The speed of light is one of the universal physical constants; it does not depend on the choice of inertial frame of reference and describes the properties of space-time as a whole. The speed of light in a vacuum is 299,792,458 meters per second, and this is the maximum speed of particle movement and the propagation of interactions. This is what school physics books teach us. You can also remember that the mass of a body is not constant and, as the speed approaches the speed of light, tends to infinity. This is why photons—particles without mass—move at the speed of light, while this is much more difficult for particles with mass.
However, an international team of scientists from the large-scale OPERA experiment, located near Rome, is ready to argue with the elementary truth.
He managed to detect neutrinos, which, as experiments showed, move at speeds greater than the speed of light,
reports the press service of the European Organization for Nuclear Research (CERN).
The OPERA (Oscillation Project with Emulsion-tRacking Apparatus) experiment studies the most inert particles in the Universe - neutrinos. They are so inert that they can fly right through the entire globe, stars and planets, and in order for them to hit an iron barrier, the size of this barrier must be from the Sun to Jupiter. Every second, about 10 14 neutrinos emitted by the Sun pass through the body of every person on Earth. The probability that at least one of them will hit human tissue throughout his life tends to zero. For these reasons, neutrinos are extremely difficult to detect and study. The laboratories that do this are located deep under the mountains and even under the ice of Antarctica.
OPERA receives a beam of neutrinos from CERN, where the Large Hadron Collider is located. Its "little brother" - the superproton synchrotron (SPS) - directs the beam directly underground towards Rome. The resulting neutrino beam passes through the thickness of the earth's crust, thereby clearing itself of other particles that the crustal substance retains, and goes straight to the laboratory in Gran Sasso, hidden under 1200 m of rock.
Neutrinos travel an underground path of 732 km in 2.5 milliseconds.
The OPERA project detector, consisting of approximately 150 thousand elements and weighing 1300 tons, “catches” neutrinos and studies them. In particular, the main goal is to study the so-called neutrino oscillations - transitions from one type of neutrino to another.
The stunning results about exceeding the speed of light are supported by serious statistics: the laboratory in Gran Sasso observed about 15 thousand neutrinos. Scientists have found that
Neutrinos travel at speeds 20 parts per million faster than the speed of light—the “infallible” speed limit.
This result came as a surprise to them, and no explanation has yet been proposed. Naturally, to refute or confirm it, independent experiments carried out by other groups on other equipment are required - this principle of “double-blind control” is also implemented at the CERN Large Hadron Collider. The OPERA collaboration immediately published its results to allow colleagues around the world to test them. A detailed description of the work is available on the preprint website Arxiv.Org.
The official presentation of the results will take place today at a seminar at CERN at 18.00 Moscow time, will be conducted on-line translation.
“These data came as a complete surprise. After months of data collection, analysis, cleaning, and cross-checking, we did not find a possible source of system error in either the data processing algorithm or the detector. Therefore, we publish our results, continue our work, and also hope that independent measurements from other groups will help understand the nature of this observation,” said OPERA experiment leader Antonio Ereditato from the University of Bern, as quoted by the CERN press service.
“When experimental scientists discover an implausible result and cannot find an artifact that would explain it, they turn to their colleagues in other groups to begin a broader study of the issue. This is a good scientific tradition, and the OPERA collaboration is now following it.
If observations of exceeding the speed of light are confirmed, it could change our understanding of physics, but we must ensure that they do not have another, more banal explanation.
This is why independent experiments are needed,” said CERN scientific director Sergio Bertolucci.
OPERA's measurements are extremely accurate. Thus, the distance from the neutrino launch point to the point of their registration (more than 730 km) is known with an accuracy of 20 cm, and the time of flight is measured with an accuracy of 10 nanoseconds.
The OPERA experiment has been running since 2006. Approximately 200 physicists from 36 institutes and 13 countries, including Russia, take part in it.
We often talk about the fact that maximum speed of light in our Universe, and that there is nothing that can move faster than the speed of light in a vacuum. And even more so - us. Approaching near-light speed, an object acquires mass and energy, which either destroys it or contradicts Einstein's general theory of relativity. Let's say we believe in this and look for workarounds (like or we'll figure it out) in order to fly to the nearest star not for 75,000 years, but for a couple of weeks. But since few of us have a higher physics education, it is not clear why they say on the streets that the speed of light is maximum, constant and equal to 300,000 km/s?
