the theory of relativity? The point is in the past. It was in the works of Poincaré that the hypothesis was put forward that high speeds in the laws of mechanics need to be rethought. Thanks to the statements French physics academia I learned about how relative the movement in the projection is to the theory of ethereal space.

In static science, a large amount of physical processes were considered for various material objects moving with . The postulates of the general concept describe the processes occurring with accelerating objects, explain the existence of graviton particles and gravity itself. The essence of the theory of relativity in explaining those facts that were previously nonsense for scientists. If it is necessary to describe the features of motion and the laws of mechanics, the relationship of space and time continuum in conditions of approaching the speed of light, the postulates of the theory of relativity should be used exclusively.

About the theory briefly and clearly

How is the teaching of the great Albert so different from what physicists did before him? Previously, physics was a rather static science, which considered the principles of development of all processes in nature in the sphere of the “here, today and now” system. Einstein made it possible to see everything that happens around not only in three-dimensional space, but also relative to various objects and points of time.

Attention! In 1905, when Einstein published his theory of relativity, she allowed to explain and in affordable option interpret motion between different inertial reference systems.

Its main provisions are the ratio of constant velocities of two objects moving relative to each other instead of taking one of the objects, which can be taken as one of the absolute reference factors.

Feature of the doctrine lies in the fact that it can be considered in relation to one exceptional case. Main factors:

1. Straightness of the direction of movement;
2. Uniformity of motion of a material body.

When changing direction or other simple parameters, when a material body can accelerate or turn sideways, the laws of the static theory of relativity are not valid. In this case, the entry into force general laws relativity, which can explain the movement of material bodies in general situation. Thus, Einstein found an explanation for all the principles of interaction physical bodies each other in space.

Principles of the Theory of Relativity

Doctrine principles

The statement about relativity has been the subject of the most lively discussions for a hundred years. Most scientists consider various options application of postulates as an application of two principles of physics. And this path is the most popular in the field of applied physics. Basic postulates theory of relativity, Interesting Facts , which today found irrefutable confirmation:

• The principle of relativity. Preservation of the ratio of bodies under all laws of physics. Accepting them as inertial frames of reference, which move at constant speeds relative to each other.
• Postulate about the speed of light. It remains an unchanging constant, in all situations, regardless of speed and relationship with light sources.

Despite the contradictions between the new teaching and the basic postulates of one of the most exact sciences based on constant static indicators, the new hypothesis attracted fresh eyes on the the world. The success of the scientist was ensured, which was confirmed by the award of Nobel Prize in the field of exact sciences.

What caused such overwhelming popularity, and How did Einstein discover his theory of relativity?? Tactics of a young scientist.

1. Until now, world-famous scientists have put forward a thesis, and only then carried out a series of practical research. If on certain moment received data that does not fit the general concept, they were recognized as erroneous with summing up the reasons.
2. The young genius used a radically different tactic, set practical experiences, they were serial. The results obtained, despite the fact that they could somehow not fit into the conceptual series, lined up in a coherent theory. And no "mistakes" and "errors", all moments relativity hypotheses, examples and the results of the observations clearly fit into the revolutionary theoretical doctrine.
3. Future Nobel laureate refuted the need to study the mysterious ether, where waves of light propagate. The belief that the ether exists has led to a number of significant misconceptions. The main postulate is the change in the velocities of the light beam relative to the one observing the process in the ethereal medium.

Relativity for dummies

The theory of relativity is the simplest explanation

Conclusion

The main achievement of the scientist is the proof of the harmony and unity of such quantities as space and time. The fundamental nature of the connection of these two continuums as part of three dimensions, combined with the time dimension, made it possible to learn many secrets of nature. material world. Thanks to Einstein's theory of gravity became available the study of the depths and other achievements modern science, after all, the full possibilities of the teachings have not been used to date.

One hundred years ago, in 1915, a young Swiss scientist, who at that time had already made revolutionary discoveries in physics, proposed a fundamentally new understanding of gravity.

In 1915, Einstein published the general theory of relativity, which characterizes gravity as a basic property of spacetime. He presented a series of equations describing the effect of the curvature of space-time on the energy and motion of the matter and radiation present in it.

One hundred years later, the general theory of relativity (GR) became the basis for the construction of modern science, it has withstood all the tests with which scientists attacked it.

But until recently it was not possible to conduct experiments in extreme conditions to test the stability of the theory.

It's amazing how strong the theory of relativity has proven to be over 100 years. We are still using what Einstein wrote!

Clifford Will, theoretical physicist, University of Florida

Scientists now have the technology to search for physics beyond general relativity.

