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Einstein's theory of relativity, we explain and read in short, understandable words. General Relativity Is it Consistent? Does it match physical reality?

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 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 effects that are paradoxical and contrary to intuitive ideas about the world, arising when moving at a speed close to the speed of light, are 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 contradictory common sense they seemed to find complete and direct experimental confirmation. In one of the most revealing experiments, scientists at the University of Michigan placed ultra-precise atomic clocks on board an airliner making regular transatlantic flights, and after each return to 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 on a par with Newton's laws of 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 ordinary equations of Newton's laws, if it is applied to describe bodies moving at a speed of 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 it is the speed of light, and not some other, that plays such a role. 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 source reach 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 the stronger its gravitational force, respectively). 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.

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 many people are mistaken in their 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 we are talking 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 exclusive, 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 on the example of classical, non-relativistic mechanics - Newtonian mechanics as applied to the simplest in principle problem of the motion of some "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 an essentially similar 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. It is quite natural that 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, at the height 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. Illuminated this final stage in building the foundation of GR was 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 currently known 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 current accuracy of about ± 0″.1 / century (Einstein in his first work used less accurate data, but within the limits of error 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 of me famous biographies Einstein expresses and substantiates the opinion that the explanation of the rotation of the perihelion of Mercury was "the most powerful emotional event in the whole scientific life Einstein, and perhaps for his entire life. Yes, it was Einstein's finest hour. But just for him. For a number of reasons (it suffices 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 is (approximately at this angle an adult is visible from a distance of 200 km), it could already be measured at that time by the optical method by photographing 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 ray deflection in the solar field was established with all certainty and is in agreement with formula (2), although the accuracy of measurements due to the smallness of the effect was low. However, a deviation half 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 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. To land instruments on Mars and Venus, when flying near Phobos, etc., calculations are 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 in the location of 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 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 is accepted by A. A. Logunov 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 any 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 speeds 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 possible to obtain fields of only 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 gravity, combined with the principle of equivalence, determines the transition in general relativity from the pseudo-Euclidean geometry of Minkowski to Riemannian geometry (in this geometry, space-time has, generally speaking, a non-zero curvature; the presence of such a curvature distinguishes the “true” gravitational field from "kinematic"). Physical Features gravitational field determine, we repeat, 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. It's obvious that detailed analysis RTG is possible only on pages scientific journals. Only after such an analysis will it 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”, at present, RTG should be considered an alternative theory of gravity that needs appropriate analysis and discussion. For those who like this theory (RTG) and who are interested in it, no one hinders (and, of course, should not hinder) its development, suggesting 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 play a significant role in science, 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 last 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 full 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. B. Zeldovich and L. P. Grischuk, see footnote 5): different results in GR when using different systems coordinates are obtained only because the located planets are compared, which 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 more mass 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 the 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 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 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 .

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

In contact with

A few general questions

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

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

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

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

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

History and roots of the theory

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

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

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

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

The works of these great scientists made it possible to create the foundation for the main postulates of the doctrine. It is this fact that provides constant material for the assertion that the works of the Nobel laureate and Albert's relativistic theory were and still are plagiarism. Many scientists today argue that many postulates were accepted much earlier, for example:

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

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

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

About the theory briefly and clearly

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

Attention! In 1905, when Einstein published his theory of relativity, it allowed to explain and in an accessible way to interpret the movement between different inertial calculation systems.

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

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

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

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

Principles of the Theory of Relativity

Doctrine principles

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

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

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

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

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

Relativity for dummies

The theory of relativity is the simplest explanation

Conclusion

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

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

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

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

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

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

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

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

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

Time spans, distances, and their uniformity

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

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

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

The connection of energy with mass

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

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

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

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

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 amazing ability give equal acceleration to bodies of different masses.

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.

It was said about this theory that only three people in the world understand it, and when mathematicians tried to express in numbers what follows from it, the author himself - Albert Einstein - joked that now he had ceased to understand it.

Special and general relativity are inseparable parts of the doctrine on which modern scientific views on the structure of the world are built.