There are many simple and intuitive explanations for why things are this way, but you can start to hate them. An internet search will lead you to the concept of “relativistic mass” and how it requires more force to accelerate an object that is already moving at a high speed. This is a familiar way of interpreting the mathematical apparatus of the special theory of relativity, but it misleads many, and especially you, our dear readers. Because many of you (and us too) are tasting high physics, as if dipping one toe into its salty water before going in for a swim. As a result, it becomes much more complex and less beautiful than it actually is.
Let's discuss this issue from the point of view of a geometric interpretation that is consistent with general relativity. It is less obvious, but a little more complicated than drawing arrows on paper, so many of you will immediately understand the theory that is hidden behind abstractions like “force” and outright lies like “relativistic mass”.
First, let's define what a direction is so we can clearly define our place. "Down" is the direction. It is defined as the direction in which things fall when you let them go. "Up" is the opposite direction to "down". Pick up a compass and determine additional directions: north, south, west and east. All these directions are defined by serious people as an “orthonormal (or orthogonal) basis,” but it’s better not to think about it now. Let us assume that these six directions are absolute, since they will exist where we deal with our complex question.
Now let's add two more directions: to the future and to the past. You can't easily move in these directions on your own, but imagining them should be easy enough for you. The future is the direction where tomorrow comes; past is the direction where yesterday is.
These eight cardinal directions—up, down, north, south, west, east, past, and future—describe the fundamental geometry of the universe. We can call each pair of these directions a “dimension,” which is why we live in a four-dimensional Universe. Another term to define this four-dimensional understanding would be "space-time", but we will try to avoid using this term. Just remember that in our context, "space-time" will be equivalent to the concept of "Universe".
Welcome to the stage. Let's take a look at the actors.
Sitting in front of your computer right now, you are in motion. You don't feel it. It seems to you that you are at rest. But this is only because everything around you is also moving relative to you. No, don’t think that we are talking about the Earth circling around the Sun or the Sun moving through the galaxy and pulling us along with it. This is, of course, true, but that’s not what we’re talking about now. By movement we mean movement towards the “future”.
Imagine that you are in a train carriage with the windows closed. You can't see the street and, let's say, the rails are so perfect that you don't feel whether the train is moving or not. Therefore, just sitting inside the train, you cannot say whether you are actually traveling or not. Look outside and you will realize that the landscape is rushing by. But the windows are closed.
There is only one way to know whether you are moving or not. Just sit and wait. If the train stays at the station, nothing will happen. But if the train is moving, sooner or later you will arrive at a new station.
In this metaphor, the carriage represents everything that we can see in the world around us - a house, Vaska the cat, stars in the sky, etc. "Next station - Tomorrow."
If you sit motionless, and the cat Vaska sleeps serenely for his allotted hours per day, you will not feel movement. But tomorrow will definitely come.
This is what it means to move towards the future. Only time will tell which is true: movement or parking.
It should all be pretty easy for you to imagine so far. It may be difficult to think of time as a direction, much less of oneself as an object passing through time. But you will understand. Now use your imagination.
Imagine that when you are driving in your car, something terrible happens: the brakes fail. By a strange coincidence, at the same moment the gas and gearbox jam. You can neither speed up nor stop. The only thing you have is a steering wheel. You can change the direction of movement, but not its speed.
Of course, the first thing you will do is try to drive into a soft bush and somehow carefully stop the car. But let's not use this technique for now. Let's just focus on the specifics of your faulty car: you can change direction, but not speed.
This is how we move through the Universe. You have a steering wheel, but no pedals. As you sit and read this article, you are rolling towards a bright future at top speed. And when you get up to make yourself some tea, you change the direction of movement in space-time, but not its speed. If you move very quickly through space, time will flow a little slower.
It's easy to imagine by drawing a couple of axes on paper. The axis that will go up and down is the axis of time, up means into the future. The horizontal axis represents space. We can only draw one dimension of space because a piece of paper is two-dimensional, but let's just imagine that this concept applies to all three dimensions of space.
Draw an arrow from the origin of the coordinate axis, where they converge, and point it up along the vertical axis. It doesn't matter how long it is, just keep in mind that it will only come in one length. This arrow, which is now pointing into the future, represents a quantity that physicists call “four-speed.” This is the speed of your movement through space-time. Right now you are in a stationary state, so the arrow is pointing only to the future.
