Einstein's theory of relativity has always been something abstract and incomprehensible to me. Let's try to describe Einstein's theory of relativity in simple words. Imagine you are outside in heavy rain and the wind is blowing on your back. If you start running fast, the rain drops will not fall on your back. Drops will be slower or not reach your back at all, this is a scientifically proven fact, and you yourself can check this in a downpour. Now imagine if you turned around and ran against the wind with rain, the drops would fall harder on your clothes and face than if you just stood.

Previously, scientists thought light acted like rain on windy days. They thought that if the Earth moves around the Sun, and the Sun moves around the galaxy, then it is possible to measure the speed of their movement in space. In their opinion, all that remains for them to do is to measure the speed of light and how it changes relative to two bodies.

Scientists have done this found something very strange. The speed of light was the same, no matter how the bodies moved and no matter in what direction to take measurements.

It was very strange. If we take a rainstorm situation, then under normal circumstances, raindrops will affect you more or less depending on your movements. Agree, it would be very strange if the downpour blew in your back with the same force, both when running and when stopping.

Scientists have discovered that light does not have the same properties as raindrops or anything else in the universe. No matter how fast you are moving, and no matter which direction you are heading, the speed of light will always be the same. This is very confusing and only Albert Einstein was able to shed light on this injustice.

Einstein and another scientist, Hendrik Lorenz, figured out that there is only one way to explain how it all could be. This is only possible if time slows down.

Imagine what would happen if time slowed down for you and you didn't know you were moving slower. You will feel like everything else is happening faster., everything around you will move like in a fast-forward movie.

So now let's pretend you're in a downpour again. How is it possible that the rain will affect you in the same way even if you are running? It turns out that if you tried to run away from the rain, then your time would slow down and the rain would speed up. Raindrops would fall on your back at the same speed. Scientists call this expansion of time. No matter how fast you move, your time slows down, at least for the speed of light, this expression is true.

Duality of measurements

Another thing that Einstein and Lorentz found out is that two people under different circumstances can get different calculated values, and the strangest thing is that they will both be right. This is another side effect of the fact that light always travels at the same speed.

Let's do a thought experiment

Imagine that you are standing in the center of your room and you have placed a lamp right in the middle of the room. Now imagine that the speed of light is very slow and you can see how it spreads, imagine that you have turned on the lamp.

As soon as you turn on the lamp, the light will begin to diverge and illuminate. Since both walls are at the same distance, the light will reach both walls at the same time.

Now imagine that your room has a large window and a friend of yours drives by. He will see something else. To him, it will look like your room is moving to the right, and when you turn on the lamp, he will see the left wall moving towards the light. and the right wall moves away from the light. He will see that the light first hit the left wall, and then the right. It seems to him that the light did not illuminate both walls at the same time.

According to Einstein's theory of relativity, both points of view would be right.. From your point of view, the light hits both walls at the same time. From your friend's point of view, this is not the case. There is nothing wrong.

That's why scientists say that "simultaneity is relative." If you are measuring two things that should happen at the same time, then someone who is moving at a different speed or in a different direction will not be able to measure them the same way as you.

This seems very strange to us, because the speed of light for us is instantaneous, and we move very slowly compared to it. Because the speed of light is so fast, we don't notice the speed of light unless we do special experiments.

The faster an object moves, the shorter and smaller it is

Another very strange side effect that the speed of light does not change. At the speed of light, moving things get shorter.

Again, let's imagine that the speed of light is very slow. Imagine that you are on a train and you have installed a lamp in the middle of the car. Now imagine that you have turned on the lamp, as in the room.

The light will spread and simultaneously reach the walls in front and behind the car. This way you can even measure the length of the wagon by measuring how long it took for the light to reach both sides.

Let's do the calculations:

Imagine that it takes 1 second to travel 10 meters and it takes 1 second for the light to travel from the lamp to the wall of the car. This means that the lamp is located at a distance of 10 meters from both sides of the car. Since 10 + 10 = 20, it means that the length of the car is 20 meters.

Now let's imagine that your friend is on the street, watching the train go by. Remember that he sees things differently. The rear wall of the car moves towards the lamp, while the front wall moves away from it. Thus, for him, the light will not touch the front and back of the wall of the car at the same time. First, the light will reach the back, and then to the front.

Thus, if you and your friend measure the speed of light from the lamp to the walls, you will get different values, while from the point of view of science, both calculations will be correct. Only for you, according to the measurements, the length of the wagon will be the same size, and for a friend, the length of the wagon will be less.

Remember, it's all about how and under what conditions you measure. If you were inside a flying rocket that moves at the speed of light, you would not feel anything unusual, unlike people on the ground measuring your movement. You wouldn't be able to tell that time was running slower for you, or that the front and back of the ship were suddenly closer together.

At the same time, if you were flying on a rocket, then it would seem to you as if all the planets and stars are flying past you at the speed of light. In this case, if you try to measure their time and size, then logically for them, time should slow down and size decrease, right?

All this was very strange and incomprehensible, but Einstein proposed a solution and combined all these phenomena into one theory of relativity.

It is said that the epiphany came to Albert Einstein in an instant. The scientist allegedly rode 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 the formulation of one of the central postulates of relativity - that different observers perceive reality differently, including such fundamental quantities as distance and time.

In scientific terms, on that day Einstein realized that the description of any physical event or phenomenon depends on reference systems where the observer is located. If a tram passenger, for example, drops her glasses, then for her they will fall vertically downwards, 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 reference system.

But although the 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 about the law of nature that causes them to fall, then the answer to it will be the same for an observer in a fixed coordinate system and for an observer in a moving coordinate system. The law of distributed traffic is equally valid both on the street and in 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 they say in scientific language, they are invariant. This is what principle of relativity.

Like any hypothesis, the principle of relativity had to be tested by correlating it with real natural phenomena. Einstein derived two separate (though related) theories from the principle of relativity. Special, or private, theory of relativity proceeds from the position that the laws of nature are the same for all frames of reference moving at a 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 contrary to intuitive ideas about the world of effects that occur when moving at a speed close to the speed of light is predicted precisely by the special theory of relativity. The most famous of these is the effect of slowing down the clock, or time dilation effect. A clock moving relative to an observer runs slower for him than exactly the same clock in his hands.

