Superluminal speed. How NASA scientists are going to exceed the speed of light in space. Outflow rate in the converging channel, mass flow rate

Very important is the note "in a vacuum", which we talked about at the very beginning. Light travels along fiber optics not as fast as it does in a vacuum. When passing through any medium we know of, light travels much slower than in the "ideal" conditions that the constant speaks of. Air doesn't really interfere with light, but glass is essential. The refractive index of light for a medium is the value of the speed of light in a vacuum divided by the speed of light in a medium. For glass, this figure is 1.5, so if you divide the speed of light (300,000 km / s approximately) by 1.5, you get 200,000 km / s - the approximate speed of light passing through the glass. Some optical fibers are made of plastic, which has an even higher refractive index of light, which means its speed is slower.

One of the reasons for the decrease in speed is the dual nature of light. It has the characteristics of both a particle and a wave. Yes, light is made of photons, but they don't travel in a straight line as they pass through the cable. And since the photons collide with the molecules of the material, they move in different directions. Refraction of light and absorption of the medium ultimately results in a loss of energy and data. That is why the signal cannot move indefinitely, and it must be constantly amplified for transmission over a long distance. It's worth noting that slowing down light is only a fraction of the bad news. Impurities are sometimes added to fiber optic cables that control the speed of light and allow the signal to be transmitted more efficiently.

Fiber optic cable, of course, transmits information much faster than copper wire and is less susceptible to electromagnetic interference. Fiber can achieve transmission speeds of several hundred Gb / s or even TB / s. A home Internet connection does not demonstrate this speed, if only because the wiring is different everywhere. Even if you have fiber optic, there may be a piece of copper in one of the data transmission sections. But even with such fiber, information will go to you at a speed of 50-100 Mb / s, which is better than 1-6 Mb / s for DSL lines. Connection speed also depends on location, provider and your data plan.

There are other things that cause signal delays (called delays) when you try to visit a web page or play an online game. Your computer and the server that stores the data are told to keep the data in sync and transfer efficiently, and this is what causes delays. The distance traveled by the data is also important, and in some places there may be "narrow passages" that will delay them even more. A system works as fast as its slowest component works.

Scientists are working to create a data transmission system over the air. Imagine Wi-Fi bulbs or Wi-Fi spraying, which we are talking about, or even laser beams from building to building. But all the same, light can move through air at a speed close to the speed of light in a vacuum, but not more. How do I get around this limitation?

FTL capability

Scientists at the National Institute of Standards and Technology (NIST) claim to have been able to transmit quantum information at superluminal speed, thanks to the so-called four-wave mixing, which, in fact, is a manifestation of a form of interference in optical fiber. The experiment consists in transmitting a short 200-nanosecond pulse through heated rubidium vapor and simultaneously transmitting a second beam of rays at a different frequency, which should amplify the first pulse. Photons from both beams interact with the vapor and create a third beam. The results show that the third ray travels faster than the speed of light in a vacuum. About 50-90 nanoseconds faster. The scientists argue that the pulse rate can be calibrated by changing the input parameters.

Another FTL option is quantum teleportation, one of which is based on entangled pairs: two particles entangled with each other will have the same characteristics, no matter how far you separate them. It also requires a third particle, which will contain the data you need to transfer. With the help of a laser, you can literally teleport one of the particles anywhere. This is not like transferring a photon, but rather replacing one photon with a copy of the original. This photon can be compared with the third particle in order to find correspondences or differences, and this information can already be used to compare two particles. It looks like instant data transfer, but not quite. The laser beam can only move at the speed of light. However, it can be used to transmit encrypted data to a satellite, as well as to create quantum computers, if we do get to them. This technology has gone much further than any other attempt to transmit information faster than the speed of light. To date, it works only to a limited extent, and scientists are constantly working to increase the teleport distance.

There is still no answer to the question of whether meaningful information can move faster than light. Now we can only move a few particles, which is good, because in the future it can lead us to the desired goal. In practice, you need to transfer organized bits of information that mean something and are intact to another machine that can read them. Otherwise, the world's fastest data transfer won't be worth a penny. But you can be sure that if scientists do exceed the threshold for the speed of light, your Internet will work faster. Much faster than interstellar travel begins.