If you want to move through space - to the right along the coordinate axis - you need to change your four-speed and include a horizontal component. It turns out that you need to turn the arrow. But as soon as you do this, you will notice that the arrow is no longer pointing upward, into the future, as confidently as before. You are now moving through space, but you have had to sacrifice future movement since the four-speed needle can only rotate, but never stretch or contract.
This is where the famous “time dilation” effect begins, which is talked about by everyone even slightly privy to the special theory of relativity. If you are moving through space, you are not moving through time as fast as you could if you were sitting still. Your watch will count down time more slowly than the watch of a person who is not moving.
And now we come to the solution to the question of why the phrase “faster than light” has no meaning in our universe. See what happens if you want to move through the space as quickly as possible. You turn the four-speed needle all the way until it points along the horizontal axis. We remember that the arrow cannot stretch. It can only rotate. So, you have increased the speed in space as much as possible. But it became impossible to move any faster. There is nowhere to turn the arrow, otherwise it will become “straighter than straight” or “horizontal than horizontal.” This is the concept we equate with “faster than light.” It is simply impossible to feed a huge people with three fish and seven loaves of bread.
This is why nothing in our universe can travel faster than light. Because the phrase “faster than light” in our universe is equivalent to the phrase “straighter than straight” or “horizontal than horizontal.”
Yes, you still have a few questions. Why can four-speed vectors only rotate but not stretch? There is an answer to this question, but it has to do with the invariance of the speed of light, and we will leave that for later. And if you simply believe this, you will be slightly less informed on this subject than the most brilliant physicists who have ever walked the planet.
Skeptics may question why we use a simplified model of the geometry of space when talking about Euclidean rotations and circles. In the real world, the geometry of spacetime obeys the geometry of Minkowski, and the rotations are hyperbolic. But a simple version of the explanation has the right to life.
As well as a simple explanation for this, .
As you know, photons, the particles of light that make up light, move at the speed of light. The special theory of relativity will help us in this matter.
In science fiction films, interstellar space ships almost always fly at the speed of light. This is usually what science fiction writers call hyperspeed. Both writers and film directors describe and show it to us using almost the same artistic technique. Most often, in order for the ship to make a rapid breakthrough, the heroes pull or press a button on the control element, and the vehicle instantly accelerates, accelerating almost to the speed of light with a deafening bang. The stars that the viewer sees overboard the ship first flicker, and then completely stretch out into lines. But is this what stars really look like through the windows of a spaceship at hyperspeed? Researchers say no. In reality, the ship's passengers would see only a bright disk instead of stars stretched out in a line.
If an object moves almost at the speed of light, it may see the Doppler effect in action. In physics, this is the name for the change in frequency and wavelength due to the rapid movement of the receiver. The frequency of the light from stars flashing in front of the viewer from the ship will increase so much that it will shift from the visible range to the X-ray part of the spectrum. The stars seem to disappear! At the same time, the length of the relict electromagnetic radiation remaining after the Big Bang will decrease. The background radiation will become visible and appear as a bright disk, fading at the edges.
But what does the world look like from the side of an object that will reach the speed of light? As is known, photons, the particles of light from which it consists, move at such speeds. The special theory of relativity will help us in this matter. According to it, when an object moves at the speed of light for any length of time, the time spent on the movement of this object becomes equal to zero. In simple terms, if you move at the speed of light, then it is impossible to perform any action, such as observing, seeing, seeing, and so on. An object traveling at the speed of light will actually see nothing.
Photons always travel at the speed of light. They do not waste time accelerating and braking, so their entire life lasts zero time for them. If we were photons, then our moments of birth and death would coincide, that is, we simply would not realize that the world exists at all. It is worth noting that if an object accelerates to the speed of light, then its speed in all reference systems becomes equal to the speed of light. This is photo physics. Applying the special theory of relativity, we can conclude that for an object moving at the speed of light, the entire surrounding world will appear infinitely flattened, and all events occurring in it will take place at one point in time.
In September 2011, physicist Antonio Ereditato shocked the world. His statement could revolutionize our understanding of the universe. If the data collected by the 160 OPERA Project scientists was correct, the incredible was observed. The particles - in this case neutrinos - moved faster than light. According to Einstein's theory of relativity, this is impossible. And the consequences of such an observation would be incredible. The very foundations of physics might have to be reconsidered.