Time in a coordinate system moving at speeds close to the speed of light is stretched relative to the observer, while the spatial extent (length) of objects along the axis of the direction of motion, on the contrary, is compressed. This effect, known as Lorentz-Fitzgerald contraction, was described in 1889 by the Irish physicist George Fitzgerald (George Fitzgerald, 1851-1901) and supplemented in 1892 by the Dutchman Hendrick Lorentz (1853-1928). The Lorentz-Fitzgerald contraction explains why the Michelson-Morley experiment to determine the speed of the Earth in outer space by measuring the "ethereal wind" gave a negative result. Later, Einstein incorporated these equations into special relativity and supplemented them with a similar transformation formula for mass, according to which the mass of a body also increases as the speed of the body approaches the speed of light. So, at a speed of 260,000 km / s (87% of the speed of light), the mass of an object from the point of view of an observer 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 been fully and directly experimentally confirmed. 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 the home airport, they compared their readings with the control clock. It turned out that the clock on the plane was gradually lagging behind the control more and more (if I may say so, when it comes to fractions of a second). For the last half century, scientists have been studying elementary particles on 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 they are fired at various nuclear targets. In such experiments on 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 along with the laws of Newton's mechanics.

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

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

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

General relativity is already applied to all frames of reference (and not just to those moving at a constant speed relative to each other) and looks mathematically much more complicated than special (which explains the gap of eleven years between their publication). It includes as a special case the special theory of relativity (and hence 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 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 that unite 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, space-time. On this continuum, observers moving relative to each other may even disagree about whether two events happened at the same time—or one preceded the other. Fortunately for our poor mind, it does not come to a violation of causal relationships - that is, the existence of coordinate systems in which two events do not occur simultaneously and in a different sequence, even the general theory of relativity does not allow.

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 revolves around the Sun, since there are forces of mutual attraction 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 (in this case, the heavier the body, for example the Sun, the more space-time “bends” under it and, accordingly, the stronger its gravitational field). Imagine a tightly stretched canvas (a kind of trampoline), on which a massive ball is placed. The canvas deforms under the weight of the ball, and a funnel-shaped depression forms around it. According to the general theory of relativity, the Earth revolves around the Sun like a small ball rolled around the cone of a funnel formed as a result of the "punching" of space-time by a heavy ball - the Sun. And what seems to us the force of gravity, in fact, is, in fact, a purely external manifestation of the curvature of space-time, and not at all a force in the Newtonian sense. To date, a better explanation of the nature of gravity than the general theory of relativity gives us has not been found.

Testing general relativity is difficult because, under normal laboratory conditions, its results are almost identical to those predicted by Newton's law of universal gravitation. 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 the slight deviations of Mercury from a stationary orbit that are inexplicable from the point of view of classical Newtonian mechanics, or the bending of electromagnetic radiation from distant stars as it passes in close proximity to the Sun.

In fact, the results predicted by general relativity differ noticeably from the results predicted by Newton's laws only in the presence of superstrong gravitational fields. This means that a full test of the general theory of relativity requires 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 for testing the theory of relativity remains one of the most important tasks of experimental physics.

GR and RTG: Some Emphasis

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 (GR) as one of the greatest achievements of our century, a remarkable theory, an indispensable tool of modern physics and astronomy. Meanwhile, they learn from A. A. Logunov's article that, in his opinion, general relativity should be abandoned, that it is bad, inconsistent, and contradictory. Therefore, general relativity requires replacement by some other theory and, specifically, by the relativistic theory of gravity (RTG) built by A. A. Logunov and his collaborators.

Is it possible that a lot of people are mistaken in the assessment of general relativity, which has existed and has been studied for more than 70 years, and only a few people, led by A. A. Logunov, really found out that general relativity should be discarded? Most readers are probably expecting the answer: it's impossible. In fact, I can only answer in the opposite way: “such” is in principle possible, because it is not about religion, but about science.

The founders and prophets of various religions and creeds created and continue to create their own "holy books", the content of which is 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. And 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’s absurd.” The scientific worldview is fundamentally the opposite: it requires not to take anything for granted, allows you to doubt everything, does not recognize dogma. Under the influence of new facts and considerations, it is not only possible, but necessary, if justified, to change one's point of view, replace an imperfect theory with a more perfect one, or, say, somehow generalize the old theory. The situation is similar for individuals. The founders of creeds are considered infallible, and, for example, among Catholics, even a living person - the "reigning" Pope - is declared infallible. Science does not know the infallible. The great, sometimes even exceptional, respect that physicists (I will speak of physicists for definiteness) 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 interests us here, then the greatest physicists were far from always and not in everything right, 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. First, such a theory must be complete in the area of ​​its applicability, or, as I will arbitrarily say for brevity, must be consistent. Secondly, the physical theory must be adequate to physical reality, or, more simply, be consistent with experiments and observations. One could mention other requirements, first of all, 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 motion of a certain "point" particle. As is known, the role of such a particle in the problems of celestial mechanics can be played by an entire planet or its satellite. Let at the moment t0 the particle is at a point A with coordinates x iA(t0) and has a speed v iA(t0) (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 speed v i at any subsequent point in time t, that is, to find well-defined quantities xiB(t) and v iB(t). And what would happen if the laws of mechanics used did not give an unambiguous answer and, say, in our example predicted that the particle at the moment t can be 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 it was said, is consistent - it gives unambiguous and quite definite answers to questions that are in the field of its competence and applicability. The mechanics of Newton also satisfies the second mentioned requirement - the results obtained on its basis (and, specifically, the values ​​of the coordinates x i(t) and speed v i (t)) are consistent with observations and experiments. That is why all celestial mechanics - the description of the motion of the 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 is somewhat different from that predicted by Newton's 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, which differs from that which would be expected when taking into account all known perturbations from other planets and their satellites. Even earlier, Le Verrier and Adams encountered a similar, in fact, situation when analyzing the motion of Uranus, the most distant planet from the Sun of all 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 indeed discovered at the predicted location, and this event is deservedly considered a triumph of Newtonian mechanics. Quite naturally, Le Verrier tried to explain the mentioned anomaly in the motion of Mercury by the existence of a still 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 the Newtonian law of universal gravitation, according to which the gravitational force as applied to the Sun-planet system changes according to the law

where ε is some small quantity. By the way, a similar technique is used (albeit without success) today to explain some obscure 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. Nobody succeeded in this, and the question of the rotation of the perihelion of Mercury 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 strenuous effort) the creation of the general theory of relativity. This last stage in building the foundation of general relativity 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 an additional rotation of the perihelion of Mercury compared to the Newtonian, which turned out to be equal (in radians for one revolution of the planet around the Sun)

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

a 3 =	GM ☼	T 2
	4π 2

where T is the orbital period of the planet. If we substitute the best known now values ​​of all quantities into formula (1), and also make an elementary recalculation from radians per revolution to rotation in arc seconds (sign ″) per century, then we will come to the value Ψ = 42″.98 / century. Observations agree with this result with the now achieved accuracy of about ± 0″.1 / century (Einstein in his first work used less accurate data, but within the limits of errors he obtained full agreement between 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 most importantly, it is clear from (1) that the rotation of perihelion 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 Einstein biographies I know of, the opinion is expressed and substantiated that the explanation of the rotation of Mercury's perihelion was "the most powerful emotional event in Einstein's entire scientific life, and perhaps in his entire life." Yes, it was Einstein's finest hour. But just for him. For a number of reasons (suffice it to mention the war), for the GR itself to enter the world stage for both this theory and its creator, another event that took place 4 years later, in 1919, became the “high point” In the work in which formula (1) was obtained, Einstein made an important prediction: the rays of light passing near the Sun must be bent, and their deviation must be

