The theory of relativity was proposed by the brilliant scientist Albert Einstein in 1905.

The scientist then spoke about a special case of his development.

Today this is commonly called the Special Theory of Relativity or STR. In SRT, the physical principles of uniform and linear motion are studied.

In particular, this is how light moves if there are no obstacles in its path; much of this theory is devoted to it.

At the heart of SRT, Einstein laid down two fundamental principles:

The principle of relativity. Any physical laws are the same for stationary objects and for bodies moving uniformly and rectilinearly.
The speed of light in vacuum is the same for all observers and is equal to 300,000 km/s.

The theory of relativity is testable in practice, Einstein presented evidence in the form of experimental results.

Let's look at the principles using examples.

Let's imagine that two objects are moving at constant speeds strictly in a straight line. Instead of considering their movements relative to a fixed point, Einstein proposed studying them relative to each other. For example, two trains travel on adjacent tracks at different speeds. In one you are sitting, in the other, on the contrary, is your friend. You see it, and its speed relative to your view will depend only on the difference in the speeds of the trains, but not on how fast they are traveling. At least until the trains start speeding up or turning.
They like to explain the theory of relativity using cosmic examples. This happens because the effects increase with increasing speed and distance, especially considering that light does not change its speed. In addition, in a vacuum nothing prevents the propagation of light. So, the second principle proclaims the constancy of the speed of light. If you strengthen and turn on the radiation source on a spaceship, then no matter what happens to the ship itself: it can move at high speed, hang motionless, or disappear altogether along with the emitter, the observer from the station will see the light after the same period of time for all incidents.

General theory of relativity.

From 1907 to 1916, Einstein worked on the creation of the General Theory of Relativity. This section of physics studies the movement of material bodies in general; objects can accelerate and change trajectories. The general theory of relativity combines the doctrine of space and time with the theory of gravity and establishes dependencies between them. Another name is also known: the geometric theory of gravity. The general theory of relativity is based on the conclusions of special relativity. The mathematical calculations in this case are extremely complex.

Let's try to explain without formulas.

Postulates of the General Theory of Relativity:

the environment in which objects and their movement are considered is four-dimensional;
all bodies fall at a constant speed.

Let's move on to the details.

So, in general relativity Einstein uses four dimensions: he supplemented the usual three-dimensional space with time. Scientists call the resulting structure the space-time continuum or space-time. It is argued that four-dimensional objects are unchanged when moving, but we are only able to perceive their three-dimensional projections. That is, no matter how hard you bend the ruler, you will only see projections of an unknown 4-dimensional body. Einstein considered the space-time continuum to be indivisible.

Regarding gravity, Einstein put forward the following postulate: gravity is the curvature of space-time.

That is, according to Einstein, the fall of an apple on the inventor’s head is not a consequence of gravity, but a consequence of the presence of mass-energy at the affected point in space-time. Using a flat example: take a canvas, stretch it on four supports, place a body on it, we see a dent in the canvas; lighter bodies that find themselves close to the first object will roll (not be attracted) as a result of the curvature of the canvas.

It has been proven that light rays are bent in the presence of gravitating bodies. Time dilation with increasing altitude has also been experimentally confirmed. Einstein concluded that space-time is curved in the presence of a massive body and gravitational acceleration is just a 3D projection of uniform motion in 4-dimensional space. And the trajectory of small bodies rolling on the canvas towards a larger object remains rectilinear for themselves.

Currently, general relativity is a leader among other theories of gravity and is used in practice by engineers, astronomers and developers of satellite navigation. Albert Einstein is actually a great transformer of science and the concept of natural science. In addition to the theory of relativity, he created the theory of Brownian motion, studied the quantum theory of light, and participated in the development of the foundations of quantum statistics.