Although Ereditato said he and his team were “extremely confident” in their results, they did not say that the data was completely accurate. Instead, they asked other scientists to help them figure out what was going on.
In the end, it turned out that OPERA's results were wrong. Due to a poorly connected cable, there was a synchronization problem and the signals from GPS satellites were inaccurate. There was an unexpected delay in the signal. As a result, measurements of the time it took neutrinos to travel a certain distance showed an extra 73 nanoseconds: it seemed that the neutrinos were traveling faster than light.
Despite months of careful testing before the experiment began and double-checking the data afterwards, the scientists were seriously wrong. Ereditato resigned despite the comments of many that such errors always occurred due to the extreme complexity of particle accelerators.
Why did the suggestion - just the suggestion - that something could travel faster than light cause such a fuss? How sure are we that nothing can overcome this barrier?
Let's look at the second of these questions first. The speed of light in a vacuum is 299,792.458 kilometers per second - for convenience, this number is rounded to 300,000 kilometers per second. It's quite fast. The sun is 150 million kilometers from the Earth, and its light reaches the Earth in just eight minutes and twenty seconds.
Can any of our creations compete in the race against light? One of the fastest man-made objects ever built, the New Horizons space probe whizzed past Pluto and Charon in July 2015. It reached a speed relative to the Earth of 16 km/s. Much less than 300,000 km/s.
However, we had tiny particles that were moving quite quickly. In the early 1960s, William Bertozzi at MIT experimented with accelerating electrons to even higher speeds.
Because electrons have a negative charge, they can be accelerated—more accurately, repelled—by applying the same negative charge to a material. The more energy is applied, the faster the electrons accelerate.
One would think that one would simply need to increase the applied energy to reach a speed of 300,000 km/s. But it turns out that electrons simply cannot move that fast. Bertozzi's experiments showed that using more energy does not lead to a directly proportional increase in electron speed.
Instead, enormous amounts of additional energy had to be applied to even slightly change the speed of the electrons. She came closer and closer to the speed of light, but never reached it.
Imagine moving towards the door in small steps, each step covering half the distance from your current position to the door. Strictly speaking, you will never reach the door, because after each step you take, you will still have a distance to cover. Bertozzi encountered approximately the same problem while dealing with his electrons.
But light is made up of particles called photons. Why can these particles travel at the speed of light, but electrons cannot?
"As objects move faster and faster, they become heavier - the heavier they become, the harder it is for them to accelerate, so you never reach the speed of light," says Roger Rassoul, a physicist at the University of Melbourne in Australia. “A photon has no mass. If it had mass, it couldn't move at the speed of light."
Photons are special. Not only do they have no mass, which provides them with complete freedom of movement in the vacuum of space, but they also do not need to accelerate. The natural energy they have moves in waves just like them, so when they are created they already have maximum speed. In some ways, it's easier to think of light as energy rather than as a stream of particles, although in truth light is both.
However, light travels much slower than we might expect. Although internet technologists like to talk about communications running at the "speed of light" in fiber optics, light travels 40% slower in glass fiber optics than in a vacuum.
In reality, photons travel at speeds of 300,000 km/s, but encounter a certain amount of interference caused by other photons emitted by glass atoms as the main light wave passes through. This may not be easy to understand, but at least we tried.
In the same way, within the framework of special experiments with individual photons, it was possible to slow them down quite impressively. But for most cases, 300,000 would be about right. We haven't seen or built anything that can move that fast, or even faster. There are special points, but before we touch on them, let's touch on our other question. Why is it so important that the speed of light rule be strictly followed?
The answer is associated with a person named , as is often the case in physics. His special theory of relativity explores the many implications of his universal speed limits. One of the most important elements of the theory is the idea that the speed of light is constant. No matter where you are or how fast you are moving, light always moves at the same speed.
But this raises several conceptual problems.
Imagine the light that falls from a flashlight onto a mirror on the ceiling of a stationary spacecraft. The light goes up, reflects off the mirror and falls on the floor of the spacecraft. Let's say he covers a distance of 10 meters.
Now imagine that this spacecraft begins to move at a colossal speed of many thousands of kilometers per second. When you turn on the flashlight, the light behaves as before: it shines upward, hits the mirror and is reflected onto the floor. But to do this, the light will have to travel a diagonal distance, not a vertical one. After all, the mirror now moves quickly along with the spacecraft.
