Experimental basis of the general theory of relativity. So was Einstein right? Testing the theory of relativity

One of the pearls of scientific thought in the tiara of human knowledge with which we entered the 21st century is the General Theory of Relativity (hereinafter referred to as GTR). This theory has been confirmed by countless experiments; I will say more, there is not a single experiment where our observations would differ even a little bit, even a tiny bit, from the predictions of the General Theory of Relativity. Within the limits of its applicability, of course.

Today I want to tell you what kind of beast this General Theory of Relativity is. Why is it so difficult and why In fact she's so simple. As you already understand, the explanation will go on your fingers™, therefore, I ask you not to judge too harshly for very free interpretations and not entirely correct allegories. I want anyone to read this explanation humanitarian, without any knowledge of differential calculus and surface integration, was able to understand the basics of general relativity. After all, historically, this is one of the first scientific theories that begin to move away from the usual everyday human experience. With Newtonian mechanics everything is simple, three fingers are enough to explain it - here is the force, here is the mass, here is the acceleration. Here is an apple falling on your head (has everyone seen how apples fall?), here is the acceleration of its free fall, here are the forces acting on it.

With general relativity, not everything is so simple - space curvature, gravitational time dilation, black holes - all this should cause (and does!) a lot of vague suspicions in an unprepared person - are you messing with my ears, dude? What are the curvatures of space? Who saw these distortions, where do they come from, how can something like this even be imagined?

Let's try to figure it out.

As can be understood from the name of the General Theory of Relativity, its essence is that in general, everything in the world is relative. Joke. Not really though.

The speed of light is the quantity relative to which all other things in the world are relative. Any reference frames are equal, no matter where they move, no matter what they do, even spinning in place, even moving with acceleration (which is a serious blow to the guts of Newton and Galileo, who thought that only uniformly and rectilinearly moving frames of reference can be relative and equal, and even then, only within the framework of elementary mechanics) - all the same, you can always find clever trick(scientifically this is called coordinate transformation), with the help of which it will be possible to painlessly move from one frame of reference to another, practically without losing anything along the way.

A postulate helped Einstein reach such a conclusion (let me remind you - a logical statement taken on faith without proof due to its obviousness) "on the equality of gravity and acceleration". (Attention, there is a strong simplification of the wording here, but in general outline that's right - equivalence of effects uniformly accelerated motion and gravity is at the very heart of General Relativity).

Prove this postulate, or at least mentally to taste quite simple. Welcome to the Einstein Elevator.

The idea of ​​this thought experiment is that if you were locked in an elevator without windows and doors, then there is not the slightest, absolutely not a single way to know what situation you are in: either the elevator continues to stand as it stood at the ground floor level, and you (and all other contents of the elevator) the usual force of attraction acts, i.e. the force of gravity of the Earth, or the entire planet Earth was removed from under your feet, and the elevator began to rise upward, with an acceleration equal to the acceleration of free fall g=9.8m/s 2 .

No matter what you do, no matter what experiments you carry out, no matter what measurements of surrounding objects and phenomena you make, it is impossible to distinguish between these two situations, and in the first and second cases, all processes in the elevator will take place exactly the same.

The reader with an asterisk (*) probably knows one tricky way out of this difficulty. Tidal forces. If the elevator is very (very, very) large, 300 kilometers across, it is theoretically possible to distinguish gravity from acceleration by measuring the force of gravity (or the magnitude of acceleration, we don’t yet know which is which) at different ends of the elevator. Such a huge elevator will be slightly compressed by tidal forces in the cross section and slightly stretched by them in the longitudinal plane. But these are already tricks. If the elevator is small enough, you won't be able to detect any tidal forces. So let's not talk about sad things.

In total, in a fairly small elevator we can assume that gravity and acceleration are the same thing. It would seem that the idea is obvious, and even trivial. What is so new or complicated here, you say, this should be clear to a child! Yes, in principle, nothing complicated. It was not Einstein who invented this; such things were known much earlier.

Einstein decided to find out how a beam of light would behave in such an elevator. But this idea had very far-reaching consequences, which no one seriously thought about until 1907. I mean, to be honest, many people thought about it, but only one decided to get so deeply involved.

Let's imagine that we shine a flashlight on Einstein in our mental elevator. A ray of light flew out of one wall of the elevator, from point 0) and flew parallel to the floor towards the opposite wall. While the elevator is standing still, it is logical to assume that the light beam will hit the opposite wall exactly opposite the starting point 0), i.e. will arrive at point 1). The rays of light travel in a straight line, everyone went to school, they all learned this at school, and so did young Albertik.

It’s easy to guess that if the elevator went up, then during the time the beam was flying across the cabin, it would have time to move a little upward.
And if the elevator moves with uniform acceleration, then the beam will hit the wall at point 2), that is when viewed from the side it will seem that the light moved as if in a parabola.

Well, it's clear that In fact there is no parabola. The beam flew straight and still does. It’s just that while it was flying in its straight line, the elevator managed to go up a little, so here we are Seems that the beam moved in a parabola.

Everything is exaggerated and exaggerated, of course. A thought experiment, why our light flies slowly, and elevators move quickly. There is still nothing particularly cool here, all this should also be understandable to any schoolchild. You can conduct a similar experiment at home. You just need to find “very slow beams” and good, fast elevators.

But Einstein was truly a genius. Today many people scold him, like he’s a nobody and nothing at all, he sat in his patent office, weaved his Jewish conspiracies and stole ideas from real physicists. Most of those who say this do not understand at all who Einstein is and what he did for science and humanity.

Einstein said - since “gravity and acceleration are equivalent” (I repeat once again, he didn’t say exactly that, I’m deliberately exaggerating and simplifying), it means that in the presence of a gravitational field (for example, near the planet Earth), light will also fly not in a straight line, but along a curve . Gravity will bend the light beam.

Which in itself was an absolute heresy for that time. Any peasant should know that photons are massless particles. This means that light “doesn’t weigh” anything. Therefore, light should not care about gravity; it should not be “attracted” by the Earth, as stones, balls and mountains are attracted. If anyone remembers Newton's formula, gravity is inversely proportional to the square of the distance between bodies and directly proportional to their masses. If a ray of light has no mass (and light really has none), then there should be no attraction! Here contemporaries began to look askance at Einstein with suspicion.

And he, the infection, went even further. He says we won’t break the peasants’ heads. Let's believe the ancient Greeks (hello, ancient Greeks!), let the light spread as before strictly in a straight line. Let's better assume that the space itself around the Earth (and any body with mass) bends. And not just three-dimensional space, but four-dimensional space-time.

Those. The light flew in a straight line and still does. Only this straight line is now drawn not on a plane, but lies on a sort of crumpled towel. And in 3D too. And it is the close presence of the mass that crumples this towel. Well, more precisely the presence of energy-momentum, to be absolutely precise.

All to him - “Albertik, you’re driving, stop with opium as soon as possible! Because LSD has not yet been invented, and you definitely wouldn’t come up with such a thing on your sober head! What a bent space, what are you talking about?”

And Einstein was like, “I’ll show you again!”

Locked yourself in your white tower (in the patent office, I mean) and let’s adjust the mathematics to the ideas. I pushed for 10 years until I gave birth to this:

More precisely, this is the quintessence of what he gave birth to. In the more detailed version there are 10 independent formulas, and in the full version there are two pages of mathematical symbols in small print.

If you decide to take a real course in General Relativity, the introductory part ends here and then two semesters of studying the harsh language must follow. And to prepare to study this math, you need at least three more years of higher mathematics, given that you graduated from high school and are already familiar with differential and integral calculus.

