The general theory of relativity is supplemented by the conclusion that. Einstein's Special Theory of Relativity: Briefly and in Simple Words
Special relativity (SRT) or private relativity is the theory of Albert Einstein, published in 1905 in the work "On the Electrodynamics of Moving Bodies" (Albert Einstein - Zur Elektrodynamik bewegter Körper. Annalen der Physik, IV. Folge 17. Seite 891-921 Juni 1905).
It explained the movement between different inertial reference frames or the movement of bodies moving relative to each other at a constant speed. In this case, none of the objects should be taken as a frame of reference, but they should be considered relative to each other. SRT provides only 1 case when 2 bodies do not change the direction of motion and move uniformly.
The laws of special relativity cease to operate when one of the bodies changes the trajectory of movement or increases speed. Here the general theory of relativity (GR) takes place, which gives a general interpretation of the motion of objects.
The two postulates on which the theory of relativity is based are:
- The principle of relativity- According to him, in all existing reference systems that move relative to each other with a constant speed and do not change direction, the same laws operate.
- The principle of the speed of light- The speed of light is the same for all observers and does not depend on the speed of their movement. This is the highest speed, and nothing in nature has a greater speed. The speed of light is 3*10^8 m/s.
Albert Einstein took experimental rather than theoretical data as a basis. This was one of the components of his success. The new experimental data served as the basis for the creation of a new theory.
Physicists with mid-nineteenth centuries have been searching for a new mysterious medium called ether. It was assumed that the ether can pass through all objects, but does not participate in their movement. According to beliefs about the ether, by changing the speed of the viewer in relation to the ether, the speed of light also changes.
Einstein, trusting experiments, rejected the notion new environment ether and assumed that the speed of light is always constant and does not depend on any circumstances, such as the speed of the person himself.
Time spans, distances, and their uniformity
The special theory of relativity links time and space. In the Material Universe, there are 3 known in space: right and left, forward and backward, up and down. If we add to them another dimension, called time, then this will form the basis of the space-time continuum.
If you are moving at a slow speed, your observations will not converge with people who are moving faster.
Later experiments confirmed that space, just like time, cannot be perceived in the same way: our perception depends on the speed of the movement of objects.
The connection of energy with mass
Einstein came up with a formula that combined energy with mass. This formula has become widespread in physics, and it is familiar to every student: E=m*s², wherein E-energy; m- body mass, c-speed spread of light.
The mass of a body increases in proportion to the increase in the speed of light. If the speed of light is reached, the mass and energy of the body become dimensionless.
By increasing the mass of an object, it becomes more difficult to achieve an increase in its speed, i.e., for a body with an infinitely huge material mass, infinite energy is needed. But in reality this is impossible to achieve.
Einstein's theory combined two separate positions: the position of mass and the position of energy into one general law. This made it possible to convert energy into material mass and vice versa.
"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 possible, after all, to find such an observation point, such a laboratory, from where we could best study the laws that govern the motion 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 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 consider as resting, can serve as a guide for us, as it were, " 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 find out 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 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 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 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 went on until late XIX 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 seen this 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 the 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. Having performed 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, Mikaelson had to apply a very complex experimental technique 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 learned world stood before 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 with perfect unexpected side, 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 door- 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, it will not seem to people on the pier that the doors did not open at the same time: for them, this is actually actually happen simultaneously. 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 in different time.
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 " classical principle 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" has become 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 a train (or, conversely, an hour will pass in a minute of station time in a 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 large in world space that even at the maximum speed for most travels, there would not be enough human life.
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, travel 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 technical reasons impossible.
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 many 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:
V1 + V2
W = _________________
V 1 x V 2
1+ ___________
C2
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 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 man is walking, this difference is still 340 thousand times smaller.
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 wrong, 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 how serious and deep changes introduced the principle of relativity into the worldview that has developed among mankind for 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 completely new picture 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 met only with a particular principle (consideration general principle was not within the scope 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.
