What can be faster than the speed of light. Particles found that move faster than the speed of light? Difficult cases of SS movement

As you know, photons, particles of light, of which it consists, move at the speed of light. The special theory of relativity will help us in this matter.

In science fiction films, interstellar spaceships fly almost at the speed of light without exception. Usually this is the so-called hyperspeed by science fiction writers. Both writers and film directors describe and show him to us in much the same way. artistic device. Most often, in order for the ship to make a swift dash, the heroes pull or press the control button, and vehicle instantly accelerates, accelerating almost to the speed of light with a deafening pop. The stars that the viewer sees over the side of the ship first flicker, and then completely stretch out in lines. But is this what the stars really look like in the windows of a spaceship at hyperspeed? Researchers say no. In reality, instead of the stars stretched out in a line, the passengers of the ship would see only a bright disk.

If the object moves at almost the speed of light, then it can see the Doppler effect in action. In physics, this is the name given to the change in frequency and wavelength due to the rapid movement of the receiver. The frequency of the light of stars flashing in front of the viewer from the ship will increase so much that it will shift from the visible range to the X-ray part of the spectrum. The stars seem to disappear! At the same time, the length of the relic electromagnetic radiation remaining after big bang. The background radiation will become visible and appear as a bright disk, fading at the edges.

But what does the world look like from the side of an object that reaches the speed of light? As you know, photons, particles of light, of which it consists, move at such speeds. The special theory of relativity will help us in this matter. According to it, when an object moves at the speed of light for an arbitrarily long time, the time spent on the movement of this object becomes equal to zero. in plain language, if you move at the speed of light, then it is impossible to perform any action, such as observing, seeing, seeing, and so on. An object traveling at the speed of light will actually see nothing.

Photons always travel at the speed of light. They do not waste time accelerating and decelerating, so their whole life for them lasts zero time. If we were photons, then our moments of birth and death would coincide, that is, we would simply not realize that the world exists at all. It is worth noting that if an object accelerates to the speed of light, then its speed in all frames of reference becomes equal to the speed of light. Here is such a photo physics. Applying the special theory of relativity, we can conclude that for an object moving at the speed of light, the entire the world will appear infinitely flattened, and all the events occurring in it will take place at one moment in time.

But it turned out that it is possible; now they believe that we will never be able to travel faster than light ... ". But in fact it is not true that someone once believed that moving faster than sound impossible. Long before there were supersonic aircraft, it was already known that bullets travel faster than sound. In fact, it was said that it was impossible controlled supersonic flight, and that was the mistake. SS movement is a completely different matter. It was clear from the start that supersonic flight was hampered by technical problems that simply had to be solved. But it is completely unclear whether the problems that hinder the SS movement can ever be solved. The theory of relativity has a lot to say about this. If SS travel or even signal transmission is possible, then causality will be violated, and absolutely incredible conclusions will follow from this.

We will first discuss simple cases of CC motion. We mention them not because they are interesting, but because they resurface again and again in discussions of the STS movement and therefore have to be dealt with. Then we will discuss what we consider to be difficult cases of STS movement or communication and consider some of the arguments against them. Finally, we will consider the most serious assumptions about the real STS movement.

Simple SS move

1. The phenomenon of Cherenkov radiation

One way to move faster than light is to first slow down the light itself! :-) In a vacuum, light travels at a speed c, and this value is a world constant (see the question Is the speed of light constant), and in a denser medium like water or glass, it slows down to the speed c/n, Where n is the refractive index of the medium (1.0003 for air; 1.4 for water). Therefore, particles can move faster in water or air than light travels there. As a result, Vavilov-Cherenkov radiation appears (see question ).

But when we talk about SS motion, we, of course, mean exceeding the speed of light in a vacuum c(299 792 458 m/s). Therefore, the Cherenkov phenomenon cannot be considered an example of SS motion.

2.Third party

If the rocket A flies away from me at a speed 0.6s west and the other B- from me with speed 0.6s east, then the total distance between A And B in my frame of reference increases with speed 1.2c. Thus, an apparent relative velocity greater than c can be observed "from a third party".

However, this speed is not what we usually understand by relative speed. Real rocket speed A regarding the rocket B- this is the rate of increase in the distance between the rockets, which is observed by the observer in the rocket B. Two velocities must be added according to the relativistic formula for adding velocities (see the question How to add velocities in particular relativity). In this case, the relative speed is approximately 0.88c, that is, is not superluminal.

3. Shadows and bunnies

Think about how fast the shadow can move? If you create a shadow on a distant wall from your finger from a nearby lamp, and then move your finger, then the shadow moves much faster than your finger. If the finger moves parallel to the wall, then the speed of the shadow will be D/d times the speed of the finger, where d is the distance from the finger to the lamp, and D- distance from the lamp to the wall. And you can get even more speed if the wall is located at an angle. If the wall is very far away, then the movement of the shadow will lag behind the movement of the finger, since the light will still have to fly from the finger to the wall, but still the speed of the shadow will be as many times greater. That is, the speed of the shadow is not limited by the speed of light.

In addition to shadows, bunnies can also move faster than light, for example, a speck from a laser beam directed at the moon. Knowing that the distance to the Moon is 385,000 km, try to calculate the speed of the bunny if you move the laser slightly. You can also think of a sea wave hitting the shore obliquely. With what speed can the point at which the wave breaks move?

Similar things can happen in nature. For example, a light beam from a pulsar can comb through a cloud of dust. A bright flash generates an expanding shell of light or other radiation. When it crosses the surface, it creates a ring of light that grows faster than the speed of light. In nature, this occurs when an electromagnetic pulse from lightning reaches the upper atmosphere.

All these were examples of things moving faster than light, but which were not physical bodies. With the help of a shadow or a bunny, you cannot transmit a CC message, so communication faster than light is not possible. And again, this is probably not what we want to understand by CC motion, although it becomes clear how difficult it is to determine what exactly we need (see the question FTL Shears).

4. Rigid bodies

If you take a long hard stick and push one end of it, does the other end move immediately or not? Is it possible to carry out the SS transmission of the message in this way?

Yes it was would could be done if such solid bodies existed. In reality, the influence of a blow to the end of a stick propagates along it at the speed of sound in a given substance, and the speed of sound depends on the elasticity and density of the material. Relativity imposes an absolute limit on the possible hardness of any bodies so that the speed of sound in them cannot exceed c.

The same thing happens if you are in the field of attraction, and first hold the string or pole vertically by the upper end, and then release it. The point that you let go will start moving immediately, and the lower end cannot begin to fall until the influence of letting go reaches it at the speed of sound.

It is difficult to formulate a general theory of elastic materials in terms of relativity, but the basic idea can also be shown using the example of Newtonian mechanics. The equation for the longitudinal motion of a perfectly elastic body can be obtained from Hooke's law. In variables mass per unit length p and Young's modulus Y, longitudinal displacement X satisfies the wave equation.

