What a magnitude appears in the general theory of relativity. Everything in the world will know

The theory of relativity was represented by Albert Einstein at the beginning of the 20th century. What is its essence? Consider the highlights and understandable language. Desiccate.

The theory of relativity practically eliminated inconsistent and contradictions of the physics of the 20th century, made in the root to change the idea of \u200b\u200bthe structure of space-time and experimentally confirmed in numerous experiments and research.

Thus, TEE fell the basis of all modern fundamental physical theories. In essence, this is a mother of modern physics!

To begin with, it is worth noting that there are 2 theories of relativity:

• The special theory of relativity (service station) - considers the physical processes in uniformly moving objects.
• The general theory of relativity (OTO) describes accelerating objects and explains the origin of such a phenomenon as gravity and existence.

It is clear that the one hundred appeared earlier and in essence is part of from. About her and let's talk first.

One hundred simple words

The theory is based on the principle of relativity, according to which any laws of nature are the same relative to fixed and moving at a constant speed of tel. And of such a seemingly simple thought it follows that the speed of light (300,000 m / s in vacuum) is the same for all bodies.

For example, imagine that you were given a spacecraft from a distant future, which can fly at a huge speed. A laser gun is installed on the ships's nose, capable of shooting forward photons.

Regarding the ship, such particles fly at the speed of light, but a relatively fixed observer, they would seem to be flying faster, as both speeds are summed up.

However, it really does not happen! Third-party observer sees photons flying 300,000 m / s, as if speed spacecraft Not added to them.

It is necessary to remember: relative to any body the speed of light will be unchanged magnitude, no matter how quickly it moved.

From this, there are amazing imagination conclusions like slowing down time, longitudinal reduction and body weight dependence on speed. Read more about the most interesting consequences of the special theory of relativity, read in the article below.

The essence of the general relativity theory (OTO)

To better understand it, we need to re-combine two facts:

• We live in four-dimensional space

Space and time is the manifestations of the same essence called the "Spatio-Temporary Continum". This is a 4-dimensional space-time with the x, y, z and t coordinate axes.

We, people, are not able to perceive 4 measurements equally. In essence, we see only the projections of the present four-dimensional object on space and time.

What is interesting, the theory of relativity does not argue that the bodies change when driving. 4-dimensional objects always remain unchanged, but with the relative movement of their projection may change. And we perceive it as a slowdown in time, cutting size, etc.

• All bodies fall at a constant speed, and not accelerate

Let's spend a terrible thought experiment. Imagine that you are driving in a closed cabin of an elevator and are in a state of weightlessness.

This situation could occur only for two reasons: either you are in space, or freely fall together with the cab under the action of earthly gravity.

Without peeping out of the booth, it is absolutely impossible to distinguish two of these cases. Just in one case, you fly evenly, and in another with acceleration. You will have to guess!

Perhaps Albert Einstein himself pondered over the imaginary elevator, and he had one amazing thought: if these two cases it is impossible to distinguish, it means that the fall due to gravity is also a uniform movement. Just uniform movement is in four-dimensional space-time, but in the presence of massive bodies (for example,) it is curved and the uniform movement is projected into the usual three-dimensional space in the form of an accelerated movement.

Let's consider another simpler, although not a completely correct example of the curvature of the two-dimensional space.

It can be imagined that any massive body under it creates some-shaped funnel. Then other bodies flying by, will not be able to continue their movement in a straight line and change their trajectory according to the bends of the curved space.

By the way, if the body has not so much energy, then its movement can generally be closed.

It is worth noting that from the point of view of moving bodies, they continue to move in a straight line, because nothing they feel that it makes them turn them. They simply got into the curved space and not realizing themselves to have an indirectural trajectory.

It should be noted that 4 measurements are twisted, including time, therefore it is worth treating this analogy.

So in general Theory Relativity Gravity is not at all strength, but only a consequence of the curvature of space-time. At the moment, this theory is the working version of the origin of gravity and is perfectly consistent with the experiments.

Amazing consequences from

Light rays can beft, fluttering near massive bodies. Indeed, there are distant objects in space that "hide" after others, but the light rays are enveloped, so that the light comes to us.

According to the stronger gravity, the slower the time flows. This fact is necessarily taken into account when working GPS and GLONASS, because their satellites have an exact atomic clock that ticks a little faster than on Earth. If this fact is not taken into account, then after a day, the error of the coordinates will be 10 km.

It is thanks to Albert Einstein that you can understand where the library or store is located in the proximity.

And finally, OTO predicts the existence of black holes, around which gravity is so strong that the time close to simply stops. Therefore, the light that was in the black hole cannot leave it (reflected).

In the center of the black hole, due to the enormous gravitational compression, an object is formed with an infinitely high density, and such, it seems to be cannot.

Thus, from can lead to very contradictory conclusions, unlike, so the bulk of physicists did not fully accept it completely and continued to look for an alternative.

But a lot of things and she succeeds to predicting successfully, for example, a recent sensational discovery confirmed the theory of relativity and made again recall the great scientist with the dried language. Love science, read Vikinauka.

material from the book Stephen Hawking and Leonard Mlodinova "The shortest history of time"

Relativity

The fundamental postulate of Einstein, referred to as the principle of relativity, it says that all the laws of physics should 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 must record the same value regardless of the speed with which it approaches the light source or is removed from it.

The requirement so that all observers come together in the speed estimate forcing the concept of time. According to the theory of relativity, the observer traveling on the train, and the one that stands on the platform will differ in the estimate of the distance traveled by the light. And since the speed is the distance divided by the time, the only way for observers to come to an agreement relative to the speed of light is also to disperse in the time evaluation. In other words, the theory of relativity put an end to the idea of \u200b\u200babsolute time! It turned out that each observer should have his own measure of time and that identical hours of different observers will not necessarily show the same time.

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

Another known consequence of the theory of relativity is the equivalence of mass and energy, expressed by the famous Einstein E \u003d MC 2 equation (where E-energy, M - body weight, C - the speed of light). Due to the equivalence of energy and mass, the kinetic energy that the material object has due to its movement increases its mass. In other words, the object becomes harder to accelerate.

This effect is essential only for bodies that move at a speed close to the speed of light. For example, at a speed of 10% of the light speed, the body weight will be only 0.5% more than at rest, but at a speed that makes up 90% of the speed of light, the mass is already more than twice as long as normal. As the light approaches light, the mass of the body increases faster, so that more energy is required to accelerate it. According to the theory of relativity, the object will never be able to achieve the speed of light, since in this case its mass would have become infinite, and by virtue of the equivalence of mass and energy for this would require endless energy. That is why the theory of relativity forever carries any ordinary body to move at a speed of less light speed. Only light or other waves that do not have their own masses are capable of moving at the speed of light.

Curved space

The general theory of the relativity of Einstein is based on a revolutionary assumption that gravity is not a common force, but a consequence of the fact that space-time is not flat, as was customary to think earlier. In the general theory of relativity, the space-time is curved or twisted with a mass and energy placed in it. Bodies, similar to the Earth, are moving at curved orbits not under the action of the force, referred to as gravity.