Big open secret
Alexander Grishaev, excerpt from the article " Spillikins and wicks of universal gravitation»
“The British don’t clean their guns with bricks: even if they don’t clean ours, otherwise, God forbid, they are not good for shooting ...” - N. Leskov.
8 parabolic mirrors of the ADU-1000 receiving and transmitting antenna complex - part of the Pluton receiving complex of the Center for Deep Space Communications ...
In the early years of the formation of deep space research, it was sadly lost whole line Soviet and American interplanetary stations. Even if the launch took place without failures, as experts say, “in normal mode”, all systems worked normally, all the pre-planned orbit corrections went through normally, communication with the vehicles was suddenly interrupted.
It got to the point that, in the next “window” favorable for the launch, the same devices with the same program were launched in batches, one after the other in pursuit - in the hope that at least one could be brought to a victorious end. But where is it! There was a certain Reason that cut off communication on approach to the planets, which did not give concessions.
Of course, they kept quiet about it. The foolish public was informed that the station passed at a distance, say, 120 thousand kilometers from the planet. The tone of these messages was so cheerful that one involuntarily thought: “Guys are shooting! One hundred twenty thousand is not bad. Could after all and on three hundred thousand pass! You give new, more accurate launches! No one had any idea about the intensity of the drama - that pundits of something there did not understand.
In the end, we decided to try this. The signal by which communication is carried out, let it be known to you, has long been represented in the form of waves - radio waves. The easiest way to imagine what these waves are can be on the "domino effect". The communication signal propagates in space like a wave of falling dominoes.
The speed of wave propagation depends on the speed of the fall of each individual of the knuckles, and since all the knuckles are the same and fall in the same time, the wave speed is a constant value. The distance between the bones of physics is called "wavelength".
An example of a wave is the "domino effect"
Now let's assume that we have a celestial body (let's call it Venus), marked in this figure with a red doodle. Let's say that if we push the initial knuckle, then each subsequent knuckle will fall on the next one in one second. If exactly 100 tiles fit from us to Venus, the wave will reach it after all 100 tiles fall in succession, spending one second each. In total, the wave from us will reach Venus in 100 seconds.
This is the case if Venus stands still. And if Venus does not stand still? Let's say, while 100 knuckles are falling, our Venus has time to "crawl" to a distance equal to the distance between several knuckles (several wavelengths) what will happen then?
The academics decided what if the wave overtakes Venus according to the very law that schoolchildren use lower grades in puzzles like: “From the point A a train leaves at a speed A km/h, and from the point B at the same time a pedestrian exits with a speed b in the same direction, how long will it take for the train to overtake the pedestrian?
That's when the academics realized that it was necessary to solve such a simple problem for younger students, then things went smoothly. If not for this ingenuity, we would not see the outstanding achievements of interplanetary astronautics.
And what is so cunning here, Dunno, inexperienced in the sciences, will throw up his hands?! And on the contrary, Znayka, experienced in the sciences, will cry out: guard, hold the rogue, this is pseudoscience! According to real, correct science, correctly, this task should be solved in a completely different way! After all, we are not dealing with some kind of low-speed fox-pedist steamers, but with a signal rushing after Venus at the speed of light, which, no matter how fast you, or Venus, run, still catches up with you at the speed of light! Moreover, if you rush towards him, you will not meet him sooner!
Principles of Relativity
- It's like, - Dunno will exclaim, - it turns out that if from the paragraph B me, who is in a starship at point A let them know that a dangerous epidemic has begun on board, for which I have a remedy, it is useless for me to turn around to meet them, because we won't meet before anyway, if the spaceship sent to me is moving at light speed? And this is what it means - I can, with a clear conscience, continue my journey to the point C to deliver a load of diapers for monkeys due to be born exactly next month?
