The special theory of relativity of Einstein and Poincaré Recall the principle of relativity of Galileo, which states that the physical laws of Newton and Galileo will remain completely unchanged if we move from a resting frame of reference to another, moving uniformly

Chapter 14 The Theory of Relativity and the Return of Time Thus, the recognition of the reality of time opens up new approaches to understanding how the universe chooses laws, as well as ways to resolve the difficulties of quantum mechanics. However, we still have to overcome serious

2.4. The theory of ontological relativity and realism From the thesis of the indeterminacy of translation and the idea of ​​ontological obligations follows ontological relativity, which means, first of all, that the reference is incomprehensible, that we cannot know what

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

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

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

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

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

Clifford Will, theoretical physicist, University of Florida

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

A new look at gravity

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

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

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

Testing Einstein's Theory

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

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

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

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

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

Clifford Will

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

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

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

unified theory

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

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

Why are these experiments needed at all?

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

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

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

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

Today it is commonly called the Special Theory of Relativity or SRT. SRT studies the physical principles of uniform and rectilinear motion.

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

Einstein laid down two fundamental principles at the basis of SRT:

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 verifiable in practice, Einstein presented evidence in the form of experimental results.

Let's look at the principles with examples.

• Imagine that two objects are moving at constant speeds in a straight line. Instead of considering their movements relative to a fixed point, Einstein proposed to study them relative to each other. For example, two trains travel on adjacent tracks at different speeds. You are sitting in one, 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 go. At least until the trains start to accelerate or turn.
• They like to explain the theory of relativity using space examples. This is 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 the spacecraft, then no matter what happens to the ship itself: it can move at high speed, hang motionless or disappear altogether together with the emitter, the observer from the station will see the light after the same time interval for all incidents.

General theory of relativity.

From 1907 to 1916 Einstein worked on the creation of the General Theory of Relativity. In this section of physics, the movement of material bodies in general is studied, objects can accelerate and change trajectories. The general theory of relativity combines the doctrine of space and time with the theory of gravitation, 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 the special one. 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, while we are able to perceive only their three-dimensional projections. That is, no matter how you bend the ruler, you will see only projections of an unknown 4-dimensional body. Einstein considered the space-time continuum to be indivisible.

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

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

So it is proved that the rays of light are bent in the presence of gravitating bodies. Also experimentally confirmed time dilation with increasing altitude. Einstein concluded that space-time is curved in the presence of a massive body and gravitational acceleration is only a projection into 3D of uniform motion in 4-dimensional space. And the trajectory of small bodies rolling down on the canvas towards a larger object remains rectilinear for them.

Currently, general relativity is the leader among other theories of gravity and is used in practice by engineers, astronomers and developers of satellite navigation. Albert Einstein is in fact a great reformer of science and the concept of natural science. In addition to the theory of relativity, he created the theory of Brownian motion, investigated 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 birthday 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 understanding of the world around us, the principle of relativity, put forward by Einstein as early as 1905, produced the same tremendous revolution that the Copernican doctrine made 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, which is in constant 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, a great knowledge of mathematics and physics is needed. However, every cultured person can and should have a general idea of ​​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.

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

Relativity we're used to

Does every statement make sense?

Obviously not. For example, if you say "bee-ba-boo", then no one will find any meaning in this exclamation. But even quite meaningful words, combined according to all the rules of grammar, can also give 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, then 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 what is now on the globe: day or night? The answer depends on where the question is asked. When it's day in Moscow, it's night in Chicago. Therefore, the statement "it is now day or night" has no meaning unless it is indicated to which place on the globe it refers. Such concepts will be called "relative".

The two drawings shown here show a shepherd and a cow. In one picture the shepherd is bigger than the cow, and in the other the cow is bigger 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 one was closer to the cow, the second one was 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 larger its angular magnitude and the larger it looks, and the farther the object, the smaller its angular magnitude and the smaller it appears.

The absolute turned out to be relative

Not always, however, the relativity of our concepts is as obvious as in the examples given.

