Einstein's theory of relativity turned out to be wrong

SRT, TOE - these abbreviations hide the familiar term “theory of relativity”, which is familiar to almost everyone. In simple language, everything can be explained, even the statement of a genius, so don’t despair if you don’t remember your school physics course, because in fact, everything is much simpler than it seems.

The origin of the theory

So, let's start the course "The Theory of Relativity for Dummies". Albert Einstein published his work in 1905, and it caused a stir among scientists. This theory almost completely covered many of the gaps and inconsistencies in the physics of the last century, but, on top of everything else, it revolutionized the idea of ​​space and time. Many of Einstein’s statements were difficult for his contemporaries to believe, but experiments and research only confirmed the words of the great scientist.

Einstein's theory of relativity explained in simple terms what people had been struggling with for centuries. It can be called the basis of all modern physics. However, before continuing the conversation about the theory of relativity, the issue of terms should be clarified. Surely many, reading popular science articles, have come across two abbreviations: SRT and GTO. In fact they mean several different concepts. The first one is special theory relativity, and the second stands for “general theory of relativity.”

Just something complicated

STR is an older theory, which later became part of GTR. It can only consider physical processes for objects moving at uniform speed. The general theory can describe what happens to accelerating objects, and also explain why graviton particles and gravity exist.

If you need to describe the movement and also the relationship of space and time when approaching the speed of light, the special theory of relativity can do this. In simple words it can be explained as follows: for example, friends from the future gave you a spaceship that can fly at high speed. On the nose of the spaceship there is a cannon capable of shooting photons at everything that comes in front.

When a shot is fired, relative to the ship these particles fly at the speed of light, but, logically, a stationary observer should see the sum of two speeds (the photons themselves and the ship). But nothing like that. The observer will see photons moving at a speed of 300,000 m/s, as if the speed of the ship was zero.

The thing is that no matter how fast an object moves, the speed of light for it is a constant value.

This statement is fundamentally astounding logical conclusions like slowing down and distorting time depending on the mass and speed of the object. The plots of many science fiction films and TV series are based on this.

General theory of relativity

In simple language one can explain more voluminous general relativity. To begin with, we should take into account the fact that our space is four-dimensional. Time and space are united in such a “subject” as the “space-time continuum”. In our space there are four coordinate axes: x, y, z and t.

But humans cannot directly perceive four dimensions, just as a hypothetical flat person living in a two-dimensional world cannot look up. In fact, our world is only a projection of four-dimensional space into three-dimensional space.

An interesting fact is that, according to the general theory of relativity, bodies do not change when they move. Objects of the four-dimensional world are in fact always unchanged, and when they move, only their projections change, which we perceive as a distortion of time, a reduction or increase in size, and so on.

Elevator experiment

The theory of relativity can be explained in simple terms using a small thought experiment. Imagine that you are in an elevator. The cabin began to move, and you found yourself in a state of weightlessness. What happened? There can be two reasons: either the elevator is in space, or it is in free fall under the influence of the planet’s gravity. The most interesting thing is that it is impossible to find out the cause of weightlessness if it is not possible to look out of the elevator car, that is, both processes look the same.

Perhaps after conducting a similar thought experiment, Albert Einstein came to the conclusion that if these two situations are indistinguishable from each other, then in fact the body under the influence of gravity is not accelerated, it is a uniform motion that is curved under the influence of a massive body (in in this case planets). Thus, accelerated motion is only a projection of uniform motion into three-dimensional space.

A good example

Another good example on the topic "The Theory of Relativity for Dummies." It is not entirely correct, but it is very simple and clear. If you put any object on a stretched fabric, it forms a “deflection” or a “funnel” underneath it. All smaller bodies will be forced to distort their trajectory according to the new bend of space, and if the body has little energy, it may not overcome this funnel at all. However, from the point of view of the moving object itself, the trajectory remains straight; they will not feel the bending of space.

Gravity "demoted"

With the advent of the general theory of relativity, gravity has ceased to be a force and is now content to be a simple consequence of the curvature of time and space. General relativity may seem fantastic, but it is a working version and is confirmed by experiments.

The theory of relativity can explain many seemingly incredible things in our world. In simple terms, such things are called consequences of general relativity. For example, rays of light flying close to massive bodies are bent. Moreover, many objects from deep space are hidden behind each other, but due to the fact that rays of light bend around other bodies, seemingly invisible objects are accessible to our eyes (more precisely, to the eyes of a telescope). It's like looking through walls.

The greater the gravity, the slower time flows on the surface of an object. This doesn't just apply to massive bodies like neutron stars or black holes. The effect of time dilation can be observed even on Earth. For example, satellite navigation devices are equipped with highly accurate atomic clocks. They are in orbit of our planet, and time ticks a little faster there. Hundredths of a second in a day will add up to a figure that will give up to 10 km of error in route calculations on Earth. It is the theory of relativity that allows us to calculate this error.

In simple terms, we can put it this way: general relativity underlies many modern technologies, and thanks to Einstein, we can easily find a pizzeria and a library in an unfamiliar area.

material from the book "A Brief History of Time" by Stephen Hawking and Leonard Mlodinow

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 is constant, then any freely moving observer should record the same value regardless of the speed with which he approaches or moves away from the light source.

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 traveling on a train and one standing on the platform will differ in their estimate of the distance traveled by light. And since speed is distance divided by time, the only way for observers to agree on the speed of light is if they also disagree on time. In other words, the theory of 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 will not necessarily show the same time.

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

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

This effect is significant only for bodies that move at speeds close to the speed of light. For example, at a speed equal to 10% of the speed of light, the body mass will be only 0.5% greater than at rest, but at a speed equal to 90% of the speed of light, the mass will be more than twice the normal one. As it approaches the speed of light, the mass of a body increases more and more rapidly, so that more and more energy is required to accelerate it. According to the theory of relativity, an object can never reach the speed of light, since in this case its mass would become infinite, and due to the equivalence of mass and energy, infinite energy would be required to do this. This is why the theory of relativity forever condemns 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 travel at the speed of light.

Warped 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 previously thought. In general relativity, spacetime is bent, or curved, by the mass and energy placed in it. Bodies like 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 guide planes along exactly these routes. For example, you could follow the compass readings and fly the 5,966 kilometers from New York to Madrid almost due east along the geographic parallel. But you'll only have to cover 5,802 kilometers if you fly along big circle, first to the northeast, and then gradually turning to the east and then to the southeast. View of these two routes on the map, where earth's surface distorted (presented flat), deceptive. When moving “straight” east from one point to another on the surface of the globe, you are not actually moving along a straight line, or rather, not along the shortest geodetic line.

If the trajectory of a spacecraft moving in a straight line through space 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, rays of light should bend slightly towards it 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, which is why an observer on Earth will see the star not exactly where it is actually located.

Let us 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 move not freely, but under the influence of a gravitational field.

In small enough 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 an empty space. There is no gravity, no “up” and “down”. You are floating freely. The elevator then begins 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 the floor. If you pick up an apple and let it go, it will fall to the floor. In fact, now that you are moving with acceleration, everything inside the elevator will happen exactly the same as if the elevator were not moving at all, but were at rest in a uniform gravitational field. Einstein realized that just as when you are in a train car you cannot tell whether it is stationary or moving uniformly, so when you are inside an elevator you cannot tell whether it is moving with constant acceleration or is in uniform motion. gravitational field. The result of this understanding was the principle of equivalence.