- That's right, - Znayka will answer you, - if you were on a bicycle, then you would need to go as the dotted arrow shows - towards the car that left you. But, if a light-speed vehicle is moving towards you, then whether you will move towards it or move away from it, or stay in place, does not matter - meeting time cannot be changed.
- How is it so, - Dunno will return to our dominoes, - will the knuckles start falling faster? It will not help - it will just be a puzzle about Achilles catching up with a turtle, no matter how fast Achilles runs, it will still take him some time to go the additional distance traveled by the turtle.
No, everything is cooler here - if a beam of light catches up with you, then you, moving, stretch the space. Put the same dominoes on a rubber bandage and pull it - the red cross on it will move, but the knuckles will also move, the distance between the knuckles increases, i.e. the wavelength increases, and thus between you and the starting point of the wave, there will always be the same number of bones. How!
It was I who popularly outlined the foundations of Einstein's Theories of Relativity, the only correct one, scientific theory, which should have been used to calculate the passage of a subluminal signal, including when calculating modes of communication with interplanetary probes.
Let's focus on one point: in relativistic theories (and there are two of them: ONE HUNDRED– the special theory of relativity and general relativity- the general theory of relativity) the speed of light is absolute and cannot be exceeded in any way. And one useful term, which refers to the effect of increasing the distance between the knuckles, this is called " Doppler effect» - the effect of increasing the wavelength, if the wave follows the moving object, and the effect of reducing the wavelength, if the object is moving towards the wave.
So the academicians considered according to the only correct theory, only the probes "for milk" left. Meanwhile, in the 60s of the 20th century, a number of countries produced Venus radar. With the radar of Venus, this postulate of the relativistic addition of velocities can be verified.
American B. J. Wallace in 1969, in the article “Radar Test of the Relative Speed of Light in Space”, he analyzed eight radar observations of Venus published in 1961. The analysis convinced him that the speed of the radio beam ( contrary to the theory of relativity) is algebraically added to the speed of the Earth's rotation. Subsequently, he had problems with the publication of materials on this topic.
We list the articles devoted to the mentioned experiments:
1. V.A. Kotelnikov et al. "The radar installation used in the radar of Venus in 1961" Radio Engineering and Electronics, 7, 11 (1962) 1851.
2. V.A. Kotelnikov et al. "The results of Venus radar in 1961" Ibid., p.1860.
3. V.A. Morozov, Z.G. Trunova "Weak signal analyzer used in the radar of Venus in 1961" Ibid., p.1880.
conclusions, which were formulated in the third article, are understandable even to Dunno, who has understood the theory of falling dominoes, which is stated here at the beginning.
In the last article, in the part where they described the conditions for detecting a signal reflected from Venus, there was the following phrase: “ The narrow-band component is understood as the component of the echo signal corresponding to the reflection from a fixed point reflector ...»
Here the “narrowband component” is the detected component of the signal returned from Venus, and it is detected if Venus is considered ... motionless! Those. guys didn't write directly that Doppler effect is not detected, they instead wrote that the signal is recognized by the receiver only if the motion of Venus in the same direction as the signal is not taken into account, i.e. when the Doppler effect is zero according to any theory, but since Venus was moving, then, therefore, the effect of wave lengthening did not take place, which was prescribed by the theory of relativity.
To the great sadness of the theory of relativity, Venus did not stretch space, and there were much more “dominoes” by the time the signal arrived at Venus than during its launch from Earth. Venus, like the Achilles tortoise, managed to crawl away from the steps of the waves catching up with her at the speed of light.
Obviously, American researchers did the same, as evidenced by the above-mentioned case with Wallace, who was not allowed to publish a paper on the interpretation of the results obtained during the Venus scan. So the commissions to combat pseudoscience functioned properly not only in the totalitarian Soviet Union.
By the way, the lengthening of the waves, as we found out, according to the theory, should indicate the removal of a space object from the observer, and it is called redshift, and this redshift, discovered by Hubble in 1929, underlies the cosmogonic theory of the Big Bang.