Hand on heart, the matan there is not so much complicated as tedious. Tensor calculus in pseudo-Riemannian space is not a very confusing topic to understand. This is not quantum chromodynamics, or, God forbid, not string theory. Everything is clear here, everything is logical. Here's a Riemann space, here's a manifold without breaks or folds, here's a metric tensor, here's a non-degenerate matrix, write out formulas for yourself, and balance the indices, making sure that covariant and contravariant representations of vectors on both sides of the equation correspond to each other. It is not difficult. It's long and tedious.

But let's not go to such lengths and return to to our fingers™. In our opinion, in a simple way, Einstein’s formula means approximately the following. To the left of the equal sign in the formula are the Einstein tensor plus the covariant metric tensor and the cosmological constant (Λ). This lambda is essentially dark energy which we still have today we don't know anything, but we love and respect. And Einstein doesn’t even know about it yet. It has its own interesting story, worthy of a whole separate post.

In a nutshell, everything to the left of the equal sign shows how the geometry of space changes, i.e. how it bends and twists under the influence of gravity.

And on the right, in addition to the usual constants like π , speed of light c and gravitational constant G there is a letter T- energy-momentum tensor. In Lammer terms, we can consider that this is the configuration of how mass is distributed in space (more precisely, energy, because what mass or energy is the same emtse square) in order to create gravity and bend space with it in order to correspond to the left side of the equation.

That, in principle, is the whole General Theory of Relativity on your fingers™.

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 SRT. 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:

1. The principle of relativity. Any physical laws are the same for stationary objects and for bodies moving uniformly and rectilinearly.
2. 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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"ZS" No. 7-11/1939

Lev Landau

This year marks the 60th anniversary of the greatest physicist of our time - Albert Einstein. Einstein is famous for his theory of relativity, which caused a real revolution in science. In our ideas about the world around us, the principle of relativity, put forward by Einstein back in 1905, produced the same enormous revolution that the teachings of Copernicus produced in its time.
Before Copernicus, people thought that they lived in an absolutely calm world, on a motionless Earth - the center of the universe. Copernicus overturned this age-old prejudice, proving that in fact the Earth is just a tiny grain of sand in an immense world, in continuous motion. This was four hundred years ago. And now Einstein has shown that such a familiar and seemingly completely clear thing for us as time also has completely different properties than those that we usually attribute to it...

In order to fully understand this very complex theory, one needs extensive knowledge of mathematics and physics. However general idea Every cultured person can and should know about it. We will try to give such a general idea of ​​Einstein’s principle of relativity in our article, which will be published in parts in three issues of “Knowledge is Power.”

The following people took part in the processing of this article for the young reader: E. Zelikovich, I. Nechaev and O. Pisarzhevsky.

Relativity to which we are accustomed

Does every statement have meaning?

Obviously not. For example, if you say “bi-ba-boo,” no one will find any meaning in this exclamation. But even completely meaningful words, combined according to all the rules of grammar, can also produce complete nonsense. Thus, it is difficult to attribute any meaning to the phrase “lyrical cheese laughs.”

However, not all nonsense is so obvious: very often a statement, at first glance quite reasonable, turns out to be essentially absurd. Tell me, for example, on which side of Pushkin Square in Moscow is the monument to Pushkin: on the right or on the left?

It is impossible to answer this question. If you go from Red Square to Mayakovsky Square, the monument will be on the left, and if you go in the opposite direction, it will be on the right. It is clear that without indicating the direction in relation to which we consider “right” and “left”, these concepts have no meaning.

In the same way, it is impossible to say that it is now day or night on the globe? The answer depends on where the question is asked. When it is day in Moscow, it is night in Chicago. Therefore, the statement “it is day or night” does not make any sense unless it is indicated to which place on the globe it refers. We will call such concepts “relative”.

The two pictures shown here show a shepherd and a cow. In one picture the shepherd is larger than the cow, and in the other the cow is larger than the shepherd. But it is clear to everyone that there is no contradiction here. The drawings were made by observers who were in different places: the first stood closer to the cow, the second stood closer to the shepherd. In paintings, it is not the size of objects that is important, but the angle at which we would see these objects in reality.

It is clear that the “angular magnitude” of an object is relative: it depends on the distance between them and the object. The closer the object, the greater its angular value and the larger it appears, and the further away the object, the smaller its angular value and the smaller it appears.

The absolute turned out to be relative

However, the relativity of our concepts is not always as obvious as in the examples given.

We often talk about "above" and "below". Are these absolute concepts or relative ones? In earlier times, when it was not yet known that the Earth was spherical, and it was imagined as a flat pancake, it was considered self-evident that the directions of “up” and “down” were the same throughout the world.

But it was discovered that the Earth is spherical, and it turned out that the vertical directions at different points earth's surface are different.

All this does not cause us any doubt now. Meanwhile, history shows that it was not so easy to understand the relativity of “top” and “bottom”. People are very prone to attribute absolute meaning to concepts whose relativity is unclear from everyday experience. Let us recall the ridiculous “objection” to the sphericity of the Earth, which enjoyed great success in the Middle Ages: on the “other side” of the Earth, they say, trees should grow downward, raindrops should fall upward, and people would walk upside down.

And indeed, if we consider the direction of the vertical in Moscow to be absolute, then it turns out that in Chicago people walk upside down. And from the absolute point of view of people living in Chicago, Muscovites are walking upside down. But in fact, the vertical direction is not absolute, but relative. And everywhere on Earth, although it is spherical, people only walk upside down.

And the movement is relative

Let's imagine two travelers traveling on the Moscow-Vladivostok express. They agree to meet every day in the same place in the dining car and write letters to their husbands. Travelers are confident that they fulfill the condition - that they are every day in the same place where they were yesterday. However, their husbands will not agree with this: they will strongly argue that the travelers met every day in a new place, a thousand kilometers away from the previous one.

Who is right: the travelers or their husbands?

We have no reason to give preference to one or the other: the concept of “same place” is relative. Regarding the train, the travelers actually met “in the same place” all the time, but relative to the earth’s surface, the place of their meeting was constantly changing.

Thus, position in space is a relative concept. When we talk about the position of a body, we always mean its position relative to other bodies. Therefore, if we were asked to indicate where such and such a body is located, without mentioning other bodies in the answer, we would have to consider such a requirement completely impossible.

It follows that the movement, or movement, of bodies is also relative. And when we say “a body moves,” it only means that it changes its position relative to some other bodies.

Let us imagine that we observe the movement of a body from various points. Let’s agree to call such points “laboratories.” Our imaginary laboratories can be anything in the world: houses, cities, trains, airplanes, the Earth, other planets, the Sun and even stars.

What will the trajectory, that is, the path of a moving body, seem to us?

It all depends on which laboratory we observe it from. Let's say that a pilot throws cargo out of an airplane. From the point of view of the pilot, the load flies down vertically in a straight line, and from the point of view of an observer on the ground, the falling load describes a curved line - a parabola. What trajectory does the load actually follow?

This question makes as little sense as the question of which photograph of a person is “real” - the one in which he is shot from the front, or the one in which he is shot from behind?

The geometric shape of the curve along which a body moves has the same relative character as a photograph of a person. By photographing a person from the front and the back, we will get different pictures, and each of them will be completely correct. In the same way, when observing the movement of a body from various laboratories, we see different trajectories, and all these trajectories are “real”.

But will they all be of equal value to us? Is it still possible to find such an observation point, such a laboratory, from where we could best study the laws governing the movement of a body?

