Dedicated to the direct measurement of the speed of movement of neutrinos. The results sound sensational: the neutrino speed turned out to be slightly - but statistically significant! - more than the speed of light. The collaboration's article contains an analysis of various sources of errors and uncertainties, but the reaction of the overwhelming majority of physicists remains very skeptical, primarily because such a result does not agree with other experimental data on the properties of neutrinos.

Rice. 1.

Experiment details

The idea of ​​the experiment (see OPERA experiment) is very simple. The neutrino beam is born at CERN, flies through the Earth to the Italian laboratory of Gran Sasso and passes there through the special OPERA neutrino detector. Neutrinos interact very weakly with matter, but due to the fact that their flux from CERN is very large, some neutrinos still collide with atoms inside the detector. There they generate a cascade of charged particles and thereby leave their signal in the detector. Neutrinos at CERN are not born continuously, but "bursts", and if we know the moment of neutrino birth and the moment of its absorption in the detector, as well as the distance between the two laboratories, we can calculate the speed of the neutrino.

The distance between the source and the detector in a straight line is approximately 730 km and it was measured with an accuracy of 20 cm (the exact distance between the reference points is 730,534.61 ± 0.20 meters). True, the process leading to the production of neutrinos is not at all localized with such precision. At CERN, a high-energy proton beam is emitted from the SPS accelerator, dropped onto a graphite target, and generates secondary particles in it, including mesons. They still fly forward at near-light speed and decay into muons on the fly, emitting neutrinos. Muons also decay and generate additional neutrinos. Then all particles, except for neutrinos, are absorbed in the bulk of the substance, and they reach the place of detection without hindrance. General scheme this part of the experiment is shown in Fig. 1.

The entire cascade leading to the appearance of a neutrino beam can stretch for hundreds of meters. However, since all particles in this bunch fly forward at a near-light speed, for the detection time there is practically no difference whether a neutrino was born immediately or after a kilometer of travel (however, it is of great importance when exactly the initial proton that led to the creation of a given neutrino flew out of the accelerator). As a result, the produced neutrinos by and large simply repeat the profile of the initial proton beam. Therefore, the key parameter here is precisely the temporal profile of the proton beam emitted from the accelerator, in particular, the exact position of its leading and trailing edges, and this profile is measured with a good temporal NS m resolution (see Fig. 2).

Each session of dumping a proton beam onto a target (in English, such a session is called spill, "Splash") lasts about 10 microseconds and leads to the creation of a huge number of neutrinos. However, almost all of them fly through the Earth (and the detector) without interaction. In those rare cases, when the detector does register a neutrino, it is impossible to say at what point during the 10 microsecond interval it was emitted. The analysis can be carried out only statistically, that is, accumulate many cases of neutrino detection and construct their distribution over time relative to the starting point for each session. In the detector, the reference point is taken to be that moment in time when the conditional signal, moving at the speed of light and emitted exactly at the moment of the leading edge of the proton beam, reaches the detector. An accurate measurement of this moment became possible thanks to the synchronization of clocks in the two laboratories with an accuracy of several nanoseconds.

In fig. 3 shows an example of such a distribution. Black dots are real neutrino data recorded by the detector and summed over a large number of sessions. The red curve shows a conventional "reference" signal that would move at the speed of light. It can be seen that the data starts at about 1048.5 ns earlier reference signal. This, however, does not mean that the neutrino is really a microsecond ahead of light, but is only a reason to carefully measure all cable lengths, the response rates of the equipment, the delay times of the electronics, and so on. This recheck was performed, and it turned out that it displaces the "reference" moment by 988 ns. Thus, it turns out that the neutrino signal actually overtakes the reference signal, but only by about 60 nanoseconds. In terms of the speed of neutrinos, this corresponds to an excess of the speed of light by about 0.0025%.

The error of this measurement was estimated by the authors of the analysis at 10 nanoseconds, which includes both statistical and systematic errors. Thus, the authors claim that they "see" the superluminal motion of neutrinos at a statistical confidence level of six standard deviations.