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General theory of relativity(GTR) is a geometric theory of gravity published by Albert Einstein in 1915–16. Within the framework of this theory, which is a further development of the special theory of relativity, it is postulated that gravitational effects are caused not by the force interaction of bodies and fields located in space-time, but by the deformation of space-time itself, which is associated, in particular, with the presence of mass-energy. Thus, in general relativity, as in other metric theories, gravity is not a force interaction. General relativity differs from other metric theories of gravity by using Einstein's equations to relate the curvature of spacetime to the matter present in space.

General relativity is currently the most successful gravitational theory, well confirmed by observations. The first success of general relativity was to explain the anomalous precession of Mercury's perihelion. Then, in 1919, Arthur Eddington reported the observation of light bending near the Sun during a total eclipse, confirming the predictions of general relativity.

Since then, many other observations and experiments have confirmed a significant number of the theory's predictions, including gravitational time dilation, gravitational redshift, 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 due to the fact that it cannot be reformulated as the classical limit of quantum theory due to the appearance of irremovable mathematical divergences when considering black holes and space-time singularities in general. A number of alternative theories have been proposed to solve this problem. Modern experimental data indicate that any type of deviation from general relativity should be very small, if it exists at all.

Basic principles of general relativity

Newton's theory of gravity is based on the concept of gravity, which is a long-range force: it acts instantly at any distance. This instantaneous nature of the action is incompatible with the field paradigm of modern physics and, in particular, with the special theory of relativity, created in 1905 by Einstein, inspired by the work of Poincaré and Lorentz. In Einstein's theory, no information can travel faster than the speed of light in a vacuum.

Mathematically, Newton's gravitational force is derived from the potential energy of a body in a gravitational field. The gravitational potential corresponding to this potential energy obeys the Poisson equation, which is not invariant under Lorentz transformations. The reason for the non-invariance is that energy in the special theory of relativity is not a scalar quantity, but goes into the time component of the 4-vector. The vector theory of gravity turns out to be similar to Maxwell’s theory of the electromagnetic field and leads to negative energy of gravitational waves, which is associated with the nature of the interaction: like charges (mass) in gravity attract and do not repel, as in electromagnetism. Thus, Newton's theory of gravity is incompatible with the fundamental principle of the special theory of relativity - the invariance of the laws of nature in any inertial frame of reference, and the direct vector generalization of Newton's theory, first proposed by Poincaré in 1905 in his work “On the Dynamics of the Electron,” leads to physically unsatisfactory results .

Einstein began searching for a theory of gravity that would be compatible with the principle of invariance of the laws of nature relative to any frame of reference. The result of this search was the general theory of relativity, based on the principle of the identity of gravitational and inertial mass.

The principle of equality of gravitational and inertial masses

In classical Newtonian mechanics, there are two concepts of mass: the first refers to Newton's second law, and the second to the law of universal gravitation. The first mass - inertial (or inertial) - is the ratio of the non-gravitational force acting on the body to its acceleration. The second mass - gravitational (or, as it is sometimes called, heavy) - determines the force of attraction of a body by other bodies and its own force of attraction. Generally speaking, these two masses are measured, as can be seen from the description, in various experiments, and therefore do not have to be proportional to each other at all. Their strict proportionality allows us to speak of a single body mass in both non-gravitational and gravitational interactions. By a suitable choice of units these masses can be made equal to each other. The principle itself was put forward by Isaac Newton, and the equality of masses was verified by him experimentally with a relative accuracy of 10?3. At the end of the 19th century, Eötvös carried out more subtle experiments, bringing the accuracy of testing the principle to 10?9. During the 20th century, experimental technology made it possible to confirm the equality of masses with a relative accuracy of 10?12-10?13 (Braginsky, Dicke, etc.). Sometimes the principle of equality of gravitational and inertial masses is called the weak equivalence principle. Albert Einstein based it on the general theory of relativity.

The principle of movement along geodetic lines

If the gravitational mass is exactly equal to the inertial mass, then in the expression for the acceleration of a body on which only gravitational forces act, both masses cancel. Therefore, the acceleration of a body, and consequently its trajectory, does not depend on the mass and internal structure of the body. If all bodies at the same point in space receive the same acceleration, then this acceleration can be associated not with the properties of the bodies, but with the properties of space itself at this point.