THE LIGHT SPEED BARRIER WILL FINALLY JUMP! An attempt has been made in the United States to refute yet another scientific dogma. The postulate, once put forward by A. Einstein, states that the speed of light, reaching 300 thousand km / s in a vacuum, is the maximum that can be achieved in nature. Professor Raymond Chu, from the University of Berkeley, in his experiments achieved a speed exceeding the classical one by 1.7 times. Now researchers from the NEC Institute in Princeton have gone even further. A POWERFUL PULSE OF LIGHT was passed through a 6-centimeter "flask" filled with specially prepared gaseous cesium, - describes the course of the experiment, the correspondent of the newspaper "Sunday Times", referring to the head of the experiment, Dr. Liju-na Wang ...

And the devices showed an incredible thing - while the main part of the light at its usual speed passed through the cesium cell, some nimble photons managed to reach the opposite wall of the laboratory, located about 18 m away, and be noted on the sensors located there. Physicists calculated and made sure: if the "hurrying" particles flew 18 m in the same time as normal photons passed through a 6-centimeter "flask", then their speed was 300 times higher than the speed of light! And this violates the inviolability of Einstein's constant, shakes the very foundations of the theory of relativity ...

In order to somehow protect the authority of the great physicist, researchers from Princeton put forward the assumption that "fast photons" do not cover the distance from the light source to the sensors at all, but seem to disappear in one place and instantly appear in another. That is, there is the so-called effect of zero-transport, or teleportation, about which science fiction writers have written so much in their novels. However, in the course of further verification experiments, it turned out that some photons seem to arrive at their destination even before their source is turned on!

Agree, this fact violates not only the postulates of Einstein's theory of relativity, but also the fundamental ideas about the nature of Time, which, as is commonly believed, flows only in one direction and cannot be turned back.

Only one explanation would be logical here - the "flask" with gaseous cesium works as a kind of "time machine" that sends part of the light photons into the past, which allows them to reach the sensors before the light source was turned on. SO INCREDIBLE EXPERIMENTS of scientists from Princeton could not fail to attract the attention of their colleagues from other research organizations. And not all of them were skeptical about this.

The leaders of the Italian State Research Council said they recently also managed to accelerate microwaves at 25% faster than the speed of light. Therefore, they do not doubt the complete reliability of the message of the Americans. And yet it is still difficult to unequivocally assess the results of the experiments at Princeton, since in reports that appeared in the foreign press, sensational experiments are described only in general terms.

The most likely explanation for them, as has happened more than once, in the end may be an elementary error of devices. But if, say, the sensation is confirmed, then this will help explain other mysterious violations of causal relationships, over which scientists are still struggling in vain. Take, for example, the strange foresight possessed by some living things. So, back in the 1930s. Microbiologist S.T. Velthofer discovered that corynebacteria (unicellular microbes living in the human respiratory tract) begin to actively multiply at certain periods of time (a few days before astronomers record another flash on the Sun).

The essence of the phenomenon is clear: increasing solar radiation (cause) is detrimental to these bacteria, and a defense mechanism is triggered, forcing them to multiply intensively (consequence) in order to preserve the population. Another thing is strange - how do microbes "determine" the time of the solar flare in advance?

The devices did not register any physical precursors that could have warned about solar emission in advance. There is a temporary phenomenon when
the effect is observed before the cause. The existence of “rushing” light photons, reaching the target even before the flash occurs, could explain it. WHILE THE EXPERIMENTS ARE DISCUSSING whether super-high-speed photons may or may not exist, theorists are trying not only to explain the observed phenomena, but also to find practical applications for them.

For example, Sergei Krasnikov, an employee of the Main Astronomical Observatory at Pulkovo, believes that the spacecraft of the near future will be able to move much faster than the speed of light. As is clear from the words of the scientist, he was able to find a kind of "loophole" in the laws of physics, which suggests that even the most remote regions of the Universe can be reached almost instantly if you use the natural tunnels that appeared during the Big Bang - the so-called "mole holes "Connecting the most distant corners of space.