Accordingly, the distance that light travels increases. Let's say 5 meters. That turns out to be 15 meters in total, not 10.
And despite this, even though the distance has increased, Einstein's theories claim that light will still travel at the same speed. Since speed is distance divided by time, since speed remains the same and distance increases, time must also increase. Yes, time itself must stretch. And although this sounds strange, it has been confirmed experimentally.
This phenomenon is called time dilation. Time moves slower for people who travel in fast-moving vehicles compared to those who are stationary.
For example, time moves 0.007 seconds slower for astronauts on the International Space Station, which is moving at 7.66 km/s relative to Earth, compared to people on the planet. Even more interesting is the situation with particles like the aforementioned electrons, which can move close to the speed of light. In the case of these particles, the degree of deceleration will be enormous.
Stephen Kolthammer, an experimental physicist at the University of Oxford in the UK, points to the example of particles called muons.
Muons are unstable: they quickly decay into simpler particles. So fast that most muons leaving the Sun should decay by the time they reach Earth. But in reality, muons arrive on Earth from the Sun in colossal volumes. Physicists have long tried to understand why.
“The answer to this mystery is that muons are generated with such energy that they travel at close to the speed of light,” says Kolthammer. “Their sense of time, so to speak, their internal clock is slow.”
Muons "stay alive" longer than expected relative to us, thanks to a real, natural time warp. When objects move quickly relative to other objects, their length also decreases and contracts. These consequences, time dilation and length reduction, are examples of how space-time changes depending on the movement of things - me, you, or a spacecraft - that have mass.
What's important, as Einstein said, is that light is not affected because it has no mass. That's why these principles go hand in hand. If things could travel faster than light, they would obey the fundamental laws that describe how the universe works. These are the key principles. Now we can talk about a few exceptions and exceptions.
On the one hand, although we haven't seen anything going faster than light, that doesn't mean that this speed limit can't theoretically be beaten under very specific conditions. For example, take the expansion of the Universe itself. Galaxies in the Universe are moving away from each other at speeds significantly exceeding light speed.
Another interesting situation concerns particles that share the same properties at the same time, no matter how far apart they are. This is the so-called “quantum entanglement.” The photon will spin up and down, randomly choosing between two possible states, but the choice of spin direction will be exactly reflected in another photon elsewhere if they are entangled.
Two scientists, each studying their own photon, would get the same result at the same time, faster than the speed of light could allow.
However, in both of these examples, it is important to note that no information travels faster than the speed of light between two objects. We can calculate the expansion of the Universe, but we cannot observe objects faster than light in it: they have disappeared from view.
As for two scientists with their photons, although they could get one result at the same time, they could not let each other know it faster than the light travels between them.
"This doesn't create any problems for us, because if you can send signals faster than light, you get weird paradoxes whereby information can somehow go back in time," says Kolthammer.
There is another possible way to make faster-than-light travel technically possible: rifts in spacetime that would allow the traveler to escape the rules of normal travel.
Gerald Cleaver of Baylor University in Texas believes that one day we will be able to build a spacecraft that travels faster than light. Which is moving through a wormhole. Wormholes are loops in space-time that fit perfectly into Einshein's theories. They could allow an astronaut to jump from one end of the universe to the other via an anomaly in spacetime, some form of cosmic shortcut.
An object traveling through a wormhole will not exceed the speed of light, but could theoretically reach its destination faster than light that takes a "normal" path. But wormholes may be completely inaccessible to space travel. Could there be another way to actively warp spacetime to move faster than 300,000 km/s relative to someone else?
Cleaver also explored the idea of an "Alcubierre engine" in 1994. It describes a situation in which spacetime contracts in front of the spacecraft, pushing it forward, and expands behind it, also pushing it forward. “But then,” says Cleaver, “the problems arose: how to do it and how much energy would be needed.”
In 2008, he and his graduate student Richard Obouzi calculated how much energy would be needed.
"We imagined a ship 10m x 10m x 10m - 1000 cubic meters - and calculated that the amount of energy required to start the process would be equivalent to the mass of the entire Jupiter."
After this, energy must be constantly “added” so that the process does not end. No one knows if this will ever be possible, or what the necessary technology will look like. “I don’t want to be quoted for centuries as if I predicted something that would never happen,” says Cleaver, “but I don’t see any solutions yet.”