We have just compared the trajectories of a moving body with photographs of a person - both can be very diverse, it all depends on where you observe the movement of the body or take the photo. But you know that in photography not all points of view are equal. For example, if you need a photo for identification, you will naturally want to be photographed from the face rather than from behind. In the same way, in mechanics, that is, when studying the laws of motion of bodies, we must choose the most suitable one from all possible points of observation.

Looking for peace

We know that the movement of bodies is influenced by external influences, which we call forces. But we can imagine a body that is free from the influence of any forces. Let us agree once and for all to assume that a body on which no forces act is at rest. Now, having introduced the concept of rest, we seem to already have some solid support in the study of the movement of bodies. In fact, this body, on which no forces act and which we have agreed to consider as at rest, can serve as a guide for us, “ guiding star"when studying the motion of all other bodies.

Let us imagine that we have removed some body so far from all other bodies that no forces will act on it. And then we will be able to establish how physical phenomena should occur on such a body at rest. In other words, we can find the laws of mechanics that prevail in this imaginary “resting” laboratory. And by comparing them with what we observe in other, real laboratories, we will be able to judge the true properties of movement in all cases.

So, it would seem that everything is working out perfectly: we have found a strong point - “peace”, albeit conditional, and now movement has lost its relativity for us.

However, in reality, this illusory “peace” achieved with such difficulty will not be absolute.

Imagine observers living on a lonely globe, lost in the vast expanses of the universe. They do not feel the influence of any extraneous forces and, therefore, must be convinced that the ball on which they live is in complete immobility, in absolute, unchanging peace.

Suddenly they notice in the distance another similar ball, on which there are the same observers. This second ball rushes with great speed, straight and evenly, towards the first. Observers on the first ball have no doubt that they are standing still, and only the second ball is moving. But the inhabitants of this second ball also believe in their immobility and are firmly convinced that this first “alien” ball is moving towards them.

Which one is right? The debate on this matter makes no sense, since the state of rectilinear and uniform motion is completely impossible to distinguish from the state of rest.

To be convinced of this, you and I don’t even need to climb into the endless depths of the universe. Get on a river boat at the pier, lock yourself in the cabin and carefully curtain the windows. Under such conditions you will never discover whether you are standing still or moving straight and evenly. All bodies in the cabin will behave in exactly the same way in both cases: the surface of the water in the glass will remain calm all the time; a ball thrown vertically upward will also fall vertically downward; The clock pendulum will swing the same way as on the wall of your apartment.

Your steamer can travel at any speed, but the same laws of motion will prevail on it as on a completely motionless steamship. Only at the moment of slowing down or accelerating can you detect its movement; when it moves straight and evenly, everything flows on it in the same way as on a stationary ship.

Thus, we did not find absolute rest anywhere, but discovered that there can be infinitely many “rests” in the world, moving relative to each other evenly and in a straight line. Therefore, when we talk about the movement of a body, we must always indicate relative to what kind of “rest” it is moving. This position is called in mechanics the “law of relativity of motion.” It was put forward three hundred years ago by Galileo.

But if motion and rest are relative, then speed, obviously, must be relative. This is how it really is. Let's say, for example, that you are running along the deck of a steamship at a speed of 5 meters per second. If the ship passes in the same direction at 10 meters per second, then relative to the shore your speed will be already 15 meters per second.

Therefore, the statement: “a body moves at such and such a speed,” without indicating what the speed is measured in relation to, does not make sense. By determining the speed of a moving body from different points, we must obtain different results.

Everything we have talked about so far was known long before Einstein’s work. The relativity of motion, rest and speed was established by the great creators of mechanics - Galileo and Newton. The laws of motion he discovered formed the basis of physics and for almost three centuries contributed greatly to the development of all natural sciences. Countless new facts and laws were discovered by researchers, and all of them again and again confirmed the correctness of the views of Galileo and Newton. These views were also confirmed in practical mechanics - in the design and operation of all kinds of machines and devices.

This continued until the end of the 19th century, when new phenomena were discovered that turned out to be in decisive contradiction with the laws of classical mechanics.

In 1881, the American physicist Michaelson undertook a series of experiments to measure the speed of light. The unexpected result of these experiments caused confusion among physicists; it was so amazing and mysterious that it baffled the world's greatest scientists.

Remarkable properties of light

Perhaps you have observed such an interesting phenomenon.

Somewhere in the distance, in a field, on a railroad track or at a construction site, a hammer is beating. You see how hard it falls on the anvil or the steel rail. However, the sound of the impact is completely inaudible. It looks like the hammer has landed on something very soft. But now he rises again. And at the moment when he is already quite high in the air, you hear a distant sharp knock.

It's not hard to understand why this happens. At normal conditions sound travels in the air at a speed of about 340 meters per second, so we hear the blow of a hammer not at the moment when it occurs, but only after the sound from it has time to reach our ear.

Here is another, more striking example. Lightning and thunder occur simultaneously, but often it seems that the lightning flashes silently, since the thunderclaps reach our ears only after a few seconds. If we hear them with a delay, for example, 10 seconds, then this means that the lightning is 340 x 10 = 3400 meters away from us, or 3.4 kilometers.

In both cases, we are talking about two moments: about when some event actually happened, and about the moment at which the echo of this event reached our ear. But how do we know when exactly the event actually happened?

We see it: we see the hammer falling, the lightning flashing. In this case, we assume that the event actually occurs at the very moment when we see it. But is this really so?

No not like this. After all, we do not perceive events directly. Light is involved in the phenomena that we observe with the help of vision. And light does not travel in space instantly: like sound, light rays take time to cover the distance.

In emptiness, light travels at a speed of about 300 thousand kilometers per second. This means: if a light flashes at a distance of 300 thousand kilometers from you, you may not notice its flash immediately, but only a second later.

In one second, the rays of light would have time to circle seven times Earth along the equator. Compared to such a colossal speed, earthly distances seem insignificant, so we can practically assume that we see all the phenomena occurring on Earth at the same moment when they occur.

The unimaginably enormous speed of light may seem surprising. Much more surprising, however, is something else: the fact that the speed of light is amazingly constant. Let's see what this consistency is.

It is known that the movement of bodies can be artificially slowed down and accelerated. If, for example, you place a box of sand in the path of a bullet, then the bullet in the box will lose some of its speed. The lost speed will not be restored: after leaving the box, the bullet will fly further not at the same speed, but at a reduced speed.

Rays of light behave differently. In air they propagate more slowly than in emptiness, in water - more slowly than in air, and in glass - even more slowly. However, having left any substance (transparent, of course) into the void, light continues to spread at its previous speed - 300 thousand kilometers per second. Moreover, the speed of light does not depend on the properties of its source: it is absolutely the same for the rays of the Sun, a spotlight, and a candle. In addition, it makes no difference whether the light source itself is moving or not - this does not affect the speed of light in any way.

To fully understand the meaning of this fact, let us once again compare the propagation of light with the movement of ordinary bodies. Imagine that you are releasing a stream of water from a fire nozzle on the street at a speed of 5 meters per second. This means that each particle of water passes relative to the street 5 meters per second. But if you place a fire hose on a car passing in the direction of the jet at 10 meters per second, then the speed of the jet relative to the street will be already 15 meters per second: the water particles are imparted speed not only by the fire nozzle, but also by the moving car, which carries the fire hose along with the jet forward.

Comparing the light source with a fire hose, and its rays with a stream of water, we will see a significant difference. For rays of light, it does not matter from what source they entered the void and what happened to them before they entered the empty space. Since they are in it, the speed of their propagation is equal to the same value - 300 thousand kilometers per second, and regardless of whether the light source is moving or not.