The difference between the results and expectations by six standard deviations is already quite large and is called in elementary particle physics by the loud word "discovery". However, this number must be understood correctly: it only means that the probability statistical fluctuations in the data are very small, but it does not say how reliable the data processing technique is and how well physicists have taken into account all instrumental errors. After all, there are many examples in particle physics where unusual signals with exceptionally high statistical confidence have not been confirmed by other experiments.

What do superluminal neutrinos contradict?

Contrary to popular belief, the special theory of relativity does not in itself prohibit the existence of particles moving at a speed faster than light. However, for such particles (they are collectively called "tachyons"), the speed of light is also a limit, but only from below - they cannot move slower than it. In this case, the dependence of the energy of the particles on the speed turns out to be inverse: the greater the energy, the closer the speed of the tachyons to the speed of light.

Much more serious problems begin in quantum field theory. This theory is replacing quantum mechanics when it comes to quantum particles with high energies. In this theory, particles are not points, but, relatively speaking, clumps of a material field, and it is impossible to consider them separately from the field. It turns out that tachyons lower the field energy, which means they make the vacuum unstable. It is then more profitable for emptiness to spontaneously disintegrate into a huge number of these particles, and therefore it is simply meaningless to consider the movement of one tachyon in ordinary empty space. We can say that the tachyon is not a particle, but an instability of the vacuum.

In the case of tachyons-fermions, the situation is somewhat more complicated, but even there, comparable difficulties arise that prevent the creation of a self-consistent tachyon quantum field theory, including the usual theory of relativity.

However, this is also not the last word in theory. Just as experimenters measure anything that can be measured, theorists also test all possible hypothetical models that do not contradict the available data. In particular, there are theories in which a small, not yet noticed deviation from the postulates of the theory of relativity is allowed - for example, the speed of light itself can be a variable. Such theories do not yet have direct experimental support, but they have not yet been closed.

This brief sketch of theoretical possibilities can be summarized as follows: although in some theoretical models movement with superluminal speed is possible, they remain purely hypothetical constructions. All the experimental data available to date are described by standard theories without superluminal motion. Therefore, if it were reliably confirmed even for some particles, the quantum field theory would have to be radically altered.

Should we consider the result of OPERA in this sense "the first sign"? Not yet. Perhaps the most important reason for skepticism is the fact that the OPERA result does not agree with other experimental data on neutrinos.

First, during the famous supernova SN1987A, neutrinos were also detected, which arrived several hours before the light pulse. This does not mean that neutrinos went faster than light, but only reflects the fact that neutrinos are emitted by more early stage core collapse in a supernova than light. However, since neutrinos and light, having spent 170 thousand years on their way, did not diverge by more than a few hours, it means that their speeds are very close and differ by no more than billionths of a fraction. The OPERA experiment shows a thousand times stronger discrepancy.

Here, of course, we can say that neutrinos produced in supernova explosions and neutrinos from CERN differ greatly in energy (several tens of MeV in supernovae and 10–40 GeV in the described experiment), and the neutrino velocity changes depending on the energy. But this change in this case works in the “wrong” direction: after all, the higher the energy of the tachyons, the closer their speed should be to the speed of light. Of course, here you can think of some modification of the tachyon theory, in which this dependence would be completely different, but in this case it will be necessary to discuss the "double-hypothetical" model.

Further, from a variety of experimental data on neutrino oscillations received for last years, it follows that the masses of all neutrinos differ from each other only by a fraction of an electron-volt. If the OPERA result is perceived as a manifestation of the superluminal motion of neutrinos, then the value of the square of the mass of at least one neutrino will be of the order of - (100 MeV) 2 (negative square of the mass is the mathematical manifestation of the fact that the particle is considered a tachyon). Then you have to admit that all sorts of neutrinos are tachyons and have approximately the same mass. On the other hand, direct measurement of the neutrino mass in beta decay of tritium nuclei shows that the neutrino mass (in absolute value) should not exceed 2 electron volts. In other words, all this data cannot be reconciled with each other.

The conclusion from this can be made as follows: the declared result of the OPERA collaboration is difficult to fit into any, even the most exotic theoretical models.

What's next?

