General theory of relativity. The principle of movement along geodetic lines

A 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 fundamental property of spacetime. He presented a series of equations that described the effect of the curvature of spacetime on the energy and motion of the matter and radiation present in it.

A hundred years later, the general theory of relativity (GTR) became the basis for the construction of modern science, it withstood all the tests with which scientists attacked it.

But until recently it was impossible to conduct experiments under extreme conditions to test the theory's stability.

It's amazing how strong the theory of relativity has proven to be in 100 years. We still use 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 you put a heavy bowling ball 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 inside, not even light. Based on the theory, evidence was found for the generally accepted opinion today that the Universe is expanding and accelerating.

General 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 relies on the effect of subtle changes in radiation bent by the gravitational field of the star around which the planet orbits.

Testing Einstein's theory

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

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

A cosmic fireworks display of this magnitude would only reflect 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 located a meter apart on Earth by one thousandth 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 of detecting gravitational waves in the next two years.

Clifford Will

The Laser Interferometer 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 spacetime ripples pass through the detectors, they stretch and compress space, causing the detector to change dimensions. And LIGO can measure them.

LIGO began a series of launches in 2002, but failed to achieve results. Improvements were made in 2010, and the organization's successor, Advanced LIGO, should be operational 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 must continue to search for evidence of general relativity in order to be sure that it is correct.

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 connect together Einstein’s research, that is, the science of the macrocosm, and quantum mechanics, the reality of the smallest objects.

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

At a speech on April 27, 1900 at the Royal Institution of Great Britain, Lord Kelvin said: “Theoretical physics is a harmonious and complete edifice. In the clear sky of physics there are only two small clouds - the constancy of the speed of light and the curve of radiation intensity depending on the wavelength. I think that these two particular questions will soon be resolved and physicists of the 20th century will have nothing left to do.” Lord Kelvin turned out to be absolutely right in indicating the key areas of research in physics, but did not correctly assess their importance: the theory of relativity and quantum theory that emerged from them turned out to be endless fields of research that have occupied scientific minds for more than a hundred years.

Since it did not describe gravitational interaction, Einstein, soon after its completion, began to develop a general version of this theory, the creation of which he spent 1907-1915. The theory was beautiful in its simplicity and consistency with natural phenomena, except for one thing: at the time Einstein compiled the theory, the expansion of the Universe and even the existence of other galaxies were not yet known, therefore scientists of that time believed that the Universe existed indefinitely and was stationary. At the same time, it followed from Newton’s law of universal gravitation that the fixed stars should at some point simply be pulled together to one point.

Not finding a better explanation for this phenomenon, Einstein introduced into his equations , which compensated numerically and thus allowed the stationary Universe to exist without violating the laws of physics. Subsequently, Einstein began to consider the introduction of the cosmological constant into his equations as his biggest mistake, since it was not necessary for the theory and was not confirmed by anything other than the seemingly stationary Universe at that time. And in 1965, cosmic microwave background radiation was discovered, which meant that the Universe had a beginning and the constant in Einstein’s equations turned out to be completely unnecessary. Nevertheless, the cosmological constant was nevertheless found in 1998: according to data obtained by the Hubble telescope, distant galaxies did not slow down their expansion due to gravitational attraction, but even accelerated their expansion.

Basic theory

In addition to the basic postulates of the special theory of relativity, something new was added here: Newtonian mechanics gave a numerical assessment of the gravitational interaction of material bodies, but did not explain the physics of this process. Einstein managed to describe this through the curvature of 4-dimensional space-time by a massive body: the body creates a disturbance around itself, as a result of which surrounding bodies begin to move along geodesic lines (examples of such lines are the lines of the earth's latitude and longitude, which to an internal observer seem to be straight lines , but in reality they are slightly curved). The rays of light also bend in the same way, which distorts the visible picture behind the massive object. With a successful coincidence of the positions and masses of objects, this leads to (when the curvature of space-time acts as a huge lens, making the source of distant light much brighter). If the parameters do not match perfectly, this can lead to the formation of an “Einstein cross” or “Einstein circle” in astronomical images of distant objects.

Among the predictions of the theory there was also gravitational time dilation (which, when approaching a massive object, acted on the body in the same way as time dilation due to acceleration), gravitational (when a beam of light emitted by a massive body goes into the red part of the spectrum as a result of its loss energy for the work function of exiting the “gravity well”), as well as gravitational waves (perturbation of space-time that is produced by any body with mass during its movement).