We often say "above" and "below". Are these concepts absolute or relative? In the old days, when it was not yet known that the Earth was spherical, and it was imagined as a flat pancake, it was taken for granted that the directions of "up" and "down" throughout the world were the same.

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

All this leaves us in no doubt now. Meanwhile, history shows that it was not so easy to understand the relativity of "up" and "down". People are very apt to assign absolute meaning to concepts whose relativity is not clear from everyday experience. Recall the ridiculous "objection" against the sphericity of the Earth, which was very successful in the Middle Ages: on the "other side" of the Earth, they say, trees would have to grow downwards, raindrops would fall upwards, and people would walk upside down.

Indeed, if we consider the direction of the vertical in Moscow as 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 walk 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 movement is relative

Let's imagine two travelers traveling in the express train Moscow - Vladivostok. They agree to meet every day in the same place in the dining car and write letters to their husbands. Travelers are sure 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 firmly assert 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 "one and the same place" is relative. Regarding the train, the travelers really met all the time “in the same place”, and relative to the earth's surface, the place of their meeting was constantly changing.

Thus, position in space is a relative concept. Speaking of 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, without mentioning other bodies in the answer, we would have to consider such a requirement as completely impracticable.

It follows from this that the movement, or movement, of bodies is also relatively. And when we say "a body is moving," 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. We will agree to call such points “laboratories”. Our imaginary laboratories can be anything in the world: houses, cities, trains, planes, Earth, other planets, the Sun and even stars.

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

It all depends on which laboratory we observe it from. Assume that the pilot is ejecting cargo from the aircraft. From the point of view of the pilot, the load flies down vertically in a straight line, and from the point of view of the observer on the ground, the falling load describes a curved line - a parabola. On what trajectory does the load actually move?

This question makes as little sense as the question of which photograph of a person is "real", the one in which he is taken from the front, or the one in which he is taken from behind?

The geometric shape of the curve along which the body moves has the same relative character as a photograph of a person. When photographing a person from the front and back, we will get different shots, and each of them will be perfectly correct. In the same way, observing the movement of any body from different laboratories, we see different trajectories, and all these trajectories are "real".

But are they all equal for us? Is it still impossible to find such an observation point, such a laboratory, from where we can best study the laws that govern the motion of a body?

We just compared the trajectories of a moving body with photographs of a person - both can be very diverse - it all depends on from which point you observe the movement of the body or take the picture. But you know that in photography, not all points of view are equal. For example, if you need a photo for ID, then you naturally want to be photographed from the front, not from behind. Similarly, in mechanics, that is, when studying the laws of motion of bodies, we must choose the most suitable from all possible points of observation.

In search of 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 whatsoever. Let us agree once and for all to consider that the 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 motion of bodies. In fact, this body, on which no forces act and which we have agreed to regard as at rest, can serve us as a guide, a "guiding star" in the study of the motion of all other bodies.

Imagine that we have removed some body so far from all other bodies that no forces will act on it any more. And then we will be able to establish how physical phenomena should proceed on such a resting body. In other words, we can find the laws of mechanics that govern this imaginary "resting" laboratory. And by comparing them with what we observe in other, real laboratories, we can already judge the true properties of motion in all cases.

So, it would seem that everything is fine: we have found a strong point - "peace", although conditional, and now the movement has lost its relativity for us.

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

Imagine observers living on a lonely ball, lost in the vast expanses of the universe. They do not feel the influence of any extraneous forces on themselves 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. With great speed, this second ball rushes, 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 “foreign” ball is moving towards them.

Which of them is right? There is no point in arguing about this, since the state of rectilinear and uniform motion is completely indistinguishable from the state of rest.

To be convinced of this, you and I do not even need to climb into the infinite depths of the universe. Get on the river steamer at the wharf, lock yourself in your cabin, and curtain the windows well. Under such conditions, you will never detect whether you are standing still or moving in a straight line 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 up will also fall vertically down; the pendulum of the clock will swing just like on the wall of your apartment.