Location of Venus showed absence this same bias, and since then, since the successful results of the location of Venus, this theory - the theory of the Big Bang - like the hypotheses of "black holes" and other relativistic nonsense, pass into the category of science fiction. Fiction for which they give Nobel Prizes not in literature, but in physics!!! Wonderful are thy works, Lord!
P.S. By the 100th anniversary of SRT and the 90th anniversary of general relativity that coincided with it, it turned out that neither one nor the other theory was experimentally confirmed! On the occasion of the anniversary, the project "Gravity Probe B (GP-B) ” worth $ 760 million, which was supposed to give at least one confirmation of these ridiculous theories, but it all ended in great embarrassment. The next article is about that...
Einstein's OTO: "But the king is naked!"
“In June 2004, the UN General Assembly decided to proclaim 2005 the International Year of Physics. The Assembly invited UNESCO (the United Nations Educational, Scientific and Cultural Organization) to organize activities for the celebration of the Year in cooperation with physical societies and other interest groups around the world...”- Message from the "Bulletin of the United Nations"
Still would! – Next year marks the 100th anniversary of the Special Theory of Relativity ( ONE HUNDRED), 90 years of the General Theory of Relativity ( general relativity) - a hundred years of uninterrupted triumph of the new physics, which overthrew the archaic Newtonian physics from the pedestal, so officials from the UN thought, anticipating next year's celebrations and celebrations greatest genius of all times and peoples as well as his followers.
But the followers knew better than others that the “brilliant” theories had not shown themselves in any way for almost a hundred years: no predictions of new phenomena were made on their basis and no explanations were made that were already discovered, but not explained by classical Newtonian physics. Nothing at all, NOTHING!
GR did not have a single experimental confirmation!
It was only known that the theory was brilliant, but no one knew what was the use of it. Well, yes, she regularly fed promises and breakfasts, for which an unmeasured dough was released, and as a result - science fiction novels about black holes, for which they gave Nobel Prizes not in literature, but in physics, colliders were built, one after another, one more than the other, gravitational interferometers were bred all over the world, in which, to paraphrase Confucius, in “dark matter”, they searched for black cat, which, moreover, was not there, and no one saw the “black matter” itself either.
Therefore, in April 2004, an ambitious project was launched, which was carefully prepared for about forty years and for the final stage of which $ 760 million was released - "Gravity Probe B (GP-B)". Gravity test B was supposed to wind on precision gyroscopes (in other words - tops), no more, no less, Einstein's space-time, in the amount of 6.6 arc seconds, approximately, for a year of flight - just in time for the great anniversary.
Immediately after the launch, they were waiting for victorious reports, in the spirit of "His Excellency's Adjutant" - the "letter" followed the Nth kilometer: "The first arc second of space-time has been successfully wound." But the victorious reports, for which the believers in the most grandiose scam of the 20th century, somehow everything should not have been.
And without victorious reports, what the hell is an anniversary - crowds of enemies of the most progressive teachings with pens and calculators at the ready are waiting to spit on the great teachings of Einstein. So they dropped "international year of physics" on the brakes - he passed quietly and imperceptibly.
There were no victorious reports even immediately after the completion of the mission, in August of the anniversary year: there was only a message that everything was on track, the ingenious theory was confirmed, but we will process the results a little, exactly in a year there will be an exact answer. There was no answer after a year or two. In the end, they promised to finalize the results by March 2010.
And where is the result? Googling the Internet, I found this curious note, in the LiveJournal of one blogger:
Gravity Probe B (GP-B) - aftertraces$760 million. $
So - modern physics has no doubts about general relativity, it would seem, why then do we need an experiment worth 760 million dollars aimed at confirming the effects of general relativity?
After all, this is nonsense - it's the same as spending almost a billion, for example, to confirm the law of Archimedes. Nevertheless, judging by the results of the experiment, this money was not directed at all to the experiment, money was used for PR.