In all major particle physics collaborations, it is normal practice when each specific analysis is carried out by a small group of participants, and only then the results are presented for general discussion. In this case, apparently, this stage was too short, as a result of which not all participants in the collaboration agreed to substitute their signatures under the article (the full list includes 216 participants in the experiment, and the preprint has only 174 authors). Therefore, in the near future, most likely, many additional checks will be carried out within the collaboration, and only after that the article will be sent to print.

Of course, now we can expect a stream of theoretical articles with a variety of exotic explanations for this result. However, until the declared result is reliably verified, it cannot be considered a full-fledged discovery.

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

We will first discuss simple cases of STS 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 to be difficult cases of STS movement or communication and consider some of the arguments against them. Finally, we look at some of the more serious speculations about the true STS movement.

Simple SS movement

1. The phenomenon of Cherenkov radiation

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

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

2.From a third party

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

However, this speed is not what we usually mean by relative speed. Real rocket speed A regarding the rocket B is the rate of growth of the distance between missiles, which is observed by an observer in a rocket B... Two velocities must be added according to the relativistic formula for the addition of velocities (see the question How to add velocities in partial relativity). In this case, the relative speed is approximately 0.88c, that is, it is not superluminal.

3. Shadows and bunnies

Think about how fast the shadow can move? If you create a shadow on a distant wall from your finger from a nearby lamp, and then move your finger, then the shadow moves much faster than your finger. If the finger moves parallel to the wall, then the speed of the shadow will be in D / d times the speed of a finger, where d is the distance from the finger to the lamp, and D- the distance from the lamp to the wall. And even higher speed can turn out if the wall is located at an angle. If the wall is very far away, then the movement of the shadow will lag behind the movement of the finger, since the light will still have to travel from the finger to the wall, but still the speed of the movement of the shadow will be as many times higher. 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 light by moving the laser slightly. You can also think of a sea wave slanting against the shore. 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 sweep a cloud of dust. A bright flash creates an expanding shell of light or other radiation. When it crosses the surface, a ring of light is created that grows faster than the speed of light. In nature, this occurs when an electromagnetic pulse from lightning reaches the upper atmosphere.

These were all examples of things moving faster than light, but which were not physical bodies... With the help of a shadow or a bunny, it is impossible to transmit an SS message, so communication faster than light does not work. And again, this, apparently, is not what we want to understand by ST motion, although it becomes clear how difficult it is to determine what exactly we need (see the question Superluminal scissors).

4. Solids

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

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

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

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

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

5. Phase velocity

Look at this wave equation:

He has solutions of the form:

These solutions are sine waves moving at a speed

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

The paradox will be resolved if you understand the difference between this speed, also called phase speed v ph from another speed called group v gr which is dated 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 wave crests move with phase velocity. It is possible to transmit information with the help of such a wave only with a group velocity, so that the phase velocity gives us another example of superluminal velocity, which cannot carry information.

7. Relativistic rocket

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

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

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

Difficult cases of SS movement

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

10. Virtual photons

11. Quantum tunneling

Real Candidates for SS Travelers

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

19. Tachyons

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

Tachyons have never been observed and most physicists doubt their existence. Somehow it was stated that experiments were carried out to measure the mass of neutrinos emitted during the decay of Tritium, and that these neutrinos were tachyon. This is highly doubtful, but still not excluded. There are problems in tachyon theories, since from the point of view of possible violations of causality, they destabilize the vacuum. It may be possible to circumvent 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 error in their field theories, and interest in them on the part of the broad masses is fueled mainly by science fiction (see Tachyons' article).

20. Wormholes

The most famous hypothesized possibility of SS travel is the use of wormholes. Wormholes are tunnels in space-time that connect one place in the universe to another. On them you can move between these points faster than light would do its usual way. Wormholes are a classical phenomenon general relativity, but to create them, you need to change the topology of space-time. The possibility of this may be included in the theory of quantum gravity.

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

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

21. Motors-deformers

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

The deformer could be a mechanism for twisting spacetime so that an object can travel faster than light. Miguel Alcabier 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 make the deformer work with it.
ref M. Alcubierre, Classical and Quantum Gravity, 11 , L73-L77, (1994)

Conclusion

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

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

Is FTL flight possible?