The principle of equivalence and the given example of its manifestation will be valid only if the inertial mass (included in Newton’s second law, which determines how much acceleration a force applied to a body gives to a body) and gravitational mass (included in Newton’s law of gravity, which determines the magnitude of gravitational attraction) are one and the same.

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

Time dilation

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

Now that we're familiar with the equivalence principle, we can follow Einstein's thinking by performing another thought experiment that 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 light a whole second to pass along it from top to bottom. Finally, suppose that there are two observers in the rocket: one at the top, near the ceiling, the other at the bottom, on the floor, and both of them are equipped with the same clock that counts the seconds.

Let us assume that the upper observer, having waited for his clock to count down, 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 would change if in this experiment, instead of floating freely in space, the rocket was standing on Earth, experiencing the action of gravity? According to Newton's theory, gravity will not affect the state of affairs in any way: if the observer above transmits signals with an interval of a second, then the observer below will receive them at the same interval. But the equivalence principle 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 constant acceleration. This is one example of how Einstein used the principle of equivalence when creating his new theory of gravity.

So let's say our rocket is accelerating. (We will assume that it is accelerating slowly, so that its speed is not approaching the speed of light.) Since the body of the rocket is moving upward, the first signal will have to travel less distance than before (before acceleration begins), and it will arrive at the lower observer sooner than in second. If the rocket were moving at a constant speed, then the second signal would arrive exactly the same 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 acceleration, the rocket is moving faster than at the moment of sending the first, so the second signal will travel a shorter distance than the first and will take even less time. The observer below, checking his watch, will record that the interval between signals is less than one second, and will disagree with the observer above, who claims that he sent the signals exactly one second later.

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

Gravity changes the flow of time. Just as special relativity tells us that time passes differently for observers moving relative to each other, general relativity tells us that time passes differently for observers in different gravitational fields. According to general relativity, the lower observer registers a shorter interval between signals because time passes more slowly at the Earth's surface because gravity is stronger there. The stronger the gravitational field, the greater this effect.

Our biological clock also responds to changes in the passage of time. If one twin lives on top of a mountain 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 the speed of light. When the wanderer returns, he will be much younger than his brother left on Earth. This case is known as the twin paradox, but it is a paradox only for those who cling 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 acquired practical significance. If the equipment ignored the predictions of general relativity, the error in determining the location could be several kilometers!

The emergence of the general theory of relativity radically changed the situation. Space and time acquired the status of 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 influence everything that happens in the Universe, but they themselves depend on it all.

Let's imagine an intrepid astronaut who remains on the surface of a collapsing star during a catastrophic contraction. At some point according to his watch, say at 11:00, the star will shrink to a critical radius, beyond which the gravitational field intensifies so much that it is impossible to escape from it. Now suppose that according to the instructions, the astronaut must 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 begins transmitting signals at 10:59:58, that is, two seconds before 11:00. What will the crew register on board the spacecraft?

Previously, 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 colleagues in orbit, so one second on his watch will last longer than a second on the ship's clock. As the astronaut moves with the surface towards 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 slight until 10:59:59, so that for astronauts in orbit the interval between the signals transmitted at 10:59:58 and at 10:59:59 will be very little more than a second. But the signal sent at 11:00 will no longer be received on the ship.

Anything that happens on the surface of the star between 10:59:59 and 11:00 on the astronaut's clock will stretch out over an infinite period of time on the spacecraft's clock. As 11:00 approaches, the intervals between the arrival in orbit of successive crests and troughs of light waves emitted by the star will become increasingly 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 crests (or troughs) arriving per second, the spacecraft will record lower and lower frequency radiation from the star. The light of the star will become increasingly red and at the same time fade. Eventually the star will become so dim that it will become invisible to observers on the spacecraft; all that will remain is a black hole in space. However, the effect of star gravity on spacecraft will remain, and it will continue to orbit.

They say that Albert Einstein had an epiphany in an instant. The scientist was allegedly riding a tram in Bern (Switzerland), looked at the street clock and suddenly realized that if the tram now accelerated to the speed of light, then in his perception this clock would stop - and there would be no time around. This led him to formulate one of the central postulates of relativity - that different observers perceive reality differently, including such fundamental quantities as distance and time.

Scientifically speaking, on that day Einstein realized that the description of any physical event or phenomenon depends on reference systems, in which the observer is located. If a tram passenger, for example, drops her glasses, then for her they will fall vertically down, and for a pedestrian standing on the street, the glasses will fall in a parabola, since the tram is moving while the glasses are falling. Everyone has their own frame of reference.

But although descriptions of events change when moving from one frame of reference to another, there are also universal things that remain unchanged. If, instead of describing the fall of glasses, we ask a question about the law of nature that causes them to fall, then the answer to it will be the same for an observer in a stationary coordinate system and for an observer in a moving coordinate system. The law of distributed movement applies equally on the street and on the tram. In other words, while the description of events depends on the observer, the laws of nature do not depend on him, that is, as is commonly said in scientific language, they are invariant. This is what it's all about principle of relativity.

Like any hypothesis, the principle of relativity had to be tested by correlating it with real natural phenomena. From the principle of relativity, Einstein derived two separate (albeit related) theories. Special or particular theory of relativity comes from the position that the laws of nature are the same for all reference systems moving at constant speed. General theory of relativity extends this principle to any frame of reference, including those that move with acceleration. The special theory of relativity was published in 1905, and the more mathematically complex general theory of relativity was completed by Einstein by 1916.

Special theory of relativity

Most of the paradoxical and counterintuitive effects that occur when moving at speeds close to the speed of light are predicted by the special theory of relativity. The most famous of them is the effect of slowing down the clock, or time dilation effect. A clock moving relative to an observer goes slower for him than the exact same clock in his hands.

Time in a coordinate system moving at speeds close to the speed of light relative to the observer is stretched, and the spatial extent (length) of objects along the axis of the direction of movement is, on the contrary, compressed. This effect, known as Lorentz-Fitzgerald contraction, was described in 1889 by the Irish physicist George Fitzgerald (1851-1901) and expanded in 1892 by the Dutchman Hendrick Lorentz (1853-1928). The Lorentz-Fitzgerald reduction explains why the Michelson-Morley experiment to determine the speed of the Earth in outer space by measuring the “ether wind” gave a negative result. Einstein later included these equations in the special theory of relativity and supplemented them with a similar conversion formula for mass, according to which the mass of a body also increases as the speed of the body approaches the speed of light. Thus, at a speed of 260,000 km/s (87% of the speed of light), the mass of the object from the point of view of an observer located in a resting frame of reference will double.

Since the time of Einstein, all these predictions, no matter how contrary to common sense they may seem, have found complete and direct experimental confirmation. In one of the most revealing experiments, scientists at the University of Michigan placed ultra-precise atomic clocks on board an airliner making regular transatlantic flights, and after each return to its home airport, they compared their readings with the control clock. It turned out that the clock on the plane gradually lagged behind the control clock more and more (so to speak, when we are talking about fractions of a second). For the last half century, scientists have been studying elementary particles using huge hardware complexes called accelerators. In them, beams of charged subatomic particles (such as protons and electrons) are accelerated to speeds close to the speed of light, then fired at various nuclear targets. In such experiments at accelerators, it is necessary to take into account the increase in the mass of accelerated particles - otherwise the results of the experiment simply will not lend themselves to reasonable interpretation. And in this sense, the special theory of relativity has long moved from the category of hypothetical theories to the field of applied engineering tools, where it is used on a par with Newton’s laws of mechanics.