Plane wave solution moves at the speed of sound s, and s 2 = Y/p. This equation does not imply the possibility of a causal influence propagating faster s. Thus, relativity imposes a theoretical limit on the amount of elasticity: Y < pc2. Practically, there are no materials even close to it. By the way, even if the speed of sound in the material is close to c, matter in itself is not required to move with relativistic velocity. But how do we know that, in principle, there can be no substance that overcomes this limit? The answer is that all substances are made up of particles, the interaction between which obeys the standard model of elementary particles, and in this model no interaction can propagate faster than light (see below about quantum field theory).

5. Phase velocity

Look at this wave equation:

It has solutions like:

These solutions are sine waves moving at a speed

But this is faster than light, so we have the equation of the tachyon field in our hands? No, this is just the usual relativistic equation of a massive scalar particle!

The paradox will be resolved if we understand the difference between this speed, also called the phase speed vph from another speed, called the group speed v gr which is given by the formula,

If the wave solution has a frequency spread, then it will take the form of a wave packet , which moves with a group velocity not exceeding c. Only wave crests move with phase velocity. It is possible to transmit information using such a wave only with a group velocity, so the phase velocity gives us another example of superluminal speed, which cannot carry information.

7. Relativistic rocket

A controller on Earth watches a spacecraft leaving at a speed of 0.8 c. According to the theory of relativity, even after taking into account the Doppler shift of the signals from the ship, he will see that the time on the ship is slowed down and the clocks there go slower by a factor of 0.6. If he calculates the quotient of the distance traveled by the ship divided by the elapsed time measured by the ship's clock, he will get 4/3 c. This means that the ship's passengers travel through interstellar space at an effective speed greater than the speed of light they would have if measured. From the perspective of the ship's passengers, interstellar distances are subject to Lorentzian contraction by the same factor of 0.6, which means they too must admit that they cover known interstellar distances at a rate of 4/3 c.

This is a real phenomenon and in principle it can be used by space travelers to overcome huge distances during their lifetime. If they accelerate at a constant acceleration equal to the acceleration of free fall on Earth, then not only will they have perfect artificial gravity on the ship, but they will still have time to cross the Galaxy in just 12 of their years! (See the question What are the equations of a relativistic rocket?)

However, this is not a real SS movement. The effective speed is calculated from distance in one frame of reference and time in another. This is not real speed. Only the ship's passengers benefit from this speed. The dispatcher, for example, will not have time in his life to see how they fly a gigantic distance.

Difficult cases of SS movement

9. Paradox of Einstein, Podolsky, Rosen (EPR)

10. Virtual photons

11. Quantum tunneling

Real Candidates for the SS Travelers

This section contains speculative but serious assumptions about the possibility of FTL travel. These will not be the kind of things that are usually put in a FAQ, as they raise more questions than they answer. They are presented here mainly to show that serious research is being carried out in this direction. Only a brief introduction is given in each direction. More detailed information can be found on the Internet.

19. Tachyons

Tachyons are hypothetical particles that locally travel faster than light. To do this, they must have an imaginary mass, but their energy and momentum must be positive. It is sometimes thought that such CC particles should be impossible to detect, but in fact, there is no reason to believe so. Shadows and bunnies tell us that stealth does not follow from the CC of the movement.

Tachyons have never been observed and most physicists doubt their existence. It was once stated that experiments were carried out to measure the mass of neutrinos emitted during the decay of Tritium, and that these neutrinos were tachyon. This is highly doubtful, but still not excluded. There are problems in tachyon theories, since from the point of view possible violations causality, they destabilize the vacuum. It may be possible to get around these problems, but then it will be impossible to use tachyons in the SS message we need.

The truth is that most physicists consider tachyons to be a sign of an error in their field theories, and interest in them from the general public is fueled mainly by science fiction (see Tachyons article).

20. Wormholes

The most well-known supposed possibility of STS travel is the use of wormholes. Wormholes are tunnels in space-time that connect one place in the universe to another. They can move between these points faster than light would take its usual path. Wormholes are a phenomenon of classical general relativity, but in order to create them, you need to change the topology of space-time. The possibility of this may be contained in the theory of quantum gravity.

Huge amounts of negative energy are needed to keep wormholes open. Misner And Thorn suggested that the large-scale Casimir effect can be used to generate negative energy and Visser proposed a solution using cosmic strings. All these ideas are highly speculative and may simply be unrealistic. An unusual substance with negative energy may not exist in the form necessary for the phenomenon.

Thorne found that if wormholes could be created, they could create closed time loops that would make time travel possible. It has also been suggested that the multivariate interpretation of quantum mechanics suggests that time travel will not cause any paradoxes, and that events will simply unfold differently when you get into the past. Hawking says that wormholes may simply be unstable and therefore unusable in practice. But the topic itself remains a fruitful area for thought experiments, allowing you to figure out what is possible and what is not possible based on both known and assumed laws of physics.
refs:
W. G. Morris and K. S. Thorne, American Journal of Physics 56 , 395-412 (1988)
W. G. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. letters 61 , 1446-9 (1988)
Matt Visser, Physical Review D39, 3182-4 (1989)
see also "Black Holes and Time Warps" Kip Thorn, Norton & co. (1994)
For an explanation of the multiverse see, "The Fabric of Reality" David Deutsch, Penguin Press.

21. Deformer motors

[I have no idea how to translate this! The original warp drive. - approx. translator
translated by analogy with the article on Membrane]

The warp could be a mechanism for twisting space-time so that an object can travel faster than light. Miguel Alcabière became famous for having developed the geometry that describes such a deformer. Space-time distortion makes it possible for an object to travel faster than light while remaining on a time-like curve. The obstacles are the same as when creating wormholes. To create a deformer, you need a substance with a negative energy density u. Even if such a substance is possible, it is still not clear how it can be obtained and how to use it to make the deformer work.
ref M. Alcubierre, Classical and Quantum Gravity, 11 , L73-L77, (1994)

Conclusion

First, it was not easy to define in general what an SS travel and SS message means. Many things, like shadows, make CC move, but in such a way that it cannot be used, for example, to transmit information. But there are also serious possibilities of real SS movement, which are proposed in the scientific literature, but their implementation is still technically impossible. The Heisenberg Uncertainty Principle makes it impossible to use apparent CC motion in quantum mechanics. In general relativity there are potential means of SS propulsion, but it may not be possible to use them. It seems extremely unlikely that in the foreseeable future, or at all, the technology will be able to create spacecraft with SS engines, but it is curious that theoretical physics, as we now know it, does not close the door to SS propulsion for good. SS movement in the style of science fiction novels is apparently completely impossible. For physicists, the question is interesting: "why, in fact, is this impossible, and what can be learned from this?"