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

Simple examples of FTL travel

1. The Cherenkov effect

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

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 to the east, then I see that the distance between A and B increasing at a rate 1.2c... Watching the missiles fly A and B from the side, the third observer sees that the total velocity of missile removal is greater than c .

but relative speed 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 seen by an observer flying on a rocket B... The 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 speed is approximately 0.88c... So in this example we didn't get the superluminal velocity.

3. Light and shadow

Consider 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 your finger moves. When you move your finger parallel to the wall, the speed of the shadow in D / d times more than the speed of a finger. Here d is the distance from the lamp to the finger, and D- from lamp to wall. The speed will be even higher 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 movement along the wall will increase even more. The speed of the 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 spot of light on the surface of the Moon by yourself, with small vibrations of the laser pointer in your hand. You might also like the example of a wave running into a straight line of the beach at a slight angle. How fast can the intersection of the wave and the shore travel along the beach?

All of these things can happen in nature. For example, a beam of light from a pulsar can travel along a dust cloud. A powerful explosion can create spherical waves of light or radiation. When these waves intersect with any surface, light circles appear on this surface, which expand faster than light. This phenomenon occurs, for example, when an electromagnetic pulse from a lightning flash travels through the upper atmosphere.

4. Solid body

If you have a long stiff rod and you hit one end of the rod, won't the other end start moving immediately? Isn't this a way to transmit information faster than light?

That would be true if ideally rigid bodies existed. 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 speed of sound in a material to the value c .

The same principle applies if you hold a string or rod upright, release it, and it begins to fall under the influence of gravity. The upper end, which you let go, begins to fall immediately, but the lower end will only begin to move after a while, since the disappearance 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 ideal elastic body can be derived from Hooke's law. We denote the linear density of the rod ρ , Young's modulus of elasticity Y... Longitudinal displacement 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 perturbations of the medium to move faster than with the speed s... In addition, the theory of relativity gives a limit to the value of elasticity: Y< ρc 2 ... In practice, no known material comes close to this limit. Note also that even if the speed of sound is close to c, then the substance itself does not necessarily move with a relativistic speed.

Although in nature there is solids, exists movement of solids that can be used to overcome the speed of light. This topic belongs to the already described section of shadows and highlights. (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 = A cos (ax - bt), c 2 a 2 - b 2 + w 2 = 0

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

But this is more than c. Is this an equation for tachyons? (see further section). No, this is the usual relativistic equation for a particle with mass.

To eliminate the paradox, it is necessary to distinguish between the "phase velocity" v ph, and "group rate" v gr, and
v ph v gr = c 2

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

6. Superluminal galaxies

7. Relativistic rocket

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

Time dilation is a real effect that, in principle, can be used in space travel to cover long distances in a short time from the point of view of astronauts. With a constant acceleration of 1g, astronauts will not only have comfortable artificial gravity, but will also be able to traverse the galaxy in just 12 years in their own time. During the trip, they will age by 12 years.

But this is still not a superluminal flight. You cannot calculate speed using distance and time defined in different frames of reference.

8. The speed of gravity

Some insist that the speed of gravity is much greater. c or even endless. Check out Does Gravity Travel at the Speed ​​of Light? and What is Gravitational Radiation? Gravitational disturbances and gravitational waves spread with speed c .

9. EPR paradox

10. Virtual photons

11. Quantum tunneling effect

In quantum mechanics, the tunneling effect allows a particle to overcome a barrier, even if there is not enough energy for it. 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 cover the same distance at a speed c... Can this be used to send messages faster than light?

Quantum Electrodynamics Says No! Nevertheless, an experiment has been performed that demonstrated superluminal information transmission using the tunneling effect. Through an 11.4 cm wide barrier at a speed of 4.7 c Mozart's Fortieth Symphony was delivered. The explanation for this experiment is highly controversial. Most physicists believe that the tunnel effect cannot transmit information faster than light. If that were possible, why not send the signal back in time by placing the equipment in a fast moving frame of reference.

17. Quantum field theory

Except for gravity, all observables physical phenomena correspond to " Standard model". The Standard Model is a relativistic quantum field theory that explains electromagnetic and nuclear interactions, as well as all known particles. In this theory, any pair of operators corresponding to physical observables separated by a spacelike interval of events" commutes "(that is, you can change the order In principle, this implies that in the standard model, the impact cannot travel faster than light, and this can be considered the quantum field equivalent of the infinite energy argument.

