In September 2011, physicist Antonio Ereditato shocked the whole world. The announcement he made promised to upend the entire understanding of the universe. And if the data that was collected by the 160 scientists who participated in the OPERA program were correct, then this meant that something incredible had been discovered. The particles, in this case neutrinos, were moving faster than the speed of light.

Incredible discovery

According to Einstein's theories of relativity, this should not be the case. And the consequences of demonstrating that it did happen would be enormous. Many points in physics would have to be revised. And although Ereditato and his team reported that they had a high level of confidence in what they found, they did not state that they were one hundred percent sure of the accuracy of their observations. In fact, they were asking other scientists to help them understand what had happened.

An error in the experiment

As a result, it turned out that the OPERA program was wrong. The problem with taking time readings was due to the fact that the cable was poorly connected, which was supposed to transmit incredibly accurate signals from GPS satellites. Accordingly, there was an unexpected delay in signal transmission. Thus, measurements of how long a neutrino took a certain distance had an error of about 73 nanoseconds. This gave the impression that these particles were moving faster than the particles of light.

Effects

Despite the months of careful checks before the start of the experiment, a large number of repeated checks of the information obtained during the experiment, this time the scientists were still mistaken. Ereditato retired, although many people noted that such errors in the extremely complex technology of particle accelerators happen quite often. But why does even the tiniest suggestion that something can travel faster than the speed of light matter so much? And do people really believe that nothing can do that?

speed of light

Let's look at the second of these questions first. The speed of light in a vacuum is 299792.458 kilometers per second - a little short of the beautiful round figure of 300,000 kilometers per second. It's very fast. The sun is 150 million kilometers from Earth, and light takes only eight minutes and twenty seconds to travel this way. Can something man-made compete with light? One of the fastest objects ever made by man is the New Horizons space probe that flew past Pluto and Charon in 2015. The maximum speed that he was able to reach is 16 kilometers per second, that is, much less than 300 thousand kilometers per second.

Experiment with electrons

However, people have managed to make tiny particles move at much faster speeds. In the early sixties, William Bertozzi of the Massachusetts Institute of Technology experimented with the acceleration of electrons. Since the electrons have a negative charge, it is possible to set them in motion by repulsion if the material is charged with the same charge. The more energy used, the faster the electrons got.

Why not apply maximum energy?

One might think that it is enough to increase the applied energy to such an extent that the speed of the particle develops to the required 300,000 kilometers per second. However, it turned out that electrons cannot move that fast. Bertozzi's experiments showed that using more energy did not create a proportional increase in the speed of the electrons. He had to apply more and more energy to get ever-decreasing increases in particle speed. They got closer and closer to the speed of light, but never reached it.

Impossibility of achievement

Imagine that you need to get to the door, taking steps, but each subsequent step will be half the previous one. Simply put, you will never reach the door, because with each subsequent step, there will still be a certain distance between you and the door. This is exactly the problem that Bertozzi encountered in his experiment with electrons. However, light is made up of particles called photons. Why can these particles move at the speed of light if the electrons can't do the job?

Features of photons

As an object moves faster and faster, it gets heavier and heavier, and so it becomes harder for them to pick up speed, which is why they can never reach the speed of light. Photons don't have mass. If they had mass, they would not be able to move at the speed of light. Photons are unique particles. They have no mass, which gives them limitless possibilities while moving in a vacuum, they do not need to accelerate. The natural energy they possess as they move in waves ensures that, at the time of creation, photons already have their speed limit.

We were taught from school that it is impossible to exceed the speed of light, and therefore the movement of a person in outer space is a big insoluble problem (how to fly to the nearest solar system if light can overcome this distance only in a few thousand years?). Perhaps American scientists have found a way to fly at superspeeds, not only without cheating, but also following the fundamental laws of Albert Einstein. In any case, Harold White, the author of the project of the space deformation engine, says so.