Doctor of Technical Sciences A. GOLUBEV.

In the middle of last year, a sensational report appeared in the magazines. A group of American researchers have discovered that a very short laser pulse travels hundreds of times faster in a specially selected medium than in a vacuum. This phenomenon seemed absolutely incredible (the speed of light in a medium is always less than in a vacuum) and even gave rise to doubts about the validity of the special theory of relativity. Meanwhile, a superluminal physical object - a laser pulse in an amplifying medium - was first discovered not in 2000, but 35 years earlier, in 1965, and the possibility of superluminal motion was widely discussed until the early 70s. Today, the discussion around this strange phenomenon has flared up with renewed vigor.

Examples of "superluminal" motion.

In the early 1960s, high-power short light pulses began to be obtained by passing a laser flash through a quantum amplifier (a medium with an inverse population).

In an amplifying medium, the initial region of a light pulse causes stimulated emission of atoms in the amplifier medium, and its final region causes energy absorption by them. As a result, it will appear to the observer that the pulse is moving faster than light.

Lijun Wong experiment.

A beam of light passing through a prism of a transparent material (such as glass) is refracted, that is, it experiences dispersion.

A light pulse is a set of oscillations of different frequencies.

Probably everyone - even people far from physics - knows that the maximum possible speed of movement of material objects or the propagation of any signals is the speed of light in vacuum. It is marked with the letter With and is almost 300 thousand kilometers per second; exact value With= 299 792 458 m/s. The speed of light in vacuum is one of the fundamental physical constants. The impossibility of achieving speeds exceeding With, follows from the special theory of relativity (SRT) of Einstein. If it were possible to prove that the transmission of signals with superluminal speed is possible, the theory of relativity would fall. So far, this has not happened, despite numerous attempts to refute the ban on the existence of speeds greater than With. However, in experimental studies Recently, some very interesting phenomena, indicating that under specially created conditions it is possible to observe superluminal speeds and at the same time the principles of the theory of relativity are not violated.

To begin with, let us recall the main aspects related to the problem of the speed of light. First of all: why not (when normal conditions) exceed the light limit? Because then the fundamental law of our world is violated - the law of causality, according to which the effect cannot outstrip the cause. No one has ever observed that, for example, a bear first fell dead, and then a hunter shot. At speeds exceeding With, the sequence of events becomes reversed, the time tape rewinds. This can be easily seen from the following simple reasoning.

Let's assume that we are on a certain cosmic miracle ship moving faster than light. Then we would gradually catch up with the light emitted by the source at earlier and earlier points in time. First, we would catch up with photons emitted, say, yesterday, then - emitted the day before yesterday, then - a week, a month, a year ago, and so on. If the light source were a mirror reflecting life, then we would first see the events of yesterday, then the day before yesterday, and so on. We could see, say, an old man who gradually turns into a middle-aged man, then into a young man, into a youth, into a child ... That is, time would turn back, we would move from the present to the past. Cause and effect would then be reversed.

Although this argument completely ignores the technical details of the process of observing light, from a fundamental point of view it clearly demonstrates that the movement at a superluminal speed leads to a situation that is impossible in our world. However, nature has set even more stringent conditions: movement is unattainable not only at superluminal speed, but also at a speed equal to the speed of light - you can only approach it. It follows from the theory of relativity that with an increase in the speed of movement, three circumstances arise: the mass of a moving object increases, its size decreases in the direction of movement, and the passage of time on this object slows down (from the point of view of an external "resting" observer). At ordinary speeds, these changes are negligible, but as we approach the speed of light, they become more and more noticeable, and in the limit - at a speed equal to With, - the mass becomes infinitely large, the object completely loses its size in the direction of motion and time stops on it. Therefore, no material body can reach the speed of light. Only light itself has such a speed! (And also the "all-penetrating" particle - the neutrino, which, like the photon, cannot move at a speed less than With.)

Now about the signal transmission speed. Here it is appropriate to use the representation of light in the form of electromagnetic waves. What is a signal? This is some information to be transmitted. An ideal electromagnetic wave is an infinite sinusoid of strictly one frequency, and it cannot carry any information, because each period of such a sinusoid exactly repeats the previous one. The speed at which the phase of the sine wave moves - the so-called phase speed - can exceed the speed of light in a vacuum under certain conditions. There are no restrictions here, since the phase speed is not the speed of the signal - it does not exist yet. To create a signal, you need to make some kind of "mark" on the wave. Such a mark can be, for example, a change in any of the wave parameters - amplitude, frequency or initial phase. But as soon as the mark is made, the wave loses its sinusoidality. It becomes modulated, consisting of a set of simple sinusoidal waves with different amplitudes, frequencies and initial phases - a group of waves. The speed of movement of the mark in the modulated wave is the speed of the signal. When propagating in a medium, this velocity usually coincides with the group velocity characterizing the propagation of the above group of waves as a whole (see "Science and Life" No. 2, 2000). Under normal conditions, the group velocity, and hence the speed of the signal, is less than the speed of light in vacuum. It is no coincidence that the expression "under normal conditions" is used here, because in some cases the group velocity can also exceed With or even lose meaning, but then it does not apply to signal propagation. It is established in the SRT that it is impossible to transmit a signal at a speed greater than With.

Why is it so? Because the obstacle to the transmission of any signal at a speed greater than With the same law of causality applies. Let's imagine such a situation. At some point A, a light flash (event 1) turns on a device that sends a certain radio signal, and at a remote point B, under the action of this radio signal, an explosion occurs (event 2). It is clear that event 1 (flash) is the cause, and event 2 (explosion) is the effect that occurs later than the cause. But if the radio signal propagated at a superluminal speed, an observer near point B would first see an explosion, and only then - that reached him with a speed With flash of light, the cause of the explosion. In other words, for this observer, event 2 would have happened before event 1, that is, the effect would have preceded the cause.

It is appropriate to emphasize that the "superluminal prohibition" of the theory of relativity is imposed only on the movement of material bodies and the transmission of signals. In many situations it is possible to move at any speed, but it will be the movement of non-material objects and signals. For example, imagine two rather long rulers lying in the same plane, one of which is located horizontally, and the other intersects it at a small angle. If the first line is moved down (in the direction indicated by the arrow) at high speed, the intersection point of the lines can be made to run arbitrarily fast, but this point is not a material body. Another example: if you take a flashlight (or, say, a laser that gives a narrow beam) and quickly describe an arc in the air, then the linear speed of the light spot will increase with distance and, at a sufficiently large distance, will exceed With. The spot of light will move between points A and B at superluminal speed, but this will not be a signal transmission from A to B, since such a spot of light does not carry any information about point A.