Your steamer can go at any speed, but the same laws of motion will prevail on it as on a completely stationary steamer. Only at the moment of slowing down or accelerating it can you detect its movement; when it goes 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 in the world there can be infinitely many “rests” moving uniformly and rectilinearly relative to each other. Therefore, when we talk about the motion of a body, we must always indicate with respect to which particular “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. So it really is. Suppose, for example, that you are running on the deck of a steamboat at a speed of 5 meters per second. If the ship is moving in the same direction at 10 meters per second, then your speed relative to the shore will be 15 meters per second.

Therefore, the statement: “a body moves with such and such a speed”, without indicating what the speed is measured against, does not make sense. Determining the speed of a moving body from different points, we should get 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 discovered by him 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 apparatus.

This continued until the end of the 19th century, when new phenomena were discovered that were 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 brought confusion to the ranks of physicists; it was so striking 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 an anvil or on a steel rail. However, the impact sound is completely inaudible. It seems that 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 is not difficult to understand why this is happening. Under normal conditions, sound travels through the air at a speed of about 340 meters per second, so we hear a hammer blow not at the moment it occurs, but only after the sound from it has time to reach our ear.

Here is another, more striking example. Lightning and thunder happen at the same time, but it often seems that lightning flashes silently, since the peals of thunder reach our ear only after a few seconds. If we hear them late, for example, 10 seconds, then this means that lightning is 340 x 10 = 3400 meters away from us, or 3.4 kilometers.

In both cases, we are talking about two moments: when an event actually happened, and 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 coming down, the lightning flashing. In this case, we assume that the event really occurs at the very moment when we see it. But is it really so?

No not like this. After all, we do not perceive events directly. In the phenomena that we observe with the help of vision, light is involved. And light does not propagate in space instantly: like sound, it takes time for light rays to overcome the distance.

In the void, light travels at about 300,000 kilometers per second. This means that if a light flashes at a distance of 300 thousand kilometers from you, you can notice its flash not immediately, but only a second later.

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

The unimaginably huge speed of light may seem surprising. Much more surprising, however, is something else: the fact that the speed of light is remarkable for its amazing constancy. Let's see what this constancy is.

It is known that the movement of bodies can be artificially slowed down and accelerated. If, for example, a box of sand is placed 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 otherwise. In air, they propagate more slowly than in emptiness, in water - more slowly than in air, and in glass - even more slowly. However, leaving any substance (of course, transparent) into the void, light continues to propagate at its former speed - 300 thousand kilometers per second. At the same time, the speed of light does not depend on the properties of its source: it is exactly the same for the rays of the Sun, and the searchlight, and the candle. In addition, it does not matter whether the light source itself is moving or not - this does not affect the speed of light in any way.

In order to fully understand the meaning of this fact, let us compare once again the propagation of light with the motion of ordinary bodies. Imagine that you are shooting a stream of water from a hose at a speed of 5 meters per second on the street. This means that each particle of water travels 5 meters per second relative to the street. But if you place a 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 already be 15 meters per second: the particles of water are given speed not only by the hose, but also by a moving car, which carries the hose along with the jet forward.

Comparing the light source with a hose, and its rays - with a jet of water, we will see a significant difference. It makes no difference to the rays of light from which source they entered the void and what happened to them before they entered the void. Once 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 velocities, and for simplicity we will assume that all the phenomena we imagine occur in a void, 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. Both of them measure the speed of light propagation. What will be the results of their work?

Since the rays propagate in all directions, and both observers move along with the steamer in one direction, the following picture will turn out: the observer located at the rear end of the steamer moves towards the rays, and the front one is constantly moving away from them.

Therefore, the first observer must find that the speed of light is 300,000 kilometers plus the speed of the steamer, and the second must find that the speed of light is 300,000 kilometers minus the speed of the steamer. And if we imagine for a moment that a steamship travels a monstrous distance of 200,000 kilometers per second, then the speed of light found by the first observer will be 500,000 kilometers, and by the second, 100,000 kilometers per second. On a stationary steamboat, both observers would get the same result - 300,000 kilometers per second.