Scientists have been suspecting the existence of such tunnels for a long time. But if earlier many believed that they are only of a tiny diameter (the presence of just such was confirmed, it seems, by experiments at Princeton), then Krasnikov, by his calculations, proves that "molehills" can be of such a solid diameter that large ones can slip through them. spaceships, instantly conquering space and time. Moreover, if we assume that time in these tunnels tends to flow in the opposite direction, then it turns out that the "wormholes" can work simultaneously and "time machines", transferring objects penetrating through them in earlier times!

So the ships jumping out of the "molehills" can simultaneously appear not only thousands of parsecs from our planet, but also millions of years earlier than our era ... Whether this is all or not, further research should show. After all, we still need to find these tunnels and examine them. But the first step in the search, it seems, has already been taken ... Back in 1994, the Russian orbiting X-ray telescope "Granat" detected in space two bursts of radiation emanating from some source of gigantic power. This data was transferred to the International Astronomical Union so that astrophysicists, who have the necessary equipment, track what will follow the unprecedented release of energy.

Traditionally denoted by the Latin letter " c (\ displaystyle c)"(Pronounced as" tse "). The speed of light in a vacuum is a fundamental constant that does not depend on the choice of an inertial reference frame (IFR). It refers to the fundamental physical constants that characterize not just individual bodies or fields, but the properties of the geometry of space-time as a whole. From the postulate of causality (any event can only affect events occurring after it and cannot affect events that occurred before it) and the postulate of the special theory of relativity that the speed of light in vacuum is independent of the choice of an inertial reference frame (the speed of light in vacuum is the same in all coordinate systems moving rectilinearly and uniformly relative to each other) it follows that the speed of any signal and elementary particle cannot exceed the speed of light. Thus, the speed of light in a vacuum is the limiting speed of movement of particles and the propagation of interactions.

In a vacuum (emptiness)

The most accurate measurement of the speed of light 299 792 458 ± 1.2 / based on a reference meter was carried out in 1975.

At the moment, it is believed that the speed of light in a vacuum is a fundamental physical constant, by definition, exactly equal to 299,792,458 m / s, or 1,079,252,848.8 km / h. The accuracy of the value is due to the fact that since 1983 a meter in the International System of Units (SI) has been defined as the distance that light travels in a vacuum for a period of time equal to 1/299 792 458 seconds .

In nature, they propagate at the speed of light (in a vacuum):

Massive particles can have a speed that comes close to the speed of light, but still does not reach it exactly. For example, the near-light speed, only 3 m / s less than the speed of light, is possessed by massive particles (protons) obtained at an accelerator (Large Hadron Collider) or included in cosmic rays. [ ]

In modern physics, it is considered a well-founded statement that a causal effect cannot be transferred at a speed greater than the speed of light in a vacuum (including through the transfer of such an effect by any physical body). There is, however, the problem of "entangled states" of particles, which, apparently, "recognize" each other's state instantly. However, even in this case, superluminal information transmission does not occur, since in order to transmit information in this way it is necessary to involve an additional classical transmission channel with the speed of light.

Although, in principle, the movement of some objects with a speed greater than the speed of light in a vacuum is quite possible, however, from a modern point of view, these can only be such objects that cannot be used to transfer information with their movement (for example, a sunbeam in principle, it can move along a wall at a speed greater than the speed of light, but it cannot in any way be used to transfer information at such a speed from one point of the wall to another).

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In a transparent environment

The speed of light in a transparent medium is the speed with which light travels in a medium other than a vacuum. In a dispersive medium, phase and group velocities are distinguished.

Phase velocity relates the frequency and wavelength of monochromatic light in a medium ( λ = c ν (\ displaystyle \ lambda = (\ frac (c) (\ nu)))). This speed is usually (but not necessarily) less c (\ displaystyle c)... The ratio of the speed of light in a vacuum to the phase speed of light in a medium is called the refractive index of the medium.

The group speed of light is defined as the speed of propagation of beats between two waves with a similar frequency and in an equilibrium medium is always less c (\ displaystyle c)... However, in nonequilibrium media, for example, strongly absorbing media, it can exceed c (\ displaystyle c)... In this case, however, the leading edge of the pulse still moves at a speed that does not exceed the speed of light in vacuum. As a result, superluminal information transmission remains impossible.