Let's see how these special properties of light are consistent with the law of relativity of motion, which was discussed in the first part of the article. To do this, let's try to solve the problem of adding and subtracting speeds, and for simplicity we will assume that all the phenomena we imagine occur in emptiness, where the speed of light is 300 thousand kilometers.

Let a light source be placed on a moving steamer, in the very middle of it, and an observer at each end of the steamer. They both measure the speed of light. What will be the results of their work?

Since the rays spread in all directions, and both observers move together with the steamer in one direction, the following picture will be obtained: the observer located at the rear end of the steamer moves towards the rays, and the front one moves away from them all the time.

Therefore, the first observer must find that the speed of light is equal to 300 thousand kilometers plus the speed of the steamship, and the second - 300 thousand kilometers minus the speed of the steamship. And if we imagine for a moment that the steamer travels a monstrous distance of 200 thousand kilometers per second, then the speed of light found by the first observer will be 500 thousand kilometers, and by the second - 100 thousand kilometers per second. On a stationary ship, both observers would get the same result - 300 thousand kilometers per second.

Thus, from the point of view of observers, on our moving ship the light seems to spread in one direction 1 2/3 times faster, and in the other three times slower, than on a stationary one. By performing simple arithmetic operations, they will be able to establish the absolute speed of the ship.

In the same way, we can establish the absolute speed of any other moving body: to do this, it is enough to place some light source on it and measure from different points body speed of propagation of light rays.

In other words, we suddenly found ourselves in a position to determine the speed, and therefore the movement of a body, regardless of all other bodies. But if there is absolute speed, then there is also a single, absolute rest, namely: any laboratory in which observers, measuring the speed of light in any direction, obtain the same value - 300 thousand kilometers per second, will be absolutely at rest.

It is not difficult to see that all this strongly contradicts the conclusions we came to in the previous issue of the journal. In fact: we talked about the fact that on a body moving uniformly in a straight line, everything proceeds the same way as on a stationary body. Therefore, whether we, for example, shoot on a ship in the direction of its movement or against its movement, the speed of the bullet relative to the ship will remain the same and will be equal to the speed on a stationary ship. At the same time, we are convinced that movement, speed and rest are relative concepts: absolute movement, speed and rest do not exist. And now it suddenly turns out that observations of the properties of light overturn all these conclusions and contradict the law of nature discovered by Galileo - the law of relativity of motion.

But this is one of its basic laws: it prevails throughout the world; its justice has been confirmed by experience countless times, and is confirmed everywhere and every minute to this day; if he suddenly ceased to be fair, unimaginable turmoil would engulf the universe. But the light not only does not obey it, but even refutes it!

Michaelson's experience

What to do with this contradiction? Before expressing any considerations on this matter, let us pay attention to the following circumstance: we have established that the properties of light contradict the law of relativity of motion solely by reasoning. True, these were very convincing arguments. But, limiting ourselves to reasoning alone, we would be like the ancient philosophers who tried to discover the laws of nature not with the help of experience and observation, but only on the basis of inferences alone. In this case, the danger inevitably arises that the picture of the world created in this way, for all its merits, will turn out to have very little resemblance to the real world around us.

The supreme judge of any physical theory is always experience, and therefore, without limiting ourselves to reasoning about how light should propagate on a moving body, we should turn to experiments that will show how it actually propagates under these conditions.

It should, however, be borne in mind that setting up such experiments is difficult for a very simple reason: it is impossible to find in practice a body that would move at a speed commensurate with the colossal speed of light. After all, such a ship as we used in our discussion, of course, does not exist and cannot exist.

In order to be able to determine an insignificant change in the speed of light on relatively slowly moving bodies accessible to us, it was necessary to create measuring instruments of extremely high accuracy. And only when such devices could be manufactured, it was possible to begin to clarify the contradiction between the properties of light and the law of relativity of motion.

Such an experiment was undertaken in 1881 by one of the greatest experimenters of modern times, the American physicist Michaelson.

Michaelson used... the globe as a moving body. Indeed, the Earth is a obviously moving body: it revolves around the Sun and, moreover, at a fairly “respectable” speed for our conditions - 30 kilometers per second. Therefore, when we study the propagation of light on Earth, we are actually studying the propagation of light in a moving laboratory.

Michaelson measured the speed of light on Earth with very high accuracy in various directions, that is, he practically accomplished what we mentally did with you on an imaginary moving steamship. To catch the tiny difference of 30 kilometers compared to the huge number of 300 thousand kilometers, Michaelson had to use very complex experimental techniques and show all his enormous ingenuity. The accuracy of the experiment was so great that Michaelson would have been able to detect a much smaller difference in speeds than the one he wanted to detect.

Out of the frying pan into the fire

The result of the experiment seemed obvious in advance. Knowing the properties of light, it was possible to foresee that the speed of light measured in different directions would be different. But perhaps you think that the result of the experiment actually turned out to be like this?

Nothing like this! Michaelson's experiment yielded completely unexpected results. Over the years it has been repeated many times under a variety of conditions, but it always leads to the same astonishing conclusion.

On the obviously moving Earth, the speed of light measured in any direction turns out to be exactly the same.

This means that light is no exception. It obeys the same law as a bullet on a moving ship - Galileo's law of relativity. It was never possible to detect the “absolute” movement of the Earth. It does not exist, as it should be according to the law of relativity.

The unpleasant contradiction that science faced was resolved. But new contradictions arose! Physicists have fallen from the frying pan into the fire.

To understand the new contradictions that Michaelson’s experience led to, let’s look at our research in order.

First we established that absolute motion and rest do not exist; Galileo's law of relativity speaks about this. Then it turned out that the special properties of light contradict the law of relativity. From this it followed that absolute motion and rest still exist. To test this, Michaelson performed an experiment. The experiment showed the opposite: there is no contradiction - and light obeys the law of relativity. Consequently, absolute motion and rest again do not exist. On the other hand, the conclusions from Michaelson's experiment obviously apply to any moving body, not just the Earth; therefore, the speed of light is the same in all laboratories, regardless of their own movement, and, therefore, the speed of light is still not a relative, but an absolute quantity.

It turned out to be a vicious circle. The greatest physicists around the world have been racking their brains over it for years. Various theories have been proposed, including the most incredible and fantastic. But nothing helped: every new assumption immediately caused new contradictions. The scientific world was faced with one of the greatest mysteries.

The most mysterious and strange thing about all this was that science here was dealing with completely clear, firmly established facts: the law of relativity, the known properties of light and Michaelson’s experiment. And they seemed to lead to complete absurdity.

Contradiction of truths... But truths cannot contradict each other, since there can only be one truth. Therefore, there must be an error in our understanding of the facts. But where? What is it?

For 24 whole years - from 1881 to 1905 - no answer was found to these questions. But in 1905, the greatest physicist of our time, Albert Einstein, gave the mystery a brilliant explanation. Coming from a completely unexpected direction, it gave physicists the impression of a bomb exploding.

Einstein's explanation is so unlike any concept to which humanity has been accustomed for millennia that it sounds exceptionally incredible. However, despite this, it turned out to be undoubtedly correct: for 34 years now, laboratory experiments and observations of various physical phenomena in the world have increasingly confirmed its validity.

When the doors open

To understand Einstein's explanation, it is necessary to first become familiar with one consequence of Michaelson's experiment. Let's look at it right away with an example. Let's use the fantastic steamship for this once again.