However, in the quantum field theory of the Standard Model, there is no flawlessly rigorous proof. No one has yet even proven that this theory is internally consistent. This is most likely not the case. In any case, there is no guarantee that there are no particles or forces that have not yet been discovered that do not obey the ban on superluminal travel. There is also no generalization of this theory, including gravity and general relativity. Many physicists working in the field of quantum gravity doubt that 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 limiting speed.

18. The grandfather paradox

In special relativity, a particle that travels faster than light in one frame of reference moves back in time in another frame of reference. Superluminal movement or transmission of information would make it possible to travel or send a message into the past. If such time travel was 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 implausible probability that some kind of limited superluminal movement is possible, which does not allow a return to the past. Or maybe time travel is possible, but causality is violated in some consistent way. This is all very implausible, but if we are discussing FTL travel, then it is better to be ready for new ideas.

The converse 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 final section, I will describe some serious ideas for possible faster-than-light travel. These topics are not often included in the FAQ, because they are not more like answers, but a lot of new questions. They are included here to show that serious research is being done in this direction. Only a short introduction to the topic is given. You can find details 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. In this case, the energy and momentum of the tachyon are real values. There is no reason to believe that superluminal particles cannot be detected. Shadows and light spots can travel faster than light and can be detected.

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

There are problems with tachyon theory. In addition to the possible violation of 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 message transmission.

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

20. Wormholes

The most famous way 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 go from one end of the hole to the other faster than the usual path. Wormholes are described general theory relativity. To create them, you need to change the topology of space-time. Perhaps this will become possible within the framework of the quantum theory of gravity.

To hold wormhole open, we 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 it may not be possible. Maybe the required form of exotic matter with negative energy does not exist.

In September 2011, physicist Antonio Ereditato shocked the world. His statement could turn our understanding of the universe upside down. If the data collected by 160 OPERA scientists were correct, the incredible was observed. 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. Perhaps the very foundations of physics would have to be revised.

Although Ereditato said that he and his team were “extremely confident” in their results, they did not say that the data was completely accurate. On the contrary, they asked other scientists to help them figure out what was going on.

In the end, it turned out that the OPERA results were wrong. A poorly connected cable caused a sync issue and the signals from the GPS satellites were inaccurate. There was an unexpected delay in the signal. As a result, measurements of the time it took for neutrinos to cover a certain distance showed an extra 73 nanoseconds: it seemed that the neutrinos flew by faster than light.

Despite months of scrutiny before starting the experiment and rechecking the data afterwards, the scientists were seriously wrong. Ereditato resigned, contrary to the remarks of many that such errors always occurred due to the extreme complexity of the device of particle accelerators.

Why did the assumption - just the assumption - that something could move faster than light cause such a noise? How confident 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 has been rounded up to 300,000 kilometers per second. It's quite fast. The sun is 150 million kilometers from Earth, and light from it 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. He 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 very quickly. Early 1960s William Bertozzi in Massachusetts Institute of Technology experimented with accelerating electrons to even higher speeds.

Since electrons have a negative charge, they can be accelerated — more precisely, repelled — by applying the same negative charge to the material. The more energy is applied, the faster the electrons accelerate.

One would think that one just needs to increase the applied energy in order to accelerate to a speed of 300,000 km / s. But it turns out that electrons just can't move that fast. Bertozzi's experiments showed that using more energy does not lead to a directly proportional increase in the speed of electrons.

Instead, huge amounts of additional energy had to be applied to alter the speed of the electrons even slightly. It was getting closer and closer to the speed of light, but it never reached it.

Imagine walking towards the door in small steps, each of which travels half the distance from your current position to the door. Strictly speaking, you will never get to the door, because after each step you take, you will have a distance to overcome. Bertozzi faced roughly the same problem when dealing with his electrons.

But light is made up of particles called photons. Why can these particles move at the speed of light, but electrons cannot?