The invariance of the speed of light is invariably confirmed by many experiments. It is possible to verify experimentally only that the speed of light in a "two-sided" experiment (for example, from a source to a mirror and back) does not depend on the frame of reference, since it is impossible to measure the speed of light in one direction (for example, from a source to a remote receiver) without additional agreement on how to synchronize the clock of the source and the receiver. However, if we apply Einstein's synchronization for this, the one-way speed of light becomes equal to two-way by definition.

Special theory of relativity explores the consequences of invariance c (\ displaystyle c) under the assumption that the laws of physics are the same in all inertial reference frames. One of the consequences is that c (\ displaystyle c)- this is the speed with which all massless particles and waves (in particular, light) must move in a vacuum.

Special relativity has many experimentally proven consequences that are counterintuitive. Such consequences include: equivalence of mass and energy (E 0 = m c 2) (\ displaystyle (E_ (0) = mc ^ (2))), shortening of length (shortening of objects as they move) and slowing down of time (moving clocks run slower). The coefficient showing how many times the length shortens and the time slows down is known as the Lorentz factor (Lorentz factor)

where v (\ displaystyle v)- the speed of the object. For speeds much less than c (\ displaystyle c)(for example, for the speeds we deal with every day) the difference between γ (\ displaystyle \ gamma) and 1 is so small that it can be neglected. In this case, the special theory of relativity is well approximated by Galileo's relativity. But at relativistic speeds, the difference increases and tends to infinity when approaching v (\ displaystyle v) To c (\ displaystyle c).

Combining the results of special relativity requires two conditions to be met: (1) space and time are a single structure known as spacetime (where c (\ displaystyle c) connects the units of measurement of space and time), and (2) physical laws satisfy the requirements of a special symmetry, which is called Lorentz invariance (Lorentz invariance), the formula of which contains the parameter c (\ displaystyle c)... Lorentz invariance is ubiquitous in modern physical theories such as quantum electrodynamics, quantum chromodynamics, the standard model of particle physics, and general relativity. So the parameter c (\ displaystyle c) occurs throughout modern physics and appears in many senses that have nothing to do with light itself. For example, general relativity suggests that gravity and gravitational waves travel at a speed c (\ displaystyle c)... In non-inertial frames of reference (in gravitationally curved space or in frames of reference moving with acceleration), the local speed of light is also constant and equal to c (\ displaystyle c), however, the speed of light along a path of finite length may differ from c (\ displaystyle c) depending on how space and time are defined.

It is believed that fundamental constants such as c (\ displaystyle c), have the same meaning in all space-time, that is, they do not depend on the place and do not change with time. However, some theories suggest that the speed of light can change over time. So far, there is no conclusive evidence of such changes, but they remain the subject of research.

In addition, it is believed that the speed of light is isotropic, that is, it does not depend on the direction of its propagation. Observations of the radiation of nuclear energy transitions as a function of the orientation of nuclei in a magnetic field (the Gugs-Drever experiment), as well as of rotating optical resonators (the Michelson-Morley experiment and its new variations), imposed severe restrictions on the possibility of bilateral anisotropy.

Event A precedes event B in the red frame of reference (CO), simultaneously with B in green CO and occurs after B in blue CO

In general, information or energy cannot travel faster in space than at the speed of light. One argument for this comes from the counterintuitive conclusion of special relativity, known as the relativity of simultaneity. If the spatial distance between two events A and B is greater than the time interval between them multiplied by c (\ displaystyle c), then there are such frames of reference in which A precedes B, and others in which B precedes A, as well as those in which events A and B are simultaneous. As a result, if an object would move faster than the speed of light relative to some inertial frame of reference, then in another frame of reference it would travel back in time, and the principle of causality would be violated. In such a frame of reference, the "effect" could be observed before its "root cause". This violation of causality has never been observed. It can also lead to paradoxes such as the tachyon anti-telephone.

History of light speed measurements

Ancient scientists, with rare exceptions, considered the speed of light to be infinite. In modern times, this issue has become the subject of discussion. Galileo and Hooke assumed that it was finite, although very large, while Kepler, Descartes and Fermat still defended the infinity of the speed of light.