α = 4GM ☼ = 1″.75 r ☼ , c 2 r r

(2)

where r is the nearest distance between the beam and the center of the Sun, and r☼ = 6.96 10 10 cm is the radius of the Sun (more precisely, the radius of the solar photosphere); thus, the maximum deviation that can be observed is 1.75 arcseconds. No matter how small such an angle (approximately at this angle an adult is visible from a distance of 200 km), it could already be measured by the optical method at that time by photographing the stars in the sky in the vicinity of the Sun. Such observations were made by two British expeditions during a total solar eclipse on May 29, 1919. The effect of deflection of rays in the field of the Sun was established in this case with all certainty and is in agreement with formula (2), although the measurement accuracy was not high due to the smallness of the effect. However, a deviation half that according to (2), i.e., by 0″.87, was excluded. The latter is very important, because the deviation by 0″.87 (with r = r☼) can already be obtained from Newtonian theory (the very possibility of light deflection in the 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 impression they made is clear from what J. J. Thomson, who chaired this meeting, said: “This is the most important result obtained in connection with the theory of gravity since the time of 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 the 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 illustrative parameter v 2 / c 2 , which for the solar system, as we have seen, does not exceed 2.12 10 - 6 . In earth orbit v = 3 10 6 cm s - 1 and v 2 / c 2 \u003d 10 - 8, for close Earth satellites v ~ 8 10 5 cm s - 1 and v 2 / c 2 ~ 7 10 - 10 . Therefore, verification of the mentioned effects of general relativity, even with the accuracy of 0.1% now achieved, that is, with an error not exceeding 10 - 3 of the measured value (say, the deviation of light rays in the solar field), does not yet allow a comprehensive verification of general relativity with an accuracy of terms of the order

One can only dream of measuring with the required accuracy, say, the deflection of rays within the solar system. However, projects of corresponding experiments are already being discussed. In connection with what has been said, physicists say that general relativity has been verified mainly only for a weak gravitational field. But we (I, 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 are already needed with an accuracy of up to meters (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 being carried out on the basis of computational schemes that organically take into account general relativity. I remember how a few years ago one speaker - a specialist in space navigation - did not even understand my questions about the accuracy of testing general relativity. He answered: we take into account general relativity in our engineering calculations, otherwise it is impossible to work, everything turns out right, what more could you want? Of course, one can wish for a lot, but one should not forget that general relativity is no longer an abstract theory, but is used in "engineering calculations".

4. In the light of the foregoing, the criticism of GRT by A. A. Logunov seems especially surprising. But in accordance with what was said at the beginning of this article, this criticism cannot be dismissed without analysis. To an even greater extent, without a detailed analysis, it is impossible to make a judgment about the RTG proposed by A. A. Logunov - the relativistic theory of gravity.

Unfortunately, it is absolutely 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. There is no other way I can do here.

So, we believe that GR is a consistent physical theory – GR gives an unambiguous answer to all correctly and clearly posed questions that are admissible in the area of ​​its applicability (the latter refers, in particular, to the delay time of signals when locating planets). It does not suffer from general relativity and any defects of a mathematical or logical nature. However, it is necessary 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 a number of 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 resolved by a majority of votes. But, on the other hand, it is quite obvious that the opinion of many physicists, generally speaking, is much more convincing, or, to put it better, 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 remarks.

Why does AA Logunov dislike GR so much? The 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 “from representing the gravitational field as a classical field of the Faraday-Maxwell type, which has a well-defined energy-momentum density. Yes, the latter is true in a certain sense, but it is explained by the fact that “in the Riemannian geometry, in the general case, there is no necessary symmetry with respect to shifts and rotations, that is, there is no ... space-time motion group.” The geometry of space-time, according to general relativity, is a Riemannian geometry. That is why, in particular, the rays of light deviate from a straight line, 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 GR, 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 geometry of Minkowski was, one might say, a product of the special theory of relativity (SRT) and replaced Newton's absolute time and absolute space. The latter, immediately before the creation of SRT in 1905, was tried to be identified with the fixed ether of Lorentz. But the Lorentz ether, as an absolutely immobile 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 the physical space-time is necessarily exactly the Minkowski space, which A. A. Logunov accepts as fundamental, is very far-reaching. It is in a sense analogous to the hypotheses about absolute space and about the mechanical ether, and it seems to us that it remains and will remain completely unfounded until some arguments based on observations and experiments are indicated in its favor. And such arguments, at least at the present time, are completely absent. References to the analogy with electrodynamics and the ideals of the remarkable physicists of the last century Faraday and Maxwell are not convincing in this respect.

5. If we talk about the difference between the electromagnetic field and, consequently, 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 (turn to zero) even locally (in a small area) the entire electromagnetic field. Therefore, if the energy density of the electromagnetic field

W =	E 2 + H 2
	8π

(E and H- the intensity of the electric and magnetic fields, respectively) is non-zero in any frame of reference, then it will be non-zero in any other frame of reference. The gravitational field, roughly speaking, depends much more strongly on the choice of the frame of reference. So, a uniform and constant gravitational field (that is, a gravitational field that causes acceleration g particles placed in it, independent of coordinates and time) can be completely “destroyed” (turned to zero) by the transition to a uniformly accelerated reference frame. This circumstance, which is the main physical content of the "principle of equivalence", was first noted by Einstein in an article published in 1907 and which was the first on the way 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 this it is clear that in the question of the density of energy (and momentum) the theory of the gravitational field must radically differ from the theory of the electromagnetic field. Such a statement does not change due to the fact that, in general, 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 by 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 by means of a relativistic transformation.” And here is an excerpt from an article of 1914: “We will first make one more remark to eliminate the obvious misunderstanding. A supporter of the usual modern theory of relativity (we are talking about SRT - V.L.G.) with a certain right calls the "apparent" speed of a material point. Namely, he can choose the frame of reference so that the material point has a speed equal to zero at the considered moment. If there is a system of material points that have different velocities, then he can no longer introduce such a reference system that the velocities of all material points relative to this system vanish. Similarly, a physicist, standing on our point of view, can call the gravitational field "apparent" because by appropriate choice of the acceleration of the frame of reference he can achieve that at a certain point in space-time the gravitational field vanishes. However, it is noteworthy that the vanishing of the gravitational field through 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 an appropriate frame of reference." Finally, already in 1916, responding to the criticism of general relativity, Einstein once again emphasized the same thing: “In no way can it also be argued that the gravitational field is to some 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 only possible to obtain fields of a certain structure, which, however, must obey the same laws as all other gravitational fields. This is another formulation of the principle of equivalence (specifically for applying this principle to gravity)."