Thus, the description of gravitational interaction between bodies can be reduced to a description of the space-time in which the bodies move. It is natural to assume, as Einstein did, that bodies move by inertia, that is, in such a way that their acceleration in their own frame of reference is zero. The trajectories of the bodies will then be geodesic lines, the theory of which was developed by mathematicians back in the 19th century.

The geodesic lines themselves can be found by specifying in space-time an analogue of the distance between two events, traditionally called an interval or a world function. An interval in three-dimensional space and one-dimensional time (in other words, in four-dimensional space-time) is given by 10 independent components of the metric tensor. These 10 numbers form the metric of space. It defines the “distance” between two infinitely close points in space-time in different directions. Geodesic lines corresponding to the world lines of physical bodies whose speed is less than the speed of light turn out to be lines of greatest proper time, that is, time measured by a clock rigidly attached to the body following this trajectory. Modern experiments confirm the movement of bodies along geodetic lines with the same accuracy as the equality of gravitational and inertial masses.

Curvature of spacetime

If you launch two bodies parallel to each other from two close points, then in the gravitational field they will gradually begin to either approach or move away from each other. This effect is called geodetic line deviation. A similar effect can be observed directly if two balls are launched parallel to each other along a rubber membrane on which a massive object is placed in the center. The balls will disperse: the one that was closer to the object pushing through the membrane will tend to the center more strongly than the more distant ball. This discrepancy (deviation) is due to the curvature of the membrane. Similarly, in space-time, the deviation of geodesics (the divergence of the trajectories of bodies) is associated with its curvature. The curvature of space-time is uniquely determined by its metric - the metric tensor. The difference between the general theory of relativity and alternative theories of gravity is determined in most cases precisely in the method of connection between matter (bodies and fields of non-gravitational nature that create the gravitational field) and the metric properties of space-time.

Space-time general relativity and the strong equivalence principle

It is often incorrectly believed that the basis of the general theory of relativity is the principle of equivalence of gravitational and inertial fields, which can be formulated as follows:
A local physical system, rather small in size, located in a gravitational field, is indistinguishable in behavior from the same system located in an accelerated (relative to the inertial reference frame) reference system, immersed in the flat space-time of the special theory of relativity.

Sometimes the same principle is postulated as the "local validity of special relativity" or called the "strong equivalence principle".

Historically, this principle really played a big role in the development of the general theory of relativity and was used by Einstein in its development. However, in the most final form of the theory, it is, in fact, not contained, since space-time, both in the accelerated and in the original frame of reference in the special theory of relativity, is uncurved - flat, and in the general theory of relativity it is curved by any body and precisely its curvature causes the gravitational attraction of bodies.

It is important to note that the main difference between the space-time of the general theory of relativity and the space-time of the special theory of relativity is its curvature, which is expressed by a tensor quantity - the curvature tensor. In the space-time of special relativity, 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 theories of gravity currently being considered by physicists, while the special theory of relativity (more precisely, its principle of the metricity of space-time) is generally accepted by the scientific community and forms the cornerstone of the basis of modern physics. It should be noted, however, that none of the other developed theories of gravity, except for General Relativity, has stood the test of time and experiment.

Main consequences of general relativity

According to the correspondence principle, in weak gravitational fields, the predictions of general relativity coincide with the results of applying Newton's law of universal gravitation with small corrections that increase as the field strength increases.

The first predicted and experimentally tested consequences of general relativity were three classical effects, listed below in the chronological order of their first testing:
1. Additional shift in the perihelion of Mercury's orbit compared to the predictions of Newtonian mechanics.
2. Deflection of a light beam in the gravitational field of the Sun.
3. Gravitational redshift, or time dilation in a gravitational field.

