# Faster than light

About light speed is a speed which is greater than the natural constant speed of light is. This is also called superluminar .

## General

A point of light projected by a rotating mirror onto a sufficiently distant wall moves faster than light there. But only the illuminated place moves, while no wave and no matter moves faster than light.

Whether matter or information can also move or spread faster than light ( superluminous , space-like ) in a vacuum is a question that the overwhelming majority of physicists denied, but has not yet been conclusively clarified. In principle, it does not depend on whether an object moves faster than light, but on whether a causal relationship can exist between two space-time points that are so far spatially or so briefly temporally separated that there is only a connection between them could be achieved by faster than light. This includes e.g. B. also the situation of an object that suddenly disappears in one place before it reappears a light year away after less than a year. In classical Newtonian mechanics , objects can be accelerated at will. Since the theory does not set any limits, the speed of light could also be exceeded. However, Newton's mechanics only applies approximately to sufficiently small velocities (v ≪ c). At higher speeds, on the other hand, relativistic effects occur that prevent the speed of light from being exceeded.

In science fiction books and films, journeys faster than light are often portrayed as reality, because otherwise interstellar journeys would take far too long from a dramaturgical point of view. The same applies to communication between two stations or spaceships. In these stories, the data transmission almost always takes place without a time delay, even if the spaceships are light years apart and therefore, according to current scientific knowledge, any information would need at least the corresponding time for the distance from the transmitter to the receiver.

The television images of the moon landings , on the other hand, only took 1.3 seconds to make their way to earth , communication between the earth and Mars, for example, takes between three and 22 minutes, depending on the position of the two planets.

The distinction between the speed of light above and below the speed of light is absolute within the framework of the theory of relativity : A process that takes place in a frame of reference with speed of light takes place in every frame of reference with speed of light, the same also applies to speed of light below. The mathematical background is the non-existence of a Lorentz transformation that transforms time- like vectors into space-like vectors. So you can z. For example, you cannot simply reach the speed of light above the earth's speed by first firing a rocket at ¾ the speed of light from the earth, and from this rocket a rocket that in turn is flying at ¾ the speed of light relative to it is launched. Due to the relativity of simultaneity , relative speeds cannot simply be added, as is still the case with the low speeds of everyday life. Instead, the relativistic addition theorem for speeds results in the following for the total speed :

${\ displaystyle v _ {\ mathrm {ges}} = {\ frac {v_ {1} + v_ {2}} {1 + {\ frac {v_ {1} \ cdot v_ {2}} {c ^ {2} }}}}}$

Accordingly, in the example the second rocket only moves away from the earth at 0.96  c (the 0.75 c to the first rocket are unaffected). From the principle of the constancy of the speed of light it follows that an acceleration of a mass-laden body to the speed of light would require an infinite amount of energy.

There are a few observations that at first glance seem to confirm superluminal movements:

1. For some years now, jets have been observed in the universe that appear to be superluminous from their place of origin. However, this is only an optical effect, in truth the jets are moving at less than the speed of light.
2. At the University of Cologne , which has meanwhile been checked several times by other institutions, it has been proven that the quantum mechanical tunneling of photons can lead to effects that some researchers interpret as superluminal velocities. However, the interpretations of these observations are currently still controversial.
3. When measuring quantum mechanically entangled particles, information seems to be transmitted instantaneously between the particles (i.e. without a time difference) (Einstein-Podolsky-Rosen effect, or EPR effect for short ). However, it is not possible to use this effect for communication at faster than light speeds.
4. In September 2011, the OPERA collaboration at Gran Sasso reported that they had found indications that neutrinos had moved faster than light. However, a new measurement by ICARUS showed agreement with the speed of light, whereby the OPERA result is very likely to be refuted. See Neutrino Velocity Measurements for more details .

However, within a medium, matter particles can move faster than light, that is, faster than electromagnetic waves within the same medium. This creates Cherenkov radiation . However, the speed of light in a vacuum is not exceeded.

## Tachyons

Superluminal velocities are not categorically excluded by the equations of the theory of relativity, only the change between above and below light speed is not possible in any direction. Theoretically, a superluminar particle could exist, a tachyon , which only moves superluminar and has an imaginary mass. However, it has a lot of paradoxical properties, for example it accelerates ("runaway solution") if it loses energy through radiation (with charged accelerated tachyons), so that it is difficult to construct a theory of interacting tachyons. The idea of ​​tachyons with formally "imaginary mass" was first expressed in the 1960s by George Sudarshan and others. However, if you look at tachyons from a quantum mechanical point of view, you will see that even these local disturbances cannot spread faster than light.

## Apparently faster than light objects in astronomy

Some jets , such as those emitted by quasars , appear to move superluminarly due to an observation effect. This generally happens when an object approaches an observer and has a speed of at least 70.7% the speed of light. For example, a jet of quasar 3C 273 observed between 1977 and 1980 moved at what appears to be eleven times the speed of light.

The possibility of this apparent faster than light speed was already discussed by Martin Rees in 1966 . In 1970 the phenomenon was observed.