Since the geodesic line is the shortest line between two airports, the navigations lead aircraft on such routes. For example, you could, follow the testimony of the compass, fly 5966 kilometers from New York to Madrid almost strictly to the east along the geographic parallel. But you will have to cover only 5802 kilometers, if you fly to a large circle, first northeast, and then gradually turning to the east and further to the southeast. View of these two routes on the map where ground surface distorted (represented by flat), deceptive. Moving "straight" to the east of one point to another on the surface of the globe, you actually move not in a straight line, more precisely, not by the shortest, geodesic line.

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

According to the general theory of relativity, gravitational fields must be curved light. For example, the theory predicts that near the sun rays of light should be slightly curled in its direction under the influence of the mass of the luminaries. So, the light of a distant star, it happens next to the sun, will reject a small angle, because of what the observer on the ground will see the star not entirely where it is in reality is located.

Recall that according to the main postulation special theory Relativity All physical laws are the same for all freely moving observers, regardless of their speed. Roughly speaking, the equivalence principle spreads this rule on those observers who are not free, but under the action of the gravitational field.

In sufficiently small areas of space it is impossible to judge whether you are at rest in the gravitational field or move with constant acceleration in an empty space.

Imagine that you are in the elevator in the middle of empty space. There is no gravity, no "top" and "Niza". You float freely. Then the elevator begins to move with constant acceleration. You suddenly feel weight. That is, you presses to one of the elevator walls, which is now perceived as the floor. If you take an apple and release it, it will fall on the floor. In fact, now, when you move with acceleration, inside the elevator everything will occur exactly the same way as if the lift did not move at all, but would rest in a homogeneous gravitational field. Einstein realized that, just like, being in a ride car, you can not say, it is worth it or evenly moves, and, in the elevator, you are not able to determine whether it moves with constant acceleration or is in homogeneous Gravitational field. The result of this understanding was the principle of equivalence.

The principle of equivalence and the given example of its manifestation will be fair only if the inert mass (included in Newton's second law, which determines, ka-some acceleration gives the body applied to it) and the gravitational mass (incoming Newton in conjunction, which determines the magnitude of the gravitational attraction) the essence of the same thing.

The use of einstein equivalence of inert and gravitational masses for the withdrawal of equivalence principle and, ultimately, the entire general theory of relativity is an example of a persistent and consistent development of logical conclusions in the history of human thought.

Slow time

Another prediction of the general theory of relativity is that near massive bodies, such as the Earth, should slow down the course.

Now, having acquainted with the equivalence principle, we can trace the course of the argument of Einstein, fulfilling another mental experiment, which shows why gravity affects the time. Imagine a rocket flying in space. For convenience, we assume that its body is so great that the light is required a whole second to pass along it from top to bottom. And finally, suppose that there are two observer in the rocket: one - at the top, the ceiling, the other - below, on the floor, and both are equipped with the same clocks leading the countdown of seconds.

Suppose that the upper observer, waiting for the countdown of its clock, immediately sends the lower light signal. The next time it sends the second signal. According to our conditions, one second will need each signal to reach the lower observer. Since the upper observer sends two lights with an interval in one second, the lower observer will register them with the same interval.

What will change, if in this experiment, instead of swimming freely in space, the rocket will stand on Earth, experiencing gravity? According to Newton's theory, gravity will not affect the state of affairs: if the observer will transmit signals at the top, then the observer will be at the bottom of the same interval. But the equivalence principle predicts a different development of events. What exactly, we will be able to understand if in accordance with the equivalence principle mentally replace the effect of gravity by constant acceleration. This is one of the examples of how Einstein used the equivalence principle when creating its new gravity theory.

So, suppose our rocket is accelerated. (We assume that it accelerates slowly, so that its speed is not approaching the speed of light.) Since the rocket housing moves up, the first signal will need to pass a smaller distance than before (before the acceleration), and it will arrive at the lower observer before give me a sec. If the rocket was moving at a constant speed, then the second signal would arrive exactly the same earlier, so the interval between the two signals would remain equal to one second. But at the time of the right of the second signal, due to the acceleration of the rocket, it moves faster than at the time of sending the first, so the second signal will pass a smaller distance than the first and spend even less time. The observer below, referring to his clock, will fix that the interval between signals is less than one second, and does not agree with the upper observer, which claims that he sent signals exactly across a second.

In the case of an accelerating rocket, this effect probably should not be particularly surprised. In the end, we just explained it! But remember: the equivalence principle says that the same thing happens when the rocket rests in the gravitational field. Therefore, yes, if the rocket is not accelerated, but, for example, it is standing on the starting table on the surface of the earth, the signals sent by the upper observer at the interval per second (according to its clock) will come to the lower observer with a smaller interval (by its o'clock) . That's really amazing!

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

Our biological clocks also react to changes in time. If one of the twins lives on top of the mountain, and the other - by the sea, the first will grow faster than the second. In this case, the difference in the ages will be insignificant, but it will significantly increase, since one of the twins will go on a long journey on a spacecraft, which accelerates to speed close to the light. When the wanderer returns, he will be much younger than brother left on Earth. This case is known as a paradox of twins, but he is only a paradox for those who hold on the idea of \u200b\u200babsolute time. There is no unique absolute time in the theory of relativity - for each individual there is its own measure of time, which depends on where it is and how it moves.

With the advent of ultra-precise navigation systems that receive signals from satellites, the difference in the course of hours at various heights acquired practical value. If the instrument ignored the predictions of the general theory of relativity, the error in determining the location could reach several kilometers!

The emergence of the general theory of relativity in the root changed the situation. Space and time found the status of dynamic entities. When the bodies are moved or forces, they cause curvature of space and time, and the structure of space-time, in turn, affects the movement of the bodies and the action of forces. Space and time not only affect everything that happens in the universe, but also depend on all this.

Imagine a fearless astronaut, which remains on the surface of a collapsing star during a catastrophic compression. At some point, on his clock, let's say at 11:00, the star will be squeezed to a critical radius, behind which the gravitational field is enhanced so much that it is impossible to break out of it. Now suppose that according to the instructions, the astronaut should have to send a signal to a space ship that is in orbit at some fixed distance from the center of the star. It begins to pass the signals at 10:59:58, that is, in two seconds until 11:00. What will register the crew on board the Space Ship?

Previously, having done a mental experiment with the transfer of light signals inside the rocket, we made sure that gravity slows down time and how it is stronger, the more important effect. The astronaut on the star surface is located in a stronger gravitational field than his colleagues in orbit, so one second on his clock will last longer than a second by the clock. Since the astronaut, together with the surface, moves to the center of the star, the field acting on it becomes more and stronger on it, so the intervals between its signals adopted aboard the spacecraft are constantly lengthened. This stretching time will be very insignificant until 10:59:59, so for astronauts in orbit the interval between signals passed at 10:59:58 and at 10:59:59:59, very slurred will exceed a second. But the signal sent at 11:00, the ship will not wait.

All that will happen on the star surface between 10:59:59 and 11:00 by the clock of the astronaut, it stretches on the clock of the spacecraft to the infinite period of time. With the approach to 11:00, the intervals between the arrival of consecutive ridges and the depression emitted by the star waves emitted are increasingly longer; The same happens with intervals between astronaut signals. Since the radiation frequency is determined by the number of ridges (or depression) coming in a second, an increasingly lower frequency of the star radiation will be recorded on the spacecraft. The star light will become more and more blushing and simultaneously flicker. In the end, the star will ensure that it will be made invisible for observers on a spacecraft; Everything that remains is a black hole in space. However, the action of the star on the spacecraft will continue, and it will continue to appeal in orbit.