Let's imagine a ship 5,400 thousand kilometers long. Let it move straight and evenly at a fabulous speed of 240 thousand kilometers per second. At some point, a light comes on in the middle of the steamer. There are doors at the bow and stern of the ship. They are designed in such a way that the moment the light from a light bulb falls on them, they automatically open. The light bulb came on. When exactly will the doors open?

To answer this question, let us recall the results of Michaelson's experiment. Michaelson's experiment showed that, relative to observers on a moving Earth, light travels in all directions at the same speed of 300 thousand kilometers per second. The same thing, naturally, will happen on a moving ship. But the distance from the light bulb to each end of the ship is 2,700,000 kilometers, and 2,700,000: 300,000 = 9. This means that the light from the light bulb will reach each door in 9 seconds. This way both doors will open at the same time.

This is how the situation will present itself to the observer on the ship. What will people see on the pier, past which the ship is moving?

Since the speed of light does not depend on the movement of the light source, then relative to the pier it is equal to the same 300 thousand kilometers per second, despite the fact that the light source is on a moving ship. But, from the point of view of an observer on the pier, the door at the stern of the ship is moving towards the beam of light at the speed of the ship. When will the door meet the beam?

We are dealing here with a problem similar to the problem of two travelers traveling towards each other. To find the meeting time, you need to divide the distance between travelers by the sum of their speeds. Let's do the same here. The distance between the light bulb and the door is 2,700 thousand kilometers, the speed of the door (that is, the steamship) is 240 thousand kilometers per second, and the speed of light is 300 thousand kilometers per second.

Therefore, the back door will open through

2700.000/(300000 + 240000)=5 seconds

After the light comes on. What about the front?

The front door, from the point of view of an observer on the pier, the beam of light has to catch up with, since it moves with the steamer in the same direction as the beam of light. Therefore, here we have a problem about travelers, one of whom catches up with the other. We will divide the distance by the difference in speed:

2700.000/(300000 - 240000)=45 seconds

So, the first door will open 5 seconds after the light comes on, and the second door will open 45 seconds later. Therefore, the doors will not open at the same time. This is what the people on the pier will see! The picture is the most amazing of all that has been said so far.

It turns out that the same events - the opening of the front and back doors - will turn out to be simultaneous for people on the ship, but not simultaneous for people on the pier, but separated by a time interval of 40 seconds.

Doesn't this sound like complete nonsense? Doesn't this look like an absurd statement from a joke - that the length of a crocodile from tail to head is 2 meters, and from head to tail 1 meter?

And, mind you, the people on the pier will not think that the doors did not open at the same time: for them it will actually happen at the same time. After all, we calculated the time when each of the doors opened. At the same time, we found that the second door actually opened 40 seconds later than the first.

However, the ship's passengers also correctly established that both doors opened at the same time. And this was shown arithmetically. What happens? Arithmetic versus arithmetic?!

No, arithmetic is not to blame here. All the contradictions that we have encountered here lie in our misconceptions about time: time turned out to be not at all what humanity has believed it to be until now.

Einstein reconsidered these thousand-year-old concepts. At the same time, he made a great discovery, thanks to which his name became immortal.

Time is relative

In the previous issue we showed what extraordinary conclusions physicists had to draw from Michaelson's experiment. We looked at the example of an imaginary steamship on which two doors open at a light signal, and we established an amazing fact: from the point of view of observers on the ship, the doors open at the same moment, but from the point of view of observers on the pier, they open at different moments.

What a person is not used to seems incredible to him. The incident with the doors on the ship seems completely incredible because we have never moved at a speed even remotely approaching the fabulous number of 240 thousand kilometers per second. But we must take into account that the phenomena occurring at such speeds may be very different from those to which we are accustomed in Everyday life.

Of course, in reality there are no steamships that travel at speeds close to the speed of light. And in fact, no one has ever observed such a case with doors as described in our example. But similar phenomena, thanks to modern highly developed experimental technology, can certainly be detected. Let us recall that the example with opening doors is not based on abstract reasoning, but solely on firmly established facts obtained through experience: Michaelson’s experience and many years of observations on the properties of light.

So, it was experience that led us to the indisputable conclusion that the concept of the simultaneity of two events is not absolute. Previously, we believed that if two events occurred in any laboratory at the same time, then for any other laboratory they would be simultaneous. Now we have found out that this is true only for laboratories at rest relative to each other. Otherwise, events that are simultaneous for one laboratory will occur for another in different time.

It follows that the concept of simultaneity is a relative concept. It acquires meaning only when it is indicated how the laboratory moves, from which events are observed.

At the beginning of the article, we talked about two travelers who came to the express dining car every day. The travelers were sure that they met in the same place all the time. Their husbands claimed that they met every day in a new place, a thousand kilometers away from the previous one.

Both were right: in relation to the train, the travelers actually met in the same place, but in relation to the railway track - in different places. This example showed us that the concept of space is not an absolute concept, but a relative one.

Both examples - about meeting travelers and opening doors on a ship - are similar to each other. In both cases we're talking about about relativity, and there are even identical words: “in the same” and “in different”. Only the first example talks about places, that is, space, and the second example talks about moments, that is, time. What follows from this?

The fact that the concept of time is as relative as the concept of space.

To finally make sure of this, let’s modify the example with the steamboat a little. Let's assume that the mechanism of one of the doors is faulty. Let this malfunction cause the people on the ship to notice that the front door opened 15 seconds before the back door. What will people see on the pier?

If in the first version of the example the front door opened for them 40 seconds later than the back door, then in the second version this will happen only 40 - 15 = 25 seconds later. It turns out, therefore, that for the people on the ship the front door opened earlier than the back door, and for the people on the pier - later.

So, what happened earlier for one laboratory happened later for another. From this it is clear that the concept of time itself is a relative concept.

This discovery was made in 1905 by twenty-six-year-old physicist Albert Einstein. Before that, man imagined time as absolute - the same everywhere in the world, independent of any laboratory. Thus, people once considered the directions of up and down to be the same all over the world.

And now time has suffered the fate of space. It turned out that the expression "at the same time" makes no more sense than the expression "at the same place" if it is not specified which laboratory they refer to.

Perhaps someone still has a question: well, in fact, regardless of any laboratory, are any two events simultaneous or not? Thinking about this question is just as absurd as thinking about the question, where in reality, regardless of any laboratories, are top and bottom in the world?

The discovery of the relativity of time made it possible, as you will see from what follows, to resolve all the contradictions to which Michaelson’s experience led physics. This discovery was one of the greatest victories of reason over the ossified ideas that had developed over thousands of years. Having amazed the scientific world with its extraordinary nature, it produced a profound revolution in mankind’s views on nature. In character and significance it can only be compared with the revolution caused by the discovery of the sphericity of the Earth or the discovery of its motion around the Sun.

Thus, Einstein, along with Copernicus and Newton, paved completely new paths for science. And it was not without reason that the discovery of this then still young scientist quickly earned him the fame of the greatest physicist of our century.

The doctrine of the relativity of time is usually called “Einstein’s principle of relativity” or simply “the principle of relativity.” It should not be confused with the law, or principle, of the relativity of motion, which was discussed earlier, that is, with the “classical principle of relativity”, or the “Galileo-Newton principle of relativity”.

Speed ​​has a limit

It is impossible to tell in a journal article about those huge changes and all the new things that the principle of relativity brought to science. In addition, to understand all this you need to have a good knowledge of physics and higher mathematics.

The purpose of our article is to explain only the very foundations of Einstein’s principle and those most important consequences that follow from the relativity of time. This alone, as you have seen, is far from an easy task. Let us note that the principle of relativity is one of the most difficult scientific questions, and it is generally impossible to look into it deeply enough without the help of mathematics.