### Theoretical consideration

A quasar in the distance ejects a jet with a bright knot at the time . The knot moves with the speed at the angle to the direction to the earth. ${\ displaystyle r_ {0}}$${\ displaystyle t = 0}$${\ displaystyle v}$${\ displaystyle \ theta}$

Actual movement

Representation of the movement of a jet

After the time has elapsed , the node will be in a place far from the quasar. ${\ displaystyle t_ {0}}$${\ displaystyle \ xi}$${\ displaystyle vt_ {0}}$

In the direction of the earth he has then to the route

${\ displaystyle \ Delta x = vt_ {0} \, \ cos (\ theta)}$

moved towards the observer. He has the transversal route

${\ displaystyle \ Delta y = vt_ {0} \, \ sin (\ theta)}$

covered.

Apparent movement The observer sees the knot at the quasar appear after the light has traversed the distance , i.e. at the point in time ${\ displaystyle r_ {0}}$

${\ displaystyle t_ {1} = {\ frac {r_ {0}} {c}}}$.

The observer sees the node at the point when the light emitted there at the time has covered the remaining distance to the observer. Since the jet is only observed in close proximity to the quasar, the light path from the observer is practically parallel to the direction of observation of the quasar. Thus its distance to the observer is ${\ displaystyle \ xi}$${\ displaystyle t_ {0}}$${\ displaystyle \ xi}$

${\ displaystyle R = r_ {0} - \ Delta x}$.

The light from the node reaches the observer at after time ${\ displaystyle \ xi}$

{\ displaystyle {\ begin {aligned} t_ {2} & = t_ {0} + {\ frac {R} {c}} \\ & = t_ {0} + {\ frac {r_ {0} - \ Delta x} {c}} \\ & = t_ {0} + {\ frac {r_ {0} -vt_ {0} \, \ cos (\ theta)} {c}} \ end {aligned}}}.

Time passes between the observation of the emission in the nucleus and the observation of the reaching of${\ displaystyle \ xi}$

{\ displaystyle {\ begin {aligned} \ Delta t & = t_ {2} -t_ {1} \\ & = t_ {0} + {\ frac {r_ {0} -vt_ {0} \, \ cos (\ theta)} {c}} - {\ frac {r_ {0}} {c}} \\ & = t_ {0} - {\ frac {vt_ {0} \, \ cos (\ theta)} {c} } \\ & = t_ {0} (1- \ beta \, \ cos (\ theta)) \ end {aligned}}},

with . ${\ displaystyle \ beta = v / c}$

For the apparent transverse speed we find with it ${\ displaystyle {\ tilde {v}}}$

{\ displaystyle {\ begin {aligned} {\ tilde {v}} & = {\ frac {\ Delta y} {\ Delta t}} \\ & = {\ frac {vt_ {0} \, \ sin (\ theta)} {t_ {0} (1- \ beta \, \ cos (\ theta))}} \\ & = {\ frac {\ sin (\ theta)} {1- \ beta \, \ cos (\ theta)}} \ cdot v \ end {aligned}}}

or with ${\ displaystyle {\ tilde {\ beta}} = {\ tilde {v}} / c}$

${\ displaystyle {\ tilde {\ beta}} = {\ frac {\ beta \, \ sin (\ theta)} {1- \ beta \, \ cos (\ theta)}}}$.

Example: For and results , thus apparently 11 times the speed of light. ${\ displaystyle \ beta = 0 {,} 996}$${\ displaystyle \ theta = 6 ^ {\ circ}}$${\ displaystyle {\ tilde {\ beta}} = 11}$

### Condition for observation of superluminality

The movement appears superluminous when is, i.e. when ${\ displaystyle {\ tilde {\ beta}}> 1}$

${\ displaystyle {\ frac {\ beta \, \ sin (\ theta)} {1- \ beta \, \ cos (\ theta)}}> 1}$.

Rearranging results

${\ displaystyle {\ frac {1} {\ beta}} <\ sin (\ theta) + \ cos (\ theta)}$,

and after trigonometric transformation of the right side:

${\ displaystyle {\ frac {1} {\ beta}} <{\ sqrt {2}} \ cos (\ theta - \ pi / 4)}$.

Because of must apply ${\ displaystyle \ beta <1}$

${\ displaystyle {\ sqrt {2}} \ cos (\ theta - \ pi / 4)> 1}$,

that's the case for

${\ displaystyle 0 \ leq \ theta <\ pi / 2 = 90 ^ {\ circ}}$.

Every jet that has a component directed towards the observer can therefore give the impression that it is moving transversely at faster than light speed. The smallest jet speed in relation to its source at which this effect can occur results from the maximum value of . This is the case at an angle of . In these circumstances it is sufficient if the jet speed meets the condition: ${\ displaystyle {\ sqrt {2}} \ cos (\ theta - \ pi / 4)}$${\ displaystyle \ theta = 45 ^ {\ circ}}$${\ displaystyle v _ {\ text {Jet}}}$

${\ displaystyle v _ {\ text {Jet}} \, \ geq \, {\ frac {c} {\ sqrt {2}}} \, \ approx \, 0 {,} 71 \, c}$.