We in the editorial office considered the news absolutely fantastic, so today, on the eve of Cosmonautics Day, we are publishing a report by Konstantin Kakaes for Popular Science magazine about a phenomenal NASA project, if successful, a person will be able to go beyond the solar system.

In September 2012, several hundred scientists, engineers and space enthusiasts came together for the group's second public meeting called 100 Year Starship. The group is led by former astronaut May Jemison and founded by DARPA. The goal of the conference is "to make possible human travel beyond the solar system to other stars within the next hundred years." Most of the conference participants admit that progress in manned space exploration is too small. Despite the billions of dollars spent in the last few quarters, the space agencies can do almost as much as they could in the 1960s. Actually, 100 Year Starship is convened to fix all this.

But more to the point. After a few days of the conference, its participants reached the most fantastic topics: organ regeneration, the problem of organized religion on board the ship, and so on. One of the more intriguing presentations at the 100 Year Starship meeting was called Warp Field Mechanics 102, and was delivered by NASA's Harold "Sonny" White. An agency veteran, White runs the Advanced Pulse Program at the Johnson Space Center (JSC). Together with five colleagues, he created the "Space Propulsion Systems Roadmap," which outlines NASA's goals for future space travel. The plan lists all kinds of propulsion projects, from advanced chemical rockets to far-reaching developments like antimatter or nuclear machines. But White's area of ​​research is the most futuristic of all: it concerns the space warp engine.

this is how Alcubierre's bubble is usually depicted

According to the plan, such an engine will provide movement in space at a speed exceeding the speed of light. It is generally accepted that this is impossible, since it is a clear violation of Einstein's theory of relativity. But White argues otherwise. As confirmation of his words, he appeals to the so-called Alcubierre bubbles (equations derived from Einstein's theory, according to which a body in outer space is capable of reaching superluminal speeds, unlike a body under normal conditions). In the presentation, he told how he recently managed to achieve theoretical results that directly lead to the creation of a real space warp engine.

It is clear that this all sounds absolutely fantastic: such developments are a real revolution that will untie the hands of all astrophysicists in the world. Instead of spending 75,000 years traveling to Alpha Centauri, the closest star system to our own, astronauts on a ship with such an engine could make the journey in a couple of weeks.

In light of the shutdown of the shuttle program and the growing role of private flights to low Earth orbit, NASA says it is refocusing on far-reaching, much bolder plans that go far beyond traveling to the moon. These goals can only be achieved through the development of new propulsion systems - the sooner the better. A few days after the conference, NASA chief Charles Bolden echoed White's words: "We want to travel faster than the speed of light and non-stop on Mars."

HOW DO WE KNOW ABOUT THIS ENGINE

The first popular use of the term "space warp drive" dates back to 1966, when Star Trek was released by Jen Roddenberry. For the next 30 years, this engine existed only as part of this fantasy series. A physicist named Miguel Alcubierre watched an episode of the series just as he was working on his doctorate in general relativity and was wondering if it was possible to create a space warp drive in reality. In 1994, he published a paper setting out this position.

Alcubierre imagined a bubble in space. In the front of the bubble, time-space is shrinking, and in the back it is expanding (as it was with the Big Bang, according to physicists). The deformation will cause the ship to glide smoothly through outer space, as if it were surfing a wave, despite the surrounding noise. In principle, a deformed bubble can move arbitrarily fast; the limitations in the speed of light, according to Einstein's theory, apply only in the context of space-time, but not in such distortions of space-time. Inside the bubble, Alcubierre predicted, space-time would not change and space travelers would not be harmed.

Einstein's equations in general relativity are tricky to solve in one direction, figuring out how matter curves space, but it's doable. Using them, Alcubierre determined that the distribution of matter is a necessary condition for the creation of a deformed bubble. The only problem is that the solutions led to an indefinite form of matter called negative energy.

In simple terms, gravity is the force of attraction between two objects. Each object, regardless of its size, exerts some force of attraction on the surrounding matter. According to Einstein, this force is a curvature of space-time. Negative energy, however, is gravitationally negative, that is, repulsive. Instead of connecting time and space, negative energy repels and separates them. Roughly speaking, for this model to work, Alcubierra needs negative energy to expand the space-time behind the ship.

