This world was shrouded in deep darkness.
Let there be light! And here comes Newton.
18th century epigram

But Satan did not wait long for revenge.
Einstein came - and everything was as before.
Epigram of the 20th century

Postulates of the theory of relativity

Postulate (axiom)- a fundamental statement underlying the theory and accepted without proof.

First postulate: all the laws of physics that describe any physical phenomena, should have the same form in all inertial frames of reference.

The same postulate can be formulated differently: in any inertial reference frames, all physical phenomena under the same initial conditions proceed in the same way.

Second postulate: in all inertial frames of reference, the speed of light in vacuum is the same and does not depend on the speed of movement of both the source and the light receiver. This speed is the limiting speed of all processes and movements accompanied by energy transfer.

The law of the relationship of mass and energy

Relativistic mechanics- a branch of mechanics that studies the laws of motion of bodies with velocities close to the speed of light.

Any body, due to the fact of its existence, has an energy that is proportional to the rest mass.

What is the theory of relativity (video)

Consequences of the theory of relativity

The relativity of simultaneity. Simultaneity of two events is relative. If events occurring at different points are simultaneous in one inertial frame of reference, then they may not be simultaneous in other inertial frames of reference.

Length reduction. The length of the body, measured in the reference frame K", in which it is at rest, is greater than the length in the reference frame K, relative to which K" moves with a speed v along the Ox axis:

Time slowdown. The time interval measured by the clock, which is stationary in the inertial frame of reference K", is less than the time interval measured in the inertial frame of reference K, relative to which K" is moving at a speed v:

Theory of relativity

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

Relativity

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

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

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

Another well-known consequence of the theory of relativity is the equivalence of mass and energy, expressed by the famous Einstein equation E = mc2 (where E is energy, m is the mass of the body, c is the speed of light). In view of the equivalence of energy and mass, the kinetic energy that a material object possesses by virtue of its motion increases its mass. In other words, the object becomes more difficult to overclock.

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

curved space

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

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

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

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

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

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

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

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

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

Time slowdown

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

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

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

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

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

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

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

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

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

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

Time around a black hole

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

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

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

The special theory of relativity, created in 1905 by A. Einstein, was the result of a generalization and synthesis of the classical mechanics of Galileo - Newton and electrodynamics of Maxwell - Lorentz. “She describes the laws of all physical processes at speeds close to the speed of light, but without taking into account the gravitational field. With a decrease in the speed of motion, it reduces to classical mechanics, which, therefore, turns out to be its special case. one

The starting point of this theory was the principle of relativity. The classical principle of relativity was formulated by G. Galileo: “If the laws of mechanics are valid in one coordinate system, then they are valid in any other system moving rectilinearly and uniformly relative to the first one.” 2 Such systems are called inertial, because the movement in them obeys the law of inertia: “Every body retains a state of rest or uniform rectilinear motion, unless it is forced to change it under the influence of moving forces.” 3

It follows from the principle of relativity that there is no fundamental difference between rest and motion - if it is uniform and rectilinear. The difference is only in the point of view.

Thus, the word "relatively" in the name of Galileo's principle does not hide anything special in itself. It has no other meaning than that which we put into motion, that motion or rest is always motion or rest relative to something that serves us as a frame of reference. This, of course, does not mean that there is no difference between rest and uniform motion. But the concepts of rest and movement acquire meaning only when a reference point is indicated.

If the classical principle of relativity asserted the invariance of the laws of mechanics in all inertial frames of reference, then in the special theory of relativity this principle was also extended to the laws of electrodynamics, and the general theory of relativity asserted the invariance of the laws of nature in any frames of reference, both inertial and non-inertial. Non-inertial reference systems are called, moving with deceleration or acceleration.

In accordance with the special theory of relativity, which combines space and time into a single four-dimensional space-time continuum, the space-time properties of bodies depend on the speed of their movement. Spatial dimensions are reduced in the direction of motion when the speed of bodies approaches the speed of light in vacuum (300,000 km/s), time processes slow down in fast-moving systems, and body mass increases.

Being in a comoving reference frame, that is, moving parallel and at the same distance from the measured frame, one cannot notice these effects, which are called relativistic, since all spatial scales and parts used in measurements will change in exactly the same way. According to the principle of relativity, all processes in inertial frames of reference proceed in the same way. But if the system is non-inertial, then relativistic effects can be noticed and changed. So, if an imaginary relativistic ship like a photon rocket goes to distant stars, then after its return to Earth, the time in the ship’s system will pass significantly less than on Earth, and this difference will be the greater, the farther the flight is made, and the speed of the ship will be closer to the speed of light. The difference can even be measured in hundreds and thousands of years, as a result of which the crew of the ship will immediately be transported to the near or distant future, bypassing the intermediate time, since the rocket, along with the crew, fell out of the course of development on Earth.