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

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

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

It is easy to see that all this is in stark contrast to the conclusions we reached in the previous issue of the journal. In fact: we talked about the fact that on a body moving uniformly in a rectilinear manner, everything proceeds the same as on a stationary one. Therefore, whether we, for example, shoot on a steamer in the direction of its movement or against its movement, the speed of the bullet relative to the steamer will remain the same and will be equal to the speed on a stationary steamer. At the same time, we were convinced that motion, speed and rest are relative concepts: absolute motion, 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 fundamental laws: it dominates the whole world; its justice has been confirmed by experience a myriad of times, is confirmed everywhere and every minute until now; if he suddenly ceased to be just, an unimaginable turmoil would engulf the universe. But the light not only does not obey him, but even refutes him!

Mikaelson's experience

What to do with this contradiction? Before expressing certain considerations on this subject, let us pay attention to the following circumstance: that the properties of light contradict the law of relativity of motion, we have established exclusively by reasoning. Admittedly, these were very persuasive 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, with all its merits, will turn out to be very little like the real world that surrounds us.

The supreme judge of any physical theory is always experience, and therefore, not limited to reasoning about how light should propagate on a moving body, one should turn to experiments that will show how it actually propagates under these conditions.

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

In order to be able to determine a slight change in the speed of light on relatively slowly moving bodies accessible to us, it was necessary to create measuring instruments of exceptionally high accuracy. And only when such devices could be made, 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 Mikaelson.

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

Mikaelson measured the speed of light on Earth in various directions with very high accuracy, that is, he practically carried out what we mentally did with you on an imaginary moving steamer. To catch the tiny difference of 30 kilometers compared to the huge number of 300,000 kilometers, Michaelson had to use very complex experimental techniques and use all his great ingenuity. The accuracy of the experiment was so great that Mikaelson would have been able to detect a much smaller difference in speeds than he wanted to detect.

Out of the frying pan into the fire

The result of the experiment seemed to be obvious in advance. Knowing the properties of light, one could 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! Mikaelson's experiment gave completely unexpected results. Over the course of a number of years it was repeated many times under the most varied conditions, but it invariably led to the same startling conclusion.

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

So light is no exception. It obeys the same law as a bullet on a moving steamboat, Galileo's law of relativity. It was not possible to detect the "absolute" motion 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 got out of the fire and into the frying pan.

In order to clarify the new contradictions to which Mikaelson's experience has led, let us review our investigations in order.

We first established that absolute motion and rest do not exist; This is what Galileo's law of relativity says. 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, Mikaelson performed an experiment. The experiment showed the opposite: there is no contradiction - and light obeys the law of relativity. Therefore, absolute motion and rest again do not exist. On the other hand, the implications of Mikaelson's experience 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 motion, and, therefore, the speed of light is still not a relative, but an absolute value.

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

The most mysterious and strange thing about all this was that science here dealt with absolutely clear, firmly established facts: with the law of relativity, the known properties of light, and Mikaelson's experiment. And they led, it would seem, to perfect absurdity.

Contradiction of truths... But truths cannot contradict each other, since there can be only 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 - they did not find an answer to these questions. But in 1905, the greatest physicist of our time, Albert Einstein, gave a brilliant explanation to the riddle. Appearing from a completely unexpected direction, it produced the impression of an exploding bomb on physicists.

Einstein's explanation is so different from all the concepts that mankind has been accustomed to 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 on various physical phenomena in the world have more and more confirmed its validity.

When the doors open

In order to understand Einstein's explanation, one must first be familiar with one consequence of Mikaelson's experiment. Let's look at it right away with an example. Let's use for this once again a fantastic steamer.

Imagine a steamship 5,400,000 kilometers long. Let it move in a straight line and uniformly with a fabulous speed of 240 thousand kilometers per second. At some point, a light bulb comes on in the middle of the steamer. There are doors at the bow and stern of the ship. They are arranged in such a way that at the moment when light from a light bulb falls on them, they automatically open. Here the lamp is lit. When exactly will the doors open?