Despite the fact that no one has ever specifically measured negative energy, according to quantum mechanics, it exists, and scientists have learned how to create it in the laboratory. One way to recreate it is through the Kazimirov effect: two parallel conductive plates placed close to each other create some amount of negative energy. The weak point of the Alcubierre model is that its implementation requires a huge amount of negative energy, several orders of magnitude higher than scientists estimate it can be produced.

White says he has found a way around this limitation. In a computer simulation, White altered the geometry of the warp field so that, in theory, it could produce a deformed bubble using millions of times less negative energy than Alcubierra estimated required, and perhaps little enough for a spacecraft to carry its means of production. "The discoveries," says White, "change Alcubierre's method from impractical to quite plausible."

REPORT FROM WHITE'S LAB

The Johnson Space Center is located next to the Houston lagoons, from where the path to Galveston Bay opens. The center is a bit like a suburban college campus, only aimed at training astronauts. On the day of my visit, White meets me at Building 15, a multi-story maze of corridors, offices, and engine testing labs. White is wearing an Eagleworks polo shirt, as he calls his engine experiments, embroidered with an eagle soaring over a futuristic spaceship.

White began his career as an engineer doing research as part of a robotic group. Over time, he took command of the entire ISS robotic wing while completing his PhD in plasma physics. It wasn't until 2009 that he shifted his focus to the study of motion, and this topic captured him enough to become the main reason he went to work for NASA.

"He's quite an unusual person," says his boss, John Applewhite, who heads the propulsion systems division. - He is definitely a big dreamer, but at the same time a talented engineer. He knows how to turn his fantasies into a real engineering product.” Around the same time he joined NASA, White asked permission to open his own laboratory dedicated to advanced propulsion systems. He himself came up with the name Eagleworks and even asked NASA to create a logo for his specialization. Then this work began.

White leads me to his office, which he shares with a colleague who searches for water on the Moon, and then leads me down to Eagleworks. On the way, he tells me about his request to open a laboratory and calls it "a long and difficult process of finding an advanced movement to help man explore space."

White shows me the object and shows me its central function, something he calls a "Quantum Vacuum Plasma Thruster" (QVPT). This device looks like a huge red velvet donut with wires tightly braided around the core. This is one of two Eagleworks initiatives (the other is the warp engine). It's also a secret development. When I ask what it is, White replies that he can only say that this technology is even cooler than the warp engine). According to a 2011 NASA report written by White, the craft uses quantum fluctuations in empty space as its fuel source, meaning that a QVPT-powered spacecraft does not require fuel.

The engine uses quantum fluctuations in empty space as a fuel source,
which means spaceship
powered by QVPT, does not require fuel.

When the device works, White's system looks cinematically perfect: the color of the laser is red, and the two beams are crossed like sabers. Inside the ring are four ceramic capacitors made of barium titanate, which White charges up to 23,000 volts. White has spent the last two and a half years developing the experiment, and he says that capacitors show tremendous potential energy. However, when I ask how to create the negative energy needed for warped space-time, he evades the answer. He explains that he signed a non-disclosure agreement, and therefore cannot reveal details. I ask with whom he made these agreements. He says: “With people. They come and want to talk. I can't give you more details."

OPPOSITORS OF THE ENGINE IDEA

So far, the warped travel theory is pretty intuitive - warping time and space to create a moving bubble - and it has a few significant flaws. Even if White significantly reduces the amount of negative energy Alcubierra asks for, it will still require more than scientists can produce, says Lawrence Ford, a theoretical physicist at Tufts University who has written numerous papers on the topic of negative energy over the past 30 years. Ford and other physicists claim that there are fundamental physical limitations, and it's not so much engineering imperfections, but that such an amount of negative energy cannot exist in one place for a long time.