The overall theory of relativity (from him. Allgemeine relativitätstheorie) - a geometric theory of gravity, developing special theory of relativity (STR), published by Albert Einstein in 1915-1916. As part of the general theory of relativity, as in other metric theories, it is postulated that the gravitational effects are due to non-power interaction of bodies and fields in space-time, but by deformation of the very space-time, which is connected, in particular, with the presence mass-energy. The general theory of relativity differs from other metric theories by the use of Einstein equations for the connection of the curvature of space-time with the matter present in it. According to the most successful theory of gravity, well confirmed by observations. The first success of the general theory of relativity was to explain the anomalous precession perihelion of Mercury. Then, in 1919, Arthur Eddington reported observing the deviation of light near the sun at the time of the complete eclipse, which qualitatively and quantitatively confirmed the predictions of the general theory of relativity. Since then, many other observations and experiments have confirmed a significant amount of the theory predictions, including a gravitational slowdown in time, gravitational red displacement, signal delay in the gravitational field and, so far only indirectly, gravitational radiation. In addition, numerous observations are interpreted as confirmation of one of the most mysterious and exotic predictions of the general theory of relativity - the existence of black holes. Despite the stunning success of the general theory of relativity, there is discomfort in the scientific community associated, firstly, so that it is not possible to reformulate as a classic limit of quantum theory, and secondly, so that the theory itself indicates the boundaries of its applicability, Since it predicts the emergence of unreassed physical divergences when considering black holes and in general the singularities of space-time. To solve these problems a number was proposed alternative theoriesSome of which are also quantum. Modern experimental data, however, indicate that any type of deviation from OTO should be very small if they exist at all. The value of the general theory of relativity goes far beyond the theory of gravity. In mathematics, the special theory of relativity stimulated research in the field of the theory of representations of Lorentz Groups in the Hilbert space, and the general theory of relativity stimulated research on the generalization of the Riemann geometry and the emergence of affinity differential geometry, as well as the development of the theory of continuous Liberals. The theory of relativity can be considered as an example showing as fundamental scientific discoverySometimes even contrary to the will of his author, gives rise to new fruitful areas, the development of which is happening further on their own path.
The basic principles of the general theory of relativity
The need to modify the Newtonian theory of gravity The classical theory of Newton is based on the concept of force of gravity, which is a long-range force: it acts instantly at any distance. This instantaneous nature of the action is incompatible with the concept of the field in modern physics. In the theory of relativity, no information can spread faster than the speed of light in vacuum. Mathematically, Newton's gravity force is derived from the potential energy of the body in the gravitational field. The gravity potential corresponding to this potential energy is subject to the Poisson equation, which is not invariant with Lorentz transforms. The cause of non-invariance lies in the fact that the energy in the special theory of relativity is not a scalar value, but passes into the temporary component of the 4th vector.
Vector Gravity Theory It turns out to be a similar theory electromagnetic field Maxwell and leads to the negative energy of gravitational waves, which is associated with the nature of the interaction: the eponymous charges (mass) in gravity are attracted, and not repel, as in electromagnetism.
Thus, the theory of Newton's gravity is incompatible with the fundamental principle of the special theory of relativity - the invariance of the laws of nature in any inertial reference system, and the direct vector generalization of Newton's theory, first proposed by Poincare in 1905 in its work "On the electron dynamics", leads to physically unsatisfactory results . Einstein began the search for the theory of gravity, which would be compatible with the principle of invariance of the laws of nature regarding any reference system. The result of this search was the general theory of relativity, based on the principle of identity of gravitational and inert mass.
The principle of equality of gravitational and inert masses
In nonrelativistic mechanics, there are two concepts of mass: the first one refers to the second law of Newton, and the second to the law of world community. The first mass is an inert (or inertial) - there is an attitude of the robe, acting on the body, to its acceleration. The second mass - gravitational - determines the strength of the body attraction by other bodies and its own strength of attraction. These two masses are measured, as can be seen from the description, in various experiments, therefore, they are not completely associated, and even more so - proportional to each other. However, their experimentally installed strict proportionality allows us to talk about a single mass of the body in both rope and gravitational interactions. A suitable choice of units can make these masses equal to each other. Sometimes the principle of equality of gravitational and inert masses is called the weak equivalence principle. The idea of \u200b\u200bprinciple goes back to Galilee, and in modern form, he was launched by Isaac Newton, and the equality of the masses was verified by it experimentally with the relative accuracy of 10-3. IN late XIX. A century, more subtle experiments spent the background of the Etvin, bringing the accuracy of the test of principle to 10-9. During the XX century, the experimental technique made it possible to confirm the equality of mass with the relative accuracy of 10-12-10-13 (Braginsky, Dickka, etc.).
The principle of general covariance
Mathematical equations describing the laws of nature should not change their species and be fair in transformations to any coordinate systems, that is, being covariant with respect to any coordinate transformations.
Principle of closestream
In contrast to Newtonian physics (which is based on the physical principle of long-range), the theory of relativity is based on the physical principle of closestream. According to him, the rate of transmission of causal interaction is finite and cannot exceed the speed of light in vacuo. Only such events can be causally connected, the square of the distance between which does not exceed the value, where - the speed of light, the time interval between events (separated by the time-like interval). Causal related events in the theory of relativity can be located only at the time-like lines of the Minkowski space. In the general theory of relativity, it is a line in a non-levelspace. The invariance of causal relationships in the theory of relativity is associated with the principle of closestream. If one event is the cause of another in some inertial reference system, this is true in any other inertial reference system moving relative to the first at a speed, lower speed.
Principle of causality
The principle of causality in the theory of relativity argues that any event can have a causal impact only on those events that occur later than it, and cannot have an impact on any events accounted for before it. Causality has the following properties:
. Causality is the ratio not between things, but between events.
. The condition for which the rate of causal action is finally and cannot exceed the speed of light in the vacuum uniquely determines the condition of the ability to exist with a causal connection between two events: only such events can be causally connected, the square of the distance between which in three-dimensional space does not exceed the value (separated by the time-like interval) . In the theory of relativity, the associated events are caused by the time-like lines in the Minkowski space.
. The causality of relativistic invariant, that is, two events that are a consequence and cause in one inertial reference system are a consequence and cause and in all other inertial reference systems moving relative to it at a speed of less light speed. Invariance of causality follows from the physical principle of closestream.
The principle of the smallest action
The principle of the smallest action plays an important role in the general theory of relativity. The principle of the smallest action for the free material point in the theory of relativity argues that it moves so that its global line is an extreme (minimal action) between the two predetermined world points. Its mathematical formulation: where. Of the principle of the smallest action, it is possible to obtain the equations of motion of the particle in the gravitational field. We get :. Therefore: . Here, when integrating in parts in the second, the term is taken into account that at the beginning and end of the segment of the integration. In the second member under the integral replace index index. Further: . The third dick can be written in the form. Entering crystaffel symbols :. We obtain the equation of motion of the material point in the gravitational field: the principle of the smallest action for the gravitational field and the matter for the first time the principle of the smallest action for the gravitational field and the matter was formulated by D. Hilbert. Its mathematical wording:, where - variation of the effect of matter, the energy-pulse tensor of matter, is the determinant of the matrix made up of the values \u200b\u200bof the metric tensor - the variation of the action of the gravitational field, where the scalar curvature. From here, the Einstein equations are obtained by variation.
Principle of energy conservation
The principle of energy conservation plays an important heuristic role in the theory of relativity. In a special theory of relativity, the requirement of invariating the laws of conservation of energy and pulse relative to Lorentz transformations uniquely determines the type of energy and pulse pulse. In the general theory of relativity, the law of conservation of energy-pulse is used as a heuristic principle in deriving the equations of the gravitational field. One of the assumptions in the conclusion of the equations of the gravitational field is the assumption that the law of conservation of power-pulse must be identically implemented as a consequence of the equations of the gravitational field.
Principle of movement in geodesic lines
If the gravitational mass is exactly equal to the inertial, then in the expression to accelerate the body on which only gravitational forcesBoth masses are reduced. Therefore, acceleration of the body, and therefore, its trajectory does not depend on the mass and inner structure of the body. If all the bodies in the same point of space receive the same acceleration, then this acceleration can be associated not with the properties of bodies, but with the properties of the space itself at this point. Thus, the description of the gravitational interaction between the bodies can be reduced to the description of the space-time in which the bodies are moving. It is natural to assume how Einstein did that the bodies move along inertia, that is, so that their acceleration in its own reference system is zero. The trajectories of the phone will then be geodesic lines, the theory of which was developed by mathematicians in the XIX century. The geodesic lines themselves can be found if set in space-time an analogue of the distance between two events, called the interval or global function. The interval in the three-dimensional space and one-dimensional time (in other words, in four-dimensional space-time) is set by 10 independent components of the metric tensor. These 10 numbers form a metric of space. It defines the "distance" between two infinitely close points of space-time In different directions. Geodesic lines corresponding to world lines physical telwhose speed is less than the speed of light, turn out to be the lines of the greatest one, that is, the time measured by hours, toughly fastened with the body next to this trajectory. Modern experiments confirm the movement of bodies by geodesic lines with the same accuracy as the equality of gravitational and inert mass.