The impossibility of a “kinematic understanding” of gravitation, combined with the principle of equivalence, causes the transition in GR 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 a curvature distinguishes the “true” gravitational field from "kinematic"). The physical features of the gravitational field determine, let us repeat this, a radical change in the role of energy and momentum in general relativity in comparison with electrodynamics. At the same time, both the use of Riemannian geometry and the impossibility of applying the energy concepts familiar from electrodynamics do not prevent, as already emphasized above, the fact that from general relativity follow and can be calculated quite unambiguous values ​​for all observable quantities (the angle of deflection of light rays, changes in the elements of orbits planets and double pulsars, etc., etc.).

It would probably be useful to note the fact that general relativity can also be formulated in the usual form from electrodynamics using the concept of energy-momentum density (for this, see the cited article by Ya. B. Zeldovich and L. P. Grischuk. However, 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, we repeat this, A. A. Logunov considers the Minkowski space used by him in the relativistic theory of gravity (RTG) to be real physical, and hence observable space.

6. In this regard, the second of the questions appearing in the title of this article is especially important: does general relativity correspond to physical reality? In other words, what does experience say - the supreme judge in deciding the fate of any physical theory? Numerous articles and books are devoted to this problem - the experimental verification of general relativity. In this case, the conclusion is quite definite – all the available data of experiments or observations either confirm GRT or do not contradict it. However, as we have already pointed out, the verification of general relativity was carried out and takes place mainly only in a weak gravitational field. In addition, any experiment has a limited accuracy. In strong gravitational fields (roughly speaking, in the case when the ratio |φ| / c 2 is not small; see above) GR has not yet been fully verified. For this purpose, it is now possible to practically use only astronomical methods related 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 by millions and billions of light years. Much has already been done and is being done in this direction. Suffice it to mention the studies of the binary pulsar PSR 1913+16, for which (as well as for neutron stars in general) the parameter |φ| / c 2 is already about 0.1. In addition, in this case it was possible to reveal 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 these breathtaking studies is, first of all, general relativity. At the same time, of course, some other possibilities are also discussed - other, as they sometimes say, alternative, theories of gravity. For example, in general relativity, as well as in Newton's theory of universal gravitation, the gravitational constant G really considered a constant. One of the most famous theories of gravity, generalizing (or, more precisely, expanding) general relativity, is a theory in which the gravitational "constant" is already considered a new scalar function - a quantity that depends on coordinates and time. Observations and measurements indicate, however, that possible relative changes G over time are very small - apparently, they amount to no more than a hundred billionth a 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 impermanence G assumption of existence in real space-time, in addition to the gravitational field gik, also some scalar field ψ is the main direction in modern physics and cosmology. In other alternative theories of gravitation (for which see the book of C. Will mentioned above in note 8), general relativity is modified or generalized in a different way. Of course, one cannot object to the corresponding analysis, because GR 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 still inaccessible to known gravitational experiments. Naturally, you can't go into more detail about all this here.

7. A. A. Logunov, starting from the criticism of general relativity, for more than 10 years has been building some alternative theory of gravity that is different from general relativity. At the same time, much has changed in the course of the work, and the currently accepted version of the theory (this is the RTG) is especially detailed in the article, which occupies about 150 pages and contains about 700 numbered formulas only. Obviously, a detailed analysis of RTG is possible only on the pages of scientific journals. Only after such an analysis it will be possible to say whether RTG is consistent, whether it contains mathematical contradictions, etc. As far as I could understand, RTG differs from GR by selecting only a part of GR solutions - all solutions of RTG differential equations satisfy the GR equations, but, as far as say the authors of the RTG, not vice versa. At the same time, it is concluded that, with regard to global issues (solutions for the entire space-time or its large regions, topology, etc.), the differences between RTG and GR are, generally speaking, radical. As for all the experiments and observations made within the solar system, then, as far as I understand, RTG cannot conflict with general relativity. If so, then it is impossible to prefer RTG (over GR) on the basis of known experiments in the solar system. As for "black holes" and the Universe, the authors of the 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 testify in favor of the RTG. In such a situation, RTG by A. A. Logunov (if RTG really differs from GR in essence, and not only in the way of presentation and choice of one of the possible classes of coordinate conditions; see the article by Ya. B. Zeldovich and L. P. Grischuk) can be considered only as one of the acceptable, in principle, alternative theories of gravity.

Some readers may be alerted by reservations like: “if this is so”, “if RTG really differs from GR”. Am I trying to insure against mistakes in this way? No, I am not afraid to make a mistake already by virtue of the conviction that there is only one guarantee of infallibility - 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. The categoricalness of statements does not always indicate the presence of genuine clarity and, in general, does not contribute to the establishment of the truth. The RTG of A. A. Logunov in its modern form was 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, in a popular science journal, a number of emerging issues cannot be discussed, and inappropriate. At the same time, of course, due to the great interest of readers in the theory of gravitation, the coverage of this range of issues, including debatable ones, on the pages of Science and Life seems justified at an accessible level.

So, guided by the wise “most favored nation principle”, RTG should now be considered an alternative theory of gravity that needs to be analyzed and discussed accordingly. For those who like this theory (RTG) and who are interested in it, no one prevents (and, of course, should not interfere) to develop it, to suggest possible ways of experimental verification.

At the same time, there are no grounds to say that the GTR has been shaken to some extent at the present time. Moreover, the range of applicability of general relativity seems to be very wide, and its accuracy is very high. Such, in our opinion, is an objective assessment of the existing state of affairs. If we talk about tastes and intuitive attitudes, and tastes and intuition in science play a significant role, although they cannot be put forward as evidence, then here we have to move from “we” to “I”. So, the more I have had and still have to deal with the general theory of relativity and its criticism, the more I get stronger the impression of its exceptional depth and beauty.

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).

Incidentally, 1987 marks the 300th anniversary of the first publication of Newton's great book The Mathematical Principles of Natural Philosophy. Acquaintance with the history of the creation of this work, not to mention himself, is very instructive. However, the same applies to all the activities of Newton, with which it is not so easy for non-specialists to get acquainted with us. I can recommend for this purpose a 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, vol. 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). 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 expedient to publish a Russian translation of this book.

The latter is possible during total solar eclipses; 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 the 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 (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 (“Uspekhi fizicheskikh nauk”, 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", v. 17, issue 1, 1986

In the works of A. A. Logunov there are other statements and it is specifically considered that for the signal delay time when, say, Mercury is located from the Earth, a value obtained from RTG is different from that following from GR. More precisely, it is argued that general relativity does not give an unambiguous prediction of the delay time of signals, that is, general relativity is inconsistent (see above). However, such a conclusion is, in our opinion, the fruit of a misunderstanding (this is indicated, for example, in the cited article by Ya. that compares the located planets that are in different orbits, and therefore have different periods of revolution around the Sun. The signal delay times observed from the Earth at the location of a certain planet, according to GR and RTG, coincide.