So, traveling faster than the speed of light remains science fiction at the moment. For now, the only way is to plunge into deep suspended animation. And yet it's not all bad. Most of the time we talked about visible light. But in reality, light is much more than that. From radio waves and microwaves to visible light, ultraviolet radiation, X-rays and gamma rays emitted by atoms as they decay, these beautiful rays are all made of the same thing: photons.
The difference is in energy, and therefore in wavelength. Together, these rays make up the electromagnetic spectrum. The fact that radio waves, for example, travel at the speed of light is incredibly useful for communications.
In his research, Kolthammer creates a circuit that uses photons to transmit signals from one part of the circuit to another, so he is well qualified to comment on the usefulness of the incredible speed of light.
“The very fact that we built the infrastructure of the Internet, for example, and radio before it, based on light, has to do with the ease with which we can transmit it,” he notes. And he adds that light acts as the communication force of the Universe. When the electrons in a mobile phone start to shake, photons are released and cause the electrons in another mobile phone to also shake. This is how a phone call is born. The trembling of electrons in the Sun also emits photons - in huge quantities - which, of course, form light, giving life on Earth heat and, ahem, light.
Light is the universal language of the Universe. Its speed - 299,792.458 km/s - remains constant. Meanwhile, space and time are malleable. Perhaps we should think not about how to move faster than light, but how to move faster through this space and this time? Go to the root, so to speak?
But it turned out that it is possible; now they believe that we will never be able to travel faster than light...” But in fact it is not true that anyone once believed that traveling faster than sound was impossible. Long before supersonic aircraft appeared, it was already known that that bullets fly faster than sound, but in reality we were talking about the fact that it is impossible controlled supersonic flight, and that was the mistake. The SS movement is a completely different matter. From the very beginning, it was clear that supersonic flight was hampered by technical problems that simply needed to be solved. But it is completely unclear whether the problems hindering the SS movement can ever be solved. The theory of relativity has a lot to say about this. If SS travel or even signal transmission is possible, then causality will be violated, and completely incredible conclusions will follow from this.
We will first discuss simple cases of CC motion. We mention them not because they are interesting, but because they come up again and again in discussions of the SS movement and therefore have to be dealt with. Then we will discuss what we consider difficult cases of STS movement or communication and consider some of the arguments against them. Finally, we will look at the most serious assumptions about the real SS movement.
Simple SS movement
1. The phenomenon of Cherenkov radiation
One way to move faster than light is to first slow down the light itself! :-) In a vacuum, light travels at speed c, and this quantity is a universal constant (see the question Is the speed of light constant), and in a denser medium like water or glass it slows down to the speed c/n, Where n is the refractive index of the medium (1.0003 for air; 1.4 for water). Therefore, particles can move faster in water or air than light travels there. As a result, Vavilov-Cherenkov radiation occurs (see question).
But when we talk about SS motion, we, of course, mean exceeding the speed of light in a vacuum c(299,792,458 m/s). Therefore, the Cherenkov phenomenon cannot be considered an example of the SS movement.
2. From the third party
If the rocket A flies away from me at speed 0.6c to the west, and the other B- from me with speed 0.6c to the east, then the total distance between A And B in my frame of reference increases with speed 1.2c. Thus, an apparent relative velocity greater than c can be observed “from the third side.”
However, such speed is not what we usually understand by relative speed. Real rocket speed A relative to the rocket B- this is the rate of increase in the distance between the rockets that is observed by the observer in the rocket B. Two velocities must be added using the relativistic formula for adding velocities (see the question How to add velocities in partial relativity). In this case, the relative speed is approximately 0.88c, that is, is not superluminal.
3. Shadows and bunnies
Think about how fast a shadow can move? If you create a shadow on a distant wall with your finger from a nearby lamp, and then move your finger, the shadow moves much faster than your finger. If the finger moves parallel to the wall, then the speed of the shadow will be D/d times the finger speed, where d- the distance from the finger to the lamp, and D- distance from the lamp to the wall. And you can get even greater speed if the wall is located at an angle. If the wall is located very far away, then the movement of the shadow will lag behind the movement of the finger, since the light will still have to reach from the finger to the wall, but still the speed of the shadow will be the same number of times greater. That is, the speed of the shadow is not limited by the speed of light.