It would seem that the question of superluminal speeds has been resolved. But in the 60s of the twentieth century, theoretical physicists put forward the hypothesis of the existence of superluminal particles, called tachyons. These are very strange particles: they are theoretically possible, but in order to avoid contradictions with the theory of relativity, they had to be assigned an imaginary rest mass. Physically imaginary mass does not exist, it is a purely mathematical abstraction. However, this did not cause much concern, since tachyons cannot be at rest - they exist (if they exist!) Only at speeds exceeding the speed of light in vacuum, and in this case the mass of the tachyon turns out to be real. There is some analogy with photons here: a photon has zero rest mass, but that simply means that the photon cannot be at rest - light cannot be stopped.

The most difficult thing was, as expected, to reconcile the tachyon hypothesis with the law of causality. Attempts made in this direction, although they were quite ingenious, did not lead to obvious success. No one has been able to experimentally register tachyons either. As a result, interest in tachyons as superluminal elementary particles gradually faded away.

However, in the 60s, a phenomenon was experimentally discovered, which at first led physicists into confusion. This is described in detail in the article by A. N. Oraevsky "Superluminal waves in amplifying media" (UFN No. 12, 1998). Here we briefly summarize the essence of the matter, referring the reader interested in the details to the said article.

Shortly after the discovery of lasers, in the early 1960s, the problem arose of obtaining short (with a duration of the order of 1 ns = 10 -9 s) high-power light pulses. To do this, a short laser pulse was passed through an optical quantum amplifier. The pulse was split by a beam-splitting mirror into two parts. One of them, more powerful, was sent to the amplifier, and the other propagated in the air and served as a reference pulse, with which it was possible to compare the pulse that passed through the amplifier. Both pulses were fed to photodetectors, and their output signals could be visually observed on the oscilloscope screen. It was expected that the light pulse passing through the amplifier would experience some delay in it compared to the reference pulse, that is, the speed of light propagation in the amplifier would be less than in air. What was the astonishment of the researchers when they discovered that the pulse propagated through the amplifier at a speed not only greater than in air, but also several times greater than the speed of light in vacuum!

After recovering from the first shock, physicists began to look for the reason for such an unexpected result. No one had even the slightest doubt about the principles of the special theory of relativity, and this is precisely what helped to find the correct explanation: if the principles of SRT are preserved, then the answer should be sought in the properties of the amplifying medium.

Without going into details here, we only point out that detailed analysis mechanism of action of the amplifying medium completely clarified the situation. The point was a change in the concentration of photons during the propagation of the pulse - a change due to a change in the gain of the medium up to a negative value during the passage of the rear part of the pulse, when the medium is already absorbing energy, because its own reserve has already been used up due to its transfer to the light pulse. Absorption does not cause an increase, but a decrease in the impulse, and thus the impulse is strengthened in the front and weakened in the back of it. Let us imagine that we observe the pulse with the help of an instrument moving at the speed of light in the medium of an amplifier. If the medium were transparent, we would see an impulse frozen in immobility. In the medium in which the process mentioned above takes place, the strengthening of the leading edge and the weakening of the trailing edge of the pulse will appear to the observer in such a way that the medium, as it were, has moved the pulse forward. But since the device (observer) moves at the speed of light, and the impulse overtakes it, then the speed of the impulse exceeds the speed of light! It is this effect that was registered by the experimenters. And here there really is no contradiction with the theory of relativity: it's just that the amplification process is such that the concentration of photons that came out earlier turns out to be greater than those that came out later. It is not photons that move with superluminal speed, but the envelope of the pulse, in particular its maximum, which is observed on the oscilloscope.

Thus, while in ordinary media there is always a weakening of light and a decrease in its speed, determined by the refractive index, in active laser media, not only amplification of light is observed, but also propagation of a pulse with superluminal speed.

Some physicists have tried to experimentally prove the presence of superluminal motion in the tunnel effect, one of the most amazing phenomena in quantum mechanics. This effect consists in the fact that a microparticle (more precisely, a microobject that exhibits both the properties of a particle and the properties of a wave under different conditions) is able to penetrate the so-called potential barrier - a phenomenon that is completely impossible in classical mechanics(in which the analogy would be: a ball thrown at a wall would end up on the other side of the wall, or the undulating motion imparted to a rope tied to the wall would be transmitted to a rope tied to the wall on the other side). The essence of the tunnel effect in quantum mechanics is as follows. If a micro-object with a certain energy encounters on its way an area with a potential energy exceeding the energy of the micro-object, this area is a barrier for it, the height of which is determined by the energy difference. But the micro-object "leaks" through the barrier! This possibility is given to him by the well-known Heisenberg uncertainty relation, written for the energy and interaction time. If the interaction of the micro-object with the barrier occurs for a sufficiently certain time, then the energy of the micro-object, on the contrary, will be characterized by uncertainty, and if this uncertainty is of the order of the barrier height, then the latter ceases to be an insurmountable obstacle for the micro-object. It is the rate of penetration through the potential barrier that has become the subject of research by a number of physicists who believe that it can exceed With.

In June 1998, an international symposium on the problems of superluminal motions was held in Cologne, where the results obtained in four laboratories - in Berkeley, Vienna, Cologne and Florence were discussed.

And finally, in 2000, two new experiments were reported in which the effects of superluminal propagation appeared. One of them was performed by Lijun Wong with employees in research institute in Princeton (USA). His result is that a light pulse entering a chamber filled with cesium vapor increases its speed by a factor of 300. It turned out that the main part of the pulse leaves the far wall of the chamber even before the pulse enters the chamber through the front wall. Such a situation contradicts not only common sense, but, in essence, the theory of relativity as well.

L. Wong's report provoked intense discussion among physicists, most of whom are not inclined to see in the results obtained a violation of the principles of relativity. The challenge, they believe, is to correctly explain this experiment.

In the experiment of L. Wong, the light pulse entering the chamber with cesium vapor had a duration of about 3 μs. Cesium atoms can be in sixteen possible quantum mechanical states, called "ground state hyperfine magnetic sublevels". Using optical laser pumping, almost all atoms were brought into only one of these sixteen states, corresponding to almost absolute zero temperature on the Kelvin scale (-273.15 o C). The length of the cesium chamber was 6 centimeters. In a vacuum, light travels 6 centimeters in 0.2 ns. As the measurements showed, the light pulse passed through the chamber with cesium in a time 62 ns shorter than in vacuum. In other words, the transit time of a pulse through a cesium medium has a "minus" sign! Indeed, if we subtract 62 ns from 0.2 ns, we get a "negative" time. This "negative delay" in the medium - an incomprehensible time jump - is equal to the time during which the pulse would make 310 passes through the chamber in vacuum. The consequence of this "time reversal" was that the impulse leaving the chamber managed to move away from it by 19 meters before the incoming impulse reached the near wall of the chamber. How can such an incredible situation be explained (unless, of course, there is no doubt about the purity of the experiment)?