To answer this question, let us recall the results of Mikaelson's experiment. Mikaelson's experiment showed that relative to observers on a moving Earth, light propagates in all directions at the same speed of 300,000 kilometers per second. The same, of course, will happen on a moving steamer. But the distance from the light bulb to each end of the ship is 2700.000 kilometers, and 2700.000: 300.000 = 9. This means that the light from the light bulb will reach each door in 9 seconds. Thus, both doors will open at the same time.

This is how the case will be presented to the observer on the ship. And what will people see on the pier, past which the steamer is moving?

Since the speed of light does not depend on the movement of the light source, it is equal to the same 300,000 kilometers per second relative to the pier, despite the fact that the light source is on a moving ship. But, from the point of view of the observer on the wharf, the door at the stern of the ship moves 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 the 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 steamer) 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 bulb is on. What about the front?

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

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. That's what the picture will be presented to people on the pier! 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, and non-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 is 1 meter?

And, mind you, the people at the pier will not think that the doors opened 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 passengers of the steamer also correctly established that both doors opened at the same time. And it was shown arithmetically. What happens? Arithmetic vs 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 completely different from what mankind considered it to be until now.

Einstein revised these old, 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 Mikaelson's experiment. We have considered an example of an imaginary steamer on which two doors open at the signal of a light, and we have established a striking fact: from the point of view of observers on the steamer, the doors open at the same moment, but from the point of view of observers on the wharf, at different moments.

What a person is not used to seems incredible to him. The case of the doors on a steamboat seems quite incredible because we have never moved at a speed even remotely approaching the fabulous number of 240,000 kilometers per second. But we must take into account that the phenomena occurring at such speeds can be very different from those to which we are accustomed in everyday life.

Of course, in fact, there are no steamships moving 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. Recall that the example with opening doors is not based on abstract reasoning, but solely on firmly established facts obtained through experience: the Mikaelson experiment 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 considered 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 at different times.

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

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

Both of them were right: with regard to the train, the travelers actually met in the same place, but with respect to the railroad tracks, 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 steamer - are similar to each other. In both cases, we are talking about relativity, and even the same words are found: “to the same” and “to different”. Only in the first example it is about places, that is, about space, and in the second - about moments, that is, about time. What follows from here?

That the concept of time is just as relative as the concept of space.

To finally verify this, let's modify the steamboat example a bit. Let's assume that the mechanism of one of the doors is faulty. Let the people on the boat notice that the front door opened 15 seconds before the back door because of this malfunction. And what will people see at the pier?

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

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

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

And now the fate of space has befallen time. 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 indicated 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 as absurd as thinking about the question, but where in fact, regardless of any laboratories, are the top and bottom in the world?

The discovery of the relativity of time made it possible, as you will see later, to resolve all the contradictions that Mikaelson's experiment led physics to. This discovery was one of the greatest victories of the mind over the stagnant ideas that have developed over the millennia. Striking the scientific world with its unusualness here, it produced a profound revolution in the views of mankind on nature. In character and significance, it can only be compared with the upheaval caused by the discovery of the sphericity of the Earth or the discovery of its movement around the Sun.

So Einstein, along with Copernicus and Newton, paved completely new paths for science. And it was not for nothing that the discovery of this then still young scientist quickly gained 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 principle of relativity of Galileo - Newton."

Speed ​​has a limit

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

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. 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.

To begin with, consider one very important consequence of the relativity of time, concerning speed.

As you know, the speed of steam locomotives, automobiles and airplanes has been continuously increasing since their invention and to this day. At present, it has reached a value 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 in the future.

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, even 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.

Mikaelson's experience shows, however, that this ideal is unattainable. Indeed, at an infinitely high transmission rate, signals from two events would under all conditions reach us instantly; 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 Mikaelson's experiment. Therefore, the transmission of signals or forces cannot be instantaneous.

In other words, the speed of any transmission cannot be infinitely large. There is a certain speed limit - a speed limit that under no circumstances can be exceeded.

It is easy to verify that the limiting speed coincides with the speed of light. Indeed, according to the principle of relativity of Galileo - Newton, the laws of nature in all laboratories moving relative to each other in a straight line and uniformly are the same. This means that for all such laboratories the same speed should be the limiting one. But what kind of speed keeps its value unchanged in all laboratories? Such amazing constancy, as we have seen, is just the speed of light, and only it! It follows from this that the speed of light is not just the speed of propagation of some one (albeit very important) action in the world: it is at the same time the limiting speed that exists in nature.