Half a century later, in 1728, the discovery of aberration allowed J. Bradley to confirm the finiteness of the speed of light and to refine its estimate: the value obtained by Bradley was 308,000 km / s.

For the first time measurements of the speed of light, based on the determination of the time of passage by light of an accurately measured distance in terrestrial conditions, were carried out in 1849 by A. I. L. Fizeau. In his experiments, Fizeau used the "interruption method" developed by him, while the distance covered by the light was 8.63 km. The value obtained as a result of the performed measurements turned out to be equal to 313,300 km / s. Subsequently, the interruption method was significantly improved and used for measurements by M.A.Cornu (1876), A.J. Perroten (1902) and E. Bergstrand... Measurements carried out by E. Bergstrand in 1950 gave a value of 299,793.1 km / s for the speed of light, while the measurement accuracy was increased to 0.25 km / s.

Another laboratory method (the "rotating mirror method"), the idea of ​​which was expressed in 1838 by F. Arago, was implemented in 1862 by Leon Foucault. Measuring short periods of time using a mirror rotating at a high speed (512 rev / s), he obtained the value of 298,000 km / s for the speed of light with an error of 500 km / s. The length of the base in Foucault's experiments was relatively short - twenty meters. Subsequently, due to the improvement of the experimental technique, an increase in the used base and a more accurate determination of its length, the measurement accuracy using the rotating mirror method was significantly increased. So, S. Newcomb in 1891 received the value of 299 810 km / s with an error of 50 km / s, and A. A. Michelson in 1926 managed to reduce the error to 4 km / s and obtain the value of 299 796 km / s for the speed. In his experiments, Michelson used a base equal to 35,373.21 m.

Further progress was associated with the appearance of masers and lasers, which are distinguished by very high stability of the radiation frequency, which made it possible to determine the speed of light by simultaneously measuring the wavelength and frequency of their radiation. In the early 1970s, the error in measuring the speed of light approached 1 m / s. After checking and agreeing the results obtained in various laboratories, the XV General Conference on Weights and Measures in 1975 recommended using the value of the speed of light in vacuum as a value equal to 299 792 458 m / s, with a relative error (uncertainty) of 4 10 - 9, which corresponds to an absolute error of 1.2 m / s.

It is significant that a further increase in the measurement accuracy became impossible due to circumstances of a fundamental nature: the limiting factor was the magnitude of the uncertainty in the implementation of the definition of the meter, which was in force at that time. Simply put, the main contribution to the error in measuring the speed of light was made by the error in the "manufacture" of the standard meter, the relative value of which was 4 · 10 -9. Based on this, and also taking into account other considerations, the XVII General Conference on Weights and Measures in 1983 adopted a new definition of the meter, based on the previously recommended value of the speed of light and defining the meter as the distance that light travels in a vacuum for a period of time equal to 1/299 792 458 seconds .

Superluminal motion

It follows from the special theory of relativity that the excess of the speed of light by physical particles (massive or massless) would violate the principle of causality - in some inertial reference frames, it would be possible to transmit signals from the future to the past. However, the theory does not exclude for hypothetical particles that do not interact with ordinary particles, motion in space-time with superluminal speed.

Hypothetical particles moving at faster than light speed are called tachyons. Mathematically, the movement of tachyons is described by the Lorentz transformations as the movement of particles with an imaginary mass. The higher the speed of these particles, the less energy they carry, and vice versa, the closer their speed is to the speed of light, the more their energy - just like the energy of ordinary particles, the energy of tachyons tends to infinity when approaching the speed of light. This is the most obvious consequence of the Lorentz transformation, which does not allow a massive particle (with both real and imaginary mass) to reach the speed of light - it is simply impossible to impart an infinite amount of energy to the particle.

It should be understood that, firstly, tachyons are a class of particles, and not one kind of particles, and secondly, tachyons do not violate the principle of causality if they do not interact with ordinary particles in any way.

Ordinary particles that travel slower than light are called tardions. Tardions cannot reach the speed of light, but only come as close to it as they like, since in this case their energy becomes infinitely large. All tardions have mass, in contrast to massless particles called luxons. Luxons in a vacuum always move at the speed of light, these include photons, gluons, and hypothetical gravitons.