See footnote 5.

Details for the curious

Deviation of light and radio waves in the gravitational field of the Sun. Usually, as an idealized model of the Sun, a static spherically symmetric ball of radius R☼ ~ 6.96 10 10 cm, solar mass M☼ ~ 1.99 10 30 kg (332958 times the mass of the Earth). The deviation of light is maximum for rays that barely touch the Sun, that is, at R ~ R☼ , and equal to: φ ≈ 1″.75 (arcseconds). This angle is very small - approximately at this angle an adult is seen from a distance of 200 km, and therefore the accuracy of measuring the gravitational curvature of rays was not high until recently. The last optical measurements, made during the solar eclipse of June 30, 1973, had an error of about 10%. Today, thanks to the advent of radio interferometers "with an extra long baseline" (more than 1000 km), the accuracy of measuring angles has increased dramatically. Radio interferometers make it possible to reliably measure angular distances and angle changes of the order of 10 - 4 arc seconds (~ 1 nanoradian).

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

GRAVITATIONAL POTENTIAL

In 1687, Newton's fundamental work "The 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:

F = G	mm	.
	r 2

Proportionality factor G became known as the gravitational constant, it is necessary to match the dimensions in the right and left parts of the Newtonian formula. Even Newton himself, with a very high accuracy for his time, showed that G- the value is constant and, therefore, the law of gravity discovered by him is universal.

Two attracting point masses M and m appear in Newton's formula equally. In other words, we can consider that both of them 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 MЗ ≈ 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 motion. Such a mass, which itself does not perturb the gravitational field, but serves as a kind of 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 to detect an electromagnetic field.) Since the test mass (or test charge) makes a negligible contribution to the field, for such a mass the field becomes "external" and it can be characterized by a quantity called tension. Essentially, the free fall acceleration g is the strength 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 the problems of 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, though not complicated, but often cumbersome way. Therefore, instead of the vector field strength, it would be convenient to use the scalar value corresponding to it, from which the strength characteristic of the field - the strength - would be obtained using some simple recipe. And such a scalar value 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 to

whence follows the equality |φ| = v 2 .

In mathematics, Newton's theory of gravitation is sometimes called "potential theory". At one time, the theory of the 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 gravitation to a special case of the Newtonian theory of gravitation exactly corresponds to the region of small values ​​of the dimensionless parameter |φ| / c 2 .

The King's New Mind [On Computers, Thinking, and the Laws of Physics] Roger Penrose

Einstein's general theory of relativity

Recall the great truth discovered by Galileo: all bodies fall equally fast under the influence of gravity. (This was a brilliant guess, hardly supported by empirical data, because due to air resistance, feathers and stones still fall unsteadily. simultaneously! Galileo suddenly realized that if air resistance could be reduced to zero, then feathers and stones would fall to Earth at the same time.) It took three centuries before the profound significance of this discovery was truly realized and became the cornerstone of a great theory. I am referring to Einstein's general theory of relativity - an amazing description of gravity, which, as we will soon become clear, required the introduction of the concept curved space-time !

What does Galileo's intuitive discovery have to do with the idea of ​​"curvature of space-time"? How could it be that this concept, so obviously different from Newton's scheme, according to which particles are accelerated under the influence of ordinary gravitational forces, was able not only to equal the accuracy of description with Newton's theory, but also to surpass it? And then, how true is the statement that there was something in the discovery of Galileo that did not have later incorporated into Newtonian theory?

Let me start with the last question because it's the easiest one to answer. What, according to Newton's theory, controls the acceleration of a body under the influence of gravity? First, the gravitational force acts on the body. force , which, according to Newton's law of universal gravitation, must be proportional to body weight. Secondly, the amount of acceleration experienced by the body under the action of given force, according to Newton's second law, inversely proportional to body weight. Galileo's amazing discovery depends on the fact that the "mass" that enters Newton's law of universal gravitation is, in fact, the same "mass" that enters Newton's second law. (Instead of "the same" one could say "proportional".) As a result, the acceleration of the body under the influence of gravity does not depend from its mass. There is nothing in Newton's general scheme to indicate that both concepts of mass are the same. This sameness Newton only postulated. Indeed, electrical forces are similar to gravitational ones in that both are inversely proportional to the square of the distance, but electrical forces depend on electric charge, which is of a completely different nature than weight in Newton's second law. The "intuitive discovery of Galileo" would not be applicable to electric forces: about bodies (charged bodies) thrown in an electric field, one cannot say that they "fall" with the same speed!

Just for a while accept Galileo's intuitive discovery regarding motion under the influence of gravity and try to find out what consequences it leads to. Imagine Galileo throwing two stones from the Leaning Tower of Pisa. Let us assume that a video camera is rigidly fastened to one of the stones and is aimed at another stone. Then the following situation will be captured on the film: the stone soars in space, as if not experiencing gravity (Fig. 5.23)! And this happens precisely because all bodies under the influence of gravity fall at the same speed.

Rice. 5.23. Galileo throws two stones (and a video camera) from the Leaning Tower of Pisa

In the above picture, we neglect air resistance. In our time, space flights offer us the best opportunity to test these ideas, since there is no air in outer space. In addition, "falling" in outer space simply means moving in a certain orbit under the influence of gravity. Such a "fall" does not necessarily have to occur in a straight line down - to the center of the Earth. It may well have some horizontal component. If this horizontal component is large enough, then the body can "fall" in a circular orbit around the Earth without approaching its surface! Traveling in free Earth orbit under the influence of gravity is a very sophisticated (and very expensive!) way of "falling". As in the video described above, an astronaut, making a “walk in outer space”, sees his spaceship hovering in front of him and, as it were, not experiencing the action of gravity from the huge ball of the Earth below him! (See Fig. 5.24.) Thus, by passing to the "accelerated reference frame" of free fall, one can locally exclude the action of gravity.

Rice. 5.24. An astronaut sees his spaceship hovering in front of him, as if unaffected by gravity.

We see that free fall allows exclude gravity because the effect of the action of the gravitational field is the same as that of acceleration. Indeed, if you are in an elevator that is moving with acceleration up, then you just feel that the apparent gravitational field is increasing, and if the elevator is moving with acceleration down, then you the gravitational field seems to be decreasing. If the rope on which the cabin is suspended were to break, then (if we neglect air resistance and friction effects) the resulting acceleration directed downward (towards the center of the Earth) would completely destroy the effect of gravity, and the people trapped in the elevator car would begin to float freely. in space, like an astronaut on a spacewalk, until the cabin hits the ground! Even in a train or aboard an airplane, the accelerations can be such that the passenger's sense of the magnitude and direction of gravity may not coincide with where normal experience shows "up" and "down" to be. This is explained by the fact that the actions of acceleration and gravity similar so much so that our senses are unable to distinguish one from the other. This fact - that the local manifestations of gravity are equivalent to the local manifestations of an accelerated reference frame - is what Einstein called equivalence principle .