"Year of Miracles"

In 1905, Annalen der Physik (Annals of Physics), a leading German scientific publication, published one after another four articles by 26-year-old Albert Einstein, who worked as a 3rd class examiner - a petty clerk - of the Federal Office for Patenting Inventions in Bern. He had collaborated with the magazine before, but the publication of so many papers in one year was an extraordinary event. It became even more outstanding when the value of the ideas contained in each of them became clear.

In the first of the articles, thoughts were expressed about the quantum nature of light, and the processes of absorption and release of electromagnetic radiation were considered. On this basis, the photoelectric effect was first explained - the emission of electrons by matter, knocked out by photons of light, formulas were proposed for calculating the amount of energy released in this case. It is for the theoretical development of the photoelectric effect, which became the beginning of quantum mechanics, and not for the postulates of the theory of relativity, Einstein will be awarded the Nobel Prize in Physics in 1922.

In another article, the foundation was laid for applied areas of physical statistics based on the study of the Brownian motion of the smallest particles suspended in a liquid. Einstein proposed methods for searching for patterns of fluctuations - random and random deviations of physical quantities from their most probable values.

And finally, in the articles “On the electrodynamics of moving bodies” and “Does the inertia of a body depend on the energy content in it?” contained the germs of what will be designated in the history of physics as Albert Einstein's theory of relativity, or rather its first part - SRT - the special theory of relativity.

Sources and predecessors

IN late XIX For centuries, it seemed to many physicists that most of the global problems of the universe had been resolved, the main discoveries had been made, and humanity would only have to use the accumulated knowledge to powerfully accelerate technological progress. Only some theoretical inconsistencies spoiled the harmonic picture of the Universe filled with ether and living according to immutable Newtonian laws.

Harmony was spoiled by Maxwell's theoretical research. His equations, which described the interactions of electromagnetic fields, contradicted the generally accepted laws of classical mechanics. This concerned the measurement of the speed of light in dynamic reference systems, when Galileo's principle of relativity ceased to work - the mathematical model of the interaction of such systems when moving at the speed of light led to the disappearance of electromagnetic waves.

In addition, the ether, which was supposed to reconcile the simultaneous existence of particles and waves, macro and microcosm, did not yield to detection. The experiment, which was conducted in 1887 by Albert Michelson and Edward Morley, was aimed at detecting the “ethereal wind”, which inevitably had to be recorded by a unique device - an interferometer. The experiment lasted a whole year - the time of the complete revolution of the Earth around the Sun. The planet had to move against the ether flow for half a year, the ether had to “blow into the sails” of the Earth for half a year, but the result was zero: no displacement of light waves under the influence of the ether was found, which cast doubt on the very existence of the ether.

Lorentz and Poincaré

Physicists have tried to find an explanation for the results of experiments to detect the ether. Hendrik Lorentz (1853-1928) proposed his mathematical model. It brought back to life the ethereal filling of space, but only under a very conditional and artificial assumption that when moving through the ether, objects can contract in the direction of movement. This model was finalized by the great Henri Poincaré (1854-1912).

In the works of these two scientists, for the first time, concepts appeared that largely constituted the main postulates of the theory of relativity, and this does not allow Einstein's accusations of plagiarism to subside. These include the conditionality of the concept of simultaneity, the hypothesis of the constancy of the speed of light. Poincaré admitted that high speeds Newton's laws of mechanics need to be revised, he made a conclusion about the relativity of motion, but in application to the ethereal theory.

Special Relativity - SRT

Problems of a correct description of electromagnetic processes became the motivation for choosing a topic for theoretical developments, and Einstein's articles published in 1905 contained an interpretation of a particular case - uniform and rectilinear motion. By 1915, the general theory of relativity was formed, which explained the interactions and gravitational interactions, but the first was the theory, called the special one.

Einstein's special theory of relativity can be summarized in two basic postulates. The first extends the effect of Galileo's principle of relativity to all physical phenomena, and not just to mechanical processes. In more general form it states: All physical laws are the same for all inertial (moving uniformly rectilinearly or at rest) frames of reference.

The second statement, which contains the special theory of relativity: the speed of propagation of light in vacuum for all inertial frames of reference is the same. Further, a more global conclusion is made: the speed of light is the maximum value of the transmission rate of interactions in nature.