Since 2006, it has been shown that in the so-called quantum teleportation effect, the apparent mutual influence of particles propagates faster than the speed of light. For example, in 2008, the research team of Dr. Nicolas Gisin from the University of Geneva, examining entangled photon states separated by 18 km in space, showed that this seeming “interaction between particles occurs at a speed of about a hundred thousand times the speed Sveta". The so-called “ Hartmann's paradox»Is the apparent superluminal speed in the tunnel effect. An analysis of these and similar results shows that they cannot be used for the superluminal transmission of any message carrying information or for the movement of matter.

As a result of processing the data of the OPERA experiment, collected from 2008 to 2011 at the Gran Sasso laboratory in conjunction with CERN, a statistically significant indication of the excess of the speed of light by muon neutrinos was recorded. This announcement was accompanied by publication in the archive of preprints. Experts questioned the results obtained, since they do not agree not only with the theory of relativity, but also with other experiments with neutrinos. In March 2012, independent measurements were carried out in the same tunnel, and they did not detect superluminal neutrino velocities. In May 2012, OPERA conducted a series of control experiments and came to the final conclusion that the reason for the erroneous assumption about superluminal speed was a technical defect (poorly inserted optical cable connector).

see also

Comments (1)

1. From the surface of the Sun - from 8 min. 8.3 sec. at perihelion up to 8 min. 25 sec. in aphelion.
2. The speed of propagation of a light pulse in a medium differs from the speed of its propagation in a vacuum (less than in a vacuum), and can be different for different media. When one speaks simply of the speed of light, it is usually the speed of light in a vacuum that is meant; if one speaks of the speed of light in a medium, this, as a rule, is stipulated explicitly.
3. Currently, the most accurate methods for measuring the speed of light are based on the independent determination of wavelength values. λ (\ displaystyle \ lambda) and frequencies ν (\ displaystyle \ nu) light or other electromagnetic radiation and subsequent calculation in accordance with the equality c = λ ν (\ displaystyle c = \ lambda \ nu).
4. See Oh-My-God Particle as an example.
5. An analogy could be sending at random two sealed envelopes with white and black paper to different places. Opening one envelope ensures that the second will contain the second sheet - if the first is black, then the second is white, and vice versa. This "information" can travel faster than the speed of light - after all, you can open the second envelope at any time, and there will always be this second sheet. In this case, the fundamental difference with the quantum case is only in the fact that in the quantum case, before the “opening of the envelope” measurement, the state of the leaf inside is fundamentally indeterminate, like in Schrödinger's cat, and any leaf can be there.
6. However, the frequency of the light depends on the movement of the light source relative to the observer, thanks to the Doppler effect.
7. While moving measurement objects appear shorter along the line of relative motion, they also appear to be rotated. This effect, known as Terrell's rotation, is associated with the time difference between the signals that came to the observer from different parts of the object.
8. It is believed that the Scharnhorst effect allows signals to propagate slightly higher c (\ displaystyle c), but the special conditions under which the effect can occur make it difficult to apply this effect to violate the principle of causality

Notes (edit)