There are a number of other effects that can be experimentally verified. Among them we can mention the deflection and retardation (Shapiro effect) of electromagnetic waves in the gravitational field of the Sun and Jupiter, the Lense-Thirring effect (precession of a gyroscope near a rotating body), astrophysical evidence of the existence of black holes, evidence of the emission of gravitational waves by close systems of double stars and the expansion of the Universe.

So far, no reliable experimental evidence refuting general relativity has been found. Deviations of the measured effect sizes from those predicted by general relativity do not exceed 0.1% (for the above three classical phenomena). Despite this, for various reasons, theorists have developed at least 30 alternative theories of gravity, and some of them make it possible to obtain results arbitrarily close to general relativity with appropriate values of the parameters included in the theory.

Einstein's theory of relativity is based on the statement that the determination of the movement of the first body is possible solely due to the movement of another body. This conclusion has become fundamental in the four-dimensional space-time continuum and its awareness. Which, when considering time and three dimensions, have the same basis.

Special theory of relativity, discovered in 1905 and studied to a greater extent at school, has a framework that ends only with a description of what is happening, from the side of observation, which is in uniform relative motion. Which led to several important consequences:

1 For every observer, the speed of light is constant.

2 The greater the speed, the greater the mass of the body; this is felt more strongly at the speed of light.

3 Energy-E and mass-m are equal and equivalent to each other, from which the formula follows in which c- will be the speed of light.
E = mc2
From this formula it follows that mass becomes energy, less mass leads to more energy.

4 At higher speeds, compression of the body occurs (Lorentz-Fitzgerald compression).

5 Considering an observer at rest and a moving object, for the second one time will go slower. This theory, completed in 1915, is suitable for an observer who is in accelerating motion. As gravity and space have shown. Following from this, it can be assumed that space is curved due to the presence of matter in it, thereby forming gravitational fields. It turns out that the property of space is gravity. Interestingly, the gravitational field bends light, which is where black holes appeared.

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The figure shows examples of Einstein's theory.

Under A depicts an observer looking at cars moving at different speeds. But the red car is moving faster than the blue car, which means that the speed of light relative to it will be absolute.

Under IN the light emanating from the headlights is considered, which, despite the obvious difference in the speeds of the cars, will be the same.

Under WITH a nuclear explosion is shown which proves that E energy = T mass. Or E = mс2.

Under D It can be seen from the figure that less mass gives more energy, while the body is compressed.

Under E change of time in space due to Mu mesons. Time flows slower in space than on earth.

Eat theory of relativity for dummies which is briefly shown in the video:

A very interesting fact about the theory of relativity, discovered by modern scientists in 2014, but remains a mystery.

This world was shrouded in deep darkness.
Let there be light! And then Newton appeared.
Epigram from the 18th century.

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

Postulates of the theory of relativity

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

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

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

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

Law of relationship between mass and energy

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

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

What is the theory of relativity (video)

Consequences of the theory of relativity

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

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

Time dilation. The time interval measured by a clock stationary in the inertial reference frame K" is less than the time interval measured in the inertial reference frame K, relative to which K" moves with speed v:

Theory of relativity

material from the book "A Brief History of Time" by Stephen Hawking and Leonard Mlodinow

Relativity

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

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

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

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

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

Warped Space

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

Since a geodetic line is the shortest line between two airports, navigators guide planes along these routes. For example, you could follow the compass readings and fly the 5,966 kilometers from New York to Madrid almost due east along the geographic parallel. But you'll only have to cover 5,802 kilometers if you fly in a large circle, first heading northeast and then gradually turning east and then southeast. The appearance of these two routes on a map, where the earth's surface is distorted (represented as flat), is deceptive. When moving “straight” east from one point to another on the surface of the globe, you are not actually moving along a straight line, or rather, not along the shortest geodetic line.