First, let's look at one very important consequence of the relativity of time concerning speed.

As you know, the speed of steam locomotives, cars and airplanes has been continuously increasing since their invention to this day. It has now reached levels that would have seemed incredible just a few decades ago. It will continue to increase.

Much higher speeds are also known in technology. This is, first of all, the speed of bullets and artillery shells. The speed of flight of bullets and shells, thanks to continuous technical improvements, has also increased from year to year and will continue to increase.

But the highest speed used in technology is the speed of signal transmission using light rays, electric current and radio waves. In all three cases, it is approximately equal to the same value - 300 thousand kilometers per second.

One might think that with the further development of technology, with the discovery of some new rays, this speed will be surpassed; By ever increasing the speeds available to us, we will eventually be able to come as close as we like to the ideal of instantaneous transmission of signals or efforts over any distance.

Michaelson's experience shows, however, that this ideal is unattainable. In fact, with an infinitely high transmission speed, signals from two events would reach us instantly under all conditions; and if in one laboratory two events occurred simultaneously, then in all other laboratories they would also be observed simultaneously - at the same moment when they occurred. And this would mean that “simultaneity” became absolute, completely independent of the movement of laboratories. But the absoluteness of time, as we have seen, is refuted by Michaelson's experience. Therefore, the transmission of signals or efforts cannot be instantaneous.

In other words, the speed of any transmission cannot be infinitely large. There is a certain speed limit - a maximum speed that cannot be exceeded under any circumstances.

It is easy to verify that the maximum speed coincides with the speed of light. Indeed, according to the Galileo-Newton principle of relativity, the laws of nature are the same in all laboratories moving relative to each other rectilinearly and uniformly. This means that for all such laboratories the maximum speed should be the same. But what speed remains constant in all laboratories? As we have seen, it is the speed of light that has such amazing constancy, and only it! It follows that the speed of light is not just the speed of propagation of any one (albeit very important) action in the world: it is at the same time the maximum speed that exists in nature.

The discovery of the existence of maximum speed in nature was also one of the greatest victories of human thought. A physicist of the last century could not have figured out that there is a limit to speed. If, during his experiments, he had stumbled upon the fact of the existence of a limiting speed, he would have decided that this was an accident, that only the limitations of his experimental capabilities were to blame. He would have the right to think that with the development of technology, the maximum speed could be surpassed.

The opposite is clear to us: to count on this would be as ridiculous as to believe that with the development of navigation it will be possible to reach a place on the earth’s surface more than 20 thousand kilometers away from the starting point (that is, more than half the earth’s circumference).

When does a minute equal an hour?

To fully explain the relativity of time and the ensuing consequences, which seem strange out of habit, Einstein uses examples with a train. Let's do the same. We will call the giant train moving at an imaginary fabulous speed “Einstein’s train.”

Let's imagine a very long railway. There are two stations at a distance of 864 million kilometers from one another. To travel the distance between them, Einstein's train, moving at a speed of, say, 240 thousand kilometers per second, would take an hour. Both stations have perfectly accurate clocks.

At the first station the traveler boards the train. First, he sets his pocket chronometer exactly according to the station clock. Upon arrival at another station, he checks it with the station clock and is surprised to notice that the chronometer is behind...

Why did this happen?

Let's assume that there is an electric light bulb on the floor of the carriage and a mirror on the ceiling. A ray of light from a light bulb falling on a mirror is reflected back to the light bulb. The path of the beam, as seen by a traveler in the carriage, is shown in the top picture: the beam is directed vertically upward and falls vertically downward.

A different picture will present itself to the observer at the station. During the time during which the light beam traveled from the light bulb to the mirror, the mirror moved along with the train. And during the fall of the reflected beam, the light bulb itself moved the same distance. The path traversed by the ray from the point of view of an observer at the station is shown in the lower figure: it makes up two sides of an equilateral triangle. The base of the triangle is formed by a light bulb being carried forward by the train.

We see that from the point of view of an observer at the station, the ray of light has traveled a greater distance than from the point of view of an observer on the train. At the same time, we know that the speed of light is constant under all conditions: it is exactly the same for both an observer at a station and a traveler on a train. What follows from this?

It is clear that if the speeds are the same, but the lengths of the paths are different, then it takes less time to travel a shorter path, and more time to travel a larger one. It is easy to calculate the ratio of both times.

Suppose that, from the point of view of the observer at the station, 10 seconds passed between the departure of the beam to the mirror and its return to the light bulb. During these 10 seconds the light passed:

300,000 x 10 = 3 million kilometers.

Consequently, sides AB and BC of the isosceles triangle ABC are equal to 1.5 million kilometers each. Side AC 1, the base of the triangle, is equal to the distance covered in 10 seconds by the train, namely:

240,000 x 10 = 2.4 million kilometers.

Half the base, AD 1 is equal to 1.2 million kilometers.

From here it is not difficult to determine the height of the car - the height of the triangle BD. From the right triangle ABD we have:

BD 2 = AB 2 - AD 2 = 1.52 - 1.22

Hence BD = 0.9 million kilometers.

The height is quite respectable, which, however, is not surprising given the astronomical dimensions of Einstein’s train.

The path traveled by the ray from the point of view of an observer on the train is obviously equal to twice the height of the triangle:

2BD = 2 x 0.9 = 1.8 million kilometers.

To travel this path the light will need:

1,800,000/300,000 = 6 seconds.

So, while the beam of light went from the light bulb to the mirror and back, 10 seconds passed at the station, and only 6 seconds on the train. The ratio of time on the train to time at stations is 6/10.

Hence the surprising consequence: according to station time, the train spent an hour traveling between stations, but according to the traveler’s chronometer, only 6/10 of an hour, that is, 36 minutes. That is why, during the movement between stations, the traveler's chronometer lagged behind the station clock and, moreover, by 24 minutes.

We need to think carefully about this fact: this is not why the traveler’s chronometer fell behind; that he walked slower or worked incorrectly. No, it worked the same way as the clocks at the stations. But time on a train moving relative to the stations passed differently than at the stations.

From the diagram with the triangle it is clear that the higher the speed of the train, the greater the lag of the chronometer from the train to the speed of light should be; it is possible to ensure that any short period of time passes on the train in an hour of station time. For example, with a train speed equal to about 0.9999 the speed of light, only 1 minute will pass in an hour of station time in the train (or, conversely, an hour will pass in a minute of station time in the train if an observer at one station checks his time using two chronometers installed at the beginning and end of the train).

Considering time to be absolute, people used to imagine it as something flowing evenly, and, moreover, everywhere and under all conditions in the world at the same speed. But Einstein's train shows that the pace of time is different in different laboratories. This relativity of time is one of the most important properties of the physical world.

From all that has been said, we can conclude that the “time machine” described by Wells in his science fiction story is not such an empty fantasy. The relativity of time opens up the possibility, at least theoretically, of traveling into the future. It is not difficult to see that Einstein’s train is precisely a “time machine.”

Time Machine

In fact, let’s imagine that Einstein’s train moves not in a straight line, but in a circular path. railway. Then, each time he returns to his original station, the traveler will discover that his clock is behind the station clock.

By bringing the speed of the train closer to the speed of light, you can, as you already know, ensure that any small amount of time passes on the train in an hour according to the station clock. This leads to surprising results: while only years will pass on the train, hundreds and thousands of years will pass at the station. Coming out of his “time machine”, our traveler will find himself in a separate future... His relatives and friends have long since died... He will find only their distant descendants alive.