Judging by the ongoing discussion, an exact explanation has not yet been found, but there is no doubt that the unusual dispersion properties of the medium play a role here: cesium vapor, consisting of atoms excited by laser light, is a medium with anomalous dispersion. Let us briefly recall what it is.

The dispersion of a substance is the dependence of the phase (ordinary) refractive index n on the wavelength of light l. With normal dispersion, the refractive index increases with decreasing wavelength, and this is the case in glass, water, air, and all other substances transparent to light. In substances that strongly absorb light, the course of the refractive index reverses with a change in wavelength and becomes much steeper: with a decrease in l (an increase in the frequency w), the refractive index sharply decreases and in a certain range of wavelengths becomes less than unity (the phase velocity V f > With). This is the anomalous dispersion, in which the pattern of light propagation in a substance changes radically. group speed V cp becomes greater than the phase velocity of the waves and can exceed the speed of light in vacuum (and also become negative). L. Wong points to this circumstance as the reason underlying the possibility of explaining the results of his experiment. However, it should be noted that the condition V gr > With is purely formal, since the concept of group velocity was introduced for the case of small (normal) dispersion, for transparent media, when a group of waves almost does not change its shape during propagation. In regions of anomalous dispersion, however, the light pulse is rapidly deformed and the concept of group velocity loses its meaning; in this case, the concepts of signal velocity and energy propagation velocity are introduced, which in transparent media coincide with the group velocity, while in media with absorption they remain less than the speed of light in vacuum. But here's what's interesting about Wong's experiment: a light pulse, passing through a medium with anomalous dispersion, does not deform - it retains its shape exactly! And this corresponds to the assumption that the impulse propagates with the group velocity. But if so, then it turns out that there is no absorption in the medium, although the anomalous dispersion of the medium is due precisely to absorption! Wong himself, recognizing that much remains unclear, believes that what is happening in his experimental setup can be clearly explained as a first approximation as follows.

A light pulse consists of many components with different wavelengths (frequencies). The figure shows three of these components (waves 1-3). At some point, all three waves are in phase (their maxima coincide); here they, adding up, reinforce each other and form an impulse. As the waves propagate further in space, they are out of phase and thus "extinguish" each other.

In the region of anomalous dispersion (inside the cesium cell), the wave that was shorter (wave 1) becomes longer. Conversely, the wave that was the longest of the three (wave 3) becomes the shortest.

Consequently, the phases of the waves also change accordingly. When the waves have passed through the cesium cell, their wavefronts are restored. Having undergone an unusual phase modulation in a substance with anomalous dispersion, the three considered waves again find themselves in phase at some point. Here they add up again and form a pulse of exactly the same shape as that entering the cesium medium.

Typically in air, and indeed in any normally dispersive transparent medium, a light pulse cannot accurately maintain its shape when propagating over a remote distance, that is, all of its components cannot be in phase at any remote point along the propagation path. And under normal conditions, a light pulse at such a remote point appears after some time. However, due to the anomalous properties of the medium used in the experiment, the pulse at the remote point turned out to be phased in the same way as when entering this medium. Thus, the light pulse behaves as if it had a negative time delay on its way to a remote point, that is, it would have arrived at it not later, but earlier than it passed the medium!

Most physicists are inclined to associate this result with the appearance of a low-intensity precursor in the dispersive medium of the chamber. The fact is that in the spectral decomposition of the pulse, the spectrum contains components of arbitrarily high frequencies with negligible amplitude, the so-called precursor, which goes ahead of the "main part" of the pulse. The nature of the establishment and the form of the precursor depend on the dispersion law in the medium. With this in mind, the sequence of events in Wong's experiment is proposed to be interpreted as follows. The incoming wave, "stretching" the harbinger in front of itself, approaches the camera. Before the peak of the incoming wave hits the near wall of the chamber, the precursor initiates the appearance of a pulse in the chamber, which reaches the far wall and is reflected from it, forming a "reverse wave". This wave, propagating 300 times faster With, reaches the near wall and meets the incoming wave. The peaks of one wave meet the troughs of another so that they cancel each other out and nothing remains. It turns out that the incoming wave "returns the debt" to the cesium atoms, which "borrowed" energy to it at the other end of the chamber. Someone who watched only the beginning and end of the experiment would see only a pulse of light that "jumped" forward in time, moving faster With.

L. Wong believes that his experiment is not consistent with the theory of relativity. The statement about the unattainability of superluminal speed, he believes, is applicable only to objects with a rest mass. Light can be represented either in the form of waves, to which the concept of mass is generally inapplicable, or in the form of photons with a rest mass, as is known, equal to zero. Therefore, the speed of light in a vacuum, according to Wong, is not the limit. Nevertheless, Wong admits that the effect he discovered does not make it possible to transmit information at a speed greater than With.

"The information here is already contained in the leading edge of the pulse," says P. Milonni, a physicist at the Los Alamos National Laboratory in the US.

Most physicists believe that new job does not deal a crushing blow to fundamental principles. But not all physicists believe that the problem is settled. Professor A. Ranfagni, of the Italian research group that carried out another interesting experiment in 2000, says the question is still open. This experiment, carried out by Daniel Mugnai, Anedio Ranfagni and Rocco Ruggeri, found that centimeter-wave radio waves propagate in ordinary air at a speed exceeding With by 25%.

Summarizing, we can say the following. Works recent years show that, under certain conditions, superluminal speed can indeed take place. But what exactly is moving at superluminal speed? The theory of relativity, as already mentioned, forbids such a speed for material bodies and for signals carrying information. Nevertheless, some researchers are very persistent in their attempts to demonstrate the overcoming of the light barrier specifically for signals. The reason for this lies in the fact that in the special theory of relativity there is no rigorous mathematical justification (based, say, on Maxwell's equations for an electromagnetic field) for the impossibility of transmitting signals at a speed greater than With. Such an impossibility in SRT is established, one might say, purely arithmetically, based on the Einstein formula for adding velocities, but in a fundamental way this is confirmed by the principle of causality. Einstein himself, considering the question of superluminal signal transmission, wrote that in this case "... we are forced to consider a signal transmission mechanism possible, when using which the achieved action precedes the cause. But, although this result from a purely logical point of view does not contain itself, in my opinion, no contradictions, it nevertheless contradicts the character of all our experience so much that the impossibility of supposing V > c appears to be sufficiently proven. "The principle of causality is the cornerstone that underlies the impossibility of superluminal signal transmission. And this stone, apparently, will stumble all searches for superluminal signals without exception, no matter how much experimenters would like to detect such signals because that is the nature of our world.