The discovery of the existence of a limiting velocity in nature was also one of the greatest victories of human thought. A physicist of the last century could not have guessed that there was a limit to speed. If, however, he would have stumbled upon the fact of the existence of the limiting speed during experiments, then he would have decided that this was an accident, that only the limitedness of his experimental capabilities was to blame. He would be justified in thinking that with the development of technology, the limiting speed could be surpassed.

The opposite is clear to us: it would be as ridiculous to count on this as to believe that with the development of navigation it will be possible to reach a place on the earth's surface that is 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?

In order to comprehensively explain the relativity of time and the consequences that follow from this, which seem strange from the habit, Einstein uses examples with a train. We will do the same. A giant train moving at an imaginary fabulous speed will be called "Einstein's train."

Imagine a very long railroad. There are two stations at a distance of 864 million kilometers from one another. To cover the distance between them, Einstein's train, moving at a speed of, say, 240 thousand kilometers per second, will need an hour of time. Both stations have perfectly accurate clocks.

A traveler gets on the train at the first station. First, he sets his pocket chronometer exactly to the station clock. Upon arrival at another station, he compares it with the station clock and is surprised to notice that the chronometer has fallen behind ...

Why did this happen?

Suppose that there is an electric light bulb on the floor of the car, and a mirror on the ceiling. A beam of light from a light bulb hitting a mirror is reflected back to the light bulb. The path of the beam, as seen by the traveler in the car, is shown in the upper figure: the beam is directed vertically upwards and falls vertically downwards.

A different picture will be presented to the observer at the station. During the time during which the beam of light went 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 traveled by the ray from the point of view of the observer at the station is shown in the lower figure: it makes up two sides of an isosceles 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 the observer at the station, the beam of light traveled a greater distance than from the point of view of the observer in the train. At the same time, we know that the speed of light is constant under all conditions: it is exactly the same for an observer at the station, and for a traveler in a train. What follows from here?

It is clear that if the speeds are the same, but the lengths of the paths are different, then less time is spent on passing a smaller path, and more time is spent on passing 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 elapsed between the departure of the beam to the mirror and its return to the light bulb. During these 10 seconds, the light has passed:

300.000 x 10 = 3 million kilometers.

Consequently, the sides AB and BC of the isosceles triangle ABC are equal to 1.5 million kilometers each. The side AC 1, the base of the triangle, is equal to the distance traveled by the train in 10 seconds, 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 easy to determine the height of the car - the height of the triangle BD. From right triangle ABD we have:

BD 2 \u003d AB 2 - AD 2 \u003d 1.52 - 1.22

Hence BD = 0.9 million kilometers.

The height is quite solid, 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 the observer in 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 the 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 hours, that is, 36 minutes. That is why during the time of movement between stations the traveler's chronometer lagged behind the station clock and, moreover, by 24 minutes.

It is necessary to comprehend this fact well: the traveler's chronometer fell behind not because; that it was slower or not working properly. No, it worked just like the clocks at the stations. But time in a train moving relative to the stations flowed differently than in the stations.

It can be seen from the diagram with a triangle that the greater 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 small period of time passes in the train in an hour of station time. For example, at a train speed of 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 by two chronometers installed at the beginning and at the end of the train).

Considering time to be absolute, a person used to imagine it as something evenly flowing, and, moreover, everywhere and under all conditions in the world with 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 a fantastic story is not such an empty fantasy. The relativity of time opens before them the possibility - theoretically at least - of traveling into the future. It is easy to see that Einstein's train is precisely the "time machine".

Time Machine

Indeed, imagine that Einstein's train does not move in a straight line, but along a circular railway. Then, each time the traveler returns to the starting station, he will find that his clock is behind the station clock.