Curvativity space-time
Deviation Geodesic lines near a massive body If you run two bodies from two close points parallel to each other, then in the gravitational field, they will gradually start either to get closer, or removed from each other. This effect is called the deviation of geodesic lines. A similar effect can be observed directly if you run two balls parallel to each other on the rubber membrane, which is included in the center of the massive item. The balls will disperse: the one that was closer to the subject of the membrane, will strive for the center stronger than the more remote ball. This discrepancy (deviation) is due to the curvature membrane. Similarly, in space-time, the deviation of geodesic lines (the discrepancy between the trajectories of the bodies) is associated with its curvature. The curvature of space-time is uniquely determined by its metric - metric tensor. The difference between the overall theory of relativity and alternative theories of gravity is determined in most cases precisely the method of communication between matter (bodies and fields of the rigorous nature, creating a gravitational field [clarify]) and the metric properties of space-time.
SPACE-TIME OTO and strong equivalence principle
It is often incorrect that the general theory of relativity is based on the equivalence principle of the gravitational and inertial field, which can be formulated as follows: the local physical system in the gravitational field, which is indistinguishable from the same system in accelerated (relatively an inertial reference system) reference system immersed in a flat space-time of a special theory of relativity. Sometimes the same principle postulate as
"Local justice of the special theory of relativity" or is called a "strong equivalence principle". Historically, this principle really played a big role in the establishment of the general theory of relativity and was used by Einstein in its development. However, in the final form of the theory, it is not actually contained, since the space-time both in the accelerated and in the original reference system in the special theory of relativity is non-excrailed - flat, and in the general theory of relativity it is twisted with any body and it is his curvature Causes gravitational tel. It is important to note that the main difference of space-time from the space-time service is its curvature, which is expressed by the tensor value - the lesor of curvature. In the space-time service station, this tensor is identically equal to zero and space-time is flat. For this reason, the name "General theory of relativity is not entirely correct. This theory is only one of a number of the theories of gravity considered by physicists at present, while the special theory of relativity (more precisely, its principle of space-time metricity) is a generally accepted scientific community and constitutes the cornerstone of the basis of modern physics. Nevertheless, it should be noted that none of the other developed theories of gravity, except from from, could not withstand checks with time and experiment.
The problem of the reference system.
The reference system problem occurs in OTO, since the physics in other areas of physics inertial reference systems in the spontaneous space-time are impossible. It includes the theoretical definition of a reference system (for example, a locally inertial coordinate system, normal coordinates, harmonic coordinates) and implementing it in practice by physical measuring instruments. The problem of measurements by physical devices is that only the projections of the measured values \u200b\u200bat the time-like direction can be measured, and the direct measurement of spatial projections is feasible only after the introduction of a spatial coordinate system, for example, by measuring metrics, connectivity and curvature near the world view of the observer, the package and reception of reflected light signals, or by referring to the geometric characteristics of space-time (along the light rays defined by geometry, the position of the light source is determined).
Einstein equations
Mathematical formulation of the general theory of relativity The Einstein equation is associated with each other properties of matter present in the spontaneous space-time, with its curvature. They are the simplest (most linear) among all the conceivable equations of this kind. They look like this: where - Ricci tensor, resulting from a tensor of the curvature of space-time, through a sweat of it in pairs of indices - scalar curvature, ricci tensor - cosmological constant, is a tensor of energy-pulse of matter, - the number of pi - The speed of light in vacuo, is Newton's gravitational constant. The tensor is called Einstein's tensor, and the magnitude of the gravitational constant Einstein. Here, the Greek indices run values \u200b\u200bfrom 0 to 3. Double contravariant metric tensor sets the ratio of the scope-time curvature, which uses crystaffel symbols, determined through the components of the twice covariant metric tensor, the symbol of Christoffel with one top index by definition is equal as Einstein equations are not They impose any restrictions on the coordinates used to describe the space-time, that is, they have the property of general covariance, they limit the choice of only 6 of the 10 independent components of the symmetric metric tensor - the system only from Einstein equations is undetended. Therefore, their solution is ambiguous without the introduction of some restrictions on the components of the metrics corresponding to the unique task of coordinates in the area under consideration of the space-time and called therefore usually coordinate conditions. Solving Einstein equations in conjunction with correctly selected coordinate conditions, you can find all 10 independent components of a symmetric metric tensor. This metric tensor (metric) describes the properties of space-time at this point and is used to describe the results of physical experiments. It allows you to set the square of the interval in the spontaneous space that determines the "distance" in the physical (metric) space. The symbols of Christoffel metric tensor determine the geodesic lines for which objects (trial bodies) are moving along inertia. In the simplest case of a blank space (energy-pulse tensor is zero) without lambda member, one of the solutions of Einstein equations is described by the Minkowski special theory of relativity for a long time, the question of the presence in Einstein's third member equations in the left part. The cosmological constant λ was introduced by Einstein in 1917 in the work "Cosmology issues and the general theory of relativity" in order to describe the static universe in accordance with the expansion of the Universe destroyed the philosophical and experimental foundations of its accounting in the theory of gravity. The data of modern quantitative cosmology, however, they speak in favor of the model of the universe expanding with acceleration, that is, with a positive cosmological constant. On the other hand, the value of this constant is so small, which makes it possible to not take into account it in any physical calculations, in addition to associated with astrophysics and cosmology across the clusters of galaxies and above. Einstein's most simple equations in the sense that the curvature and energy-impulse in them are only linear, and in addition, in the left part there are all the tensor values \u200b\u200bof valence 2, which can characterize space-time. They can be derived from the principle of the smallest action for the action of Einstein - Hilbert: where the designations are decrypted above, is a Lagrangian density of material fields, but gives an invariant element of the 4-volume space-time. Here is a determinant composed of the elements of the matrix twice the covariant metric tensor. The minus sign is introduced in order to show that the determinant is always negative (for the Minkowski metric it is -1). From a mathematical point of view, the Einstein equation is a system of nonlinear differential equations in private derivatives relative to the metric tensor of space-time, so the sum of their solutions is not a new solution. Approximately the linearity can be restored only in the study of small perturbations of a given space-time, for example, for weak gravitational fields, when small deviations of metric coefficients from their values \u200b\u200bfor a flat space-time and are as small as the curvature generated by them. An additional circumstance that makes it difficult to solve these equations, is that the source (energy-pulse tensor) is subject to its own set of equations - the equations of the movement of the environment, which fills in the region under consideration. Interest is the fact that the equations of motion, if there are less than four, follow from Einstein equations due to the local law of preservation of energy-impulse. This property is known as the self-consistency of Einstein equations and was first shown by D. Hilbert in his famous work "Foundations of physics." If the equations of motion are more than four, then it is necessary to solve a system from coordinate conditions, Einstein equations and equations environmentsWhat is even more difficult. That is why such importance is attached to the well-known accurate solutions of these equations. The most important accurate solutions of the Einstein equations include: Schwarzschald solution (for space-time surrounding a spherically symmetrical uncharged and non-breaking massive object), the decision of the Rissenger - Nordstraum (for a charged spherically symmetric massive object), the Kerra solution (for a rotating massive object), Kerra's solution - Newman (for a charged rotating massive object), as well as the Cosmological solution of Friedman (for the Universe as a whole) and accurate gravitational wave solutions. Among the approximated solutions it is necessary to distinguish the approximate gravitational and wave solutions of the solutions obtained by the methods of postththtymonary decomposition. The numerical solution of Einstein equations also represents the difficulties that were solved only in the 2000s, which led to the emergence of dynamically developing numerical relativity (eng.). Einstein without cosmological constant was almost simultaneously derived in November 1915 by David Hilbert (November 20, the conclusion from the principle of the smallest action) and Albert Einstein (November 25, the conclusion from the principle of general covariance of the equations of the gravitational field in combination with the local power preservation). The work of Hilbert was published later than Einsteinovskaya (1916). For priority issues, there are different opinions covered in an article about Einstein, and more fully in the "priority issues in the theory of relativity (eng.)", But Hilbert himself never claimed and considered it from the creation of Einstein.