1. . Voyager - The Interstellar Mission... Jet Propulsion Laboratory, California Istitute of Technology. Retrieved July 12, 2011. Archived February 3, 2012.
2. New galaxy "most distant" yet discovered
3. , With. 169.
4. , With. 122.
5. Chudinov E. M. Theory of relativity and philosophy. - M .: Politizdat, 1974 .-- S. 222-227.
6. , With. 167.
7. , With. 170.
8. , With. 184.
9. Sazhin M.V. The speed of light // Physics of space. Little encyclopedia / Ch. ed. R. A. Sunyaev. - 2nd ed. - M.: Soviet Encyclopedia, 1986 .-- P. 622 .-- 783 p.
10. GOST 8.417-2002. State system for ensuring the uniformity of measurements. Units of quantities.
11. Abbott B. P. et al. (LIGO Scientific Collaboration, Virgo Collaboration, Fermi Gamma-ray Burst Monitor, and INTEGRAL). Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A // The Astrophysical Journal. - 2017. - Vol. 848. - P. L13. - DOI: 10.3847 / 2041-8213 / aa920c.[to correct ]
12. Bolotovsky B.M., Ginzburg V.L.// Phys. - 1972. - T. 106, No. 4. - S. 577-592.
13. Stachel, JJ. Einstein from "B" to "Z" - Volume 9 of Einstein studies. - Springer, 2002. - P. 226. - ISBN 0-8176-4143-2.
14. Einstein, A (1905). Zur Elektrodynamik bewegter Körper (German). Annalen der Physik 17 : 890-921. DOI: 10.1002 / andp.19053221004. English translation: Perrett, W On the Electrodynamics of Moving Bodies. Fourmilab... Retrieved November 27, 2009. Archived February 1, 2013.
15. Alexandrov E. B. Theory of Relativity: Direct Experiment with a Curved Beam // Chemistry and Life. - 2012. - No. 3.
16. Hsu, J-P. Lorentz and Poincaré Invariance / J-P Hsu, Zhang. - World Scientific, 2001. - Vol. 8. - P. 543 ff... - ISBN 981-02-4721-4.
17. Zhang, YZ. Special Relativity and Its Experimental Foundations. - World Scientific, 1997. - Vol. 4. - P. 172–3. - ISBN 981-02-2749-3.
18. d "Inverno, R. Introducing Einstein's Relativity. - Oxford University Press, 1992. - P. 19-20. - ISBN 0-19-859686-3.
19. Sriranjan, B. Postulates of the special theory of relativity and their consequences // The Special Theory to Relativity. - PHI Learning, 2004. - P. 20 ff... - ISBN 81-203-1963-X.
20. Roberts, T What is the experimental basis of Special Relativity? ... Usenet Physics FAQ... University of California, Riverside (2007). Retrieved November 27, 2009. Archived February 1, 2013.
21. Terrell, J (1959). Invisibility of the Lorentz Contraction. Physical Review 116 (4): 1041-5. DOI: 10.1103 / PhysRev. 116.1041. Bibcode: 1959PhRv..116.1041T.
22. Penrose, R (1959). "The Apparent Shape of a Relativistically Moving Sphere." Proceedings of the Cambridge Philosophical Society 55 (01): 137-9. DOI: 10.1017 / S0305004100033776. Bibcode: 1959PCPS ... 55..137P.
23. Hartle, JB. Addison-Wesley, 2003. P. 52-9. - ISBN 981-02-2749-3.
24. Hartle, JB. Gravity: An Introduction to Einstein's General Relativity. - Addison-Wesley, 2003. - P. 332. - ISBN 981-02-2749-3.
25. The interpretation of observations on binary systems used to determine the speed of gravity is considered doubtful by some authors, leaving the experimental situation uncertain; see Schäfer, G. Propagation of light in the gravitational filed of binary systems to quadratic order in Newton "s gravitational constant: Part 3: 'On the speed-of-gravity controversy' // Lasers, clocks and drag-free control: Exploration of relativistic gravity in space / G Schäfer, Brügmann - Springer, 2008 - ISBN 3-540-34376-8.
26. Gibbs, P Is The Speed ​​of Light Constant? ... Usenet Physics FAQ... University of California, Riverside (1997). Retrieved November 26, 2009. Archived November 17, 2009.

SUPER LIGHT SPEED

A speed faster than the speed of light. relativity theory, the transmission of any signals and movement of material bodies cannot occur at a speed greater than the speed of light in a vacuum With. However, everyone is shaken. the process is characterized by two different propagation velocities: group velocity = and phase velocity , where w p k - frequency and wave vector of the wave. u gr determines the rate of energy transfer by a group of waves with close frequencies. Therefore, in accordance with the principle of relativity, u gr any fluctuate. With. On the contrary, w phases, k-raycharacterizes the speed of propagation of the phase of each monochromatic. component of this group of waves is not associated with the transfer of energy in the wave. Therefore, it can take any values, in particular, values> With. In the latter case, they speak of her as S. with.