The experiment was carried out using a satellite launched on April 20, 2004, equipped with equipment for measuring the Lense-Thirring effect (as a direct consequence of general relativity). Satellite Gravity Probe B carried on board the most accurate gyroscopes in the world to that day. The scheme of the experiment is well described in Wikipedia.
Already during the period of data collection, questions began to arise regarding the experimental design and the accuracy of the equipment. After all, despite the huge budget, the equipment designed to measure ultrafine effects has never been tested in space. During the data collection, vibrations were revealed due to the boiling of helium in the Dewar, there were unforeseen stops of the gyros, followed by spinning up due to failures in the electronics under the influence of energetic cosmic particles; there were computer failures and loss of "science data" arrays, and the "polhode" effect turned out to be the most significant problem.
Concept "polhode" The roots go back to the 18th century, when the outstanding mathematician and astronomer Leonhard Euler obtained a system of equations for the free motion of rigid bodies. In particular, Euler and his contemporaries (D'Alembert, Lagrange) investigated fluctuations (very small) in measurements of the Earth's latitude, which took place, apparently, due to the Earth's oscillations about the rotation axis (polar axis) ...
GP-B gyroscopes listed by Guinness as the most spherical objects ever made by human hands. The sphere is made of quartz glass and coated with a thin film of superconducting niobium. Quartz surfaces are polished to the atomic level.
Following the discussion of axial precession, you are right to ask a direct question: why do GP-B gyroscopes, listed in the Guinness book as the most spherical objects, also exhibit axial precession? Indeed, in a perfectly spherical and homogeneous body, in which all three main axes of inertia are identical, the polhode period around any of these axes would be infinitely large and, for all practical purposes, it would not exist.
However, GP-B rotors are not "perfect" spheres. The sphericity and homogeneity of the fused quartz substrate make it possible to balance the moments of inertia relative to the axes up to one millionth part - this is already enough to take into account the polholde period of the rotor and fix the track along which the end of the rotor axis will move.
All this was expected. Before the launch of the satellite, the behavior of the GP-B rotors was simulated. Yet the prevailing consensus was that, since the rotors were nearly perfect and nearly uniform, they would give a very small amplitude polhode track and such a large period that the polhode rotation of the axis would not change significantly throughout the experiment.
However, contrary to favorable forecasts, GP-B rotors in real life made it possible to see a significant axial precession. Given the almost perfectly spherical geometry and uniform composition of the rotors, there are two possibilities:
– internal decomposition of energy;
– external influence with a constant frequency.
It turned out that their combination works. Although the rotor is symmetrical, but, like the Earth described above, the gyroscope is still elastic and sticks out at the equator by about 10 nm. Since the axis of rotation drifts, the bulge of the body surface also drifts. Due to small defects in the structure of the rotor and local boundary defects between the base material of the rotor and its niobium coating, rotational energy can be dissipated internally. This causes the drift track to change without changing the total angular momentum (kind of like it does when spinning a raw egg).
If the effects predicted by general relativity really manifest themselves, then for each year of finding Gravity Probe B in orbit, the axes of rotation of its gyroscopes should deviate by 6.6 arc seconds and 42 arc milliseconds, respectively
Two of the gyroscopes in 11 months due to this effect turned a few tens of degrees, because were untwisted along the axis of minimum inertia.
As a result, gyroscopes designed to measure milliseconds angular arc, were exposed to unplanned effects and errors up to several tens of degrees! In fact it was mission failure, however, the results were simply hushed up. If it was originally planned to announce the final results of the mission at the end of 2007, then they postponed it to September 2008, and then to March 2010 altogether.