Status of the theory

The first confirmation of the general theory of relativity was obtained by Einstein himself in the same 1915, when it was published: the theory described with absolute accuracy the displacement of the perihelion of Mercury, which previously could not be explained using Newtonian mechanics. Since then, many other phenomena have been discovered that were predicted by the theory, but at the time of its publication were too weak to be detected. The latest such discovery to date was the discovery of gravitational waves on September 14, 2015.

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

The origin of the theory

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

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

Just something complicated

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

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

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

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

This statement is the basis of amazing logical conclusions such as slowing down and distorting time, depending on the mass and speed of the object. The plots of many science fiction films and TV series are based on this.

General theory of relativity

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

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

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

Elevator experiment

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

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

A good example

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

Gravity "demoted"

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

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

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

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

The general theory of relativity, along with the special theory of relativity, is the brilliant work of Albert Einstein, who at the beginning of the 20th century changed the way physicists looked at the world. A hundred years later, general relativity is the fundamental and most important theory of physics in the world, and together with quantum mechanics claims to be one of the two cornerstones of the “theory of everything.” The general theory of relativity describes gravity as a consequence of the curvature of space-time (united in general relativity into one whole) under the influence of mass. Thanks to general relativity, scientists have derived many constants, tested a bunch of unexplained phenomena and come up with things like black holes, dark matter and dark energy, the expansion of the Universe, the Big Bang and much more. GTR also vetoed exceeding the speed of light, thereby literally trapping us in our surroundings (the Solar System), but left a loophole in the form of wormholes - short possible paths through space-time.

A RUDN University employee and his Brazilian colleagues questioned the concept of using stable wormholes as portals to various points in space-time. The results of their research were published in Physical Review D. - a rather hackneyed cliché in science fiction. A wormhole, or “wormhole,” is a kind of tunnel that connects distant points in space, or even two universes, through the curvature of space-time.

Who would have thought that a small postal worker would changethe foundations of the science of his 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.

Most scientific discoveries are made through experiments: scientists repeat 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 carried out 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 person, motionless relative to the Earth, at the same time rotates with the Earth around the Sun. Or let’s say 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 moves 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 were walking against the traffic, then his speed relative to a stationary observer would be 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, moving away 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 size decreases, and 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 contradict 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 start on Earth. According to Einstein's theory, time flows slower on board a ship, and, for example, only ten years have passed there. It turns out that the one of the twins who remained on Earth became sixty years older than the second. This effect is called " twin paradox" It sounds simply incredible, but laboratory experiments have confirmed that time dilation at speeds close to the speed of light actually exists.

Ruthless conclusion

Einstein's theory also includes the famous formula E=mc 2, in which E is energy, m is mass, and c is the speed of light. Einstein argued 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 theoretician. He left the experiments that were supposed to prove the correctness of his theory to others. Many of these experiments could not be done until sufficiently accurate measuring instruments became available.

Facts and events

  • The following experiment was carried out: an airplane, on which a very accurate clock was installed, took off and, flying around the Earth at high speed, landed at the same point. The clocks on board the plane were a tiny fraction of a second behind the clocks on Earth.
  • If you drop a ball in an elevator falling with free fall acceleration, the ball will not fall, but will seem to hang in the air. This happens because the ball and the elevator fall 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. Thus, two bodies that begin to move parallel to each other will eventually meet at one point.

Bending time and space

Ten years later, in 1915-1916, Einstein developed a new theory of gravity, which he called general relativity. He argued that acceleration (change in speed) acts on bodies in the same way as the force of gravity. An astronaut cannot determine from his feelings whether a large planet is attracting him, or whether the rocket has begun to slow down.


If a spaceship 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 goes.

Its differences from Newton's theory of gravitation appear when studying cosmic objects with enormous mass, such as planets or stars. Experiments have confirmed the bending of light rays passing near bodies with large masses. In principle, it is possible for a gravitational field to be so strong that light cannot escape beyond it. This phenomenon is called " black hole" "Black holes" have apparently been discovered within 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. This was truly an epoch-making discovery. Sir Isaac Newton's law of universal gravitation was amended.

The beginning of the arms race

Einstein's work provided the key to many of the secrets 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 was not only concerned with theory in his life. 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, although he opposed the war, Einstein wrote a letter to President Roosevelt warning him that a bomb could be made that would have enormous destructive power, and that Nazi Germany had already begun developing such a bomb. The President gave the order to begin work. This started an arms race.