Similar processes of slowing down the passage of time depending on the speed of movement are actually recorded now in measurements of the length of the path of mesons arising from the collision of particles of primary cosmic radiation with the nuclei of atoms on Earth. Mesons exist for 10 -6 - 10 -15 s (depending on the type of particles) and after their appearance they decay at a small distance from the place of birth. All this can be registered by measuring devices on traces of particle runs. But if the meson moves at a speed close to the speed of light, then the time processes in it slow down, the decay period increases (by thousands and tens of thousands of times), and the path length from birth to decay increases accordingly.

So, the special theory of relativity is based on Galileo's extended principle of relativity. In addition, it uses another new position: the speed of light propagation (in vacuum) is the same in all inertial frames of reference.

But why is this speed so important that the judgment about it is equated in value with the principle of relativity? The fact is that we are confronted here with the second universal physical constant. The speed of light is the largest of all speeds in nature, the limiting speed of physical interactions. The movement of light is fundamentally different from the movement of all other bodies, the speed of which is less than the speed of light. The speed of these bodies always adds up with other speeds. In this sense, the speeds are relative: their magnitude depends on the point of view. And the speed of light does not add up with other speeds, it is absolute, always the same, and, speaking of it, we do not need to specify the frame of reference.

The absoluteness of the speed of light does not contradict the principle of relativity and is fully compatible with it. The constancy of this speed is a law of nature, and therefore - precisely in accordance with the principle of relativity - it is valid in all inertial frames of reference.

The speed of light is upper limit for the speed of movement of any bodies in nature, for the speed of propagation of any waves, any signals. It is maximum - this is an absolute speed record.

“For all physical processes, the speed of light has the property of infinite speed. In order to give a body a speed equal to the speed of light, an infinite amount of energy is required, and that is why it is physically impossible for any body to reach this speed. This result was confirmed by measurements that were carried out on electrons. The kinetic energy of a point mass grows faster than the square of its speed, and becomes infinite for a speed equal to the speed of light” 1 . Therefore, it is often said that the speed of light is the limiting speed of information transfer. And the ultimate speed of any physical interactions, and indeed of all conceivable interactions in the world.

Closely related to the speed of light is the solution to the problem of simultaneity, which also turns out to be relative, that is, depending on the point of view. In classical mechanics, which considered time to be absolute, simultaneity is also absolute.

In the general theory of relativity, new aspects of the dependence of space-time relations on material processes were revealed. This theory summed up the physical foundations for non-Euclidean geometries and connected the curvature of space and the deviation of its metric from the Euclidean one with the action of gravitational fields created by the masses of bodies. The general theory of relativity proceeds from the principle of equivalence of inertial and gravitational masses, the quantitative equality of which was established long ago in classical physics. The kinematic effects arising under the action of gravitational forces are equivalent to the effects arising under the action of acceleration. So, if a rocket takes off with an acceleration of 2g, then the rocket crew will feel as if they are in twice the Earth's gravity field. It was on the basis of the principle of equivalence of masses that the principle of relativity was generalized, which asserts in the general theory of relativity the invariance of the laws of nature in any frames of reference, both inertial and non-inertial.

How can one imagine the curvature of space that general relativity speaks of? Let's imagine a very thin sheet of rubber, and we will consider that this is a model of space. Let's place on this sheet large and small balls - models of stars. These balls will bend the rubber sheet the more, the greater the mass of the ball. This clearly demonstrates the dependence of the curvature of space on the mass of the body and also shows that the usual Euclidean geometry does not work in this case (the geometries of Lobachevsky and Riemann work).

The theory of relativity established not only the curvature of space under the influence of gravitational fields, but also the slowing down of time in strong gravitational fields. Even the gravity of the Sun - a rather small star by cosmic standards - affects the rate of time passing, slowing it down near itself. Therefore, if we send a radio signal to some point, the path to which passes near the Sun, the journey of the radio signal in this case will take longer than when there is nothing in the way of this signal. The deceleration near the Sun is about 0.0002 s.

One of the most fantastic predictions of general relativity is the complete stoppage of time in a very strong gravitational field. The slowing down of time is the greater, the stronger the gravity. Time dilation is manifested in the gravitational redshift of light: the stronger the gravitation, the more the wavelength increases and its frequency decreases. Under certain conditions, the wavelength can tend to infinity, and its frequency - to zero.