Another complication: to create a deformation ball that moves faster than light, scientists will need to generate negative energy around the spacecraft, including above it. White doesn't think this is a problem; he replies rather vaguely that the engine will most likely work due to some existing "apparatus that creates the necessary conditions." However, creating these conditions in front of the ship would mean providing a constant supply of negative energy traveling faster than the speed of light, again contradicting general relativity.

Finally, the space warp engine raises a conceptual question. In general relativity, FTL travel is equivalent to time travel. If such an engine is real, White creates a time machine.

These obstacles give rise to some serious doubts. “I don’t think the physics we know and its laws allow us to assume that he will achieve anything with his experiments,” says Ken Olum, a physicist at Tufts University, who also participated in the debate about exotic movement at the Starship 100th Anniversary meeting. ". Noah Graham, a physicist at Middlebury College who read two of White's papers at my request, emailed me: "I see no valuable scientific evidence other than references to his previous work."

Alcubierre, now a physicist at the National Autonomous University of Mexico, has his own doubts. “Even if I'm standing on a spaceship and I have negative energy available, there's no way I can put it where it's needed,” he tells me over the phone from his home in Mexico City. - No, the idea is magical, I like it, I wrote it myself. But it has a couple of serious flaws that I already see over the years, and I don’t know a single way to fix them. ”

THE FUTURE OF SUPERSPEEDS

To the left of the Johnson Science Center's main gate, a Saturn-B rocket lies on its side, its stages disengaged to reveal its contents. It's gigantic - the size of one of the many engines is the size of a small car, and the rocket itself is a couple of feet longer than a football field. This, of course, is quite eloquent evidence of the peculiarities of space navigation. Besides, she's 40 years old and the time she represents - when NASA was part of a huge national plan to send a man to the moon - is long gone. JSC today is just a place that was once great but has since left the space avant-garde.

A breakthrough in traffic could mean a new era for JSC and NASA, and to some extent part of that era is already beginning. The Dawn probe, launched in 2007, studies the ring of asteroids using ion thrusters. In 2010, the Japanese commissioned the Icarus, the first interplanetary starship powered by a solar sail, another kind of experimental propulsion. And in 2016, the scientists plan to test VASMIR, a plasma-powered system made specifically for high propulsion at the ISS. But when these systems possibly get astronauts to Mars, they still won't be able to take them outside the solar system. To achieve this, White said, NASA will need to take on more risky projects.

The Warp Drive is perhaps the most far-fetched of NASA's motion design efforts. The scientific community says that White cannot create it. Experts say it works against the laws of nature and physics. Despite this, NASA is behind the project. “It's not being subsidized at the high government level it should be,” says Applewhite. - I think that the management has some special interest in him continuing his work; it's one of those theoretical concepts that, if successful, completely changes the game."

In January, White assembled his warp interferometer and moved on to his next target. Eagleworks has outgrown its own home. The new lab is larger and, as he enthusiastically states, "seismically isolated," meaning that it is protected from vibrations. But perhaps the best thing about the new lab (and most impressive) is that NASA gave White the same conditions that Neil Armstrong and Buzz Aldrin had on the Moon. Well, let's see.

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, 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 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 amazement 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 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.

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 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 microobject with the barrier occurs for a sufficiently definite time, then the energy of the microobject, 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 microobject. 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 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.

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 to 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 discussion that has unfolded, 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 (increase in frequency w), the refractive index sharply decreases and in a certain range of wavelengths becomes less than unity (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 impulse," says P. Milonni, a physicist at the Los Alamos National Laboratory in the United States.

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 team 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. 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 with. Such an impossibility in SRT is established, one might say, purely arithmetically, based on Einstein's 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 limitation of the speed of movement 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

Shadows can travel faster than light, but cannot carry matter or information

Is superluminal flight possible?

Sections in this article have subheadings and you can refer to each section separately.

Simple examples of FTL travel

1. Cherenkov effect

When we talk about superluminal motion, we mean the speed of light in a vacuum. c(299 792 458 m/s). Therefore, the Cherenkov effect cannot be considered as an example of superluminal motion.