As Francis Everitt cheerfully reported, “Due to the interaction of electric charges “frozen” in gyroscopes and the walls of their chambers (the patch effect), and previously unaccounted for effects of reading readings, which have not yet been completely excluded from the data obtained, the measurement accuracy at this stage is limited to 0.1 arc seconds, which makes it possible to confirm with an accuracy better than 1% the effect of geodetic precession (6.606 arc seconds per year), but so far not makes it possible to isolate and verify the phenomenon of entrainment of an inertial frame of reference (0.039 arc seconds per year). Intensive work is underway to calculate and extract measurement interference ... "
That is, as commented on this statement ZZCW : “tens of degrees are subtracted from tens of degrees and angular milliseconds remain, with one percent accuracy (and then the declared accuracy will be even higher, because it would be necessary to confirm the Lense-Thirring effect for complete communism) corresponding key effect OTO…”
No wonder that NASA refused give further millions of dollars in grants to Stanford for an 18-month "advance data analysis" program that was scheduled for the period October 2008 - March 2010.
Scientists who want to get RAW(raw data) for independent confirmation, we were surprised to find that instead of RAW and sources NSSDC they are given only "data of the second level". “Second level” means that “the data has been slightly processed…”
As a result, the Stanfordites, deprived of funding, published the final report on February 5th, which reads:
After subtracting corrections for the solar geodetic effect (+7 marc-s/yr) and the proper motion of the guide star (+28 ± 1 marc-s/yr), the result is −6.673 ± 97 marc-s/yr, to be compared with the predicted −6,606 marc-s/yr of General Relativity
This is the opinion of a blogger unknown to me, whose opinion we will consider the voice of the boy who shouted: “ And the king is naked!»
And now we will cite the statements of highly competent specialists, whose qualifications are difficult to challenge.
Nikolay Levashov "Theory of relativity is a false foundation of physics"
Nikolai Levashov "Einstein's theory, astrophysicists, hushed up experiments"
More detailed And various information about the events taking place in Russia, Ukraine and other countries of our beautiful planet, you can get on Internet conferences, constantly held on the website "Keys of Knowledge". All Conferences are open and completely free. We invite all waking up and interested ...
Who would have thought that a small postal clerk would changefoundations of science of its time? But this happened! Einstein's theory of relativity forced us to reconsider the usual view of the structure of the Universe and opened up new areas of scientific knowledge.
Majority scientific discoveries done by experiment: scientists repeated their experiments many times to be sure of their results. The work was usually carried out in universities or research laboratories of large companies.
Albert Einstein completely changed scientific picture the world without conducting a single practical experiment. His only tools were paper and pen, and he did all his experiments in his head.
moving light
(1879-1955) based all his conclusions on the results of a "thought experiment". These experiments could only be done in the imagination.
The speeds of all moving bodies are relative. This means that all objects move or remain stationary only relative to some other object. For example, a man, motionless relative to the Earth, at the same time rotates with the Earth around the Sun. Or suppose that a person is walking along the carriage of a moving train in the direction of movement at a speed of 3 km / h. The train is moving at a speed of 60 km/h. Relative to a stationary observer on the ground, the speed of a person will be 63 km / h - the speed of a person plus the speed of a train. If he went against the movement, then his speed relative to a stationary observer would be equal to 57 km / h.
Einstein argued that the speed of light cannot be discussed in this way. The speed of light is always constant, regardless of whether the light source is approaching you, receding from you, or standing still.
The faster the less
From the very beginning, Einstein made some surprising assumptions. He argued that if the speed of an object approaches the speed of light, its dimensions decrease, while its mass, on the contrary, increases. No body can be accelerated to a speed equal to or greater than the speed of light.
His other conclusion was even more surprising and seemed to be contrary to common sense. Imagine that of two twins, one remained on Earth, while the other traveled through space at a speed close to the speed of light. 70 years have passed since the launch on Earth. According to Einstein's theory, time flows more slowly on board the ship, and only ten years have passed there, for example. It turns out that one of the twins who remained on Earth became sixty years older than the second. This effect is called " twin paradox". It sounds incredible, but laboratory experiments have confirmed that time dilation at speeds close to the speed of light really exists.