In addition to shadows, bunnies can also move faster than light, for example, a speck from a laser beam aimed at the Moon. Knowing that the distance to the Moon is 385,000 km, try to calculate the speed of the bunny by moving the laser slightly. You can also think about a sea wave hitting the shore obliquely. How fast can the point at which the wave breaks move?
Similar things can happen in nature. For example, a light beam from a pulsar can comb through a cloud of dust. A bright flash creates an expanding shell of light or other radiation. When it crosses the surface, it creates a ring of light that grows faster than the speed of light. In nature, this occurs when an electromagnetic pulse from lightning reaches the upper layers of the atmosphere.
These were all examples of things moving faster than light, but which were not physical bodies. Using a shadow or a bunny cannot convey a SS message, so communication faster than light does not work. And again, this is apparently not what we want to understand by SS movement, although it becomes clear how difficult it is to determine what exactly we need (see the question FTL scissors).
4. Solids
If you take a long hard stick and push one end, does the other end move in immediately or not? Is it possible to carry out CC transmission of a message in this way?
Yes it was would can be done if such solids existed. In reality, the influence of a blow on the end of a stick propagates along it at the speed of sound in a given substance, and the speed of sound depends on the elasticity and density of the material. Relativity imposes an absolute limit on the possible hardness of any body so that the speed of sound in them cannot exceed c.
The same thing happens if you are in a field of attraction, and first hold a string or pole vertically by the upper end, and then release it. The point you released will begin to move immediately, and the lower end will not be able to begin to fall until the influence of the release reaches it at the speed of sound.
It is difficult to formulate a general theory of elastic materials within the framework of relativity, but the basic idea can be demonstrated using the example of Newtonian mechanics. The equation for the longitudinal motion of an ideally elastic body can be obtained from Hooke's law. In mass variables per unit length p and Young's modulus of elasticity Y, longitudinal displacement X satisfies the wave equation.
The plane wave solution moves at the speed of sound s, and s 2 = Y/p. This equation does not imply the possibility of causal influence spreading faster s. Thus, relativity imposes a theoretical limit on the magnitude of elasticity: Y < PC 2. In practice, there are no materials even close to it. By the way, even if the speed of sound in the material is close to c, matter itself is not at all obliged to move at a relativistic speed. But how do we know that, in principle, there cannot be a substance that overcomes this limit? The answer is that all matter consists of particles, the interaction between which obeys the standard model of elementary particles, and in this model no interaction can propagate faster than light (see below about quantum field theory).
5. Phase speed
Look at this wave equation:
It has solutions of the form:
These solutions are sinusoidal waves moving at a speed
But this is faster than light, which means we have the tachyon field equation in our hands? No, this is just an ordinary relativistic equation of a massive scalar particle!
The paradox will be resolved if we understand the difference between this speed, also called the phase speed vph from another speed called group speed v gr which is given by the formula,
If the wave solution has a frequency spread, then it will take the form of a wave packet that moves with a group speed not exceeding c. Only the wave crests move with phase velocity. It is possible to transmit information using such a wave only at group speed, so phase speed gives us another example of superluminal speed, which cannot carry information.
7. Relativistic rocket
A controller on Earth monitors a spacecraft flying away at a speed of 0.8 c. According to the theory of relativity, even after taking into account the Doppler shift of signals from the ship, he will see that time on the ship is slowed down and the clock there runs slower by a factor of 0.6. If he calculates the quotient of the distance traveled by the ship by the time taken, measured by the ship's clock, he will get 4/3 c. This means that the ship's passengers are traveling through interstellar space at an effective speed greater than the speed of light they would experience if it were measured. From the point of view of the ship's passengers, interstellar distances are subject to Lorentz contraction by the same factor of 0.6 and therefore they too must recognize that they cover known interstellar distances at a rate of 4/3 c.
This is a real phenomenon and could, in principle, be used by space travelers to cover vast distances during their lives. If they accelerate with a constant acceleration equal to the acceleration of free fall on Earth, then they will not only have ideal artificial gravity on their ship, but they will also have time to cross the Galaxy in just 12 of their years! (see the question What are the equations of a relativistic rocket?)
However, this is not a real SS movement. Effective speed is calculated from distance in one frame of reference and time in another. This is not real speed. Only the ship's passengers benefit from this speed. The dispatcher, for example, will not have time in his lifetime to see how they fly a gigantic distance.