2. Third observer

If the rocket A flies away from me with speed 0.6c to the west, and the rocket B flies away from me with speed 0.6c east, then I see that the distance between A and B increases with speed 1.2c. Watching the missiles fly A and B from the outside, the third observer sees that the total removal velocity of the missiles is greater than c .

However relative speed is not equal to the sum of the speeds. rocket speed A regarding the rocket B is the rate at which the distance to the rocket increases A, which is seen by an observer flying on a rocket B. Relative velocity must be calculated using the relativistic velocity addition formula. (See How do You Add Velocities in Special Relativity?) In this example, the relative velocity is approximately 0.88c. So in this example we didn't get FTL.

3. Light and shadow

Think about how fast the shadow can move. If the lamp is close, then the shadow of your finger on the far wall moves much faster than the finger moves. When moving the finger parallel to the wall, the speed of the shadow in D/d times greater than the speed of a finger. Here d is the distance from the lamp to the finger, and D- from the lamp to the wall. The speed will be even greater if the wall is 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 takes time to reach the wall, but the speed of the shadow moving along the wall will increase even more. The speed of a shadow is not limited by the speed of light.

Another object that can travel faster than light is a spot of light from a laser aimed at the moon. The distance to the Moon is 385,000 km. You can calculate the speed of movement of the light spot on the surface of the Moon by yourself with small fluctuations of the laser pointer in your hand. You might also like the example of a wave hitting a straight line of beach at a slight angle. With what speed can the point of intersection of the wave and the shore move along the beach?

All these things can happen in nature. For example, a beam of light from a pulsar can run along a dust cloud. A powerful explosion can create spherical waves of light or radiation. When these waves intersect with a surface, circles of light appear on that surface and expand faster than light. Such a phenomenon is observed, for example, when an electromagnetic pulse from a lightning flash passes through the upper atmosphere.

4. Solid body

If you have a long, rigid rod and you hit one end of the rod, doesn't the other end immediately move? Is this not a way of superluminal transmission of information?

That would be right if there were perfectly rigid bodies. In practice, the impact is transmitted along the rod at the speed of sound, which depends on the elasticity and density of the rod material. In addition, the theory of relativity limits the possible speeds of sound in a material by the value c .

The same principle applies if you hold a string or rod vertically, release it, and it begins to fall under the influence of gravity. The top end you let go starts to fall immediately, but the bottom end will only start moving after a while, as the loss of the holding force is transmitted down the rod at the speed of sound in the material.

The formulation of the relativistic theory of elasticity is rather complicated, but the general idea can be illustrated using Newtonian mechanics. The equation of longitudinal motion of an ideally elastic body can be derived from Hooke's law. Denote the linear density of the rod ρ , Young's modulus Y. Longitudinal offset X satisfies the wave equation

ρ d 2 X/dt 2 - Y d 2 X/dx 2 = 0

Plane wave solution travels at the speed of sound s, which is determined from the formula s 2 = Y/ρ. The wave equation does not allow the perturbations of the medium to move faster than with the speed s. In addition, the theory of relativity gives a limit to the amount of elasticity: Y< ρc 2 . In practice, no known material approaches this limit. Note also that even if the speed of sound is close to c, then the matter itself does not necessarily move with relativistic speed.

Although there are no solid bodies in nature, there is motion of rigid bodies, which can be used to overcome the speed of light. This topic belongs to the already described section of shadows and light spots. (See The Superluminal Scissors, The Rigid Rotating Disk in Relativity).

5. Phase velocity

wave equation
d 2 u/dt 2 - c 2 d 2 u/dx 2 + w 2 u = 0

has a solution in the form
u \u003d A cos (ax - bt), c 2 a 2 - b 2 + w 2 \u003d 0

These are sinusoidal waves propagating at a speed v
v = b/a = sqrt(c 2 + w 2 /a 2)

But it's more than c. Maybe this is the equation for tachyons? (see section below). No, this is the usual relativistic equation for a particle with mass.