Returning to Newton's laws, I would like to especially note that the special theory of relativity, although it outwardly contradicts the laws of classical Newtonian mechanics, in fact almost exactly reproduces all the usual equations of Newton's laws, if it is applied to describe bodies moving at speeds significantly less than the speed of light. That is, the special theory of relativity does not cancel Newtonian physics, but expands and complements it.

The principle of relativity also helps to understand why it is the speed of light, and not any other, that plays such an important role in this model of the structure of the world - this is a question asked by many of those who first encountered the theory of relativity. The speed of light stands out and plays special role a universal constant, because it is determined by natural science law. Due to the principle of relativity, the speed of light in a vacuum c is the same in any reference system. This would seem to contradict common sense, since it turns out that light from a moving source (no matter how fast it moves) and from a stationary source reaches the observer at the same time. However, this is true.

Due to its special role in the laws of nature, the speed of light occupies a central place in the general theory of relativity.

General theory of relativity

The general theory of relativity applies to all reference systems (and not just to those moving at a constant speed relative to each other) and looks mathematically much more complex than the special one (which explains the eleven-year gap between their publication). It includes as a special case the special theory of relativity (and therefore Newton's laws). At the same time, the general theory of relativity goes much further than all its predecessors. In particular, it gives a new interpretation of gravity.

The general theory of relativity makes the world four-dimensional: time is added to the three spatial dimensions. All four dimensions are inseparable, so we are no longer talking about the spatial distance between two objects, as is the case in the three-dimensional world, but about the space-time intervals between events, which combine their distance from each other - both in time and in space . That is, space and time are considered as a four-dimensional space-time continuum or, simply, spacetime. In this continuum, observers moving relative to each other may even disagree about whether two events occurred simultaneously—or whether one preceded the other. Fortunately for our poor mind, it does not come to the point of violating cause-and-effect relationships - that is, even the general theory of relativity does not allow the existence of coordinate systems in which two events do not occur simultaneously and in different sequences.

Newton's law of universal gravitation tells us that between any two bodies in the Universe there is a force of mutual attraction. From this point of view, the Earth rotates around the Sun, since mutual forces of attraction act between them. General relativity, however, forces us to look at this phenomenon differently. According to this theory, gravity is a consequence of the deformation (“curvature”) of the elastic fabric of space-time under the influence of mass (the heavier the body, for example the Sun, the more space-time “bends” under it and the, accordingly, the stronger its gravitational force field). Imagine a tightly stretched canvas (a kind of trampoline) on which a massive ball is placed. The canvas is deformed under the weight of the ball, and a funnel-shaped depression is formed around it. According to the general theory of relativity, the Earth revolves around the Sun like a small ball launched to roll around the cone of a funnel formed as a result of “pushing” space-time by a heavy ball - the Sun. And what seems to us to be the force of gravity is, in fact, essentially a purely external manifestation of the curvature of space-time, and not at all a force in the Newtonian understanding. To date, no better explanation of the nature of gravity than the general theory of relativity gives us.

Testing general relativity is difficult because, under normal laboratory conditions, its results are almost exactly the same as what Newton's law of gravity predicts. Nevertheless, several important experiments were carried out, and their results allow us to consider the theory confirmed. In addition, general relativity helps explain phenomena that we observe in space, such as minor deviations of Mercury from its stationary orbit that are inexplicable from the point of view of classical Newtonian mechanics, or the bending of electromagnetic radiation from distant stars when it passes in close proximity to the Sun.

In fact, the results predicted by general relativity differ markedly from those predicted by Newton's laws only in the presence of super-strong gravitational fields. This means that to fully test the general theory of relativity, we need either ultra-precise measurements of very massive objects, or black holes, to which none of our usual intuitive ideas are applicable. So the development of new experimental methods testing the theory of relativity remains one of the most important tasks of experimental physics.

GTO and RTG: some accents

1. In countless books - monographs, textbooks and popular science publications, as well as in various types of articles - readers are accustomed to seeing references to the general theory of relativity (GTR) as one of the greatest achievements of our century, a wonderful theory, an indispensable tool of modern physics and astronomy. Meanwhile, from A. A. Logunov’s article they learn that, in his opinion, GTR should be abandoned, that it is bad, inconsistent and contradictory. Therefore, GTR requires replacement by some other theory and, specifically, by the relativistic theory of gravity (RTG) constructed by A. A. Logunov and his collaborators.

Is such a situation possible when many people are mistaken in their assessment of GTR, which has existed and been studied for more than 70 years, and only a few people, led by A. A. Logunov, really figured out that GTR needs to be discarded? Most readers probably expect the answer: this is impossible. In fact, I can only answer in the exact opposite way: “this” is possible in principle, because we are not talking about religion, but about science.

Founders and Prophets different religions and creeds have created and are creating their own “sacred books”, the contents of which are declared to be the ultimate truth. If someone doubts, so much the worse for him, he becomes a heretic with the ensuing consequences, often even bloody. It’s better not to think at all, but to believe, following the well-known formula of one of the church leaders: “I believe, because it is absurd.” The scientific worldview is fundamentally opposite: it demands not to take anything for granted, allows one to doubt everything, and does not recognize dogmas. Under the influence of new facts and considerations, it is not only possible, but also necessary, if justified, to change your point of view, replace an imperfect theory with a more perfect one, or, say, somehow generalize an old theory. The situation is similar with regard to individuals. The founders of religious doctrines are considered infallible, and, for example, among Catholics, even a living person - the “reigning” Pope - is declared infallible. Science knows no infallible people. The great, sometimes even exceptional, respect that physicists (to be clear, I will talk about physicists) have for the great representatives of their profession, especially for such titans as Isaac Newton and Albert Einstein, has nothing to do with the canonization of saints, with deification. And great physicists are people, and all people have their weaknesses. If we talk about science, which only interests us here, then the greatest physicists were not always right in everything; respect for them and recognition of their merits is based not on infallibility, but on the fact that they managed to enrich science with remarkable achievements, to see further and deeper than their contemporaries.

2. Now it is necessary to dwell on the requirements for fundamental physical theories. Firstly, such a theory must be complete in the field of its applicability, or, as I will say for brevity, it must be consistent. Secondly, a physical theory must be adequate to physical reality, or, more simply put, consistent with experiments and observations. Other requirements could be mentioned, primarily compliance with the laws and rules of mathematics, but all this is implied.

Let us explain what has been said using the example of classical, non-relativistic mechanics - Newtonian mechanics as applied to the simplest in principle problem of the movement of some “point” particle. As is known, the role of such a particle in problems of celestial mechanics can be played by an entire planet or its satellite. Let in the moment t 0 the particle is at a point A with coordinates x iA(t 0) and has speed v iA(t 0) (Here i= l, 2, 3, because the position of a point in space is characterized by three coordinates, and the speed is a vector). Then, if all the forces acting on the particle are known, the laws of mechanics allow us to determine the position B and particle velocity v i at any subsequent time t, that is, find well-defined values xiB(t) and v iB(t). What would happen if the laws of mechanics used did not give an unambiguous answer and, say, in our example they predicted that the particle at the moment t can be located either at the point B, or at a completely different point C? It is clear that such a classical (non-quantum) theory would be incomplete, or, in the terminology mentioned, inconsistent. It would either need to be supplemented, making it unambiguous, or discarded altogether. Newton's mechanics, as stated, is consistent - it gives unambiguous and well-defined answers to questions within its area of ​​competence and applicability. Newtonian mechanics also satisfies the second mentioned requirement - the results obtained on its basis (and, specifically, the coordinate values x i(t) and speed v i (t)) are consistent with observations and experiments. That is why all celestial mechanics - the description of the movement of planets and their satellites - for the time being was entirely based, and with complete success, on Newtonian mechanics.