The main consequences of the orbit of Newton (Red) and Einstein (blue) of one planet rotating around the star according to the principle of conformity, in weak gravitational fields of prediction of the OTO coincide with the results of the application of the Newtonian law of world-wide, with minor amendments that grow as the field strength increases . The first predicted and proven experimental consequences of the overall theory of relativity were the three classical effects listed below in chronological order Their first check:
1. Additional perihelium shift of the orbit of Mercury compared to the predictions of Newton's mechanics.
2. Deviation of the light beam in the gravitational field of the Sun.
3. Gravitational red shift, or slowing down the time in the gravitational field.
There are a number of other effects that are experimental verification. Among them, you can mention the deviation and delay (Shapiro effect) of electromagnetic waves in the gravitational field of the Sun and Jupiter, the effect of Lensee - Tyrarring (the precession of the gyroscope near the rotating body), astrophysical evidence of the existence of black holes, evidence of radiation of gravitational waves with close systems double stars and expansion of the universe. Until now, the reliable experimental testimonies that disprove the OTO have not been detected. Deviations of measured values \u200b\u200bof effects from predicted by OTO do not exceed 0.01% (for the above three classic phenomena). Despite this, due to various causes, theorists were developed at least 30 Alternative theories of gravity, and some of them make it possible to obtain an arbitrarily close to the results with the corresponding values \u200b\u200bof the parameters included in the theory.
Experimental confirmations from OTO
Prediction General theory of relativity.
The effects associated with the acceleration of reference systems first of these effects is a gravitational slowdown in time, due to which any clock will go the slower, the deeper in the gravitational hole (closer to the gravel body) they are located. This effect was directly confirmed in the experiment of the hafel - king, as well as in the experiment GRAVITY PROBE A. and constantly confirmed in GPS. The effect directly associated with this is a gravitational red light offset. Under this effect, it is understood to reduce the frequency of light relative to the local hours (respectively, the shift of the spectrum lines to the red end of the spectrum relative to the local scale) when the light is propagated from the gravitational hole to the outside (from the region with a smaller gravitational potential to the region with great potential). The gravitational red bias was found in the spectra of stars and the sun and is reliably confirmed already in controlled earthly conditions in the Porend and Rebb experiment.
The gravitational slowdown in time and the curvature of the space entails another effect called the Shapiro effect (also known as the gravitational signal delay). Because of this effect, the electromagnetic signals go longer than in the absence of this field. This phenomenon was detected during radar planets of the solar system and space ships passing behind the sun, as well as when observing the signals from double pulsars. With the highest accuracy for 2011 (about 7.10-9), this type of effects was measured in the experiment conducted by the Holger Muller Group from the University of California. In the experiment, the cesium atoms whose speed was directed upwards to the surface of the Earth, the action of two laser beams was translated into superposition of states with different pulses. Due to the fact that the force of gravitational exposure depends on the height above the surface of the Earth, the phases of the wave function of each of these states when returning to the starting point differed. The difference between these raids caused the interference of the atoms inside the cloud, so instead of a homogeneous distribution of atoms, alternating thickening and vacuum were observed, which were measured by the effect on the cloud of atoms with laser beams and the measurement of the probability of detection of atoms in a certain selected point of space.
Gravitational deviation of light
The most famous early check of OTO has become possible due to the total solar eclipse of 1919. Arthur Eddington showed that the visible positions of stars vary near the sun in exactly according to the predictions of the OTO. The curvature of the light path occurs in any accelerated reference system. A detailed view of the observed trajectory and gravitational effects of lenzing depend, however, from the curvature of space-time. Einstein learned about this effect in 1911, and when he was heuristic through the magnitude of the curvature of the trajectories, it turned out to be the same as it was predicted by classical mechanics for particles moving at the speed of light. In 1916, Einstein discovered that in fact, in an angular shift, the direction of the spread of light is twice as large as in Newtonian theory, in contrast to the previous consideration. Thus, this prediction has become another way to check from. Since 1919, this phenomenon has been confirmed by astronomical observations of stars in the process of the eclipse of the Sun, as well as with high accuracy checked by radio interferometric observations of quasars passing near the sun during its path by ecliptic.
Gravitational linance It occurs when one remote massive object is near or directly on the line connecting the observer with another object, much more remote. In this case, the curvature of the trajectory of light closer leads to distorting the form of a remote object, which, with a small resolution resolution, leads mainly to an increase in the total brightness of the remote object, so this phenomenon was called linzing. The first example of gravitational leinzing was obtaining two close images of the same QSO 0957 + 16 A quasar in 1979, B (Z \u003d 1.4) by English astronomers D. Walsh and others. "When it turned out that both quasar change their shine in Unison, astronomers realized that in reality these are two images of one quasar, the obliged effect of the gravitational lens. Soon found the lens itself - a distant galaxy (z \u003d 0.36), lying between the earth and quasar "\u003d. Since then, many other examples of remote galaxies and quasars affected by gravitational linlication have been found.
For example, known so-called Einstein Cross, Where the galaxy accounts for the image of a distant quasar in the form of a cross. Special type of gravitational linance is called an Einstein ring or arc. The Einstein ring occurs when the observed object is directly behind another object with a spherically symmetric field of gravity. In this case, the light from a more distant object is observed as a ring around a closer object. If the remote object is slightly displaced in one direction and / or the field is not spherically symmetric, then instead will appear partial rings called arcs. Finally, any star can increase the brightness when a compact massive object passes in front of it. In this case, the larger and distorted due to the gravitational deviation of light images of the farmer cannot be allowed (they are too close to each other), and it is observed just an increase in the brightness of the star. This effect is called microlynzing, and it is now observed regularly within the projects studying the invisible bodies of our galaxy on gravitational microlensing of light from stars - Molno \u003d, Eros (English) and others.
Black holes