In the mathematical calculations of SRT, the formula E=mc² is given, which has appeared in physical publications before, but it was thanks to Einstein that it became the most famous and popular in the history of science. The conclusion about the equivalence of mass and energy is the most revolutionary formula of the theory of relativity. The concept that any object with mass contains a huge amount of energy became the basis for developments in the use of nuclear energy and, above all, led to the appearance of the atomic bomb.

Effects of special relativity

Several consequences follow from SRT, which are called relativistic (relativity English - relativity) effects. Time dilation is one of the most striking. Its essence is that in a moving frame of reference time passes more slowly. Calculations show that for spaceship, who made a hypothetical flight to the star system Alpha Centauri and back at a speed of 0.95 c (c is the speed of light) will take 7.3 years, and on Earth - 12 years. Such examples are often given when explaining the theory of relativity for dummies, as well as the related twin paradox.

Another effect is the reduction of linear dimensions, that is, from the point of view of the observer, objects moving relative to him at a speed close to c will have smaller linear dimensions in the direction of travel than their own length. This effect predicted by relativistic physics is called the Lorentz contraction.

According to the laws of relativistic kinematics, the mass of a moving object is greater than the rest mass. This effect becomes especially significant in the development of instruments for the study of elementary particles - it is difficult to imagine the operation of the LHC (Large Hadron Collider) without taking it into account.

space-time

One of critical components SRT is a graphical representation of relativistic kinematics, a special concept of a single space-time, which was proposed by the German mathematician Hermann Minkowski, who at one time was a teacher of mathematics to student Albert Einstein.

The essence of the Minkowski model lies in a completely new approach to determining the position of interacting objects. The special theory of relativity of time pays special attention. Time becomes not just the fourth coordinate of the classical three-dimensional coordinate system, time is not an absolute value, but an inseparable characteristic of space, which takes the form of a space-time continuum, graphically expressed as a cone, in which all interactions take place.

Such a space in the theory of relativity, with its development to a more general character, was later subjected to further curvature, which made such a model suitable for describing gravitational interactions as well.

Further development of the theory

SRT did not immediately find understanding among physicists, but gradually it became the main tool for describing the world, especially the world of elementary particles, which became the main subject of study of physical science. But the task of supplementing SRT with an explanation of gravitational forces was very relevant, and Einstein did not stop working, honing the principles of the general theory of relativity - GR. The mathematical processing of these principles took quite a long time - about 11 years, and specialists from the fields of exact sciences adjacent to physics took part in it.

Thus, the leading mathematician of that time, David Hilbert (1862-1943), who became one of the co-authors of the equations of the gravitational field, made a huge contribution. They were the last stone in the construction of a beautiful building, which received the name - the general theory of relativity, or GR.

General relativity - GR

The modern theory of the gravitational field, the theory of the "space-time" structure, the geometry of "space-time", the law of physical interactions in non-inertial frames of reference - all these are the various names that Albert Einstein's general theory of relativity is endowed with.

The theory of universal gravitation, which for a long time determined the views of physical science on gravity, on the interactions of objects and fields of various sizes. Paradoxically, but its main drawback was the intangibility, illusory, mathematical nature of its essence. There was a void between the stars and planets, the attraction between celestial bodies was explained by the long-range action of certain forces, and instantaneous ones. Albert Einstein's general theory of relativity filled gravity with physical content, presented it as a direct contact of various material objects.

The geometry of gravity

The main idea with which Einstein explained gravitational interactions is very simple. He declares the physical expression of the forces of gravity to be space-time, endowed with quite tangible features - metrics and deformations, which are influenced by the mass of the object around which such curvatures are formed. At one time, Einstein was even credited with calls to return to the theory of the universe the concept of ether, as an elastic material medium that fills space. He also explained that it was difficult for him to call a substance that has many qualities that can be described as a vacuum.

Thus, gravity is a manifestation of the geometric properties of four-dimensional space-time, which was designated in SRT as non-curved, but in more general cases it is endowed with curvature that determines the movement of material objects, which are given the same acceleration in accordance with the principle of equivalence declared by Einstein.