The above considerations are "local". But if it is allowed to make (not only local) measurements with a sufficiently high accuracy, then in principle it is possible to establish difference between the "true" gravitational field and pure acceleration. On fig. 5 25 I have depicted in a slightly exaggerated way how the initially stationary spherical configuration of particles, freely falling under the influence of gravity, begins to deform under the influence of inhomogeneities(Newtonian) gravitational field.

Rice. 5.25. Tidal effect. Double arrows indicate relative acceleration (WEIL)

This field is heterogeneous in two respects. First, since the center of the Earth is located at some finite distance from the falling body, particles located closer to the Earth's surface move downward with greater acceleration than particles located above (recall Newton's law of inverse proportionality to the square of Newton's distance). Secondly, for the same reason, there are small differences in the direction of acceleration for particles occupying different horizontal positions. Due to this inhomogeneity, the spherical shape begins to deform slightly, turning into an "ellipsoid". The original sphere is elongated towards the center of the Earth (and also in the opposite direction), since those parts of it that are closer to the center of the Earth move with slightly more acceleration than those parts that are farther from the center of the Earth, and narrows horizontally , since the accelerations of its parts located at the ends of the horizontal diameter are slightly beveled "inward" - towards the center of the Earth.

This deforming action is known as tidal effect gravity. If we replace the center of the Earth with the Moon, and the sphere of material particles with the surface of the Earth, we get exactly the description of the action of the Moon, causing tides on the Earth, with "humps" being formed towards the Moon and away from the Moon. The tidal effect is a common feature of gravitational fields that cannot be "eliminated" by free fall. The tidal effect serves as a measure of the inhomogeneity of the Newtonian gravitational field. (The amount of tidal warp actually decreases with the inverse cube, not the square of the distance from the center of gravity.)

Newton's law of universal gravitation, according to which force is inversely proportional to the square of distance, can, as it turns out, be easily interpreted in terms of the tidal effect: volume ellipsoid into which the sphere is initially deformed, equals the volume of the original sphere - assuming that the sphere surrounds the vacuum. This volume conservation property is characteristic of the inverse square law; it does not hold for any other laws. Suppose further that the original sphere is surrounded not by vacuum, but by a certain amount of matter with a total mass M . Then there is an additional acceleration component directed inside the sphere due to the gravitational attraction of matter inside the sphere. The volume of the ellipsoid into which our sphere of material particles is initially deformed, shrinking- by the amount proportional M . We would encounter an example of the effect of shrinking the volume of an ellipsoid if we chose our sphere so that it surrounds the Earth at a constant height (Fig. 5.26). Then the usual acceleration due to gravity and directed downward (ie, inside the Earth) will be the very reason why the volume of our sphere shrinks.

Rice. 5.26. When a sphere surrounds some substance (in this case, the Earth), there is a net acceleration directed inward (RICCI)

In this property of volume contraction lies the remainder of Newton's law of universal gravitation, namely, that force is proportional to mass attracting body.

Let's try to get a space-time picture of such a situation. On fig. In Figure 5.27, I have drawn the world lines of the particles of our spherical surface (represented as a circle in Figure 5.25), and I have used to describe the frame of reference in which the center point of the sphere appears to be at rest ("free fall").

Rice. 5.27. Curvature of spacetime: the tidal effect depicted in spacetime

The position of general relativity is to regard free fall as "natural motion" - analogous to the "uniform rectilinear motion" that is dealt with in the absence of gravity. Thus, we trying describe free fall by "straight" world lines in space-time! But if you look at Fig. 5.27, it becomes clear that the use the words "straight lines" in relation to these world lines can mislead the reader, therefore, for terminological purposes, we will call the world lines of freely falling particles in space-time - geodetic .

But how good is this terminology? What is commonly understood by a "geodesic" line? Consider an analogy for a two-dimensional curved surface. Geodesics are those curves that on a given surface (locally) serve as "shortest paths". In other words, if we imagine a piece of thread stretched over a specified surface (and not too long so that it cannot slip), then the thread will be located along some geodesic line on the surface.

Rice. 5.28. Geodesic lines in curved space: lines converge in space with positive curvature and diverge in space with negative curvature

On fig. 5.28 I gave two examples of surfaces: the first (left) is the surface of the so-called "positive curvature" (like the surface of a sphere), the second is the surface of "negative curvature" (saddle surface). On a surface of positive curvature, two adjacent geodesic lines starting parallel to each other from the starting points begin to curve afterwards towards each other; and on the surface of negative curvature they bend into sides from each other.

If we imagine that the world lines of freely falling particles behave in some sense like geodesic lines on a surface, then it turns out that there is a close analogy between the gravitational tidal effect discussed above and the effects of surface curvature - moreover, as a positive curvature, so negative. Take a look at fig. 5.25, 5.27. We see that in our space-time the geodesic lines begin diverge in one direction (when they "line up" towards the Earth) - as it happens on the surface negative curvature in fig. 5.28 - and approach in other directions (when they move horizontally relative to the Earth) - as on the surface positive curvature in fig. 5.28. Thus, it seems that our space-time, like the aforementioned surfaces, also has a “curvature”, only more complex, because due to the high dimension of space-time, with various displacements, it can be of a mixed nature, without being purely positive. , nor purely negative.

It follows that the concept of "curvature" of space-time can be used to describe the action of gravitational fields. The possibility of using such a description ultimately follows from Galileo's intuitive discovery (equivalence principle) and allows us to eliminate the gravitational "force" with the help of free fall. Indeed, nothing I have said so far goes beyond the scope of Newtonian theory. The picture just drawn gives simply reformulation this theory. But when we try to combine the new picture with that of Minkowski's description of special relativity, the geometry of space-time that we know applies to absence gravity - new physics comes into play. The result of this combination is general theory of relativity Einstein.

Let us recall what Minkowski taught us. We have (in the absence of gravity) space-time endowed with a special kind of measure of "distance" between points: if we have in space-time a world line describing the trajectory of some particle, then "distance" in the sense of Minkowski, measured along this world line lines, gives time , actually lived by the particle. (In fact, in the previous section we considered this "distance" only for those world lines that consist of straight line segments - but the above statement is also true for curved world lines, if the "distance" is measured along a curve.) Minkowski's geometry is considered accurate if there is no gravitational field, i.e. if space-time has no curvature. But in the presence of gravity, we consider Minkowski's geometry only as an approximate one - just as a flat surface only approximately corresponds to the geometry of a curved surface. Let's imagine that, while studying a curved surface, we take a microscope, which gives an increasing magnification - so that the geometry of the curved surface seems to be more and more stretched. In this case, the surface will appear to us more and more flat. Therefore, we say that the curved surface has the local structure of the Euclidean plane. In the same way, we can say that in the presence of gravity, space-time locally is described by the geometry of Minkowski (which is the geometry of flat space-time), but we allow some "curvature" on larger scales (Fig. 5.29).