Merciless conclusion
Einstein's theory also includes the famous formula E=mc 2, where E is energy, m is mass, and c is the speed of light. Einstein claimed that mass can be converted into pure energy. As a result of applying this discovery to practical life atomic energy and the nuclear bomb appeared.
Einstein was a theorist. The experiments that were supposed to prove the correctness of his theory, he left to others. Many of these experiments could not be done until sufficiently accurate measuring instruments were available.
Facts and events
- The following experiment was carried out: an airplane, on which a very accurate clock was set, took off and, having flown around the Earth at high speed, sank at the same point. The clock on board the aircraft was a tiny fraction of a second behind the clock that remained on Earth.
- If a ball is dropped in an elevator falling with free fall acceleration, then the ball will not fall, but, as it were, will hang in the air. This is because the ball and the elevator are falling at the same speed.
- Einstein proved that gravity affects the geometric properties of space-time, which in turn affects the movement of bodies in this space. So, two bodies that started moving parallel to each other will eventually meet at one point.
Curving time and space
Ten years later, in 1915-1916, Einstein developed a new theory of gravity, which he called general relativity. He argued that acceleration (change in speed) acts on bodies in the same way as the force of gravity. The astronaut cannot determine by his own sensations whether he is being attracted by a large planet, or whether the rocket has begun to slow down.
If the spacecraft accelerates to a speed close to the speed of light, then the clock on it slows down. The faster the ship moves, the slower the clock runs.
Its differences from the Newtonian theory of gravitation are manifested in the study of space objects with a huge mass, such as planets or stars. Experiments have confirmed the curvature of light rays passing near bodies with a large mass. In principle, such a strong gravitational field is possible that light cannot go beyond it. This phenomenon is called " black hole". "Black holes" appear to have been found in some star systems.
Newton argued that the orbits of the planets around the sun are fixed. Einstein's theory predicts a slow additional rotation of the orbits of the planets associated with the presence of the gravitational field of the Sun. The prediction was confirmed experimentally. It was truly a milestone discovery. Sir Isaac Newton's law of universal gravitation was amended.
Beginning of the arms race
Einstein's work gave the key to many of the mysteries of nature. They influenced the development of many branches of physics, from elementary particle physics to astronomy - the science of the structure of the universe.
Einstein in his life was engaged not only in theory. In 1914 he became director of the Institute of Physics in Berlin. In 1933, when the Nazis came to power in Germany, he, as a Jew, had to leave this country. He moved to the USA.
In 1939, despite being opposed to the war, Einstein wrote a letter to President Roosevelt warning him that it was possible to make a bomb with tremendous destructive power and that Nazi Germany had already begun to develop such a bomb. The President gave the order to start work. This marked the beginning of an arms race.
The general theory of relativity, along with the special theory of relativity, is the brilliant work of Albert Einstein, who at the beginning of the 20th century turned the view of physicists on the world. A hundred years later, general relativity is the main and most important theory of physics in the world, and together with quantum mechanics claims to be one of the two cornerstones of the “theory of everything”. The general theory of relativity describes gravity as a consequence of the curvature of space-time (combined into a single whole in general relativity) under the influence of mass. Thanks to general relativity, scientists have deduced many constants, tested a bunch of unexplained phenomena, and come up with things like black holes, dark matter and dark energy, the expansion of the universe, the Big Bang, and much more. Also, GTR vetoed the speed of light, thereby literally imprisoning us in our vicinity (the solar system), but left a loophole in the form of wormholes - short possible ways through space-time.
A RUDN University employee and his Brazilian colleagues questioned the concept of using stable wormholes as portals to various points in space-time. The results of their research were published in Physical Review D. - a rather hackneyed cliché in science fiction. A wormhole, or "wormhole", is a kind of tunnel that connects distant points in space, or even two universes, by curving space-time.