To eliminate the paradox, you need to distinguish between "phase velocity" v ph , and "group velocity" v gr , and
v ph v gr = c 2

The solution in the form of a wave may have dispersion in frequency. In this case, the wave packet moves with a group velocity that is less than c. Using a wave packet, information can only be transmitted at the group velocity. Waves in a wave packet move with phase velocity. Phase velocity is another example of FTL motion that cannot be used to communicate.

6. Superluminal galaxies

7. Relativistic rocket

Let an observer on Earth see a spacecraft moving away at a speed 0.8c According to the theory of relativity, he will see that the clock on the spacecraft is running 5/3 times slower. If we divide the distance to the ship by the time of flight according to the onboard clock, we get the speed 4/3c. The observer concludes that, using his on-board clock, the pilot of the ship will also determine that he is flying at a superluminal speed. From the pilot's point of view, his clock is running normally, and interstellar space has shrunk by a factor of 5/3. Therefore, it flies the known distances between the stars faster, at a speed 4/3c .

But it's still not superluminal flight. You can't calculate speed using distance and time defined in different frames of reference.

8. Gravity speed

Some insist that the speed of gravity is much faster c or even infinite. See Does Gravity Travel at the Speed ​​of Light? and What is Gravitational Radiation? Gravitational perturbations and gravitational waves propagate at a speed c .

9. EPR paradox

10. Virtual photons

11. Quantum tunnel effect

In quantum mechanics, the tunnel effect allows a particle to overcome a barrier, even if its energy is not enough for this. It is possible to calculate the tunneling time through such a barrier. And it may turn out to be less than what is required for light to overcome the same distance at a speed c. Can it be used to send messages faster than light?

Quantum electrodynamics says "No!" Nevertheless, an experiment was carried out that demonstrated the superluminal transmission of information using the tunnel effect. Through a barrier 11.4 cm wide at a speed of 4.7 c Mozart's Fortieth Symphony was presented. The explanation for this experiment is very controversial. Most physicists believe that with the help of the tunnel effect it is impossible to transmit information faster than light. If it were possible, then why not send a signal to the past by placing the equipment in a rapidly moving frame of reference.

17. Quantum field theory

With the exception of gravity, all observed physical phenomena correspond to the "Standard Model". The Standard Model is a relativistic quantum field theory that explains the electromagnetic and nuclear forces and all known particles. In this theory, any pair of operators corresponding to physical observables separated by a spacelike interval of events "commutes" (that is, one can change the order of these operators). In principle, this implies that in the Standard Model the force cannot travel faster than light, and this can be considered the quantum field equivalent of the infinite energy argument.

However, there are no impeccably rigorous proofs in the quantum field theory of the Standard Model. No one has yet even proven that this theory is internally consistent. Most likely, it is not. In any case, there is no guarantee that there are no yet undiscovered particles or forces that do not obey the ban on superluminal movement. There is also no generalization of this theory, including gravity and general relativity. Many physicists working in the field of quantum gravity doubt that the simple concepts of causality and locality will be generalized. There is no guarantee that in a future more complete theory the speed of light will retain the meaning of the limiting speed.

18. Grandpa Paradox

In special relativity, a particle traveling faster than light in one frame of reference moves back in time in another frame of reference. FTL travel or information transmission would make it possible to travel or send a message to the past. If such time travel were possible, then you could go back in time and change the course of history by killing your grandfather.

This is a very strong argument against the possibility of FTL travel. True, there remains an almost improbable possibility that some limited superluminal travel is possible that does not allow a return to the past. Or maybe time travel is possible, but causality is violated in some consistent way. All this is very implausible, but if we are discussing FTL, it is better to be ready for new ideas.

The reverse is also true. If we could travel back in time, we could overcome the speed of light. You can go back in time, fly somewhere at low speed, and arrive there before the light sent in the usual way arrives. See Time Travel for details on this topic.