Rice. 5.29. A picture of curved space-time

In particular, as in Minkowski space, any point in spacetime is a vertex light cone- but in this case, these light cones are no longer located in the same way. In Chapter 7, we will look at individual space-time models that clearly show this non-uniform arrangement of light cones (see Figures 7.13, 7.14). World lines of material particles are always directed inside light cones, and lines of photons - along light cones. Along any such curve, we can introduce "distance" in the Minkowski sense, which serves as a measure of the time lived by particles in the same way as in Minkowski space. As with a curved surface, this "distance" measure determines geometry surface, which may differ from the geometry of the plane.

Geodesic lines in spacetime can now be given an interpretation similar to the interpretation of geodesic lines on two-dimensional surfaces, while taking into account the differences between the geometries of Minkowski and Euclid. Thus, our geodesic lines in space-time are not (locally) shortest curves, but, on the contrary, curves that are (locally) maximize"distance" (i.e. time) along the world line. The world lines of particles freely moving under the action of gravity, according to this rule, are indeed are geodetic. In particular, celestial bodies moving in a gravitational field are well described by similar geodesic lines. In addition, light rays (photon world lines) in empty space also serve as geodesic lines, but this time - null"length". As an example, I have schematically drawn in Fig. 5.30 world lines of the Earth and the Sun. The motion of the Earth around the Sun is described by a "corkscrew" line winding around the world line of the Sun. In the same place, I depicted a photon coming to Earth from a distant star. Its world line appears slightly "curved" due to the fact that light (according to Einstein's theory) is actually deflected by the Sun's gravitational field.

Rice. 5.30. World lines of the Earth and the Sun. A light beam from a distant star is deflected by the sun

We still need to figure out how Newton's inverse square law can be incorporated (after appropriate modification) into Einstein's general theory of relativity. Let us turn again to our sphere of material particles falling in a gravitational field. Recall that if only vacuum is enclosed inside the sphere, then, according to Newton's theory, the volume of the sphere initially does not change; but if inside the sphere there is matter with a total mass M , then there is a reduction in volume proportional to M . In Einstein's theory (for a small sphere) the rules are exactly the same, except that not all change in volume is determined by the mass M ; there is a (usually very small) contribution from pressure arising in the material surrounded by the sphere.

The complete mathematical expression for the curvature of four-dimensional spacetime (which should describe the tidal effects for particles moving at any given point in all possible directions) is given by the so-called Riemann curvature tensor . This is a somewhat complex object; to describe it, it is necessary to indicate twenty real numbers at each point. These twenty numbers are called his components . Different components correspond to different curvatures in different space-time directions. The Riemann curvature tensor is usually written as R tjkl, but since I don't feel like explaining what these sub-indices mean here (and, of course, what a tensor is), I'll write it simply as:

RIMAN .

There is a way to split this tensor into two parts, called, respectively, the tensor WEIL and tensor RICCHI (each with ten components). Conventionally, I will write this partition like this:

RIMAN = WEIL + RICCHI .

(A detailed record of the Weyl and Ricci tensors is completely unnecessary for our purposes now.) The Weil tensor WEIL serves as a measure tidal deformation our sphere of freely falling particles (i.e., changes in the initial shape, not size); while the Ricci tensor RICCHI serves as a measure of the change in the initial volume. Recall that the Newtonian theory of gravity requires that weight contained within our falling sphere was proportional to this change in the original volume. This means that, roughly speaking, the density masses matter - or, equivalently, density energy (as E = mc 2 ) - follows equate Ricci tensor.

Essentially, this is exactly what the field equations of general relativity state, namely - Einstein field equations . True, there are some technical subtleties here, which, however, it is better for us not to go into now. Suffice it to say that there is an object called a tensor energy-momentum , which brings together all the essential information about the energy, pressure and momentum of matter and electromagnetic fields. I will call this tensor ENERGY . Then the Einstein equations can be very schematically represented in the following form,

RICCHI = ENERGY .

(It is the presence of "pressure" in the tensor ENERGY together with certain requirements for the consistency of the equations as a whole lead with the need to take into account the pressure in the volume reduction effect described above.)

The above relation seems to say nothing about the Weyl tensor. However, it reflects one important property. The tidal effect produced in empty space is due to WEILEM . Indeed, it follows from the above Einstein equations that there are differential equations relating WEIL with ENERGY - almost like in the Maxwell equations we encountered earlier. Indeed, the point of view that WEIL should be considered as a kind of gravitational analogue of the electromagnetic field (in fact, the tensor - Maxwell tensor) described by the pair ( E , AT ) appears to be very fruitful. In this case WEIL serves as a kind of measure of the gravitational field. "source" for WEIL is an ENERGY - just as a source for an electromagnetic field ( E , AT ) is an ( ? , j ) - a set of charges and currents in Maxwell's theory. This point of view will be useful to us in Chapter 7.

It may seem quite surprising that with such significant differences in formulation and underlying ideas, it is rather difficult to find observable differences between Einstein's theories and the theory put forward by Newton two and a half centuries earlier. But if the velocities under consideration are small compared to the speed of light with , and the gravitational fields are not too strong (so that the escape velocity is much less with , see Chapter 7, "The Dynamics of Galileo and Newton"), then Einstein's theory gives essentially the same results as Newton's theory. But in those situations where the predictions of these two theories diverge, the predictions of Einstein's theory turn out to be more accurate. To date, a number of very impressive experimental tests have been carried out, which allow us to consider Einstein's new theory as well-founded. Clocks, according to Einstein, run a little slower in a gravitational field. This effect has now been directly measured in several ways. Light and radio signals do bend near the Sun and are slightly delayed for an observer moving towards them. These effects, originally predicted by the general theory of relativity, have now been confirmed by experience. The movement of space probes and planets require small corrections to Newtonian orbits, as follows from Einstein's theory - these corrections are now also verified empirically. (In particular, the anomaly in the motion of the planet Mercury, known as the "perihelion shift," which has plagued astronomers since 1859, was explained by Einstein in 1915.) Perhaps most impressive of all is a series of observations of a system called double pulsar, which consists of two small massive stars (possibly two "neutron stars", see Chapter 7 "Black Holes"). This series of observations agrees very well with Einstein's theory and serves as a direct test of an effect that is completely absent in Newton's theory - the emission gravitational waves. (A gravitational wave is an analogue of an electromagnetic wave and propagates at the speed of light with .) There are no verified observations that contradict Einstein's general theory of relativity. For all its strangeness (at first glance), Einstein's theory works to this day!