In conclusion, it should be emphasized that all of the above applies specifically to our world, to our Universe. Such a reservation was made because recently new hypotheses have appeared in astrophysics and cosmology that allow the existence of many Universes hidden from us, connected by topological tunnels - jumpers. This point of view is shared, for example, by the well-known astrophysicist N. S. Kardashev. For an outside observer, the entrances to these tunnels are marked by anomalous gravitational fields, similar to black holes. Movements in such tunnels, as suggested by the authors of the hypotheses, will make it possible to circumvent the speed limit imposed in ordinary space by the speed of light, and, consequently, to realize the idea of creating a time machine... things. And although so far such hypotheses are too reminiscent of plots from science fiction, one should hardly categorically reject the fundamental possibility of a multi-element model of the structure of the material world. Another thing is that all these other Universes, most likely, will remain purely mathematical constructions of theoretical physicists living in our Universe and trying to find the worlds closed to us with the power of their thoughts...

See in a room on the same topic

Astrophysicists from Baylor University (USA) have developed a mathematical model of a hyperspace drive that allows you to overcome space distances at a speed higher than the speed of light by 10³² times, which allows you to fly to a neighboring galaxy within a couple of hours and return back.

During the flight, people will not feel the overloads that are felt in modern airliners, however, such an engine can only appear in metal in a few hundred years.

The drive mechanism is based on the principle of the space deformation engine (Warp Drive), which was proposed in 1994 by the Mexican physicist Miguel Alcubierre. The Americans only had to refine the model and make more detailed calculations.
“If you compress space in front of the ship, and expand behind it, on the contrary, then a space-time bubble appears around the ship,” says one of the authors of the study, Richard Obousi. “It envelops the ship and pulls it out of the ordinary world into its own coordinate system. due to the pressure difference of space-time, this bubble is able to move in any direction, overcoming the light threshold by thousands of orders of magnitude.

Presumably, the space around the ship will be able to deform due to dark energy, which has not been studied so far. “Dark energy is a very poorly studied substance, discovered relatively recently and explaining why galaxies seem to fly apart from each other,” said Sergei Popov, senior researcher at the Department of Relativistic Astrophysics at the Sternberg State Astronomical Institute of Moscow State University. “There are several models of it, but which one "There is no generally accepted one yet. The Americans have taken a model based on extra dimensions as a basis, and they say that it is possible to change the properties of these dimensions locally. Then it turns out that there can be different cosmological constants in different directions. And then the ship in the bubble will start moving."

Such "behavior" of the Universe can be explained by "string theory", according to which our entire space is permeated with many other dimensions. Their interaction with each other generates a repulsive force, which is capable of expanding not only matter, such as galaxies, but also the body of space itself. This effect is called "inflation of the Universe".

"From the first seconds of its existence, the Universe has been stretching, - explains Ruslan Metsaev, Doctor of Physical and Mathematical Sciences, an employee of the Astro-Space Center of the Lebedev Physics Institute. - And this process continues to this day." Knowing all this, you can try to expand or narrow the space artificially. To do this, it is supposed to influence other dimensions, thereby a piece of the space of our world will begin to move in the right direction under the influence of the forces of dark energy.

In this case, the laws of the theory of relativity are not violated. Inside the bubble, the same laws of the physical world will remain, and the speed of light will be the limit. This situation does not apply to the so-called twin effect, which tells that when space travel with light speeds, time inside the ship slows down significantly and the astronaut, returning to Earth, will meet his twin brother, already a very old man. The Warp Drive engine eliminates this hassle, because it pushes the space, not the ship.

The Americans have already found a target for the future flight. This is the planet Gliese 581 (Gliese 581), on which climatic conditions and gravity approach those of the earth. The distance to it is 20 light-years, and even if the Warp Drive operates a trillion times weaker than maximum power, the travel time to it will be only a few seconds.

FTL travel is one of the foundations of space science fiction. However, probably everyone - even people far from physics - knows that the maximum possible speed of movement of material objects or the propagation of any signals is the speed of light in vacuum. It is denoted by the letter c and is almost 300 thousand kilometers per second; exact value c = 299 792 458 m/s.

The speed of light in vacuum is one of the fundamental physical constants. The impossibility of achieving speeds exceeding c follows from Einstein's special theory of relativity (SRT). If it were possible to prove that the transmission of signals with superluminal speed is possible, the theory of relativity would fall. So far, this has not happened, despite numerous attempts to refute the ban on the existence of velocities greater than c. However, recent experimental studies have revealed some very interesting phenomena, indicating that under specially created conditions it is possible to observe superluminal velocities without violating the principles of the theory of relativity.

To begin with, let us recall the main aspects related to the problem of the speed of light.

First of all: why is it impossible (under normal conditions) to exceed the light limit? Because then the fundamental law of our world is violated - the law of causality, according to which the effect cannot outstrip the cause. No one has ever observed that, for example, a bear first fell dead, and then a hunter shot. At speeds exceeding c, the sequence of events becomes reversed, the time tape rewinds. This can be easily seen from the following simple reasoning.

Although this argument completely ignores the technical details of the process of observing light, from a fundamental point of view it clearly demonstrates that the movement at a superluminal speed leads to a situation that is impossible in our world. However, nature has set even more stringent conditions: movement is unattainable not only at superluminal speed, but also at a speed equal to the speed of light - you can only approach it. It follows from the theory of relativity that with an increase in the speed of movement, three circumstances arise: the mass of a moving object increases, its size decreases in the direction of movement, and the passage of time on this object slows down (from the point of view of an external "resting" observer). At ordinary speeds, these changes are negligible, but as we approach the speed of light, they become more and more noticeable, and in the limit - at a speed equal to c - the mass becomes infinitely large, the object completely loses its size in the direction of motion and time stops on it. Therefore, no material body can reach the speed of light. Only light itself has such a speed! (And also an "all-penetrating" particle - a neutrino, which, like a photon, cannot move at a speed less than c.)

Now about the signal transmission speed. Here it is appropriate to use the representation of light in the form of electromagnetic waves. What is a signal? This is some information to be transmitted. An ideal electromagnetic wave is an infinite sinusoid of strictly one frequency, and it cannot carry any information, because each period of such a sinusoid exactly repeats the previous one. The speed of movement of the phase of a sinusoidal wave - the so-called phase speed - can in a medium under certain conditions exceed the speed of light in a vacuum. There are no restrictions here, since the phase speed is not the speed of the signal - it does not exist yet. To create a signal, you need to make some kind of "mark" on the wave. Such a mark can be, for example, a change in any of the wave parameters - amplitude, frequency or initial phase. But as soon as the mark is made, the wave loses its sinusoidality. It becomes modulated, consisting of a set of simple sinusoidal waves with different amplitudes, frequencies and initial phases - a group of waves. The speed of movement of the mark in the modulated wave is the speed of the signal. When propagating in a medium, this velocity usually coincides with the group velocity characterizing the propagation of the above group of waves as a whole (see "Science and Life" No. 2, 2000). Under normal conditions, the group velocity, and hence the speed of the signal, is less than the speed of light in vacuum. It is no coincidence that the expression "under normal conditions" is used here, because in some cases the group velocity may exceed c or even lose its meaning, but then it does not apply to signal propagation. In SRT, it is established that it is impossible to transmit a signal at a speed greater than c.