“As objects move faster and faster, they get heavier - the heavier they get, the harder it is for them to accelerate, so you never get to the speed of light,” says Roger Rassoul, a physicist at the University of Melbourne in Australia. “A photon has no mass. If he had mass, he could not move at the speed of light. "

Photons are special. They not only lack mass, which provides them complete freedom displacements in the vacuum of space, they also do not need to accelerate. The natural energy that they have at their disposal moves in waves, just like they do, so at the time of their creation they already have maximum speed. In a sense, it's easier to think of light as energy rather than a stream of particles, although in truth, light is both.

However, light travels much slower than we might expect. Although internet techs like to talk about communications that operate at "the speed of light" in fiber, light travels 40% slower in the glass of that fiber than it does in a vacuum.

In reality, photons travel at a speed of 300,000 km / s, but they encounter a certain amount of interference, interference caused by other photons that are emitted by glass atoms when the main light wave passes through. This may not be easy to understand, but at least we tried.

In the same way, in the framework of special experiments with individual photons, it was possible to slow them down quite impressively. But for most cases, the number of 300,000 will be valid. We have not seen or created anything that could move as 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 is strictly followed?

The answer has to do with the person by name, 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 has several conceptual problems.

Imagine light falling from a flashlight onto a mirror on the ceiling of a stationary spacecraft. The light goes up, is reflected from 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 on the floor. But to do this, the light will have to travel a diagonal distance, not a vertical one. After all, the mirror is now moving rapidly with the spacecraft.

Accordingly, the distance that the light travels increases. Let's say 5 meters. It turns out 15 meters in total, not 10.

Despite this, although the distance has increased, Einstein's theories state that light will still move at the same speed. Since speed is distance divided by time, since the speed is the same and the distance has increased, time must also increase. Yes, the time itself must stretch. Although it sounds strange, it has been confirmed experimentally.

This phenomenon is called time dilation. Time moves more slowly for people who move in fast moving vehicles, relative to those who are stationary.

For example, time runs 0.007 seconds slower for astronauts on the International space station, which moves at a speed of 7.66 km / s relative to the Earth, when compared with people on the planet. Even more interesting is the situation with particles like the aforementioned electrons, which can travel close to the speed of light. In the case of these particles, the degree of deceleration will be enormous.

Stephen Colthammer, an experimental physicist at the University of Oxford in the UK, points to an example with particles called muons.

Muons are unstable: they quickly decay into simpler particles. So fast that most of the 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 been trying to figure out why for a long time.

“The answer to this mystery is that muons are generated with such energy that they move at speeds close to light,” says Kolthammer. "Their sense of time, so to speak, their internal clock runs slowly."

Muons "stay alive" longer than expected relative to us, thanks to the present, natural curvature of time. When objects move rapidly relative to other objects, their length also decreases, contracts. These consequences, time dilation and length decrease, are examples of how spacetime changes depending on the movement of things - me, you, or a spacecraft - with mass.

What is important, as Einstein said, does not affect the light, since it has no mass. This is why these principles go hand in hand. If objects could move faster than light, they would obey fundamental laws that describe how the universe works. These are key principles. Now we can talk about a few exceptions and derogations.

On the one hand, although we have not seen anything moving faster than light, this does not mean that this speed limit cannot theoretically be broken under very specific conditions. Take, for example, the expansion of the universe itself. Galaxies in the Universe are moving away from each other at a speed much faster than light.

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 rotate up and down, randomly choosing from two possible states, but the choice of the direction of rotation will accurately reflect on the other photon elsewhere if they are entangled.

Two scientists, each studying their own photon, will get the same result simultaneously, faster than the speed of light would allow.

However, in both of these examples, it is important to note that no information moves. faster speed 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 the field of view.

As for the two scientists with their photons, although they could get the same result at the same time, they could not let each other know about it faster than the light travels between them.

“This does not pose any problem for us, because if you are able to send signals faster than light, you get bizarre paradoxes according to which information can somehow travel back in time,” says Kolthammer.

There is another possible way to make faster-than-light travel technically possible: rifts in space-time that would allow the traveler to avoid the rules of normal travel.