However, Einstein's train is still very different from Wells' car. After all, according to the novelist, she could move in time not due to her high speed, but due to some special technical device. But in reality no such device can be created; this is complete nonsense. There is only one way to get to the future: to give the train colossal speed - close to the speed of light.

One more property distinguishes Einstein's train from Wells's time machine: it is not able to move “backward” in time, that is, it is deprived of the ability to go into the past, and thereby return from the future to the present.

In general, the very idea of ​​​​moving backwards in time is completely meaningless. We can only influence what has not yet happened, but we are not able to change what has already happened. This is clear even from this example: if it were possible to move back in time, it could happen that a person went back in time and killed his parents when they were still babies. And if he returned to the present, he would find himself in the absurd position of a man whose parents died long before he was born!

Moving at a speed close to the speed of light theoretically opens up another possibility: to overcome any distance along with time. And they can be so large in world space that even at maximum speed, a human life would not be enough for most travel.

An example would be a star that is, say, two hundred light years away from us. Since the speed of light is the highest speed in nature, it is therefore impossible to reach this star earlier than two hundred years after launch. And since the duration of human life is less than two hundred years, it would seem to be safe to say that man is fundamentally deprived of the opportunity to reach distant stars.

Yet this reasoning is flawed. The mistake is that we talk about two hundred years as something absolute. But time is relative, that is, there is no common time for all laboratories. At the stations there was one time count, but on Einstein's train there was another.

Let's imagine an astronaut traveling into outer space. By the time it reaches a star two hundred light years away from us, according to earthly time, two hundred years will actually pass. In a rocket, depending on its speed relative to the Earth, as we know, any short period of time can pass.

Thus, the astronaut will reach the star according to his time calculation not in two hundred years, but, say, in one year. At a sufficiently high speed, it is theoretically possible to “fly” to a star and return according to the rocket clock, even in one minute...

Moreover: when moving at the maximum speed in the world - 300 thousand kilometers per second - time becomes extremely small, that is, equal to zero. In other words, if a rocket could move at the speed of light, time would completely stop for the observer in it, and from the point of view of this observer, the moment of start would coincide with the moment of finish.

We repeat that all this is conceivable only theoretically. In practice, traveling to the future and to distant stars is impossible, since the movement of cars and people at speeds close to the speed of light is impossible for technical reasons.

And the sizes of objects are relative

The reasoning and entertaining examples given in the previous chapters seem fantastic. But their goal is not to captivate the reader with fantasy, but to show the depth and seriousness of the consequences arising from the relativity of time.

It is not difficult to see that the relativity of time also implies the relativity of the sizes of bodies.

Let the length of the platform past which Einstein's train passes be 2.4 million kilometers. At a speed of 240 thousand kilometers per second, the train will pass the platform within 10 seconds. But in 10 seconds of station time, only 6 seconds will pass on the train. From here, the traveler will rightfully conclude that the length of the platform is 240 thousand x 6 = 1.44 million kilometers, and not 2.40 million kilometers.

This means that an object at rest relative to any laboratory is longer than a moving one. The platform was moving relative to the train, but relative to the station it was at rest. Therefore, for the observer at the station it was longer than for the traveler. The train cars, on the contrary, were 10/6 times shorter for the observer at the station than for the traveler.

As speed increases, the length of objects decreases more and more. Therefore, at the highest speed it should become the lowest, that is equal to zero.

So, every moving body contracts in the direction of its movement. In this regard, it is necessary to amend one of the examples we gave in No. 9 of the magazine, namely: during an experiment with opening doors on a steamship, we found that for an observer on the pier, the second door opened 40 seconds later than the first. But since the length of the steamship, moving at a speed of 240 thousand kilometers per second, was reduced by 10/6 times relative to the pier, the actual time interval between opening the doors will be equal to 40 seconds, not 40 seconds according to the clock on the pier: 10/6 = 24 seconds . This numerical correction, of course, does not change the fundamental conclusions we drew from the experience with the steamer.

The relativity of the sizes of bodies immediately entails a new, perhaps the most striking, consequence of the principle of relativity. “The most striking” because it explains the unexpected result of Michaelson’s experiment, which at one time brought confusion to the ranks of physicists. The matter concerned, as you remember, the addition of velocities, which for some unknown reason did not “want” to obey ordinary arithmetic.

Man has always been accustomed to adding up velocities directed in a straight line and in one direction, purely arithmetically, that is, as simply as tables or apples. For example, if a ship is sailing in a certain direction at a speed of 20 kilometers per hour, and a passenger is walking along its deck in the same direction at a speed of 5 kilometers per hour, then the speed of the passenger relative to the pier will be equal to 20 + 5 = 25 kilometers per hour hour.

Until recently, physicists were confident that this method of addition was absolutely correct and suitable for finding the sum of any speeds. But the principle of relativity did not leave this rule of mechanics untouched.

Try, for example, adding up speeds of 230 and 270 thousand kilometers per second. What will happen? 500 thousand kilometers per second. But such a speed cannot exist, since 300 thousand kilometers per second is the highest speed in the world. From this it is at least clear that the sum of any and how many speeds, in any case, cannot exceed 300 thousand kilometers per second.

But perhaps it is permissible to add arithmetically lower speeds, for example, 150 and 130 thousand kilometers per second? After all, their sum, 280 thousand kilometers per second, does not exceed the maximum speed in the world.

It is easy to see that the arithmetic sum is incorrect here too. Let, for example, let a steamship move past a pier at a speed of 150 thousand kilometers per second, and a ball roll along the deck of a steamship at a speed of 130 thousand kilometers per second. The sum of these velocities must express the speed of the ball relative to the pier. However, from the previous chapter we know that a moving body contracts in size. Therefore, a distance of 130 thousand kilometers on a ship is not at all equal to 130 thousand kilometers for an observer on the pier, and 150 thousand kilometers along the shore are not at all equal to 150 thousand kilometers for a passenger on a ship.

Next, to determine the speed of the ball relative to the pier, the observer uses a clock on the pier. But the speed of the ball on a steamship is determined by the steamship time. And time on a moving ship and on the pier, as we know, are not at all the same.

This is how the question of adding velocities looks in practice: we have to take into account the relativity of both distances and time. How should the speeds be added?

Einstein gave a special formula for this, corresponding to the principle of relativity. Until now we have not given formulas from the theory of relativity, not wanting to burden this difficult article with them. However, the concise and clear language of mathematics makes many things immediately clear, replacing long arguments with a lot of words. The formula for adding velocities is not only much simpler than all previous arguments, but in itself is so simple and interesting that it is worth citing:

Here V 1 and V 2 are the speed components, W is the total speed, c is the highest speed in the world (the speed of light), equal to 300 thousand kilometers per second.

This wonderful formula has just the right property: no matter what speeds we add together, we will never get more than 300 thousand kilometers per second. Try adding 230 thousand and 270 thousand kilometers per second or even 300 thousand and 300 thousand kilometers per second using this formula and see what happens.

When adding small speeds - such as we encounter in most cases in practice - the formula gives the result we are accustomed to, which differs little from the arithmetic sum. Let’s take, for example, even the highest modern speeds of movement. Let two planes move towards each other, each flying 650 kilometers per hour. What is the speed of their approach?

Arithmetically - (650 + 650) = 1300 kilometers per hour. According to Einstein's formula, it is only 0.72 microns per hour less. And in the above example with a slowly moving ship with a person walking along the deck, this difference is even 340 thousand times less.