Complex cases of SS movement
9. Einstein, Podolsky, Rosen paradox (EPR)
10. Virtual photons
11. Quantum tunneling
Real candidates for SS travelers
This section contains speculative but serious speculation about the possibility of superluminal travel. These will not be the kinds of things that would normally be put in a FAQ, as they raise more questions than they answer. They are presented here mainly to show that serious research is being carried out in this direction. Only a brief introduction is given to each direction. More detailed information can be found on the Internet.
19. Tachyons
Tachyons are hypothetical particles that locally move faster than light. To do this, they must have an imaginary mass, but their energy and momentum must be positive. It is sometimes thought that such SS particles should be impossible to detect, but in fact, there is no reason to think so. Shadows and bunnies tell us that SS movement does not yet imply invisibility.
Tachyons have never been observed and most physicists doubt their existence. It was once stated that experiments had been carried out to measure the mass of neutrinos emitted during the decay of Tritium, and that these neutrinos were tachyon. This is highly doubtful, but still not excluded. There are problems in tachyon theories, since from the point of view of possible violations of causality, they destabilize the vacuum. It may be possible to bypass these problems, but then it will be impossible to use tachyons in the SS message we need.
The truth is that most physicists consider tachyons to be a sign of an error in their field theories, and interest in them among the general public is fueled mainly by science fiction (see the article Tachyons).
20. Wormholes
The most famous proposed possibility of STS travel is the use of wormholes. Wormholes are tunnels in space-time that connect one place in the Universe to another. You can use them to move between these points faster than light would take its normal path. Wormholes are a phenomenon of classical general relativity, but to create them you need to change the topology of spacetime. The possibility of this may be contained in the theory of quantum gravity.
To keep wormholes open, huge amounts of negative energy are needed. Misner And Thorne proposed that the large-scale Casimir effect can be used to generate negative energy, and Visser proposed a solution using cosmic strings. All these ideas are highly speculative and may simply be unrealistic. An unusual substance with negative energy may not exist in the form required for the phenomenon.
Thorne discovered that if wormholes could be created, they could be used to create closed time loops that would make time travel possible. It has also been suggested that the multivariate interpretation of quantum mechanics indicates that time travel will not cause any paradoxes, and that events will simply unfold differently when you go back in time. Hawking says that wormholes may simply be unstable and therefore not practical. But the topic itself remains a fruitful area for thought experiments, allowing one to understand what is possible and what is not possible based on the known and assumed laws of physics.
refs:
W. G. Morris and K. S. Thorne, American Journal of Physics 56
,
395-412 (1988)
W. G. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Letters 61
, 1446-9 (1988)
Matt Visser, Physical Review D39, 3182-4 (1989)
see also "Black Holes and Time Warps" Kip Thorn, Norton & co. (1994)
For an explanation of the multiverse see, "The Fabric of Reality" David Deutsch, Penguin Press.
21. Deformer engines
[I have no idea how to translate this! In the original warp drive. - approx. translator;
translated by analogy with the article on Membrane]
A warp could be a mechanism for twisting spacetime so that an object can travel faster than light. Miguel Alcabière became famous for developing the geometry that describes such a deformer. The distortion of space-time makes it possible for an object to travel faster than light while remaining on a time-like curve. The obstacles are the same as when creating wormholes. To create a deformer, you need a substance with a negative energy density and. Even if such a substance is possible, it is still unclear how it can be obtained and how to use it to make a deformer work.
ref M. Alcubierre, Classical and Quantum Gravity, 11
, L73-L77, (1994)
Conclusion
Firstly, it turned out to be difficult to generally define what SS travel and SS message mean. Many things, like shadows, perform CC movement, but in such a way that it cannot be used, for example, to transmit information. But there are also serious possibilities for real SS movement, which are proposed in the scientific literature, but their implementation is not yet technically possible. The Heisenberg uncertainty principle makes it impossible to use apparent SS motion in quantum mechanics. There are potential means of SS propulsion in general relativity, but they may not be possible to use. It seems extremely unlikely that in the foreseeable future, or at all, technology will be capable of creating spacecraft with SS propulsion, but it is curious that theoretical physics, as we now know it, does not close the door to SS propulsion for good. An SS movement in the style of science fiction novels is apparently completely impossible. An interesting question for physicists is: “why, in fact, is this impossible, and what can be learned from this?”