With the light emitted by the Sun, this could happen if our luminary were suddenly compressed and turned into a ball with a radius of 3 km or less (the radius of the Sun is 700,000 km). Because of this contraction, the gravitational force on the surface, where the light comes from, increases so much that the gravitational redshift turns out to be truly infinite.

With our Sun, this will never actually happen. But other stars, whose masses are three or more times the mass of the Sun, at the end of their lives and really experience, most likely, a rapid catastrophic compression under the influence of their own gravity. This will lead them to the state of a black hole. A black hole is a physical body that creates such a strong gravity that the redshift for light emitted near it can go to infinity.

Physicists and astronomers are absolutely sure that black holes exist in nature, although so far they have not been detected. The difficulties of astronomical searches are connected with the very nature of these unusual objects. After all, the infinite redshift, due to which the frequency of the received light vanishes, makes them simply invisible. They do not shine, and therefore in the full sense of the word they are black. Only by a number of indirect signs can we hope to notice a black hole, for example, in a binary star system, where an ordinary star would be its partner. From observations of the movement of a visible star in the general gravitational field of such a pair, it would be possible to estimate the mass of an invisible star, and if this value exceeds the mass of the Sun by three or more times, it will be possible to assert that we have found a black hole.

Now there are several well-studied binary systems in which the mass of the invisible partner is estimated at 5 or even 8 solar masses. Most likely, these are black holes, but astronomers prefer to call these objects candidates for black holes until these estimates are refined.

Gravitational time dilation, measured and evidenced by redshift, is very significant near a neutron star, and near a black hole, near its gravitational radius, it is so great that time seems to freeze there.

For a body falling into the gravitational field of a black hole formed by a mass equal to 3 solar masses, the fall from a distance of 1 million km to the gravitational radius takes only about an hour. But according to the clock that rests far from the black hole, the free fall of the body in its field will stretch in time to infinity. The closer the falling body is to the gravitational radius, the slower this flight will appear to a distant observer. A body observed from afar will approach the gravitational radius indefinitely and never reach it. This is how time slows down near a black hole. Thus, matter influences the properties of space and time.

The concepts of space and time formulated in Einstein's theory of relativity are by far the most consistent. But they are macroscopic, as they are based on the experience of studying macroscopic objects, large distances and long time intervals. When constructing theories describing the phenomena of the microcosm, this classical geometric picture, assuming the continuity of space and time (space-time continuum), was transferred to a new area without any changes. There are no experimental data that contradict the application of the theory of relativity in the microcosm. But the very development of quantum theories may require a revision of ideas about physical space and time. The developed theory of superstrings, which represents elementary particles as harmonic vibrations of these strings and links physics with geometry, proceeds from the multidimensionality of space. And this means that at a new stage in the development of science, at a new level of knowledge, we are returning to the predictions of A. Einstein in 1930: “We come to a strange conclusion: now it begins to seem to us that space plays the primary role, while matter must be obtained from space, so to speak, in the next step. We have always regarded matter as primary and space as secondary. Space, figuratively speaking, is now taking revenge and “eats” matter” 1 . Perhaps there is a quantum of space, a fundamental length L. By introducing this concept, we can avoid many of the difficulties of modern quantum theories. If its existence is confirmed, then L will become the third (besides Planck's constant and the speed of light in a vacuum) fundamental constant in physics. The existence of a quantum of space also implies the existence of a quantum of time (equal to L/c), which limits the accuracy of determining time intervals.

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, 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. special theory 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 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 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 it is the speed of light, and not some other, that 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 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 like special case special 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.

Law gravity Newton 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.

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 in terms 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 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 dogmas. 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, physical theory must be adequate to physical reality, or, more simply, 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 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 finest hour» Einstein. 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 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 scientific 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, 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. supporter of the usual modern theory 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 gravitational field of the Earth cannot be made 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 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 differential equations RTGs satisfy the GR equations, but, according to the authors of 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 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 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 elementary particles And atomic nucleus”, vol. 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 measurement accuracy gravitational curvature rays until recently was low. 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 .

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

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

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

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

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

Clifford Will, theoretical physicist, University of Florida

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

A new look at gravity

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

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

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

Testing Einstein's Theory

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

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

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

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

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

Clifford Will

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

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

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

unified theory

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

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

Why are these experiments needed at all?

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

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

Who would have thought that a small postal clerk would changefoundations of science of its time? But this happened! Einstein's theory of relativity forced us to reconsider the usual view of the structure of the Universe and opened up new areas of scientific knowledge.