Black hole artist drawing: accretion disk hot plasma rotating around a black hole. Black hole - an area bounded by the so-called event horizon, which neither matter nor information can leave. It is assumed that such areas can be formed, in particular, as the result of the collapse of massive stars. Since matterium can fall into a black hole (for example, from the interstellar medium), but it can not leave it, the mass of the black hole can only increase over time. Stephen Hawking, however, showed that black holes can lose weight due to radiation called Hawking radiation. Hawking radiation is a quantum effect that does not violate the classical from. There are many candidates for black holes, in particular a supermassive object associated with radio source Sagittarius A * in the center of our galaxy. The overwhelming majority of scientists are convinced that the observed astronomical phenomena associated with this and other similar objects reliably confirm the existence of black holes, however, there are other explanations: for example, instead of black holes are offered fermion balls, bosomous stars and other exotic objects.
Orbital effects OTO Corrects the predictions of the Newtonian theory of heavenly mechanics regarding the dynamics of gravitationally related systems: solar system, double stars, etc.
The first effect According to the perihelials of all planetary orbits will be preceded, since Newton's gravitational potential will have a small relativistic additive, leading to the formation of unclosed orbits. This prediction was the first confirmation of OTO, since the size of the precession, derived by Einstein in 1916, fully coincided with anomalous precession perihelia Mercury. Thus, the problem of heavenly mechanics known at that time was solved. Later, the relativistic precession perihelium was also observed at Venus, land, an Icar asteroid and as a stronger effect in dual pulsar systems. For the opening and study of the first double pulsar PSR B1913 + 16 in 1974 by R. Khals and D. Taylor received Nobel Prize In 1993.