A new look at gravity

General relativity describes gravity not as a force (as it appears in Newtonian physics), but as a curvature of space-time due to the mass of objects. The Earth revolves around the Sun, not because the star attracts it, but because the Sun deforms space-time. If a heavy bowling ball is placed on a stretched blanket, the blanket will change shape - gravity affects space in much the same way.

Einstein's theory predicted some crazy discoveries. For example, the possibility of the existence of black holes, which bend space-time to such an extent that nothing can escape from the inside, not even light. Based on the theory, evidence was found for the generally accepted opinion today that the universe is expanding and accelerating.

The general theory of relativity has been confirmed by numerous observations. Einstein himself used general relativity to calculate the orbit of Mercury, whose motion cannot be described by Newton's laws. Einstein predicted the existence of objects so massive that they bend light. This is a gravitational lensing phenomenon that astronomers often encounter. For example, the search for exoplanets is based on the effect of subtle changes in the radiation curved by the gravitational field of the star around which the planet revolves.

Testing Einstein's Theory

General relativity works well for ordinary gravity, as shown by experiments on Earth and observations of the planets of the solar system. But it has never been tested in extreme conditions. strong impact fields in spaces lying on the boundaries of physics.

The most promising way to test a theory under such conditions is to observe changes in spacetime, which are called gravitational waves. They appear as a result major events, during the merger of two massive bodies, such as black holes, or especially dense objects - neutron stars.

A cosmic firework of this magnitude would only have the smallest ripples in space-time. For example, if two black holes collided and merged somewhere in our galaxy, gravitational waves could stretch and compress the distance between objects on Earth a meter apart by one thousandth of the diameter of an atomic nucleus.

Experiments have appeared that can record changes in space-time due to such events.

There is a good chance to fix gravitational waves in the next two years.

Clifford Will

The Laser Interferometric Gravitational Wave Observatory (LIGO), with observatories near Richland, Washington, and Livingston, Louisiana, uses a laser to detect minute distortions in dual L-shaped detectors. As space-time ripples pass through the detectors, they stretch and compress space, causing the detector to change dimensions. And LIGO can measure them.

LIGO started a series of launches in 2002 but didn't hit the mark. Improvements were made in 2010, and the organization's successor, the Advanced LIGO Observatory, should be up and running again this year. Many of the planned experiments are aimed at finding gravitational waves.

Another way to test the theory of relativity is to look at the properties of gravitational waves. For example, they can be polarized, like light passing through polarized glasses. The theory of relativity predicts the features of such an effect, and any deviations from the calculations may become a reason to doubt the theory.

unified theory

Clifford Will believes that the discovery of gravitational waves will only strengthen Einstein's theory:

I think we need to keep looking for proof of general relativity to be sure it's right.

Why are these experiments needed at all?

One of the most important and elusive tasks of modern physics is the search for a theory that will link together Einstein's research, that is, the science of the macrocosm, and quantum mechanics, the reality of the smallest objects.

Advances in this direction, quantum gravity, may require changes to the general theory of relativity. It is possible that experiments in the field quantum gravity will require so much energy that it will be impossible to conduct them. “But who knows,” says Will, “maybe in quantum universe there is an effect, insignificant, but searchable.

material from the book "The Shortest History of Time" by Stephen Hawking and Leonard Mlodinov

Relativity

Einstein's fundamental postulate, called the principle of relativity, states that all laws of physics must be the same for all freely moving observers, regardless of their speed. If the speed of light constant, then any freely moving observer must fix the same value, regardless of the speed with which he approaches the light source or moves away from it.

The requirement that all observers agree on the speed of light forces a change in the concept of time. According to the theory of relativity, an observer riding a train and one standing on a platform will disagree on the distance traveled by light. Since speed is distance divided by time, the only way for observers to agree on the speed of light is to disagree on time as well. In other words, relativity put an end to the idea of ​​absolute time! It turned out that each observer must have his own measure of time, and that identical clocks for different observers would not necessarily show the same time.

Saying that space has three dimensions, we mean that the position of a point in it can be conveyed using three numbers - coordinates. If we introduce time into our description, we get a four-dimensional space-time.

Another well-known consequence of the theory of relativity is the equivalence of mass and energy, expressed by the famous Einstein equation E = mc 2 (where E is energy, m is the mass of the body, c is the speed of light). Due to the equivalence of energy and mass kinetic energy, which a material object has due to its motion, increases its mass. In other words, the object becomes more difficult to overclock.