3. But in 1859, Le Verrier discovered that the movement of the planet closest to the Sun, Mercury, was somewhat different from that predicted by Newtonian mechanics. Specifically, it turned out that the perihelion - the point of the planet's elliptical orbit closest to the Sun - rotates with an angular velocity of 43 arc seconds per century, different from what would be expected when taking into account all known disturbances from other planets and their satellites. Even earlier, Le Verrier and Adams encountered an essentially similar situation when analyzing the motion of Uranus, the most distant planet from the Sun known at that time. And they found an explanation for the discrepancy between calculations and observations, suggesting that the movement of Uranus is influenced by an even more distant planet, called Neptune. In 1846, Neptune was actually discovered at its predicted location, and this event is rightly considered a triumph of Newtonian mechanics. Quite naturally, Le Verrier tried to explain the mentioned anomaly in the movement of Mercury by the existence of another unknown planet- in this case, a certain planet Vulcan, moving even closer to the Sun. But the second time “the trick failed” - no Vulcan exists. Then they began to try to change Newton's law of universal gravitation, according to which the gravitational force, when applied to the Sun-planet system, changes according to the law

where ε is some small value. By the way, a similar technique is used (though without success) in our days to explain some unclear questions of astronomy (we are talking about the problem of hidden mass; see, for example, the author’s book “On Physics and Astrophysics” cited below, p. 148). But in order for a hypothesis to develop into a theory, it is necessary to proceed from some principles, indicate the value of the parameter ε, and build a consistent theoretical scheme. No one succeeded, and the question of the rotation of Mercury's perihelion remained open until 1915. It was then, in the midst of the First World War, when so few were interested in the abstract problems of physics and astronomy, that Einstein completed (after about 8 years of intense effort) the creation of the general theory of relativity. This last stage in building the foundation of GTR was covered in three short articles reported and written in November 1915. In the second of them, reported on November 11, Einstein, on the basis of general relativity, calculated the additional rotation of the perihelion of Mercury compared to the Newtonian one, which turned out to be equal (in radians per revolution of the planet around the Sun)

And c= 3·10 10 cm s –1 – speed of light. When moving to the last expression (1), Kepler's third law was used

Where T– period of revolution of the planet. If we substitute the best currently known values ​​of all quantities into formula (1), and also make an elementary conversion from radians per revolution to rotation in arc seconds (sign ″) per century, then we arrive at the value Ψ = 42″.98 / century. Observations agree with this result with the currently achieved accuracy of about ± 0″.1 / century (Einstein in his first work used less accurate data, but within the limits of error he obtained complete agreement between the theory and observations). Formula (1) is given above, firstly, to make clear its simplicity, which is so often absent in mathematically complex physical theories, including in many cases in General Relativity. Secondly, and this is the main thing, it is clear from (1) that the perihelion rotation follows from general relativity without the need to involve any new unknown constants or parameters. Therefore, the result obtained by Einstein became a true triumph of general relativity.

In the best of me famous biographies Einstein expresses and substantiates the opinion that the explanation of the rotation of the perihelion of Mercury was “the most powerful emotional event in Einstein’s entire scientific life, and perhaps in his entire life.” Yes, it was " finest hour» Einstein. But just for himself. For a number of reasons (it’s enough to mention the war) for GR itself, for both this theory and its creator to enter the world stage, the “finest hour” was another event that occurred 4 years later - in 1919. The fact is that in the same work in which formula (1) was obtained, Einstein made an important prediction: rays of light passing near the Sun must bend, and their deviation should be

Where r is the closest distance between the ray and the center of the Sun, and r☼ = 6.96·10 10 cm – radius of the Sun (more precisely, radius solar photosphere); thus the maximum deviation that can be observed is 1.75 arcseconds. No matter how small such an angle is (approximately at this angle an adult is visible from a distance of 200 km), it could already be measured at that time by the optical method by photographing stars in the sky in the vicinity of the Sun. It was these observations that were made by two English expeditions during the total solar eclipse of May 29, 1919. The effect of deflection of rays in the field of the Sun was established with certainty and is in agreement with formula (2), although the accuracy of measurements due to the smallness of the effect was low. However, a deviation half as large as according to (2), i.e., 0″.87, was excluded. The latter is very important, because the deviation is 0″.87 (with r = r☼) can already be obtained from Newton’s theory (the very possibility of light deflection in a gravitational field was noted by Newton, and the expression for the deflection angle, half that according to formula (2), was obtained in 1801; another thing is that this prediction was forgotten and Einstein did not know about it). On November 6, 1919, the results of the expeditions were reported in London at a joint meeting of the Royal Society and the Royal Astronomical Society. What an impression they made is clear from what the chairman, J. J. Thomson, said at this meeting: “This is the most important result obtained in connection with the theory of gravitation since Newton ... It represents one of the greatest achievements of human thought.”

The effects of general relativity in the solar system, as we have seen, are very small. This is explained by the fact that the gravitational field of the Sun (not to mention the planets) is weak. The latter means that the Newtonian gravitational potential of the Sun

Let us now recall the result known from the school physics course: for circular orbits of planets |φ ☼ | = v 2, where v is the speed of the planet. Therefore, the weakness of the gravitational field can be characterized by a more visual parameter v 2 / c 2, which is for solar system, as we have seen, does not exceed the value 2.12·10 – 6. In Earth orbit v = 3 10 6 cm s – 1 and v 2 / c 2 = 10 – 8, for close satellites of the Earth v ~ 8 10 5 cm s – 1 and v 2 / c 2 ~ 7 ·10 – 10 . Consequently, testing the mentioned effects of general relativity even with the currently achieved accuracy of 0.1%, that is, with an error not exceeding 10 – 3 of the measured value (say, the deflection of light rays in the field of the Sun), does not yet allow us to comprehensively test general relativity with an accuracy of terms of the order

We can only dream of measuring, say, the deflection of rays within the Solar System with the required accuracy. However, projects for relevant experiments are already being discussed. In connection with the above, physicists say that general relativity has been tested mainly only for a weak gravitational field. But we (me, in any case) somehow did not even notice one important circumstance for quite a long time. It was after the launch of the first Earth satellite on October 4, 1957 that space navigation began to develop rapidly. For landing instruments on Mars and Venus, when flying near Phobos, etc., calculations with precision up to meters are needed (at distances from the Earth of the order of one hundred billion meters), when the effects of general relativity are quite significant. Therefore, calculations are now carried out on the basis of computational schemes that organically take into account general relativity. I remember how several years ago one speaker - a specialist in space navigation - did not even understand my questions about the accuracy of the general relativity test. He answered: we take into account general relativity in our engineering calculations, it’s impossible to work otherwise, everything turns out correctly, what more could you want? Of course, you can wish for a lot, but you shouldn’t forget that GTR is no longer an abstract theory, but is used in “engineering calculations.”

4. In light of all of the above, A. A. Logunov’s criticism of GTR seems especially surprising. But in accordance with what was said at the beginning of this article, it is impossible to dismiss this criticism without analysis. Back in to a greater extent impossible without detailed analysis express a judgment about the RTG proposed by A. A. Logunov - the relativistic theory of gravity.