It is impossible to detect such quantities in such cases by measurements. And their practical value is zero. From here it is clear why people for thousands of years did not notice that the arithmetic addition of velocities is fundamentally incorrect: the inaccuracy in such addition is much less than the most stringent requirements of practice. And therefore, in technology, everything always agreed with the calculations, if only the calculations were correct.

But it is no longer possible to add arithmetically speeds comparable to the speed of light: here we can fall into gross errors. For example, at speeds of 36 thousand kilometers per second the error will exceed 1 thousand kilometers, and at 100 thousand kilometers per second it will already reach 20 thousand kilometers per second.

The fact that the arithmetic addition of velocities is incorrect, but Einstein's formula is correct, is confirmed by experience. It could not be otherwise: after all, it was experience that forced physicists to reconsider old concepts in mechanics and led them to the principle of relativity.

Knowing how to actually add velocities, we can now understand the “mysterious” results of Michaelson’s experiment. Carrying out this experiment when the Earth was moving towards the light beam at a speed of 30 kilometers per second, Michaelson expected to get a result of 300,000 + 30 = 300,030 kilometers per second.

But you can’t add up speeds like that!

Substitute V 1 = c (c is the speed of light) and V 2 = 30 into the formula for adding speeds, and you will find that the total speed is only equal to c1, and not more. This was exactly the result of Michaelson's experiment.

The same result will be obtained for all other values ​​of V 2, if only V 1 is equal to the speed of light. Let the Earth travel any number of kilometers per second: 30 - around the Sun, 275 - together with solar system and thousands of kilometers - with the entire Galaxy. This doesn't change things. In all cases of adding the Earth's speed to the speed of light, the formula will give the same value c.

So, the results of Michaelson's experiment surprised us only because we did not know how to correctly add velocities. We did not know how to do this, since we did not know that bodies contract in the direction of their movement and that time passes differently in different laboratories.

Mass and energy

It remains to consider the last question.

One of the most important properties of any body is its mass. We are accustomed to thinking that it always remains unchanged. But calculations based on the principle of relativity show something else: when a body moves, its mass increases. It increases as many times as the length of the body decreases. Thus, the mass of Einstein's train, moving at a speed of 240 thousand kilometers per second, is 10/6 times greater than the mass at rest.

As the speed approaches the limit, the mass grows faster and faster. At maximum speed, the mass of any body must become infinitely large. The usual speeds that we encounter in practice cause a completely insignificant increase in mass.

However, it is still possible to test this phenomenon experimentally: modern experimental physics is able to compare the mass of rapidly moving electrons with the mass of resting electrons. And experience completely confirms the law of dependence of mass on speed.

But in order to impart speed to bodies, it is necessary to expend energy. And so it turns out that in general any work done on a body, any increase in the energy of the body entails an increase in mass proportional to this expended energy. Therefore, the mass of a heated body is greater than that of a cold body, the mass of a compressed spring is greater than that of a free one.

Insignificant amounts of units of mass correspond to enormous amounts of units of energy. For example, to increase the mass of a body by just 1 gram, 25 million kilowatt-hours of work must be done on it. In other words, the mass is 25 million kilowatt-hours electrical energy equal to 1 gram. To obtain this gram, all the energy generated by the Dnieper hydroelectric station is required for two days. Calculating just one kopeck per kilowatt-hour, we find that 1 gram of the cheapest electrical energy costs 250 thousand rubles. And if you turn electricity into light, then 1 gram of light will cost about 10 million rubles. This is many times more expensive than the most expensive substance - radium.

If you burn 1 ton of coal indoors, the combustion products will weigh, after cooling, only 1/3000th of a gram less than the coal and oxygen from which they were formed. The missing fraction of mass is lost by heat radiation. And heating 1 ton of water from 0 to 100 degrees will entail an increase in its mass by less than 5/1,000,000 parts of a gram.

It is quite understandable that such insignificant changes in the mass of bodies when they lose or gain energy elude the most accurate measurements. However, modern physics knows of phenomena in which a change in mass becomes noticeable. These are processes that occur during the collision of atomic nuclei, when the nuclei of some elements form the nuclei of other elements.

For example, when the nucleus of a lithium atom collides with the nucleus of a hydrogen atom, two nuclei of a helium atom are formed. The mass of these two nuclei is already a significant amount - 1/4 part - less total mass hydrogen and lithium nuclei. Therefore, when 1 gram of a mixture of lithium and hydrogen is converted into helium, 1/400th of a gram of energy should be released, which in kilowatt-hours will be:

25,000,000/ 400 = 62.5 thousand kilowatt-hours.

Thus, if we could easily carry out nuclear transformations, we would become the owners of a rich source of energy: to obtain the power of the Dnieper Hydroelectric Station, it would be enough to convert only 4 grams of a mixture of lithium and hydrogen into helium every hour.

New and old physics

This concludes our brief introduction to the principle of relativity.

We have seen what serious and profound changes the principle of relativity has brought to the worldview that has developed among humanity over many centuries. Doesn't this mean that old ideas are completely destroyed? That they should be completely rejected? That all physics created before the discovery of the principle of relativity should be crossed out as incorrect?

No, because the discrepancy between old physics (called “classical”) and physics that takes into account the principle of relativity (“relativistic”, from the Latin word “relatio”, which means “reference”) is too small in almost all areas of our practical activity.

If, for example, a passenger on an ordinary, even the fastest train (but, of course, not Einstein’s train) decided to introduce a time correction based on the principle of relativity, he would be laughed at. Over the course of a day, such an amendment would be expressed in ten billionths of a second. The shaking of the train and the inaccurate operation of the best watch mechanism have an incomparably greater effect on the watch's readings.

An engineer who would introduce into calculations the increase in the mass of water when it is heated could be called crazy. But a physicist who studies the collision of atomic nuclei, but does not take into account the possible changes in mass, should be expelled from the laboratory for ignorance.

Designers will always design cars using the laws of classical physics: corrections to the principle of relativity will have less impact on cars than a microbe landing on a flywheel. But a physicist observing fast electrons must take into account the change in their mass depending on the speed.

So, the laws of nature, discovered before the emergence of the principle of relativity, are not canceled; the theory of relativity does not refute, but only deepens and refines the knowledge obtained by the old science. It sets the boundaries within which this knowledge can be used without making mistakes.

In conclusion, it must be said that the theory of relativity is not limited to the issues that we considered in this article. Continuing the development of his teaching, Einstein later gave a completely new picture of such an important phenomenon as universal gravity. In this regard, the doctrine of relativity was divided into two parts. The first of them, not relating to gravitation, was called the “particular” or “special” “principle of relativity”; the second part, covering issues of gravitation, is called the “general principle of relativity.” Thus, we became acquainted only with a particular principle (consideration of the general principle was not the purpose of this article).

It only remains to note that with a sufficiently deep study of physics, all the labyrinths of the complex building of the theory of relativity become completely clear. But getting into them, as we know, was far from easy. This required a brilliant guess: it was necessary to be able to draw the correct conclusions from Michaelson’s experiment - to discover the relativity of time with all the ensuing consequences.

Thus, humanity, in its eternal quest to understand the world more widely and deeply, won one of its greatest victories.

It owes it to the genius of Albert Einstein.

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 can be explained this way: for example, friends from the future gave you a spaceship that can fly at high speed. On the nose 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 by 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 "The Theory of Relativity for Dummies." It is not entirely correct, but it is very simple and clear. If on stretched fabric When you put any object down, it forms a “sag” 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 applies not only 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 the most accurate atomic clock. 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.

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 = mс2
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:

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