This fundamental principle The theory of relativity explains many of the "bottlenecks" of the Newtonian theory of universal gravitation: the curvature of light observed when it passes near massive space objects during some astronomical phenomena and, noted by the ancients, the same acceleration of the fall of bodies, regardless of their mass.

Modeling the curvature of space

A common example that explains the general theory of relativity for dummies is the representation of space-time in the form of a trampoline - an elastic thin membrane on which objects (most often balls) are laid out, imitating interacting objects. Heavy balls bend the membrane, forming a funnel around them. A smaller ball launched on the surface moves in full accordance with the laws of gravity, gradually rolling into the depressions formed by more massive objects.

But this example is rather arbitrary. The real space-time is multidimensional, its curvature also does not look so elementary, but the principle of the formation of gravitational interaction and the essence of the theory of relativity become clear. In any case, a hypothesis that would more logically and coherently explain the theory of gravity does not yet exist.

Proofs of Truth

General relativity quickly came to be seen as a powerful foundation upon which modern physics could be built. The theory of relativity from the very beginning struck with its harmony and harmony, and not only specialists, and soon after its appearance began to be confirmed by observations.

The closest point to the Sun - the perihelion - of Mercury's orbit is gradually shifting relative to the orbits of other planets in the solar system, which was discovered back in the middle of the 19th century. Such a movement - precession - did not find a reasonable explanation within the framework of Newton's theory of universal gravitation, but was calculated with accuracy on the basis of the general theory of relativity.

The solar eclipse that occurred in 1919 provided an opportunity for yet another proof of general relativity. Arthur Eddington, who jokingly called himself the second person out of three who understand the basics of the theory of relativity, confirmed the deviations predicted by Einstein during the passage of photons of light near the star: at the time of the eclipse, a shift in the apparent position of some stars became noticeable.

The experiment to detect clock slowdown or gravitational redshift was proposed by Einstein himself, among other proofs of general relativity. Only after many years was it possible to prepare the necessary experimental equipment and conduct this experiment. The gravitational frequency shift of radiation from the emitter and receiver, spaced apart in height, turned out to be within the limits predicted by general relativity, and Harvard physicists Robert Pound and Glen Rebka, who conducted this experiment, further only increased the accuracy of measurements, and the formula of the theory of relativity again turned out to be correct.

In substantiation of the most significant research projects outer space Einstein's theory of relativity is a must. Briefly, we can say that it has become an engineering tool for specialists, in particular those involved in satellite navigation systems - GPS, GLONASS, etc. It is impossible to calculate the coordinates of an object with the required accuracy, even in a relatively small space, without taking into account the slowdowns of signals predicted by general relativity. Especially if we are talking about objects spaced apart by cosmic distances, where the error in navigation can be huge.

Creator of the theory of relativity

Albert Einstein was still a young man when he published the foundations of the theory of relativity. Subsequently, its shortcomings and inconsistencies became clear to him. In particular, the main problem General relativity became the impossibility of its growing into quantum mechanics, since the description of gravitational interactions uses principles that are radically different from each other. IN quantum mechanics the interaction of objects in a single space-time is considered, and according to Einstein, this space itself forms gravity.

Writing the "formula of everything that exists" - a unified field theory that would eliminate the contradictions of general relativity and quantum physics - was Einstein's goal for for long years, he worked on this theory until the last hour, but did not achieve success. The problems of general relativity have become a stimulus for many theorists in the search for more perfect models of the world. This is how string theories, loop quantum gravity and many others appeared.

The personality of the author of general relativity left a mark in history comparable to the importance for science of the theory of relativity itself. She does not leave indifferent so far. Einstein himself wondered why so much attention was paid to him and his work by people who had nothing to do with physics. Thanks to his personal qualities, famous wit, active political position and even expressive appearance, Einstein became the most famous physicist on Earth, the hero of many books, films and computer games.

The end of his life is described dramatically by many: he was lonely, considered himself responsible for the appearance of terrible weapon, which became a threat to all life on the planet, his unified field theory remained an unrealistic dream, but the best result can be considered the words of Einstein, spoken shortly before his death, that he completed his task on Earth. It's hard to argue with this.

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