By approximating the speed of the train to the speed of light, you can, as you already know, ensure that any small amount of time passes in an hour according to the station clock in the train. This leads to surprising results: while only years pass in the train, hundreds and thousands of years pass at the station. Coming out of his "time machine", our traveler will find himself in a separated 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's. After all, according to the novelist, she could move in time not due to her high speed, but thanks to some special technical device. But in reality no such device can be created; this is utter nonsense. There is only one way to get into the future: to give the train an enormous speed - close to the speed of light.

Another property distinguishes Einstein's train from the Wellsian time machine: it is unable to move "back" in time, that is, it is unable to go into the past, and thereby return from the future to the present.

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

Movement at a speed close to the speed of light opens up theoretically one more possibility: along with time, to overcome any distances. And they can be so great in world space that even at the maximum speed for most travels, a human life would not be enough.

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 the start. And since the duration of human life is less than two hundred years, it would seem that one can say with confidence that a person is fundamentally deprived of the opportunity to reach distant stars.

Yet this reasoning is erroneous. The mistake is that we speak of two hundred years as something absolute. But time is relative, that is, there is no common time for all laboratories. The stations had one count of time, while Einstein's train had another.

Let us imagine an astronaut who has set off for the space of the world. By the time it reaches a star two hundred light-years away from us, two hundred years will indeed have passed according to earthly time. In a rocket, depending on its speed relative to the Earth, as we know, any small period of time can flow.

Thus, the astronaut will reach the star in his own time not in two hundred years, but, say, in one year. With 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 - and time becomes extremely small, that is, equal to zero. In other words, if the rocket could move at the speed of light, time for the observer in it would stop altogether, 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 not feasible, since the movement of cars and people at speeds close to the speed of light is impossible for technical reasons.

And sizes 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 full depth and seriousness of the consequences arising from the relativity of time.

It is easy to see that the relativity of the sizes of bodies also follows from the relativity of time.

Let the length of the platform through 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 in 10 seconds. But in 10 seconds of station time, only 6 seconds will pass on the train. From this the traveler will rightfully conclude that the length of the platform is 240,000 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. Relative to the train, the platform was moving, and relative to the station, it was at rest. Therefore, for the observer at the station, it was longer than for the traveler. The carriages of the train, on the contrary, were 10/6 times shorter for the observer at the station than for the traveler.

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

So, every moving body contracts in the direction of its motion. In this regard, it is necessary to amend one of the examples given by us in No. 9 of the magazine, namely: in the experiment with opening doors on a steamer, 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 steamer, moving at a speed of 240 thousand kilometers per second, decreased by 10/6 times relative to the pier, the actual time interval between opening the doors will be equal to the clock on the pier not 40 seconds, but 40: 10/6 = 24 seconds . Of course, this numerical correction does not change the fundamental conclusions drawn by us from the experience with the steamer.

The relativity of the dimensions 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 the Mikaelson experiment, which at one time brought confusion to the ranks of physicists. The case concerned, as you remember, the addition of velocities, which, for some unknown reason, did not "wanted" to obey ordinary arithmetic.

Man has always been accustomed to adding speeds 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 20 + 5 = 25 kilometers per hour. hour.

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

Try, for example, adding the speeds of 230 and 270 thousand kilometers per second. What will happen? 500 thousand kilometers per second. And 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 any number of speeds, in any case, cannot exceed 300,000 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 speed limit in the world.

It is easy to see that the arithmetic sum is also incorrect here. Let, for example, a steamer move past the pier at a speed of 150,000 kilometers per second, and a ball roll along the deck of the steamer at a speed of 130,000 kilometers per second. The sum of these speeds should express the speed of the ball relative to the pier. However, we know from the previous chapter that a moving body shrinks in size. Therefore, a distance of 130,000 kilometers on a steamer is not at all equal to 130,000 kilometers for an observer on the pier, and 150,000 kilometers along the coast is not at all equal to 150,000 kilometers for a passenger on a steamer.

Further, to determine the speed of the ball relative to the pier, the observer uses the clock on the pier. But the speed of a ball on a steamboat is determined by steamboat time. And time on a moving steamer and on a wharf, as we know, are not at all the same thing.