Unfortunately, it is completely impossible to carry out such an analysis on the pages of popular science publications. In his article, A. A. Logunov, in fact, only declares and comments on his position. I can’t do anything else here either.

So, we believe that GTR is a consistent physical theory - to all correctly and clearly posed questions that are permissible in the area of ​​its applicability, GTR gives an unambiguous answer (the latter applies, in particular, to the delay time of signals when locating planets). It does not suffer from general relativity or any defects of a mathematical or logical nature. It is necessary, however, to clarify what is meant above when using the pronoun “we”. “We” is, of course, myself, but also all those Soviet and foreign physicists with whom I had to discuss general relativity, and in some cases, its criticism by A. A. Logunov. The great Galileo said four centuries ago: in matters of science, the opinion of one is more valuable than the opinion of a thousand. In other words, scientific disputes are not decided by a majority vote. But, on the other hand, it is quite obvious that the opinion of many physicists, generally speaking, is much more convincing, or, better said, more reliable and weighty, than the opinion of one physicist. Therefore, the transition from “I” to “we” is important here.

It will be useful and appropriate, I hope, to make a few more comments.

Why does A. A. Logunov not like GTR so much? Main reason is that in General Relativity, generally speaking, there is no concept of energy and momentum in the form familiar to us from electrodynamics and, in his words, there is a refusal “to represent the gravitational field as a classical field of the Faraday-Maxwell type, having a well-defined energy density -impulse." Yes, the latter is true in a sense, but it is explained by the fact that “in Riemannian geometry, in the general case, there is no necessary symmetry with respect to shifts and rotations, that is, there is no... group of motion of space-time.” The geometry of space-time according to general relativity is Riemannian geometry. This is why, in particular, light rays deviate from a straight line when passing near the Sun.

One of the greatest achievements of mathematics of the last century was the creation and development of non-Euclidean geometry by Lobachevsky, Bolyai, Gauss, Riemann and their followers. Then the question arose: what is actually the geometry of the physical space-time in which we live? As stated, according to GTR, this geometry is non-Euclidean, Riemannian, and not the pseudo-Euclidean geometry of Minkowski (this geometry is described in more detail in the article by A. A. Logunov). This Minkowski geometry was, one might say, a product of the special theory of relativity (STR) and replaced Newton’s absolute time and absolute space. Immediately before the creation of SRT in 1905, they tried to identify the latter with the motionless Lorentz ether. But the Lorentz ether, as an absolutely motionless mechanical medium, was abandoned because all attempts to notice the presence of this medium were unsuccessful (I mean Michelson’s experiment and some other experiments). The hypothesis that physical space-time is necessarily exactly Minkowski space, which A. A. Logunov accepts as fundamental, is very far-reaching. It is in some sense similar to the hypotheses about absolute space and the mechanical ether and, as it seems to us, remains and will remain completely unfounded until any arguments based on observations and experiments are indicated in its favor. And such arguments, at least at present, are completely absent. References to the analogy with electrodynamics and the ideals of the remarkable physicists of the last century Faraday and Maxwell do not have any convincing in this regard.

5. If we talk about the difference between the electromagnetic field and, therefore, electrodynamics and the gravitational field (GR is precisely the theory of such a field), then the following should be noted. By choosing a reference system, it is impossible to destroy (reduce to zero) even locally (in a small area) the entire electromagnetic field. Therefore, if the energy density of the electromagnetic field

(E And H– the strength of the electric and magnetic fields, respectively) is different from zero in some reference system, then it will be different from zero in any other reference system. The gravitational field, roughly speaking, depends much more strongly on the choice of reference system. Thus, a uniform and constant gravitational field (that is, a gravitational field causing acceleration g particles placed in it, independent of coordinates and time) can be completely “destroyed” (reduced to zero) by transition to a uniformly accelerated reference system. This circumstance, which constitutes the main physical content of the “principle of equivalence,” was first noted by Einstein in an article published in 1907 and was the first on the path to the creation of General Relativity.

If there is no gravitational field (in particular, the acceleration it causes g is equal to zero), then the density of the energy corresponding to it is also equal to zero. From here it is clear that in the question of energy (and momentum) density, the theory of the gravitational field must differ radically from the theory of the electromagnetic field. This statement does not change due to the fact that in the general case the gravitational field cannot be “destroyed” by the choice of reference frame.

Einstein understood this even before 1915, when he completed the creation of General Relativity. Thus, in 1911 he wrote: “Of course, it is impossible to replace any gravitational field with the state of motion of a system without a gravitational field, just as it is impossible to transform all points of an arbitrarily moving medium to rest through a relativistic transformation.” And here is an excerpt from an article from 1914: “First, let’s make one more remark to eliminate the misunderstanding that arises. Supporter of the usual modern theory relativity (we are talking about STR - V.L.G.) with a certain right calls the speed of a material point “apparent”. Namely, he can choose a reference system so that the material point at the moment under consideration has a speed equal to zero. If there is a system material points, which have different velocities, then he can no longer introduce a reference system such that the velocities of all material points relative to this system become zero. In a similar way, a physicist taking our point of view can call the gravitational field “apparent”, since by appropriate choice of acceleration of the reference frame he can achieve that at a certain point in space-time the gravitational field becomes zero. However, it is noteworthy that the vanishing of the gravitational field through a transformation in the general case cannot be achieved for extended gravitational fields. For example, the Earth's gravitational field cannot be made equal to zero by choosing a suitable reference frame." Finally, already in 1916, responding to criticism of general relativity, Einstein once again emphasized the same thing: “It is in no way possible to assert that the gravitational field is to any extent explained purely kinematically: “a kinematic, non-dynamic understanding of gravity” is impossible. We cannot obtain any gravitational field by simply accelerating one Galilean coordinate system relative to another, since in this way it is possible to obtain fields only of a certain structure, which, however, must obey the same laws as all other gravitational fields. This is another formulation of the equivalence principle (specifically for applying this principle to gravity)."

The impossibility of a “kinematic understanding” of gravity, combined with the equivalence principle, determines the transition in general relativity from the pseudo-Euclidean geometry of Minkowski to Riemannian geometry (in this geometry, space-time has, generally speaking, a non-zero curvature; the presence of such curvature is what distinguishes the “true” gravitational field from “kinematic”). Physical Features The gravitational field determines, let us repeat this, a radical change in the role of energy and momentum in general relativity compared to electrodynamics. At the same time, both the use of Riemannian geometry and the inability to apply energy concepts familiar from electrodynamics do not prevent, as already emphasized above, the fact that from general relativity it follows and can be calculated quite unambiguous values ​​for all observable quantities (the angle of deflection of light rays, changes in orbital elements for planets and double pulsars, etc., etc.).

It would probably be useful to note the fact that general relativity can also be formulated in the form familiar from electrodynamics using the concept of energy-momentum density (for this see the cited article by Ya. B. Zeldovich and L. P. Grishchuk. However, what is introduced at In this case, the Minkowski space is purely fictitious (unobservable), and we are talking only about the same general relativity, written in a non-standard form. Meanwhile, let us repeat this, A. A. Logunov considers the Minkowski space he uses in the relativistic theory of gravity (RTG) to be real physical, and therefore observable space.