Why is it so? Because the obstacle to the transmission of any signal with a speed greater than c is the same law of causality. Let's imagine such a situation. At some point A, a light flash (event 1) turns on a device that sends a certain radio signal, and at a remote point B, under the action of this radio signal, an explosion occurs (event 2). It is clear that event 1 (flash) is the cause, and event 2 (explosion) is the effect that occurs later than the cause. But if the radio signal propagated at a superluminal speed, an observer near point B would first see an explosion, and only then - a flash of light that reached him at a speed of a light flash, the cause of the explosion. In other words, for this observer, event 2 would have happened before event 1, that is, the effect would have preceded the cause.

It is appropriate to emphasize that the "superluminal prohibition" of the theory of relativity is imposed only on the movement of material bodies and the transmission of signals. In many situations it is possible to move at any speed, but it will be the movement of non-material objects and signals. For example, imagine two rather long rulers lying in the same plane, one of which is located horizontally, and the other intersects it at a small angle. If the first line is moved down (in the direction indicated by the arrow) at high speed, the intersection point of the lines can be made to run arbitrarily fast, but this point is not a material body. Another example: if you take a flashlight (or, say, a laser that gives a narrow beam) and quickly describe an arc in the air, then the linear speed of the light spot will increase with distance and, at a sufficiently large distance, will exceed c. The spot of light will move between points A and B at superluminal speed, but this will not be a signal transmission from A to B, since such a spot of light does not carry any information about point A.

Shortly after the discovery of lasers - in the early 1960s - the problem arose of obtaining short (with a duration of the order of 1 ns = 10-9 s) high-power light pulses. To do this, a short laser pulse was passed through an optical quantum amplifier. The pulse was split by a beam-splitting mirror into two parts. One of them, more powerful, was sent to the amplifier, and the other propagated in the air and served as a reference pulse, with which it was possible to compare the pulse that passed through the amplifier. Both pulses were fed to photodetectors, and their output signals could be visually observed on the oscilloscope screen. It was expected that the light pulse passing through the amplifier would experience some delay in it compared to the reference pulse, that is, the speed of light propagation in the amplifier would be less than in air. What was the astonishment of the researchers when they discovered that the pulse propagated through the amplifier at a speed not only greater than in air, but also several times greater than the speed of light in vacuum!

Without going into details here, we only point out that a detailed analysis of the mechanism of action of the amplifying medium has completely clarified the situation. The point was a change in the concentration of photons during the propagation of the pulse - a change due to a change in the gain of the medium up to a negative value during the passage of the rear part of the pulse, when the medium is already absorbing energy, because its own reserve has already been used up due to its transfer to the light pulse. Absorption does not cause an increase, but a decrease in the impulse, and thus the impulse is strengthened in the front and weakened in the back of it. Let us imagine that we observe the pulse with the help of an instrument moving at the speed of light in the medium of an amplifier. If the medium were transparent, we would see an impulse frozen in immobility. In the medium in which the process mentioned above takes place, the strengthening of the leading edge and the weakening of the trailing edge of the pulse will appear to the observer in such a way that the medium, as it were, has moved the pulse forward. But since the device (observer) moves at the speed of light, and the impulse overtakes it, then the speed of the impulse exceeds the speed of light! It is this effect that was registered by the experimenters. And here there really is no contradiction with the theory of relativity: it's just that the amplification process is such that the concentration of photons that came out earlier turns out to be greater than those that came out later. It is not photons that move with superluminal speed, but the envelope of the pulse, in particular its maximum, which is observed on the oscilloscope.

Some physicists have tried to experimentally prove the presence of superluminal motion in the tunnel effect, one of the most amazing phenomena in quantum mechanics. This effect consists in the fact that a microparticle (more precisely, a microobject that exhibits both the properties of a particle and the properties of a wave under different conditions) is able to penetrate the so-called potential barrier - a phenomenon that is completely impossible in classical mechanics (in which such a situation would be analogous : a ball thrown at a wall would end up on the other side of the wall, or the undulating motion given by a rope tied to the wall would be transmitted to a rope tied to the wall on the other side). The essence of the tunnel effect in quantum mechanics is as follows. If a micro-object with a certain energy encounters on its way an area with a potential energy exceeding the energy of the micro-object, this area is a barrier for it, the height of which is determined by the energy difference. But the micro-object "leaks" through the barrier! This possibility is given to him by the well-known Heisenberg uncertainty relation, written for the energy and interaction time. If the interaction of the micro-object with the barrier occurs for a sufficiently certain time, then the energy of the micro-object, on the contrary, will be characterized by uncertainty, and if this uncertainty is of the order of the barrier height, then the latter ceases to be an insurmountable obstacle for the micro-object. It is the rate of penetration through the potential barrier that has become the subject of research by a number of physicists, who believe that it can exceed c.

And finally, in 2000, two new experiments were reported in which the effects of superluminal propagation appeared. One of them was carried out by Lijun Wong and co-workers at a research institute in Princeton (USA). His result is that a light pulse entering a chamber filled with cesium vapor increases its speed by a factor of 300. It turned out that the main part of the pulse leaves the far wall of the chamber even before the pulse enters the chamber through the front wall. Such a situation contradicts not only common sense, but, in essence, the theory of relativity as well.

In the experiment of L. Wong, the light pulse entering the chamber with cesium vapor had a duration of about 3 μs. Cesium atoms can be in sixteen possible quantum mechanical states, called "ground state hyperfine magnetic sublevels". Using optical laser pumping, almost all atoms were brought to only one of these sixteen states, corresponding to almost absolute zero temperature on the Kelvin scale (-273.15 ° C). The length of the cesium chamber was 6 centimeters. In a vacuum, light travels 6 centimeters in 0.2 ns. As the measurements showed, the light pulse passed through the chamber with cesium in a time 62 ns shorter than in vacuum. In other words, the transit time of a pulse through a cesium medium has a "minus" sign! Indeed, if we subtract 62 ns from 0.2 ns, we get a "negative" time. This "negative delay" in the medium - an incomprehensible time jump - is equal to the time during which the pulse would make 310 passes through the chamber in vacuum. The consequence of this "time reversal" was that the impulse leaving the chamber managed to move away from it by 19 meters before the incoming impulse reached the near wall of the chamber. How can such an incredible situation be explained (unless, of course, there is no doubt about the purity of the experiment)?