Loading the arrival time of pulses from PSR B1913 + 16 pulsar compared to strictly periodic (blue dots) and predicted by the effect associated with the emission of gravitational waves (black line)
Another effect - Changing the orbit associated with the gravitational radiation of the double and more multiple system of tel. This effect is observed in systems with close stars and is to reduce the appeal period. It plays an important role in the evolution of close dual and multiple stars. The effect was first observed in the aforementioned PSR B1913 + 16 system and with an accuracy of 0.2% coincided with the predictions of the OTO.
Another effect - Geodesic precession. It represents the precession of the poles of the rotating object due to the effects of parallel transfer in the spark-time-time-time. This effect is completely absent in the Newtonian theory of gravity. The prediction of the geodesic precession was verified in the experiment with the NASA Probe "Gravity Probe B). The head of the data obtained by the probe, Francis Everitt at the plenary meeting of the American physical society on April 14, 2007, announced that the analysis of these gyroscopes allowed to confirm the predicted Einstein geodesic precession with accuracy exceeding 1%. In May 2011, the final results of the processing of these data were published: the geodesic precession was -6601.8 ± 18.3 milliseconds of the arc (MAS) per year, which within the experimentary error coincides with the predicted -6606.1 MAS / year. This effect was previously verified by the observations of the shift of the LageOS geodesic satellites; Within the errors of deviations from theoretical predictions, OTO has not been detected.
Fasting inertial reference systems
The passing of inertial reference systems of the rotating body lies in the fact that the rotating massive object "pulls" space-time towards its rotation: the remote observer at rest relative to the center of the masses of the rotating body will find that the fastest clocks (that is, resting relative to the locally inertial reference system ) At a fixed distance from the object there are hours having a motion component around the rotating object in the direction of rotation, and not those that are in peace relative to the observer, as it happens for the nonruptive massive object. In the same way, the remote observer will be found that the light moves faster in the direction of rotation of the object than against its rotation. Hobbating inertial reference systems will also cause a change in the orientation of the gyroscope in time. For a spacecraft in the polar orbit, the direction of this effect perpendicular to the geodesic precession mentioned above. Since the effect of hobbies inertial reference systems is 170 times weaker the effect of the geodesic precession, Stanford scientists have extracted its "prints" from the information obtained on a specially launched in order to measure this effect of Gravity Probe B. In May 2011, the final results of the mission were announced: the measured value of the hobbies was -37.2 ± 7.2 milliseconds of the arc (MAS) per year, which within accuracy coincides with the prediction of OTO: -39.2 MAS / year.
Other predictions
. The equivalence of inertial and gravitational mass: the consequence of the fact that the free fall is inertia. o The principle of equivalence: even the self-prompt object will respond to the external field of gravity as far as the test particle.
. Gravitational radiation: orbital movement of any gravitationally related systems (in particular, close pairs of compact stars - white dwarfs, neutron stars, black holes), as well as the processes of merge neutron stars and / or black holes, are expected to be accompanied by the emission of gravitational waves. There are indirect evidence of the existence of gravitational radiation in the form of measurements of the rate of growth of the frequency of orbital rotation of close pairs of compact stars. The effect was first observed in the aforementioned system of dual pulsar PSR B1913 + 16 and with an accuracy of 0.2% coincided with predictions from OTO.
The fusion of double pulsars and other pairs of compact stars can create gravitational waves, strong enough to be observed on Earth. For 2011, there were (or planned in the near future to build) several gravitational telescopes to observe such waves. o Gravitons. According to quantum mechanics, gravitational radiation must be made up of quanta called graviton. OTO predicts that they will be massless particles with spin equal
The detection of individual gravitons in the experiments is associated with significant problems, so that the existence of the quantum of the gravitational field so far (2015) is not shown.
Cosmology
Although the general theory of relativity was created as a theory of gravity, it soon became clear that this theory could be used to simulate the universe as a whole, and so physical cosmology appeared. Physical cosmology explores the Universe Friedman, which is a cosmological solution of Einstein equations, as well as its perturbation, giving the observed structure of astronomical metagalaxy. These decisions predict that the universe should be dynamic: it should expand, shrink or perform permanent fluctuations. Einstein first could not reconcile with the idea of \u200b\u200bthe dynamic universe, although it clearly followed Einstein equations without a cosmological member. Therefore, in an attempt to reformulate this so that the solutions described the static universe, Einstein added a cosmological constant to field equations (see above). However, the resulting static universe was unstable. Later in 1929, Edwin Habble showed that the red shift of the light from the remote galaxies indicates that they are removed from our own galaxy at a speed, which is proportional to their distance from us. This demonstrated that the universe is really unptiplined and expands. The opening of Hubble showed the failure of the views of Einstein and using the cosmological constant. The theory of the nonstationary universe (including the accounting of a cosmological member) was created, however, before the opening of the Hubble law by the efforts of Friedman, Lemeter and de Sitter. Equations describing the extension of the Universe show that it becomes singular if it is far enough to go back in time. This event is called a large explosion. In 1948, Georgy Gamov issued an article describing the processes in the early universe under the assumption of its high temperature and the predictive existence of a cosmic microwave background radiation derived from the hot blast plasma; In 1949, R. Alfer and Herman conducted more detailed calculations. In 1965, A. Penzias and R. Wilson for the first time identified relic radiation, thus confirming the theory of a large explosion and a hot early universe.
Problems OTO.
Energy
Since energy, from the point of view of mathematical physics, is a value that remains due to the homogeneity of the time, and in the general theory of relativity, unlike the special, time is inhomogeneously, the law of energy conservation can be expressed in the only locally, that is, From no such value equivalent to a hundred to the integral from her in space remained when the time moves. The local impulse energy conservation law exists and is a consequence of Einstein equations - this is the disappearance of the covariant divergence of the energy-pulse of matter: where the point with the comma refers to the capture of the covariant derivative. The transition from it to the global law is impossible, because so integrate tensor fields, except for scalar, in the Riemannian space, to obtain tensor (invariant) results, mathematically impossible. Indeed, the equation above can be rewritten so in the spinless space-time, where the second term is not equal to zero, this equation does not express any law of conservation. Many physicists consider it a significant disadvantage of OTO. On the other hand, it is obvious that if you follow the sequence to the end, in full energy, in addition to the energy of matter, it is also necessary to include the energy of the gravitational field itself. The corresponding conservation law should be recorded in the form where the value is energy-pulse of the gravitational field. It turns out that the magnitude cannot be a tensor, and is a pseudoenterzor - the value transforming as the tensor is only with linear transformations. This means that the energy of the gravitational field in principle cannot be localized (which follows from a weak equivalence principle). Various authors are introduced their pseudotenzors of the energy-pulse of the gravitational field, which have some "correct" properties, but one manifold shows that the task has no satisfactory solution. Nevertheless, the energy in OTO is always preserved in the sense that it is impossible to build an eternal engine in OTO. In general, the problem of energy and pulse can be considered solved only for island systems in OTO without a cosmological constant, that is, for such mass distributions, which are limited in space and space-time of which in the spatial infinity goes into the Minkowski space. Then, highlighting a group of asymptotic symmetry of space-time (Bondi - Saks group), one can determine the 4-vector magnitude of the system-pulse system, correctly leading itself relative to Lorentz transformations on infinity. There is an unbelried point of view, ascending to Lorentz and Levi-Civita, which determines the tensor of the energy-pulse of the gravitational field as the Einstein tensor with an accuracy of a constant multiplier. Then the Einstein equations argue that the energy-pulse of the gravitational field in any volume accurately balances the energy-pulse of matter in this volume, so that their total amount is always identically equal to zero.
OTO and quantum physics
The main problem from the current point of view is the inability to build for it a quantum field model canonically. The canonical quantization of any physical model is that the Euler - Lagrange equations are constructed in the nevantic model and the Lagrangian system is determined from which Hamiltonian H is released. Then the Hamiltonian is translated from the usual function of dynamic variables in the operator function corresponding to dynamic variables - quantity. At the same time, the physical meaning of the Hamilton operator is that its eigenvalues \u200b\u200bare the levels of energy of the system. Key feature The described procedure is that it implies the selection of the parameter - the time for which the Schredinger type equation is further composed of where - already quantum Hamiltonian, which is further solved to find the wave function. The difficulties in implementing such a program for OTO are as follows: first, the transition from the classic Hamiltonian to quantum is ambiguous, since the operators of dynamic variables do not switch together; secondly, the gravitational field refers to the type of fields with connections, for which the structure of the classical phase space is quite complex, and their quantization is impossible to be the most direct method; Thirdly, there is no pronounced direction of time, which is the difficulty in its necessary allocation and generates the problem of the interpretation of the decision. Nevertheless, the quantization program of the gravitational field was successfully solved by the 50s of the 20th century by the efforts of M. P. Bronstein, P. A. M. Dirac, Brys Devitta and other physicists. It turned out that (at least weak) the gravitational field can be considered as a quantum massless field of spin 2. Additional complexity occurred when attempting to secondary quantization of the system of the gravitational field, conducted by R. Feynman, Brys Devittite and other physicists in the 1960s after the development of quantum electrodynamics . It turned out that the field of such a high spin in three-dimensional space is not renormal about any traditional (and even unconventional) ways. Moreover, there is no reasonable determination of its energy, such that the law of conservation of energy, it would be localized and non-negative anywhere (see above the "Energy Problem" point). The resulting result remains unshakable to the present (2012). Divergence in high energies in quantum gravity, appearing in each new order by the number of loops, cannot be reduced by the introduction of any final number of renormal controls into the Hamiltonian. It is impossible and reduced renormalization to a finite number of permanent values \u200b\u200b(as it was possible to do in quantum electrodynamics with respect to the elementary electrical charge and the mass of the charged particle). To date, many theories are built, alternative from (string theory, which has been developed in the M-theory, loop quantum gravity and others), which allow quantum gravity, but they all are either not finished or have unresolved paradoxes within themselves. Also, the overwhelming majority of them have a huge disadvantage, which does not allow them to be able to talk about them as "physical theories," they are not falsified, that is, they cannot be checked experimentally.
The problem is causality
Closed time-like curve
Solutions of Einstein equations in some cases allow closed time-like lines. On the one hand, if a closed time-like line returns to the same point, from where the movement was started, it describes the arrival at the same time, which already "was", despite the fact that the time passed for an observer zero. Thus, we get along this line a closed chain of reasons and consequences - time travel. Similar problems also arise when considering solutions - passable mobbo. Perhaps such solutions demonstrate the potential to the creation of "Time Machines" and "Super Lummy Travels" in the framework of the general theory of relativity. Questions of "Physicality" of such decisions - one of the actively debaped currently. A. Einstein highly appreciated the result of closed time-like lines, first received by K. Gedelem in 1949. I believe that the article Kurt Gödel is an important contribution to the overall theory of relativity, especially in the analysis of the concept of time. At the same time, he considered closed time-like lines as interesting theoretical structures devoid of real physical meaning. It would be interesting to find out whether such decisions should be excluded from consideration on the basis of physical considerations.
The problem of singularity
In many decisions of Einstein equations, singularities are present, that is, according to one of the definitions, incomplete geodesic curves that cannot be continued. There are a number of criteria for the presence of singularities and a number of problems associated with criteria for the presence of gravitational singularities ..
Philosophical aspects of the theory of relativity
A. Einstein emphasized the importance of philosophical problems of modern physics. Nowadays, the physicist is forced to engage in philosophical problems in a much greater degree than it had to do the physicists of previous generations. This physicists force the difficulties of their own science. The philosophical basis of the theory of relativity is the episodeological principles of observability (it is forbidden to use the concepts of fundamentally unobservable objects), simplicity (all consequences of the theory should be derived from the smallest number of assumptions), unity (the idea of \u200b\u200bthe unity of knowledge and the unity of the objective world described by him is implemented in the process of generalizing the laws of nature, transition from private laws to more common in the course of the development of physics), the methodological hypotheses-deductive principle (hypotheses are formulated, including in mathematical form, and on their basis are derived from the experimental way), the ontological principle of dynamic determinism (this condition is closed physical system Definitely determines all its subsequent states) and the principle of conformity (the laws of the new physical theory with the proper value of the key characteristic parameter included in the new theory, go into the laws of the old theory).
Firstly, In the center of the entire consideration there is a question: do physically dedicated (privileged) status of motion exist in nature? ( Physical problem relativity).
Secondly, The fundamental is the following epistemological postulate: concepts and judgments make sense only inspired, since they can uniquely compare the observed facts (the requirement of the content of concepts and judgments). The entire previous experience convinces us that nature is the realization of the simplest mathematically conceived elements. There is a different, more subtle reason that plays a no less role, namely, the desire for the unity and simplicity of the prerequisites of the theory ... Belief in the existence of an external world, independent of the perceive subject, underlies all natural science. Based on the principle of observability, when creating a special theory of relativity, Einstein rejected the concept of ether and the interpretation of Michelson's experience based on Lorenz. Using the principle of simplicity, when creating a general theory of relativity, Einstein summarized the principle of relativity on non-inertial reference systems. Exercising the principle of unity, the special theory of relativity united the concepts of space and time into a single essence (four-dimensional space-time of Minkovsky), gave the laws of various industries of physics, mechanics and electrodynamics a single Lorenz-invariant form, and the general theory of relativity revealed the relationship between matter and the space geometry time, which is expressed by general counseling gravitational equations. The most striking role of the hypotheses-deductive method was manifested in the creation of a general theory of relativity. The general theory of relativity is based on the hypothesis on the geometric nature of gravity and the relationship of the geometric properties of space-time with matter. The principle of compliance plays a large heuristic role in the general theory of relativity. Based on the requirement of the transition of Einstein equations to the Poisson equation for the gravitational field of Newtonian physics, and one can determine the numerical coefficient in the right-hand side of the Einstein equations. When creating the theory of relativity on Einstein, a great influence of the work of Yuma, Mach and Kant was provided: as for me, I have to admit that I was directly or indirectly helped by the work of Yuma and Mach, the idea of \u200b\u200bthe division of logical and empirical truths was stimulated by Einstein a critical presentation analysis About space-time and causality. The criticism of the nice Newtonian concepts of space and time was influenced by Einstein's refusal of the concepts of absolute space and time in the process of creating a special theory of relativity. The thought of Kant on the independent value of logical categories regarding the experience was used by Einstein when creating a common theory of relativity. A person is committed to reliable knowledge. That is why the mission of Yum is doomed to failure. The raw material coming from the senses is the only source of our knowledge, can lead us gradually to faith and hope, but not for knowledge, and even more so by understanding patterns. Here the scene comes out Kant. The idea proposed by him, although it was unacceptable in its initial wording, meant a step forward in the decision of the Yummy dilemma: everything in knowledge, which has an empirical origin, unreliable (YUM). Consequently, if we have reliable knowledge, it should be based on pure thinking. For example, it is the case with geometric theorems and with the principle of causality. These and other types of knowledge are, so to speak, part of the means of thinking and therefore should not be first obtained from sensations (i.e. they are a priori knowledge). Currently, everything, of course, it is known that the above concepts do not have any reliability nor inner necessity that Cant attributed to them. However, the problem in the Kantian formulation is, in my opinion, the following: if we consider from a logical point of view, it turns out that in the process of thinking we, with some "base", use concepts that are not related to sensations.
Material in full