Open questions of FTL travel

In this last section, I will describe some serious ideas about possible faster-than-light travel. These topics are not often included in the FAQ, because they are more like a lot of new questions than answers. They are included here to show that serious research is being done in this direction. Only a short introduction to the topic is given. Details can be found on the Internet. As with everything on the Internet, be critical of them.

19. Tachyons

Tachyons are hypothetical particles that travel faster than light locally. To do this, they must have an imaginary mass value. In this case, the energy and momentum of the tachyon are real quantities. There is no reason to believe that superluminal particles cannot be detected. Shadows and highlights can travel faster than light and can be detected.

So far, tachyons have not been found, and physicists doubt their existence. There were claims that in experiments to measure the mass of neutrinos produced by the beta decay of tritium, neutrinos were tachyons. This is doubtful, but has not yet been definitively refuted.

There are problems in the theory of tachyons. In addition to possibly violating causality, tachyons also make the vacuum unstable. It may be possible to circumvent these difficulties, but even then we will not be able to use tachyons for superluminal transmission of messages.

Most physicists believe that the appearance of tachyons in a theory is a sign of some problems with this theory. The idea of ​​tachyons is so popular with the public simply because they are often mentioned in fantasy literature. See Tachyons.

20. Wormholes

The most famous method of global FTL travel is the use of "wormholes". A wormhole is a slit in space-time from one point in the universe to another, which allows you to get from one end of the hole to the other faster than the usual path. Wormholes are described by the general theory of relativity. To create them, you need to change the topology of space-time. Maybe this will become possible within the framework of the quantum theory of gravity.

To keep a wormhole open, you need areas of space with negative energies. C.W.Misner and K.S.Thorne proposed to use the Casimir effect on a large scale to create negative energy. Visser suggested using cosmic strings for this. These are very speculative ideas and may not be possible. Maybe the required form of exotic matter with negative energy does not exist.

Even if we could build prototype ships designed by NASA scientists to move at relativistic speeds, and find an obscenely large source of power to launch them into the skies, our journey would not be as pleasant as it could be. appear from the Millennium Falcon. It is not technology that separates us from the ability to fly to neighboring stars, it is only a matter of several centuries. The problem is how dangerous space is if it turns into a habitat, and how fragile the human body can actually be.

If we began to move at the speed of light (300,000 km / s) in interstellar space, we would die in a couple of seconds. Despite the fact that the density of matter in space is very low, at this speed even a few hydrogen atoms per cubic centimeter will crash into the bow of the ship with an acceleration that on Earth is achievable only at the Large Hadron Collider. Because of this, we will receive a radiation dose equal to ten thousand sieverts per second. Given that the lethal dose for humans is six sieverts, such a radioactive beam would damage the ship and destroy all life on board.

“If we started moving at the speed of light in space, we would die in a couple of seconds”

According to research by scientists from Johns Hopkins University, no amount of armor can protect us from this ionizing radiation. A ten-centimeter-thick aluminum bulkhead would then absorb less than 1% of the energy—and you can't increase the size of bulkheads indefinitely without risking the possibility of taking off. However, in addition to radioactive hydrogen, our spacecraft at the speed of light will be threatened by erosion due to the impact of interstellar dust. In the best case, we will have to settle for 10% of the speed of light, which will make it difficult to reach only the closest star - Proxima Centauri. Given a distance of 4.22 light years, such a flight will take 40 years - that is, one incomplete human life.

Cosmic radiation still remains an insurmountable obstacle for us, however, if in the distant future we can overcome it, traveling at the speed of light will be the most incredible experience available to man. At this speed, time will slow down, and aging will become a much longer process (after all, even astronauts on the ISS manage to age 0.007 seconds less in six months than people on Earth). Our visual field during such a flight is bent, turning into a tunnel. We will fly forward through this tunnel towards a brilliant flash of white, seeing no trace of the stars and leaving behind us the most pitch-black, the most absolute darkness imaginable.