6. In this regard, the second of the questions appearing in the title of this article is especially important: does GTR correspond to physical reality? In other words, what does experience, the supreme judge, say when deciding the fate of any physical theory? Numerous articles and books are devoted to this problem - the experimental verification of general relativity. The conclusion is quite definite - all available experimental or observational data either confirm general relativity or do not contradict it. However, as we have already indicated, the verification of general relativity has been carried out and occurs mainly only in a weak gravitational field. In addition, any experiment has limited accuracy. In strong gravitational fields (roughly speaking, in the case when the ratio |φ| / c 2 is not enough; see above) General Relativity has not yet been sufficiently verified. For this purpose, it is now possible to practically use only astronomical methods relating to very distant space: the study of neutron stars, double pulsars, “black holes”, the expansion and structure of the Universe, as they say, “in the big” - in vast expanses measured in millions and billions of light years years. Much has already been done and is being done in this direction. It is enough to mention the studies of the double pulsar PSR 1913+16, for which (as in general for neutron stars) the parameter |φ| / c 2 is already about 0.1. In addition, in this case it was possible to identify the order effect (v / c) 5 associated with the emission of gravitational waves. In the coming decades, even more opportunities will open up for studying processes in strong gravitational fields.

The guiding star in this breathtaking research is primarily general relativity. At the same time, naturally, some other possibilities are also discussed - other, as they sometimes say, alternative theories of gravity. For example, in general relativity, as in Newton’s theory of universal gravitation, the gravitational constant G is indeed considered a constant value. One of the most famous theories of gravity, generalizing (or, more precisely, expanding) General Relativity, is a theory in which the gravitational “constant” is considered a new scalar function - a quantity depending on coordinates and time. Observations and measurements indicate, however, that possible relative changes G over time, very small - apparently amounting to no more than a hundred billion per year, that is | dG / dt| / G < 10 – 11 год – 1 . Но когда-то в прошлом изменения G could play a role. Note that even regardless of the question of inconstancy G assumption of existence in real space-time, in addition to the gravitational field g ik, also some scalar field ψ is the main direction in modern physics and cosmology. In other alternative theories of gravity (about them, see the book by K. Will mentioned above in note 8), GTR is changed or generalized in a different way. Of course, one cannot object to the corresponding analysis, because GTR is not a dogma, but a physical theory. Moreover, we know that General Relativity, which is a non-quantum theory, obviously needs to be generalized to the quantum region, which is not yet accessible to known gravitational experiments. Naturally, you can’t tell us more about all this here.

7. A. A. Logunov, starting from criticism of GTR, has been building some alternative theory of gravity for more than 10 years, different from GTR. At the same time, much changed during the course of the work, and the now accepted version of the theory (this is the RTG) is presented in particular detail in an article that occupies about 150 pages and contains about 700 numbered formulas only. Obviously, a detailed analysis of RTG is only possible on the pages scientific journals. Only after such an analysis will it be possible to say whether RTG is consistent, whether it does not contain mathematical contradictions, etc. As far as I could understand, RTG differs from GTR in the selection of only part of the solutions of GTR - all solutions of RTG differential equations satisfy the equations of GTR, but how say the authors of RTG, not the other way around. At the same time, the conclusion is made that with regard to global issues (solutions for the entire space-time or its large regions, topology, etc.), the differences between RTG and GTR are, generally speaking, radical. As for all experiments and observations carried out within the Solar System, as far as I understand, RTG cannot conflict with General Relativity. If this is so, then it is impossible to prefer RTG (compared to GTR) on the basis of known experiments in the Solar System. As for “black holes” and the Universe, the authors of RTG claim that their conclusions are significantly different from the conclusions of General Relativity, but we are not aware of any specific observational data that testifies in favor of RTG. In such a situation, RTG by A. A. Logunov (if RTG really differs from GTR in essence, and not just in the way of presentation and the choice of one of the possible classes of coordinate conditions; see the article by Ya. B. Zeldovich and L. P. Grishchuk) can be considered only as one of the acceptable, in principle, alternative theories of gravity.

Some readers may be wary of clauses such as: “if this is so”, “if RTG really differs from GTR”. Am I trying to protect myself from mistakes in this way? No, I am not afraid of making a mistake simply because of the conviction that there is only one guarantee of errorlessness - not to work at all, and in this case not to discuss scientific issues. Another thing is that respect for science, familiarity with its character and history encourage caution. Categorical statements do not always indicate the presence of genuine clarity and, in general, do not contribute to establishing the truth. RTG A. A. Logunova in her modern form formulated quite recently and has not yet been discussed in detail in the scientific literature. Therefore, naturally, I do not have a final opinion about it. In addition, it is impossible, and even inappropriate, to discuss a number of emerging issues in a popular science magazine. At the same time, of course, due to the great interest of readers in the theory of gravitation, coverage at an accessible level of this range of issues, including controversial ones, on the pages of Science and Life seems justified.

So, guided by the wise “principle of most favored nation,” RTG should now be considered an alternative theory of gravity that needs appropriate analysis and discussion. For those who like this theory (RTG), who are interested in it, no one bothers (and, of course, should not interfere) with developing it, suggesting possible ways of experimental verification.

At the same time, there is no reason to say that GTR is currently in any way shaken. Moreover, the range of applicability of general relativity seems to be very wide, and its accuracy is very high. This, in our opinion, is an objective assessment of the current state of affairs. If we talk about tastes and intuitive attitudes, and tastes and intuition play a significant role in science, although they cannot be put forward as evidence, then here we will have to move from “we” to “I”. So, the more I had and still have to deal with the general theory of relativity and its criticism, the more my impression of its exceptional depth and beauty strengthens.

Indeed, as indicated in the imprint, the circulation of the journal “Science and Life” No. 4, 1987 was 3 million 475 thousand copies. IN recent years the circulation was only a few tens of thousands of copies, exceeding 40 thousand only in 2002. (note – A. M. Krainev).

By the way, 1987 marks the 300th anniversary of the first publication of Newton’s great book “Mathematical Principles of Natural Philosophy.” Getting acquainted with the history of the creation of this work, not to mention the work itself, is very instructive. However, the same applies to all of Newton’s activities, which are not so easy for non-specialists to get acquainted with. I can recommend for this purpose the very good book by S.I. Vavilov “Isaac Newton”; it should be republished. Let me also mention my article written on the occasion of Newton’s anniversary, published in the journal “Uspekhi Fizicheskikh Nauk”, v. 151, no. 1, 1987, p. 119.

The magnitude of the turn is given according to modern measurements (Le Verrier had a turn of 38 seconds). Let us recall for clarity that the Sun and Moon are visible from the Earth at an angle of about 0.5 arc degrees - 1800 arc seconds.

A. Pals “Subtle is the Lord...” The Science and Life of Albert Einstein. Oxford Univ. Press, 1982. It would be advisable to publish a Russian translation of this book.

The latter is possible during full solar eclipses; By photographing the same part of the sky, say, six months later, when the Sun has moved on the celestial sphere, we obtain for comparison a picture that is not distorted as a result of the deflection of rays under the influence of the gravitational field of the Sun.

For details, I must refer to the article by Ya. B. Zeldovich and L. P. Grishchuk, recently published in Uspekhi Fizicheskikh Nauk (vol. 149, p. 695, 1986), as well as to the literature cited there, in particular to the article by L. D. Faddeev (“Advances in Physical Sciences”, vol. 136, p. 435, 1982).

See footnote 5.

See K. Will. "Theory and experiment in gravitational physics." M., Energoiedat, 1985; see also V. L. Ginzburg. About physics and astrophysics. M., Nauka, 1985, and the literature indicated there.

A. A. Logunov and M. A. Mestvirishvili. "Fundamentals of the relativistic theory of gravity." Journal "Physics of Elementary Particles and the Atomic Nucleus", vol. 17, issue 1, 1986.