The dispersion of a substance is the dependence of the phase (usual) refractive index n on the wavelength of light l. With normal dispersion, the refractive index increases with decreasing wavelength, and this is the case in glass, water, air, and all other substances transparent to light. In substances that strongly absorb light, the course of the refractive index reverses with a change in wavelength and becomes much steeper: with a decrease in l (increase in frequency w), the refractive index sharply decreases and in a certain range of wavelengths becomes less than unity (phase velocity Vf > s ). This is the anomalous dispersion, in which the pattern of light propagation in a substance changes radically. The group velocity Vgr becomes greater than the phase velocity of the waves and can exceed the speed of light in vacuum (and also become negative). L. Wong points to this circumstance as the reason underlying the possibility of explaining the results of his experiment. However, it should be noted that the condition Vgr > c is purely formal, since the concept of group velocity was introduced for the case of small (normal) dispersion, for transparent media, when a group of waves almost does not change its shape during propagation. In regions of anomalous dispersion, however, the light pulse is rapidly deformed and the concept of group velocity loses its meaning; in this case, the concepts of signal velocity and energy propagation velocity are introduced, which in transparent media coincide with the group velocity, while in media with absorption they remain less than the speed of light in vacuum. But here's what's interesting about Wong's experiment: a light pulse, passing through a medium with anomalous dispersion, does not deform - it retains its shape exactly! And this corresponds to the assumption that the impulse propagates with the group velocity. But if so, then it turns out that there is no absorption in the medium, although the anomalous dispersion of the medium is due precisely to absorption! Wong himself, recognizing that much remains unclear, believes that what is happening in his experimental setup can be clearly explained as a first approximation as follows.

Most physicists are inclined to associate this result with the appearance of a low-intensity precursor in the dispersive medium of the chamber. The fact is that in the spectral decomposition of the pulse, the spectrum contains components of arbitrarily high frequencies with negligible amplitude, the so-called precursor, which goes ahead of the "main part" of the pulse. The nature of the establishment and the form of the precursor depend on the dispersion law in the medium. With this in mind, the sequence of events in Wong's experiment is proposed to be interpreted as follows. The incoming wave, "stretching" the harbinger in front of itself, approaches the camera. Before the peak of the incoming wave hits the near wall of the chamber, the precursor initiates the appearance of a pulse in the chamber, which reaches the far wall and is reflected from it, forming a "reverse wave". This wave, propagating 300 times faster than c, reaches the near wall and meets the incoming wave. The peaks of one wave meet the troughs of another so that they cancel each other out and nothing remains. It turns out that the incoming wave "returns the debt" to the cesium atoms, which "borrowed" energy to it at the other end of the chamber. Anyone who observed only the beginning and end of the experiment would only see a pulse of light that "jumped" forward in time, moving faster than c.

L. Wong believes that his experiment is not consistent with the theory of relativity. The statement about the unattainability of superluminal speed, he believes, is applicable only to objects with a rest mass. Light can be represented either in the form of waves, to which the concept of mass is generally inapplicable, or in the form of photons with a rest mass, as is known, equal to zero. Therefore, the speed of light in a vacuum, according to Wong, is not the limit. However, Wong admits that the effect he discovered makes it impossible to transmit information faster than c.

"The information here is already contained in the leading edge of the pulse," says P. Milonni, a physicist at the Los Alamos National Laboratory in the US.

Most physicists believe that the new work does not deal a crushing blow to fundamental principles. But not all physicists believe that the problem is settled. Professor A. Ranfagni, of the Italian research group that carried out another interesting experiment in 2000, says the question is still open. This experiment, carried out by Daniel Mugnai, Anedio Ranfagni and Rocco Ruggeri, found that centimeter-wave radio waves propagate in normal air at a speed 25% faster than c.

Summarizing, we can say the following.

The works of recent years show that under certain conditions, superluminal speed can indeed take place. But what exactly is moving at superluminal speed? The theory of relativity, as already mentioned, forbids such a speed for material bodies and for signals carrying information. Nevertheless, some researchers are very persistent in their attempts to demonstrate the overcoming of the light barrier specifically for signals. The reason for this lies in the fact that in the special theory of relativity there is no rigorous mathematical justification (based, say, on Maxwell's equations for an electromagnetic field) for the impossibility of transmitting signals at a speed greater than c. Such an impossibility in SRT is established, one might say, purely arithmetically, based on the Einstein formula for adding velocities, but in a fundamental way this is confirmed by the principle of causality. Einstein himself, considering the question of superluminal signal transmission, wrote that in this case "... we are forced to consider a signal transmission mechanism possible, when using which the achieved action precedes the cause. But, although this result from a purely logical point of view does not contain itself, in my opinion, no contradictions, it nevertheless contradicts the character of all our experience to such an extent that the impossibility of the assumption V > c seems to be sufficiently proved. The principle of causality is the cornerstone that underlies the impossibility of superluminal signaling. And, apparently, all searches for superluminal signals, without exception, will stumble over this stone, no matter how much experimenters would like to detect such signals, because such is the nature of our world.

But still, let's imagine that the mathematics of relativity will still work at superluminal speeds. This means that theoretically we can still find out what would happen if the body happened to exceed the speed of light.

Imagine two spaceship, heading from the Earth towards a star, which is 100 light years away from our planet. The first ship leaves Earth at 50% the speed of light, so it will take 200 years to complete the journey. The second ship, equipped with a hypothetical warp drive, will depart at 200% the speed of light, but 100 years after the first. What will happen?

According to the theory of relativity, the correct answer largely depends on the perspective of the observer. From Earth, it will appear that the first ship has already traveled a considerable distance before being overtaken by the second ship, which is moving four times as fast. But from the point of view of the people on the first ship, everything is a little different.

Ship #2 is moving faster than light, which means it can outrun even the light it emits. This leads to a kind of "light wave" (analogous to sound, only light waves vibrate here instead of air vibrations), which gives rise to several interesting effects. Recall that the light from ship #2 moves slower than the ship itself. The result will be a visual doubling. In other words, at first the crew of ship #1 will see that the second ship appeared next to them as if from nowhere. Then, the light from the second ship will reach the first ship with a slight delay, and the result will be a visible copy that will move in the same direction with a slight lag.

Something similar can be seen in computer games when, as a result of a system failure, the engine loads the model and its algorithms at the end point of the movement faster than the motion animation itself ends, so that multiple takes occur. This is probably why our consciousness does not perceive that hypothetical aspect of the Universe in which bodies move at superluminal speed - perhaps this is for the best.

P.S. ... but in the last example, I didn’t understand something, why is the real position of the ship associated with the "light emitted by it"? Well, even though they will see him somehow in the wrong place, but in reality he will overtake the first ship!

sources