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General relativity is already applied to all frames of reference (and not just to those moving at a constant speed relative to each other) and looks mathematically much more complicated than special (which explains the gap of eleven years between their publication). It includes as a special case the special theory of relativity (and hence 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 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 that unite 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, space-time. On this continuum, observers moving relative to each other may even disagree about whether two events happened at the same time—or one preceded the other. Fortunately for our poor mind, it does not come to a violation of causal relationships - that is, the existence of coordinate systems in which two events do not occur simultaneously and in a different sequence, even the general theory of relativity does not allow.

Classical physics considered gravity as an ordinary force among many natural forces (electrical, magnetic, etc.). Gravity was prescribed "long-range action" (penetration "through the void") and an amazing ability to give equal acceleration to bodies of different masses.

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 revolves around the Sun, since there are forces of mutual attraction 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 (in this case, the heavier the body, for example the Sun, the more space-time "bends" under it and, accordingly, the stronger its gravitational field). Imagine a tightly stretched canvas (a kind of trampoline), on which a massive ball is placed. The canvas deforms under the weight of the ball, and a funnel-shaped depression forms around it. According to the general theory of relativity, the Earth revolves around the Sun like a small ball rolled around the cone of a funnel formed as a result of "punching" space-time by a heavy ball - the Sun. And what seems to us the force of gravity, in fact, is, in fact, a purely external manifestation of the curvature of space-time, and not at all a force in the Newtonian sense. To date, a better explanation of the nature of gravity than the general theory of relativity gives us has not been found.

First, the equality of accelerations of free fall for bodies of different masses is discussed (the fact that a massive key and a light match equally quickly fall from the table to the floor). As Einstein noted, this unique property makes gravity very similar to inertia.

In fact, the key and the match behave as if they were moving in weightlessness by inertia, and the floor of the room was moving towards them with acceleration. Having reached the key and the match, the floor would experience their impact, and then pressure, because. the inertia of the key and the match would have affected the further acceleration of the floor.

This pressure (astronauts say - "overload") is called the force of inertia. A similar force is always applied to bodies in accelerated frames of reference.

If the rocket flies with an acceleration equal to the free fall acceleration on the earth's surface (9.81 m/s), then the inertia force will play the role of the weight of the key and the match. Their "artificial" gravity will be exactly the same as the natural one on the surface of the Earth. This means that the acceleration of the reference frame is a phenomenon quite similar to gravity.

On the contrary, in a free-falling elevator, natural gravity is eliminated by the accelerated movement of the cabin reference system "chasing" the key and the match. Of course, classical physics does not see in these examples the true emergence and disappearance of gravity. Gravity is only simulated or compensated by acceleration. But in general relativity, the similarity between inertia and gravity is recognized to be much deeper.

Einstein put forward the local principle of the equivalence of inertia and gravity, stating that on sufficiently small scales of distances and durations, one phenomenon cannot be distinguished from another by any experiment. Thus, general relativity has changed the scientific understanding of the world even more profoundly. The first law of Newtonian dynamics has lost its universality - it turned out that the movement by inertia can be curvilinear and accelerated. The need for the concept of a heavy mass has disappeared. The geometry of the Universe has changed: instead of direct Euclidean space and uniform time, a curved space-time, a curved world, has appeared. The history of science has never known such a sharp restructuring of views on the physical fundamental principles of the universe.

Testing general relativity is difficult because, under normal laboratory conditions, its results are almost identical to those predicted by Newton's law of universal gravitation. Nevertheless, several important experiments were carried out, and their results allow us to consider the theory confirmed. In addition, general relativity helps explain the phenomena we observe in space, one example is a beam of light passing near the sun. Both Newtonian mechanics and general relativity recognize that it must deviate towards the Sun (fall). However, general relativity predicts twice the beam shift. Observations during solar eclipses proved the correctness of Einstein's prediction. Another example. The planet Mercury closest to the Sun has minor deviations from a stationary orbit, inexplicable from the point of view of classical Newtonian mechanics. But just such an orbit is given by the calculation by the GR formulas. The slowing down of time in a strong gravitational field explains the decrease in the frequency of light oscillations in the radiation of white dwarfs - stars of very high density. And in recent years, this effect has been registered in laboratory conditions. Finally, the role of general relativity in modern cosmology, the science of the structure and history of the entire universe, is very important. Many proofs of Einstein's theory of gravitation have also been found in this field of knowledge. In fact, the results predicted by general relativity differ noticeably from the results predicted by Newton's laws only in the presence of superstrong gravitational fields. This means that a full test of the general theory of relativity requires 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 for testing the theory of relativity remains one of the most important tasks of experimental physics.

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

Theory of relativity- physical theory of space-time, that is, a theory that describes the universal space-time properties of 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).

In a 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 introduced 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 should have propagated, like acoustic waves, 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 change with the speed of the observer with respect to the aether. Albert Einstein abandoned the concept of aether and assumed that all physical laws, including the speed of light, remain unchanged regardless of the speed of the observer - as experiments showed.

SRT explained how to interpret motions between different inertial frames of reference - simply put, objects that are moving at a constant speed relative to each other. Einstein explained that when two objects move 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 frames of reference are equal. He formulated two important postulates that formed the basis of a new theory of space and time, called the Special Theory of Relativity (SRT):

1. Einstein's principle of relativity - this principle was a generalization of Galileo's principle of relativity (states the same, but not for all laws of nature, but only for the laws of classical mechanics, leaving open the question of 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 carried out inside a closed IRF can determine whether it is at rest or moving uniformly and rectilinearly. Thus, all IFRs are completely equal, and physical laws are invariant with respect to the choice of IFR (ie, the equations expressing these laws have the same form in all inertial frames of reference).

2. The principle of constancy of the speed of light- the speed of light in vacuum is constant and does not depend on the movement of the 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 the data of 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 - lost their validity independent of each other and turned out to be combined into a single law, which can be called the law of conservation of energy or mass." Due to the fundamental connection between these two concepts, matter can be turned into energy, and vice versa - energy into matter.

General theory of relativity- The theory of gravity published by Einstein in 1916, which he worked on for 10 years. It is a further development of the 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 principle of equivalence plays an 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.

A number of important conclusions have been drawn from GR:

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.

For a long time, there were few experimental confirmations of general relativity. 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; the gravitational deflection of radio waves by the Sun was measured, the planets of the solar system were radar-located; 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, the special theory of 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 large masses there is a curvature of the paths of movement of light rays. 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 fundamental difference between the general theory of relativity and the fundamental physical theories preceding it is 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. On its basis, various models of the Universe have appeared.