This effect is significant only for bodies that move at a speed close to the speed of light. For example, at a speed equal to 10% of the speed of light, the mass of the body will be only 0.5% more than at rest, but at a speed of 90% of the speed of light, the mass will already be more than twice the normal. As we approach the speed of light, the mass of the body increases faster and faster, so everything is required to accelerate it. more energy. According to the theory of relativity, an object can never reach the speed of light, because in this case its mass would become infinite, and due to the equivalence of mass and energy, this would require infinite energy. That is why the theory of relativity forever dooms any ordinary body to move at a speed less than the speed of light. Only light or other waves that have no mass of their own can move at the speed of light.

curved space

Einstein's general theory of relativity is based on the revolutionary assumption that gravity is not an ordinary force, but a consequence of the fact that space-time is not flat, as was once thought. In general relativity, spacetime is curved or warped by the mass and energy placed in it. Bodies like the Earth move in curved orbits not under the influence of a force called gravity.

Since the geodesic line is shortest line between two airports, navigators fly planes along such routes. For example, you could follow a compass to fly 5,966 kilometers from New York to Madrid almost due east along the geographic parallel. But you only have to cover 5802 kilometers if you fly in a big circle, first to the northeast and then gradually turning to the east and further to the southeast. View of these two routes on the map, where earth's surface distorted (represented flat), deceptive. Moving "straight" east from one point to another on the surface the globe, you are not really moving in a straight line, or rather, not in the shortest, geodesic line.

If the trajectory of a spacecraft that moves in space in a straight line is projected onto the two-dimensional surface of the Earth, it turns out that it is curved.

According to general relativity, gravitational fields should bend light. For example, the theory predicts that near the Sun, the rays of light should be slightly bent in its direction under the influence of the mass of the star. This means that the light of a distant star, if it happens to pass near the Sun, will deviate by a small angle, due to which an observer on Earth will see the star not quite where it is actually located.

Recall that according to the basic postulate of the special theory of relativity, all physical laws are the same for all freely moving observers, regardless of their speed. Roughly speaking, the principle of equivalence extends this rule to those observers who do not move freely, but under the influence of a gravitational field.

In sufficiently small regions of space, it is impossible to judge whether you are at rest in a gravitational field or moving with constant acceleration in empty space.

Imagine that you are in an elevator in the middle of empty space. There is no gravity, no up and down. You float freely. Then the elevator starts to move with constant acceleration. You suddenly feel weight. That is, you are pressed against one of the walls of the elevator, which is now perceived as a floor. If you pick up an apple and let it go, it will fall to the floor. In fact, now when you are moving with acceleration, inside the elevator everything will happen in exactly the same way as if the elevator did not move at all, but rested in a uniform gravitational field. Einstein realized that just as you can't tell when you're in a train car whether it's stationary or moving uniformly, so when you're inside an elevator you can't tell whether it's moving at a constant speed or is in a uniform motion. gravitational field. The result of this understanding was the principle of equivalence.

The equivalence principle and the given example of its manifestation will be valid only if inertial mass(included in Newton's second law, which determines what kind of acceleration gives the body the force applied to it) and gravitational mass (included in Newton's law of gravity, which determines the value gravitational attraction) are essentially the same.

Einstein's use of the equivalence of inertial and gravitational masses to derive the principle of equivalence and, ultimately, the entire theory of general relativity is unprecedented in history. human thought an example of persistent and consistent development of logical conclusions.

Time slowdown

Another prediction of general relativity is that around massive bodies like the Earth, time should slow down.

Now, having become acquainted with the principle of equivalence, we can follow the course of Einstein's reasoning by doing another thought experiment, which shows why gravity affects time. Imagine a rocket flying in space. For convenience, we will assume that its body is so large that it takes a whole second for light to pass along it from top to bottom. Finally, suppose that there are two observers in the rocket, one on the top, near the ceiling, the other on the floor below, and both of them are equipped with the same clock that counts seconds.

Let us assume that the upper observer, having waited for the countdown of his clock, immediately sends a light signal to the lower one. At the next count, it sends a second signal. According to our conditions, it will take one second for each signal to reach the lower observer. Since the upper observer sends two light signals with an interval of one second, the lower observer will also register them with the same interval.

What will change if, in this experiment, instead of floating freely in space, the rocket will stand on the Earth, experiencing the action of gravity? According to Newton's theory, gravity will not affect the situation in any way: if the observer above transmits signals at intervals of a second, then the observer below will receive them at the same interval. But the principle of equivalence predicts a different development of events. Which one, we can understand if, in accordance with the principle of equivalence, we mentally replace the action of gravity with a constant acceleration. This is one example of how Einstein used the principle of equivalence to create his new theory of gravity.