On speech on April 27, 1900, Lord Kelvin said in the Royal Institute: "Theoretical physics is a slim and finished building. On the clear sky of physics there are only two small clouds - this is the constancy of the speed of light and the radiation intensity curve depending on the wavelength. I think that these two private questions will soon be allowed and the physicists of the 20th century will have nothing to do. " Lord Kelvin turned out to be absolutely right with key areas of research in physics, but did not correctly appreciate their importance: the theory of relativity and quantum theory of them were endless expanses for studies that occupy the minds for more than a hundred years.

Since the gravitational interaction did not describe, Einstein shortly after its completion, began to develop a common version of this theory, for the creation of which he spent 1907-1915. The theory was excellent in its simplicity and consistency with natural phenomena, with the exception of the only moment: during the preparation of the Einstein theory, it was not yet known about expanding the universe and even the existence of other galaxies, so scientists were considered that the universe existed infinitely for a long time and was stationary. At the same time, the World of Newton's World followed that fixed stars should have been at some point to be pulled at one point.

Without finding a better explanation for this, Einstein introduced into its equations, which novelly compensated and thus allowed the stationary universe to exist without violation of the laws of physics. In the consequence, Einstein began to consider the introduction of a cosmological constant in his equations with his biggest mistake, since it was not necessary for the theory and nothing but looking at that time the stationary universe was not confirmed. And in 1965, a relic radiation was discovered, which meant that the universe had the beginning and constant in Einstein equations was not needed at all. Nevertheless, the cosmological constant was still found in 1998: according to the obtained telescope "Hubble" data, distant galaxies did not slow down their relaxation in the resulting gravity attraction, but even accelerated their split.

Basics of theory

In addition to the main postulates of the special theory of relativity, a new one was added here: Newton's mechanics gave a numerical assessment of the gravitational interaction of material bodies, but did not explain the physics of this process. Einstein was able to describe it by curvature by a massive body of 4-dimensional space-time: the body creates around himself a perturbation, as a result of which the surrounding bodies begin to move along geodesic lines (examples of such lines are the lines of earthly latitude and longitude, which for an internal observer seem straight lines. But in reality a little twisted). The rays of light are spoken in the same way, which distorts the visible picture for a massive object. With a successful coincidence of the provisions and masses of objects, this leads to (when the curvature of space-time acts as a huge lens making the source of the distant light much brighter). If the parameters do not match perfectly - this can lead to the formation of the "cross of Einstein" or "Einstein Circle" on astronomical pictures of distant objects.

Among the predictions of the theory there was also a gravitational slowdown in time, (which approached the massive object acted on the body exactly as well as a slowdown in time in a consequence of acceleration), gravitational (when the beam of light emitted with a massive body goes into the red part of the spectrum as a result of the loss of them Energy to work out from the "gravitational well"), as well as gravitational waves (the perturbation of space-time, which produces any body having a mass in the process of its movement).

Theory status

The first confirmation of the general theory of relativity was obtained by Einstein himself in the same 1915, when it was published: the theory with absolute accuracy described the displacement of the perihelion of Mercury, which before that could not be explained using Newtonian mechanics. From that moment on, many other phenomena were opened, which were predicted by theory, but at the time of its publication were too weak so that they could be thrown. The latter such discovery was at the moment the opening of gravitational waves on September 14, 2015.