Majority scientific discoveries done by experiment: scientists repeated their experiments many times to be sure of their results. The work was usually carried out in universities or research laboratories of large companies.

Albert Einstein completely changed the scientific picture of the world without conducting a single practical experiment. His only tools were paper and pen, and he did all his experiments in his head.

moving light

(1879-1955) based all his conclusions on the results of a "thought experiment". These experiments could only be done in the imagination.

The speeds of all moving bodies are relative. This means that all objects move or remain stationary only relative to some other object. For example, a man, motionless relative to the Earth, at the same time rotates with the Earth around the Sun. Or suppose that a person is walking along the carriage of a moving train in the direction of movement at a speed of 3 km / h. The train is moving at a speed of 60 km/h. Relative to a stationary observer on the ground, the speed of a person will be 63 km / h - the speed of a person plus the speed of a train. If he went against the movement, then his speed relative to a stationary observer would be equal to 57 km / h.

Einstein argued that the speed of light cannot be discussed in this way. The speed of light is always constant, regardless of whether the light source is approaching you, receding from you, or standing still.

The faster the less

From the very beginning, Einstein made some surprising assumptions. He argued that if the speed of an object approaches the speed of light, its dimensions decrease, while its mass, on the contrary, increases. No body can be accelerated to a speed equal to or greater than the speed of light.

His other conclusion was even more surprising and seemed to be contrary to common sense. Imagine that of two twins, one remained on Earth, while the other traveled through space at a speed close to the speed of light. 70 years have passed since the launch on Earth. According to Einstein's theory, time flows more slowly on board the ship, and only ten years have passed there, for example. It turns out that one of the twins who remained on Earth became sixty years older than the second. This effect is called " twin paradox". It sounds incredible, but laboratory experiments have confirmed that time dilation at speeds close to the speed of light really exists.

Merciless withdrawal

Einstein's theory also includes the famous formula E=mc 2, where E is energy, m is mass, and c is the speed of light. Einstein claimed that mass can be converted into pure energy. As a result of the application of this discovery in practical life, atomic energy and the nuclear bomb appeared.

Einstein was a theorist. The experiments that were supposed to prove the correctness of his theory, he left to others. Many of these experiments could not be done until sufficiently accurate measuring instruments were available.

Facts and events

• The following experiment was carried out: an airplane, on which a very accurate clock was set, took off and, having flown around the Earth at high speed, sank at the same point. The clock on board the aircraft was a tiny fraction of a second behind the clock that remained on Earth.
• If a ball is dropped in an elevator falling with free fall acceleration, then the ball will not fall, but, as it were, will hang in the air. This is because the ball and the elevator are falling at the same speed.
• Einstein proved that gravity affects the geometric properties of space-time, which in turn affects the movement of bodies in this space. So, two bodies that started moving parallel to each other will eventually meet at one point.

Curving time and space

Ten years later, in 1915-1916, Einstein built new theory gravity, which he named general relativity. He argued that acceleration (change in speed) acts on bodies in the same way as the force of gravity. The astronaut cannot determine by his sensations whether he is attracted big planet, or the rocket began to slow down.

If the spacecraft accelerates to a speed close to the speed of light, then the clock on it slows down. The faster the ship moves, the slower the clock runs.

Its differences from the Newtonian theory of gravity are manifested in the study of space objects with a huge mass, such as planets or stars. Experiments have confirmed the curvature of light rays passing near bodies with a large mass. In principle, such a strong gravitational field is possible that light cannot go beyond it. This phenomenon is called " black hole". "Black holes" appear to have been found in some star systems.

Newton argued that the orbits of the planets around the Sun are fixed. Einstein's theory predicts a slow additional rotation of the orbits of the planets associated with the presence of the gravitational field of the Sun. The prediction was confirmed experimentally. It was truly a milestone discovery. Sir Isaac Newton's law of universal gravitation was amended.

Beginning of the arms race

Einstein's work gave the key to many of the mysteries of nature. They influenced the development of many branches of physics, from elementary particle physics to astronomy - the science of the structure of the universe.

Einstein in his life was engaged not only in theory. In 1914 he became director of the Institute of Physics in Berlin. In 1933, when the Nazis came to power in Germany, he, as a Jew, had to leave this country. He moved to the USA.

In 1939, despite being opposed to the war, Einstein wrote a letter to President Roosevelt warning him that it was possible to make a bomb with a huge destructive force, and that Nazi Germany had already started developing such a bomb. The President gave the order to start work. This marked the beginning of an arms race.