The simplest example of S. with. Is the phase velocity of propagation of an electric magnet. , where k z - projection of the wave vector fc onto the waveguide axis z. The wave vector fc is related to frequency with the relation k 2 = w 2 / s 2, where , a is the projection of the wave vector k onto the cross section of the waveguide z= const. Then the w phases of the wave along the waveguide axis

there will be more s, a

less With.

Let us give one more example of the existence of S. with. If you rotate the electron beam with the help of an appropriate electron gun around a certain axis of the angle. velocity, then the linear velocity of the spot from the electron beam at sufficiently large distances R the speed of light may increase from the axis. However, the movement of the electron spot from the gun along a circle of radius R 0 with velocity is equivalent to the movement of the beam phase in space. In this case, the beam energy is transferred in the radial direction and the transfer rate cannot increase With.

When a signal propagates in a medium with a refractive index P wavevector fc electromagnet wave and its frequency satisfy the relation In this case, u phases = s / n. For environment with P< 1and phasesWith. An example of such a medium is fully ionized plasma, at a swarm, where e and T - the charge and mass of the electron, and N - the density of electrons in the plasma. In an environment with P 1 >u phases = s / n< с. However, in this case, real movement of material particles with a speed v, greater speed of light in the medium (i.e. The movement is charged. particles with such a speed ( vs / n, but v< с!) приводит к возникновению Cherenkov - Vavilov radiation.

Lit .: Vainshtein L.A., Electromagnetic waves, 2nd ed., M., 1988; Ginzburg V.L., Theoretical physics and astrophysics, 3rd ed., M., 1987; Bolotovsky B. M., Bykov V.P., Radiation at superluminal motion of charges, "UFN", 1990, v. 160. v. 6, p. 141. S. Ya. Stolyarov.

• - a physical concept denoting the path traversed by Ph.D. a moving body per unit of time, for example. in 1 sec. Usually, the average C is taken, which is the result of the addition of all marked Cs at different times and division ...

  Agricultural dictionary-reference

• - it is impossible, according to the special theory of relativity, for particles that actually exist and have rest mass, but it is possible as a phase velocity in any medium, or as the speed of any particle in a medium, ...
• - one of the main kinematic characteristics of the movement of material bodies, numerically equal to the value of the path traveled per unit of time ...

  Beginnings of Modern Natural Science

• - one of the main characteristics of the movement of a material point ...

  Astronomical Dictionary

• - 1983, 93 min., Color, sh / e, sh / f, 1to. genre: drama ...

  Lenfilm. Annotated Film Catalog (1918-2003)

• - numerically equal to the distance traveled by the ship per unit of time; determined by lag. For surface ships are distinguished: the largest; full; economic; the smallest ...

  Dictionary of military terms

• - the degree of duration of the carriage of goods by rail ...
• - see small ...

  Reference commercial vocabulary

• - the characteristic of the translational motion of a point, which is numerically equal, with uniform motion, to the ratio of the distance traveled s to the intermediate time t, that is, v = s / t. With the rotational movement of the body, they use the concept ...

  Modern encyclopedia

• - the characteristic of the movement of a point, numerically equal to the ratio of the distance traveled s to the time interval t for uniform movement, i.e. v = s / t. The vector S. is directed tangentially to the trajectory of the body. When they rotate ....

  Natural science. encyclopedic Dictionary

• -: See also: - rate of chemical reaction - rate of sintering - rate of deformation - rate of deformation - speed of drawing - critical rate of hardening - rate of heating - rate of thermal ...

  Encyclopedic Dictionary of Metallurgy

• Big Dictionary of Economics

• - the degree of speed of movement, the spread of action ...

  Big accounting dictionary

• - - The concept of S. is derived from the concepts of average S. in the way and average S. of movement ...

  Encyclopedic Dictionary of Brockhaus and Euphron

• - I Velocity in mechanics, one of the main kinematic characteristics of a point's movement, which is numerically equal to the ratio of the distance traveled s to the time interval t during uniform movement, during which this path ...

  Great Soviet Encyclopedia

• - the characteristic of the movement of a point, numerically equal to the ratio of the distance traveled s to the time interval t for uniform movement, i.e.? = s / t. When the body rotates, the concept of angular velocity is used ...

  Big encyclopedic dictionary

SUPER LIGHT SPEED in books

Type Speed