Overcoming the speed of light. Superluminal speed: how realistic is it?

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 Sergey 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. The so-called twin effect does not apply to this situation, which tells that during space travel at 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.

The theme of "The engine that allows you to fly at superluminal speed", "Travel in multidimensional space" and everything related to the topic of flight at a speed exceeding the speed of light, so far does not go beyond speculation, although in some aspects it comes into contact with the world science. Today we are at the stage where we know that we know some things and do not know some things, but we certainly do not know if it is possible to travel faster than the speed of light.

The bad news is that the basis of current scientific knowledge to date suggests that faster-than-light travel is impossible. It's an artifact of Einstein's Special Theory of Relativity. Yes, there are other concepts - superluminal particles, wormholes ( tunnels in space - approx. transl.), inflationary universe, deformation of space and time, quantum paradoxes... All these ideas are discussed in serious scientific literature, but it is too early to talk about their reality.

One of the questions that comes up in connection with FTL is temporal paradoxes: the violation of causality and what is meant by time travel. As if the topic of superluminal flight is not enough, is it also possible to develop a scenario in which superluminal speed will enable time travel. Time travel is considered far more impossible than light travel.

What is the main difference?

Barely breaking the sound barrier, people wondered: “Why don’t we now also break the light barrier, is it really that different?” It's too early to talk about breaking the light barrier, but something is already known for sure - this is a completely different problem than breaking the sound barrier. The sound barrier was broken by an object made of material, not sound. The atoms and molecules of a material are connected by electromagnetic fields, which is what light is made of. In the case of breaking through the light speed barrier, the object trying to break through this barrier is made up of the same thing as the barrier itself. How can an object move faster than what binds its atoms? As we have already noted, this is a completely different problem than breaking the sound barrier.

You can very briefly state the "Special Theory of Relativity". In fact, it is very simple in its design... Start with two simple rules.

Rule #1: the distance you have traveled (d) depends on your speed (v) and your travel time (t). If you are driving at 55 miles per hour, you will travel 55 miles in an hour. Just.

Rule #2: This is an amazing thing - no matter how fast you move, you will constantly notice that the speed of light remains the same.

Put them together and compare what one traveler "sees" compared to someone traveling at a different speed - that's where the problems come in. Let's try a different picture. Close your eyes. Imagine that of all your senses, only hearing is involved. You perceive only sounds. You identify objects only by the sound they make. So, if a locomotive passed by, did its whistle change in any way? We know that it sounds on a certain note, but due to the movement of the train, it changes due to the action of the so-called Doppler effect. The same thing happens with light. Everything around us we know due to the presence of light or, more generally, electromagnetism. What we see, what we feel (air molecules bounce off our skin), what we hear (molecules collide with each other under the pressure of waves), even the passage of time - all this is controlled by electromagnetic forces. So if we start moving at speeds approaching the speed at which we receive all the information, our information is distorted. All in all, it's that simple. Understanding this is enough if you are trying to do something about it. But that's another question.

The light speed barrier is one of the consequences of the Special Theory of Relativity. You can look at this differently. To move faster, you need to add energy. But when you start approaching the speed of light, the amount of energy required for movement skyrockets to infinity. It takes infinite energy to move a mass at the speed of light. It turns out that here you are facing a real barrier.

Is it possible to bypass the Special Theory of Relativity? Probably.

Is there any research being done in this direction? Yes, but on a small scale.

In addition to the individual theoretical work of physicists such as Matt Visser, Michael Morris, Miguel Alcubierre and others, there is a brand new NASA program in jet propulsion physics.

The materials of InoSMI contain only assessments of foreign media and do not reflect the position of the editors of InoSMI.

Today we are at the stage where we know that we know some things and do not know some things, but we certainly do not know if it is possible to travel faster than the speed of light.

The bad news is that the basis of current scientific knowledge to date suggests that faster-than-light travel is impossible. It's an artifact of Einstein's Special Theory of Relativity.

Yes, there are other concepts - superluminal particles, wormholes (tunnels in space - approx. Transl.), inflationary universe, space and time warps, quantum paradoxes ... All these ideas are discussed in serious scientific literature, but it is still too early to talk about their reality.

What is the main difference?

The atoms and molecules of a material are connected by electromagnetic fields, which is what light is made of. In the case of breaking through the light speed barrier, the object trying to break through this barrier is made up of the same thing as the barrier itself. How can an object move faster than what binds its atoms? As we have already noted, this is a completely different problem than breaking the sound barrier.

Special theory of relativity

You can very briefly state the "Special Theory of Relativity". In fact, it is very simple in its design... Start with two simple rules.

Rule #1: the distance you have traveled (d) depends on your speed (v) and your travel time (t). If you are driving at 55 miles per hour, you will travel 55 miles in an hour. Just.

Rule #2: This is an amazing thing - no matter how fast you move, you will constantly notice that the speed of light remains the same.

So, if a locomotive passed by, did its whistle change in any way? We know that it sounds on a certain note, but due to the movement of the train, it changes due to the action of the so-called Doppler effect. The same thing happens with light. Everything around us we know due to the presence of light or, more generally, electromagnetism. What we see, what we feel (air molecules bounce off our skin), what we hear (molecules collide with each other under the pressure of waves), even the passage of time - all this is controlled by electromagnetic forces.

So if we start moving at speeds approaching the speed at which we receive all the information, our information is distorted. All in all, it's that simple. Understanding this is enough if you are trying to do something about it. But that's another question.

light speed barrier

Is it possible to bypass the Special Theory of Relativity? Probably.

Is there any research being done in this direction? Yes, but on a small scale.

In addition to the individual theoretical work of physicists such as Matt Visser, Michael Morris, Miguel Alcubierre and others, there is a brand new NASA program in jet propulsion physics.

Original publication.

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 in only 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 nonstop 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 PhD in general relativity and was wondering if it was possible to create a 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 hovering 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 a rather 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 specialty. 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, e-mailed 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 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.

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 speed

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.

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