Gerald Cleaver of Baylor University in Texas believes that one day we may be able to build a spacecraft that travels faster than light. Which moves through a wormhole. Wormholes are loops in space-time that fit perfectly into Einstein's theories. They could allow an astronaut to jump from one end of the universe to the other using 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 traveling along a "normal" path. But wormholes may not be accessible at all. space travel... Could there be another way to actively distort spacetime to travel faster than 300,000 km / s relative to someone else?

Cleaver also explored the idea of ​​an "Alcubierre engine" in 1994. He 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, "problems arose: how to do it and how much energy would be needed."

In 2008, he and his graduate student Richard Aubosie calculated how much energy would be needed.

"We imagined a 10m x 10m x 10m spacecraft - 1,000 cubic meters - and calculated that the amount of energy needed to start the process would be equivalent to the mass of a whole Jupiter."

After that, the energy must be constantly "poured" so that the process does not end. No one knows if this will ever be possible, or what the required technologies will be like. “I don’t want to be quoted for centuries as predicting something that will never happen,” Cleaver says, “but I don’t see a solution yet.”

So, travel faster than the speed of light remains a fantasy at the moment. So far, the only way is to plunge into deep suspended animation. And yet it's not all bad. In most cases, we talked about visible light. But in reality, light is much more. From radio waves and microwaves to visible light, ultraviolet radiation, x-rays and the gamma rays emitted by atoms in the process of decay - all these beautiful rays are made of the same thing: photons.

The difference is in energy, which means 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 communication.

In his research, Kolthammer creates a circuit that uses photons to transfer signals from one part of the circuit to another, so it deserves a right 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 before that the radio 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 fly out and cause the electrons in the other mobile phone to shake as well. This is how a phone call is born. The tremors of electrons in the Sun also emit photons - in huge quantities - which, of course, form the light that gives life on Earth warmth and, ahem, light.

Light is universal language The universe. Its speed - 299,792.458 km / s - remains constant. Meanwhile, space and time are malleable. Perhaps we should not think about how to move faster than light, but how to move faster through this space and this time? To mature at the root, so to speak?

A group of scientists from the OPERA experiment in collaboration with the European Organization for Nuclear Research (CERN) have published the sensational results of an experiment to overcome the speed of light. Experimental results refute special theory relativity of Albert Einstein, on which all modern physics... The theory says that the speed of light is 299 792 458 m / s, and elementary particles cannot move faster than the speed of light.

Nevertheless, scientists recorded an excess of it by a neutrino beam by 60 nanoseconds when overcoming 732 km. It happened on September 22 during an experiment conducted by international group nuclear physicists from Italy, France, Russia, Korea, Japan and other countries.

The experiment proceeded as follows: the proton beam was accelerated in a special accelerator and hit with it in the center of a special target. This is how mesons were born - particles composed of quarks.

When mesons decay, neutrinos are born, ”RAS Academician Valery Rubakov, Chief Researcher at the RAS Institute for Nuclear Research, explained to Izvestia. - The beam is located so that the neutrino flies 732 km and falls into the Italian underground laboratory in Gran Sasso. It contains a special detector that records the speed of the neutrino beam.

The research results split the scientific world. Some scientists refuse to believe the results.

What was done at CERN is impossible from the modern point of view of physics, - Academician of the Russian Academy of Sciences Spartak Belyaev told Izvestia. scientific director Institute of General and Nuclear Physics. - It is necessary to check this experiment and its results - perhaps they were just wrong. All the experiments carried out before this fit into the existing theory, and it is not worth raising a panic because of one experiment carried out once.

Academician Belyaev at the same time admits: if it is possible to prove that the neutrino can move faster than the speed of light, it will be a coup.

We then have to break all physics, ”he said.

If the results are confirmed, this is a revolution, - Academician Rubakov agrees. - It's hard to say how this will turn out for the townsfolk. In general, it is, of course, possible to change the special theory of relativity, but it is extremely difficult to do this, and what kind of theory will crystallize as a result is not entirely clear.

Rubakov noted that the report says that over the three years of the experiment, 15 thousand events were recorded and measured.

The statistics are very good, and an international group of reputable scientists took part in the experiment, - sums up Rubakov.

Academicians stressed that the world regularly attempts to experimentally refute the special theory of relativity. However, none of them has yielded positive results so far.