So, suppose our rocket is accelerating. (We will assume that it is accelerating slowly, so that its speed does not approach the speed of light.) Since the rocket body is moving upwards, the first signal will need to travel a shorter distance than before (before the acceleration begins), and will arrive at the lower observer before give me a sec. If the rocket were moving at a constant speed, then the second signal would arrive exactly the same amount earlier, so that the interval between the two signals would remain equal to one second. But at the moment of sending the second signal, due to the acceleration, the rocket moves faster than at the moment of sending the first, so that the second signal will travel a shorter distance than the first, and spend even less time. The observer below, checking his watch, will note that the interval between signals is less than one second, and will disagree with the observer above, who claims that he sent signals exactly one second later.

In the case of an accelerating rocket, this effect should probably not be particularly surprising. After all, we just explained it! But remember: the principle of equivalence says that the same thing happens when the rocket is at rest in a gravitational field. Therefore, even if the rocket is not accelerating, but, for example, standing on the launch pad on the surface of the Earth, the signals sent by the upper observer at intervals of a second (according to his clock) will arrive at the lower observer at a shorter interval (according to his clock) . This is truly amazing!

Gravity changes the flow of time. Just as special relativity tells us that time runs differently for observers moving relative to each other, general relativity declares that the course of time is different for observers in different gravitational fields. According to the general theory of relativity, the lower observer registers a shorter interval between signals, because time flows more slowly near the surface of the Earth, since gravity is stronger here. The stronger the gravitational field, the greater this effect.

Our The biological clock also respond to changes in the passage of time. If one of the twins lives on a mountain top and the other lives by the sea, the first will age faster than the second. In this case, the difference in ages will be negligible, but it will increase significantly as soon as one of the twins goes on a long journey in a spaceship that accelerates to a speed close to the speed of light. When the wanderer returns, he will be much younger than his brother, who remained on Earth. This case is known as the twin paradox, but it is only a paradox for those who hold on to the idea of ​​absolute time. In the theory of relativity there is no unique absolute time - each individual has his own measure of time, which depends on where he is and how he moves.

With the advent of ultra-precise navigation systems that receive signals from satellites, the difference in clock rates at different altitudes has become practical value. If the equipment ignored the predictions of general relativity, the error in determining the position could reach several kilometers!

The advent of the general theory of relativity radically changed the situation. Space and time have gained status dynamic entities. When bodies move or forces act, they cause the curvature of space and time, and the structure of space-time, in turn, affects the movement of bodies and the action of forces. Space and time not only affect everything that happens in the universe, but they themselves depend on it all.

Imagine an intrepid astronaut who remains on the surface of a collapsing star during a cataclysmic collapse. At some point on his watch, say at 11:00, the star will shrink to a critical radius, beyond which the gravitational field becomes so strong that it is impossible to escape from it. Now suppose that the astronaut is instructed to send a signal every second on his watch to a spacecraft that is in orbit at some fixed distance from the center of the star. It starts transmitting signals at 10:59:58, that is, two seconds before 11:00. What will the crew register on board the spacecraft?

Earlier, having done a thought experiment with the transmission of light signals inside a rocket, we were convinced that gravity slows down time and the stronger it is, the more significant the effect. An astronaut on the surface of a star is in a stronger gravitational field than his counterparts in orbit, so one second on his clock will last longer than a second on the ship's clock. As the astronaut moves with the surface toward the center of the star, the field acting on him becomes stronger and stronger, so that the intervals between his signals received on board the spacecraft are constantly lengthening. This time dilation will be very small until 10:59:59, so for astronauts in orbit, the interval between the signals transmitted at 10:59:58 and 10:59:59 will be very little more than a second. But the signal sent at 11:00 am will not be expected on the ship.

Anything that happens on the surface of a star between 10:59:59 and 11:00 am according to the astronaut's clock will be stretched out over an infinite period of time by the spacecraft's clock. As we approach 11:00, the intervals between the arrival of successive crests and troughs of light waves emitted by the star will become longer and longer; the same will happen with the time intervals between the astronaut's signals. Since the frequency of the radiation is determined by the number of ridges (or troughs) arriving per second, more and more low frequency star radiation. The light of the star will become more and more reddening and fading at the same time. Eventually the star will dim so much that it will become invisible to spacecraft observers; all that remains is a black hole in space. However, the effect of the star's gravity on spaceship persists, and it continues to orbit.