In the works of A. A. Logunov there are other statements and specifically it is believed that for the signal delay time when locating, say, Mercury from the Earth, a value different from the following from GTR is obtained from RTG. More precisely, it is argued that General Relativity does not give an unambiguous prediction of signal delay times at all, that is, General Relativity is inconsistent (see above). However, such a conclusion, as it seems to us, is the fruit of a misunderstanding (this is indicated, for example, in the cited article by Ya. B. Zeldovich and L. P. Grishchuk, see footnote 5): different results in general relativity when using different coordinate systems are obtained only because , which compares the located planets located in different orbits, and therefore having different periods of revolution around the Sun. The delay times of signals observed from Earth when locating a certain planet, according to general relativity and RTG, coincide.

See footnote 5.

Details for the curious

Deflection of light and radio waves in the gravitational field of the Sun. Usually, a static spherically symmetric ball of radius is taken as an idealized model of the Sun R☼ ~ 6.96·10 10 cm, solar mass M☼ ~ 1.99 10 30 kg (332958 times more mass Earth). The deflection of light is maximum for rays that barely touch the Sun, that is, when R ~ R☼ , and equal to: φ ≈ 1″.75 (arcseconds). This angle is very small - approximately at this angle an adult is visible from a distance of 200 km, and therefore the accuracy of measuring the gravitational curvature of rays was low until recently. The latest optical measurements taken during the solar eclipse of June 30, 1973 had an error of approximately 10%. Today, thanks to the advent of radio interferometers “with an ultra-long base” (more than 1000 km), the accuracy of measuring angles has increased sharply. Radio interferometers make it possible to reliably measure angular distances and changes in angles on the order of 10 – 4 arcseconds (~ 1 nanoradian).

The figure shows the deflection of only one of the rays coming from a distant source. In reality, both rays are bent.

GRAVITY POTENTIAL

In 1687, Newton’s fundamental work “Mathematical Principles of Natural Philosophy” appeared (see “Science and Life” No. 1, 1987), in which the law of universal gravitation was formulated. This law states that the force of attraction between any two material particles is directly proportional to their masses M And m and inversely proportional to the square of the distance r between them:

Proportionality factor G began to be called the gravitational constant, it is necessary to reconcile the dimensions on the right and left sides of the Newtonian formula. Newton himself showed with very high accuracy for his time that G– the quantity is constant and, therefore, the law of gravity discovered by him is universal.

Two attracting point masses M And m appear equally in Newton's formula. In other words, we can consider that they both serve as sources of the gravitational field. However, in specific problems, in particular in celestial mechanics, one of the two masses is often very small compared to the other. For example, the mass of the Earth M 3 ≈ 6 · 10 24 kg is much less than the mass of the Sun M☼ ≈ 2 · 10 30 kg or, say, the mass of the satellite m≈ 10 3 kg cannot be compared with the Earth's mass and therefore has practically no effect on the Earth's movement. Such a mass, which itself does not disturb the gravitational field, but serves as a probe on which this field acts, is called a test mass. (In the same way, in electrodynamics there is the concept of a “test charge,” that is, one that helps detect an electromagnetic field.) Since the test mass (or test charge) makes a negligibly small contribution to the field, for such a mass the field becomes “external” and can be characterized by a quantity called tension. Essentially, the acceleration due to gravity g is the intensity of the earth's gravitational field. The second law of Newtonian mechanics then gives the equations of motion of a point test mass m. For example, this is how problems in ballistics and celestial mechanics are solved. Note that for most of these problems, Newton's theory of gravitation even today has quite sufficient accuracy.

Tension, like force, is a vector quantity, that is, in three-dimensional space it is determined by three numbers - components along mutually perpendicular Cartesian axes X, at, z. When changing the coordinate system - and such operations are not uncommon in physical and astronomical problems - the Cartesian coordinates of the vector are transformed in some, although not complex, but often cumbersome way. Therefore, instead of the vector field strength, it would be convenient to use the corresponding scalar quantity, from which the force characteristic of the field - the strength - would be obtained using some simple recipe. And such a scalar quantity exists - it is called potential, and the transition to tension is carried out by simple differentiation. It follows that the Newtonian gravitational potential created by the mass M, is equal

hence the equality |φ| = v 2 .

In mathematics, Newton's theory of gravity is sometimes called "potential theory". At one time, the theory of Newtonian potential served as a model for the theory of electricity, and then the ideas about the physical field, formed in Maxwell's electrodynamics, in turn, stimulated the emergence of Einstein's general theory of relativity. The transition from Einstein's relativistic theory of gravity to the special case of Newton's theory of gravity precisely corresponds to the region of small values ​​of the dimensionless parameter |φ| / c 2 .

General theory of relativity(GTR) is a geometric theory of gravity published by Albert Einstein in 1915–16. Within the framework of this theory, which is a further development of the special theory of relativity, it is postulated that gravitational effects are caused not by the force interaction of bodies and fields located in space-time, but by the deformation of space-time itself, which is associated, in particular, with the presence of mass-energy. Thus, in general relativity, as in other metric theories, gravity is not a force interaction. General relativity differs from other metric theories of gravity by using Einstein's equations to relate the curvature of spacetime to the matter present in space.

General relativity is currently the most successful gravitational theory, well confirmed by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported the observation of light bending near the Sun during a total eclipse, confirming the predictions of general relativity.

Since then, many other observations and experiments have confirmed a significant number of the theory's predictions, including gravitational time dilation, gravitational redshift, signal delay in the gravitational field, and, so far only indirectly, gravitational radiation. In addition, numerous observations are interpreted as confirmation of one of the most mysterious and exotic predictions of the general theory of relativity - the existence of black holes.

Despite the stunning success of the general theory of relativity, there is discomfort in the scientific community due to the fact that it cannot be reformulated as the classical limit of quantum theory due to the appearance of irremovable mathematical divergences when considering black holes and space-time singularities in general. A number of alternative theories have been proposed to solve this problem. Modern experimental data indicate that any type of deviation from general relativity should be very small, if it exists at all.

Basic principles of general relativity

Newton's theory of gravity is based on the concept of gravity, which is a long-range force: it acts instantly at any distance. This instantaneous nature of the action is incompatible with the field paradigm of modern physics and, in particular, with the special theory of relativity, created in 1905 by Einstein, inspired by the work of Poincaré and Lorentz. In Einstein's theory, no information can travel faster than the speed of light in a vacuum.

Mathematically, Newton's gravitational force is derived from the potential energy of a body in a gravitational field. The gravitational potential corresponding to this potential energy obeys the Poisson equation, which is not invariant under Lorentz transformations. The reason for non-invariance is that energy in special relativity is not scalar quantity, and goes into the time component of the 4-vector. The vector theory of gravity turns out to be similar to Maxwell’s theory of the electromagnetic field and leads to negative energy of gravitational waves, which is associated with the nature of the interaction: like charges (mass) in gravity attract, and do not repel, as in electromagnetism. Thus, Newton's theory of gravity is incompatible with the fundamental principle of the special theory of relativity - the invariance of the laws of nature in any inertial frame of reference, and the direct vector generalization of Newton's theory, first proposed by Poincaré in 1905 in his work “On the Dynamics of the Electron,” leads to physically unsatisfactory results .

Einstein began searching for a theory of gravity that would be compatible with the principle of invariance of the laws of nature relative to any frame of reference. The result of this search was the general theory of relativity, based on the principle of the identity of gravitational and inertial mass.