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

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

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

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

Imagine that you are in an elevator in the middle of an empty space. There is no gravity, no “up” and “down”. You are floating freely. The elevator then begins to move with constant acceleration. You suddenly feel weight. That is, you are pressed against one of the walls of the elevator, which is now perceived as the floor. If you pick up an apple and let it go, it will fall to the floor. In fact, now that you are moving with acceleration, everything inside the elevator will happen exactly the same as if the elevator were not moving at all, but were at rest in a uniform gravitational field. Einstein realized that just as when you are in a train car you cannot tell whether it is stationary or moving uniformly, so when you are inside an elevator you cannot tell whether it is moving with constant acceleration or is in a uniform 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 valid only if the inertial mass (part of Newton’s second law, which determines how much acceleration a force applied to it gives to a body) and gravitational mass (part of Newton’s law of gravity, which determines the magnitude of the gravitational force) attraction) are one and the same thing.

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

Time dilation

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

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

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

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

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

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

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

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

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

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

Time near a black hole

Let's imagine an intrepid astronaut who remains on the surface of a collapsing star during a catastrophic contraction. At some point according to his watch, say at 11:00, the star will shrink to a critical radius, beyond which the gravitational field intensifies so much that it is impossible to escape from it. Now suppose that according to the instructions, the astronaut must send a signal every second on his watch to a spacecraft that is in orbit at some fixed distance from the center of the star. It begins transmitting signals at 10:59:58, that is, two seconds before 11:00. What will the crew register on board the spacecraft?

Previously, having done a thought experiment with the transmission of light signals inside a rocket, we were convinced that gravity slows down time and the stronger it is, the more significant the effect. An astronaut on the surface of a star is in a stronger gravitational field than his colleagues in orbit, so one second on his watch will last longer than a second on the ship's clock. As the astronaut moves with the surface towards the center of the star, the field acting on him becomes stronger and stronger, so that the intervals between his signals received on board the spacecraft are constantly lengthening. This time dilation will be very slight until 10:59:59, so that for astronauts in orbit the interval between the signals transmitted at 10:59:58 and at 10:59:59 will be very little more than a second. But the signal sent at 11:00 will no longer be received on the ship.

Anything that happens on the surface of the star between 10:59:59 and 11:00 on the astronaut's clock will stretch out over an infinite period of time on the spacecraft's clock. As 11:00 approaches, the intervals between the arrival in orbit of successive crests and troughs of light waves emitted by the star will become increasingly longer; the same will happen with the time intervals between the astronaut's signals. Since the frequency of the radiation is determined by the number of crests (or troughs) arriving per second, the spacecraft will record lower and lower frequencies of the star's radiation. The light of the star will become increasingly red and at the same time fade. Eventually the star will become so dim that it will become invisible to observers on the spacecraft; all that will remain is a black hole in space. However, the effect of the star's gravity on the spacecraft will remain, and it will continue to orbit.

material from the book "A Brief History of Time" by Stephen Hawking and Leonard Mlodinow

Relativity

Another well-known consequence of the theory of relativity is the equivalence of mass and energy, expressed by Einstein’s famous equation E = mс 2 (where E is energy, m is body mass, c is the speed of light). Due to the equivalence of energy and mass, the kinetic energy that a material object possesses due to its motion increases its mass. In other words, the object becomes more difficult to accelerate.

Warped Space

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

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

Imagine that you are in an elevator in the middle of an empty space. There is no gravity, no “up” and “down”. You are floating freely. The elevator then begins to move with constant acceleration. You suddenly feel weight. That is, you are pressed against one of the walls of the elevator, which is now perceived as the floor. If you pick up an apple and let it go, it will fall to the floor. In fact, now that you are moving with acceleration, everything inside the elevator will happen exactly the same as if the elevator were not moving at all, but were at rest in a uniform gravitational field. Einstein realized that just as when you are in a train car you cannot tell whether it is standing still or moving uniformly, so when you are inside an elevator you cannot tell whether it is moving with constant acceleration or is in uniform motion. 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 valid only if the inertial mass (part of Newton’s second law, which determines how much acceleration a force applied to a body gives to a body) and gravitational mass (part of Newton’s law of gravity, which determines the magnitude of gravitational attraction) are the same thing.

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

Time dilation

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

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