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

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

Here V 1 and V 2 are the terms of the speed, 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 to it, we will never get more than 300 thousand kilometers per second. Try adding 230,000 and 270,000 kilometers per second using this formula, or even 300,000 and 300,000 kilometers per second, and see what happens.

When adding small speeds - such as we in most cases encounter in practice - the formula gives us the usual result, 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, flying 650 kilometers per hour each. What is the speed of their convergence?

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

It is impossible to detect such quantities in such cases by measurements. Yes, and their practical value is zero. From this it is clear why for thousands of years man did not notice that the arithmetic addition of velocities is fundamentally wrong: the inaccuracy with such addition is much less than the most stringent requirements of practice. And therefore, in technology, everything always converged with 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, and Einstein's formula is correct, is confirmed by experience. It could not be otherwise: after all, it was the experience that made physicists reconsider the old concepts in mechanics and led them to the principle of relativity.

Knowing how to actually add the speeds, we can now understand the "mysterious" results of the Michaelson experiment. Performing this experiment when the Earth was moving towards the beam of light 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 speed 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 c1, and no more. Just such was the result of Mikaelson's experiment.

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

So, the results of Mikaelson's experiment surprised us only because we did not know how to add the speeds correctly. We did not know how to do this, because 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 believe 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 the limiting speed, the mass of any body must become infinitely large. The usual speeds that we encounter in practice cause a completely negligible 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 those at rest. And experience fully confirms the law of the dependence of mass on speed.

But, in order to tell the bodies speed, it is necessary to expend energy. And 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 one, the mass of a compressed spring is greater than that of a free one.

Insignificant quantities of units of mass correspond to huge quantities of units of energy. For example, to increase the mass of a body by only 1 gram, it is necessary to work on it in 25 million kilowatt-hours. In other words, the mass of 25 million kilowatt-hours of electrical energy is equal to 1 gram. To get this gram, all the energy generated by Dneproges for two days is required. Counting only 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, then the combustion products will weigh only 1/3000 of a gram less than the coal and oxygen from which they were formed after they are cooled. The missing fraction of the 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 fractions of a gram.

It is quite clear that such insignificant changes in the mass of bodies when they lose or gain energy elude the most accurate measurements. However, modern physics knows phenomena in which a change in mass becomes noticeable. These are the processes that occur during the collision of atomic nuclei, when the nuclei of other elements are formed from the nuclei of some 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 than the total mass of hydrogen and lithium nuclei. Therefore, when converting 1 gram of a mixture of lithium and hydrogen into helium, 1/400 of a gram of energy should be released, which will be in kilowatt-hours:

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

Thus, if we could easily carry out nuclear transformations, we would become the owners of the richest source of energy: in order to get the power of the Dneproges, 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 cursory introduction to the principle of relativity.

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

No, because the difference between the old physics (it is called “classical”) and the 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 of an ordinary, even the fastest train (but, of course, not Einstein's train) took it into his head to introduce a time correction for the principle of relativity, he would be ridiculed. For a day, such an amendment would be expressed in ten-billionths of a second. The shaking of the train and the inaccurate workings of the best clockwork have an incomparably stronger effect on the readings of the clock.

An engineer who would enter into the calculations the increase in the mass of water when it is heated could be called crazy. On the other hand, 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 machines using the laws of classical physics: amendments to the principle of relativity will have less effect on machines than a microbe that has landed 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 have considered in this article. Continuing the development of his teachings, Einstein later gave a completely new picture of such an important phenomenon as universal gravitation. In this regard, the doctrine of relativity was divided into two parts. The first of these, which does not concern gravitation, has been called the "private" or "special" "principle of relativity"; the second part, covering the questions of gravitation, is the "general principle of relativity". Thus, we got acquainted only with the particular principle (the consideration of the general principle was not included in the task of this article).

It remains only 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 right conclusions from Mikaelson's experiment - to discover the relativity of time with all the ensuing consequences.

Thus, humanity, in its eternal desire to know the world wider and deeper, won one of its greatest victories.

It owes it to the genius of Albert Einstein.