The principle of equality of gravitational and inertial masses

In classical Newtonian mechanics, there are two concepts of mass: the first refers to Newton's second law, and the second to the law of universal gravitation. The first mass - inertial (or inertial) - is the ratio of the non-gravitational force acting on the body to its acceleration. The second mass - gravitational (or, as it is sometimes called, heavy) - determines the force of attraction of a body by other bodies and its own force of attraction. Generally speaking, these two masses are measured, as can be seen from the description, in various experiments, and therefore do not have to be proportional to each other at all. Their strict proportionality allows us to speak of a single body mass in both non-gravitational and gravitational interactions. By a suitable choice of units these masses can be made equal to each other. The principle itself was put forward by Isaac Newton, and the equality of masses was verified by him experimentally with a relative accuracy of 10?3. IN late XIX centuries, more subtle experiments were carried out by Eötvös, bringing the accuracy of testing the principle to 10?9. During the 20th century, experimental technology made it possible to confirm the equality of masses with a relative accuracy of 10?12-10?13 (Braginsky, Dicke, etc.). Sometimes the principle of equality of gravitational and inertial masses is called the weak equivalence principle. Albert Einstein based it on the general theory of relativity.

The principle of movement along geodetic lines

If the gravitational mass is exactly equal to the inertial mass, then in the expression for the acceleration of a body on which only gravitational forces act, both masses cancel. Therefore, the acceleration of the body, and therefore its trajectory, does not depend on the mass and internal structure bodies. If all bodies at the same point in space receive the same acceleration, then this acceleration can be associated not with the properties of the bodies, but with the properties of space itself at this point.

Thus, the description of gravitational interaction between bodies can be reduced to a description of the space-time in which the bodies move. It is natural to assume, as Einstein did, that bodies move by inertia, that is, in such a way that their acceleration in their own frame of reference is zero. The trajectories of the bodies will then be geodesic lines, the theory of which was developed by mathematicians back in the 19th century.

The geodesic lines themselves can be found by specifying in space-time an analogue of the distance between two events, traditionally called an interval or a world function. An interval in three-dimensional space and one-dimensional time (in other words, in four-dimensional space-time) is given by 10 independent components of the metric tensor. These 10 numbers form the metric of space. It defines the “distance” between two infinitely close points in space-time in different directions. Geodesic lines corresponding to the world lines of physical bodies whose speed is less than the speed of light turn out to be lines of greatest proper time, that is, time measured by a clock rigidly attached to the body following this trajectory. Modern experiments confirm the movement of bodies along geodetic lines with the same accuracy as the equality of gravitational and inertial masses.

Curvature of spacetime

If you launch two bodies parallel to each other from two close points, then in the gravitational field they will gradually begin to either approach or move away from each other. This effect is called geodetic line deviation. A similar effect can be observed directly if two balls are launched parallel to each other along a rubber membrane on which a massive object is placed in the center. The balls will disperse: the one that was closer to the object pushing through the membrane will tend to the center more strongly than the more distant ball. This discrepancy (deviation) is due to the curvature of the membrane. Similarly, in space-time, the deviation of geodesics (the divergence of the trajectories of bodies) is associated with its curvature. The curvature of space-time is uniquely determined by its metric - the metric tensor. The difference between the general theory of relativity and alternative theories of gravity is determined in most cases precisely in the method of connection between matter (bodies and fields of non-gravitational nature that create the gravitational field) and the metric properties of space-time.

Space-time general relativity and the strong equivalence principle

It is often incorrectly believed that the basis of the general theory of relativity is the principle of equivalence of gravitational and inertial fields, which can be formulated as follows:
A local physical system, rather small in size, located in a gravitational field, is indistinguishable in behavior from the same system located in an accelerated (relative to the inertial reference frame) reference system, immersed in the flat space-time of the special theory of relativity.

Sometimes the same principle is postulated as the "local validity of special relativity" or called the "strong equivalence principle".

Historically, this principle really played a big role in the development of the general theory of relativity and was used by Einstein in its development. However, in the most final form of the theory, it is, in fact, not contained, since space-time, both in the accelerated and in the original frame of reference in the special theory of relativity, is uncurved - flat, and in the general theory of relativity it is curved by any body and precisely its curvature causes the gravitational attraction of bodies.

It is important to note that the main difference between the space-time of the general theory of relativity and the space-time of the special theory of relativity is its curvature, which is expressed by a tensor quantity - the curvature tensor. In the space-time of special relativity, this tensor is identically equal to zero and space-time is flat.

For this reason, the name “general theory of relativity” is not entirely correct. This theory is only one of a number of theories of gravity currently being considered by physicists, while the special theory of relativity (more precisely, its principle of the metricity of space-time) is generally accepted by the scientific community and forms the cornerstone of the basis of modern physics. It should be noted, however, that none of the other developed theories of gravity, except for General Relativity, has stood the test of time and experiment.

Main consequences of general relativity

According to the correspondence principle, in weak gravitational fields the predictions of general relativity coincide with the results of applying Newton's law of universal gravitation with small corrections that increase as the field strength increases.

The first predicted and experimentally verified consequences of general relativity were the three classical effects listed below in chronological order their first check:
1. Additional shift in the perihelion of Mercury's orbit compared to the predictions of Newtonian mechanics.
2. Deflection of a light beam in the gravitational field of the Sun.
3. Gravitational redshift, or time dilation in a gravitational field.

There are a number of other effects that can be experimentally verified. Among them we can mention deviation and lag (Shapiro effect) electromagnetic waves in the gravitational field of the Sun and Jupiter, the Lense-Thirring effect (precession of a gyroscope near a rotating body), astrophysical evidence of the existence of black holes, evidence of the emission of gravitational waves by close systems of double stars and the expansion of the Universe.

So far, no reliable experimental evidence refuting general relativity has been found. Deviations of the measured effect sizes from those predicted by general relativity do not exceed 0.1% (for the above three classical phenomena). Despite this, for various reasons, theorists have developed at least 30 alternative theories of gravity, and some of them make it possible to obtain results arbitrarily close to general relativity with appropriate values ​​of the parameters included in the theory.

The special theory of relativity (STR) or partial theory of relativity is a 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 motion between different inertial frames of reference or the motion of bodies moving in relation to each other with constant speed. In this case, none of the objects should be taken as a reference system, 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 SRT cease to apply when one of the bodies changes its trajectory or increases its speed. Here the general theory of relativity (GTR) takes place, giving general interpretation movement of objects.

Two postulates on which the theory of relativity is built:

1. The principle of relativity- According to him, in all existing reference systems, which move in relation to each other at a constant speed and do not change direction, the same laws apply.
2. The Speed ​​of Light Principle- 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 greater speed. The speed of light is 3*10^8 m/s.

Albert Einstein used 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 the creation of a new theory.

Since the mid-19th century, physicists have been searching for a new mysterious medium called the ether. It was believed that the ether can pass through all objects, but does not participate in their movement. According to beliefs about the aether, by changing the speed of the viewer in relation to the aether, the speed of light also changes.

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

Time intervals, 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, 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 movement of objects.

Connecting energy with mass

Einstein came up with a formula that combined energy with mass. This formula is widely used in physics, and it is familiar to every student: E=m*c², in which E-energy; m - body mass, c - speed propagation of light.

The mass of a body increases in proportion to the increase in the speed of light. If you reach the speed of light, the mass and energy of a 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 required. But in reality this is impossible to achieve.

Einstein's theory combined two separate provisions: 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.