Where is the speed of light. ${\ displaystyle c}$

## Superlight effects in quantum mechanics

### Superluminous tunneling

At the University of Cologne was under the direction of Günter Nimtz the quantum mechanical effect of Superluminaren tunneling of microwave - photons , which the tunnel effect underlies when first detected.

Experiments of the Nimtz type with photons of different wavelengths, especially with visible light, have been carried out by other groups and have confirmed the observations of Nimtz (including Steinberg and Raymond Chiao from the University of Berkeley ), but are interpreted differently by experimenters such as Chiao and Steinberg . In all experiments it is found that a superluminal speed is established when there is a barrier between the source and the detector , which the photons first have to overcome (tunnel through).

In 1994, part of a Mozart symphony was broadcast there in a media -effective manner using frequency-modulated microwaves , whereby Nimtz, according to his own statements, measured 4.7 times the speed of light for the maximum and the leading edge of the wave packet. Nimtz claims to have shown the possibility of transmitting information at faster than light speed, but this has been denied. If the speed of information transfer is defined by the response time of a detector, there is no information transfer with faster than light speed: A detector on a comparative distance of the same length without a "tunnel", on which the same information (pulse shape) propagates at the speed of light, responds first because that Signal on the tunnel section is much weaker regardless of the sensitivity of the detector.

According to the general opinion, these experiments are in full agreement with one of the basic statements of the theory of relativity, according to which no information propagation takes place at a speed faster than light. So you can z. B. show that a wave train is more attenuated in the rear part than in the front part when tunneling, so that its maximum intensity is shifted to the front. If the position of the maximum is defined as the position of the wave train, a faster than light speed can be calculated without any part of the wave train having advanced faster than light.

In tunnel experiments with single photons, tunneling faster than light has already been demonstrated, see, for example, experiments by the Chiao group. However, since a large part of the tunneling photons and thus the information is lost during tunneling, the possibility of faster information transmission than light is also controversial here, see also this bibliography.

Other physicists, for example in the review article by Privitera et al., Point out that the superluminality of what is happening is an artifact of the definition of speed used. For example , Léon Brillouin and Arnold Sommerfeld knew that the group speed of pulses in media with strong absorption and dispersion can be greater than the speed of light, but is not a signal speed . Horst Aichmann and Günter Nimtz, on the other hand, defend their interpretation of the experiments that superluminal signal speeds can actually occur during the tunnel process, and accuse their critics of misinterpretations.

### EPR effect

Another phenomenon that at first glance suggests the occurrence of superluminal speed is the EPR effect: If you have two entangled particles in different places, quantum mechanics predicts that, on the one hand, the state of each individual particle is indefinite before the measurement ( the value of the measured variable is therefore not fixed), on the other hand, after the measurement of one particle, the state of the other particle is also determined immediately . This property of quantum mechanics, rejected by Einstein as a “spooky action at a distance ”, has been experimentally confirmed. However, the EPR effect cannot be used to communicate faster than light, as the individual measurement results taken individually are random. The correlation can only be determined when the measurement results on both particles are compared . For this, however, a “classic”, sublight-fast information transmission is first necessary. For example, quantum teleportation is based on this combination of the EPR effect and subsequent classically transmitted information .

In the early 1980s, Nick Herbert proposed an experiment in which information in quantum mechanics could be transmitted at faster than light speed, if it were possible to produce perfect quantum copiers. As Wojciech Zurek and William Wootters showed shortly afterwards in 1982, however, such copiers are fundamentally impossible ( no-cloning theorem ).

Whether information is transmitted at all with the EPR effect is controversial and depends very much on the interpretation of quantum mechanics and the concept of information . One interpretation is that the particles contain additional information in hidden variables, i.e. H. non-measurable properties that control the correlation. However, it can be shown that the measurement results would then have to obey certain statistical rules, Bell's inequalities . Violation of these inequalities has been confirmed experimentally. Other attempts at explanation also consider time-reversed causal relationships for quantum mechanical systems.

## Time travel

According to the special theory of relativity , faster than light speed would enable time travel or at least in the form of an anti-telephony the sending of messages into the past. The connection between the speed of lightning and time travel can be derived from the properties of the Lorentz transformation in the Minkowski diagram . Because of the resulting paradoxes, the possibility of time travel in physical theories is mostly excluded. Without additional assumptions, the equations of general relativity do not forbid time travel, as Kurt Gödel first showed.

## Superluminal speed in cosmology

### Speed ​​above light due to the expansion of space

The light spectrum of most galaxies has a red shift on. Edwin P. Hubble initially interpreted this shift as a Doppler effect . This means that the respective galaxy is moving away from the earth at a considerable speed . When comparing the redshift of galaxies with a known distance to Earth, Hubble found a linear relationship. This is Hubble's law with the Hubble constant . According to this law, galaxies should travel faster than the speed of light from Earth if they are far enough away. ${\ displaystyle v}$${\ displaystyle d}$${\ displaystyle v = H_ {0} \, d}$ ${\ displaystyle H_ {0}}$

The interpretation of the cosmological redshift attributes this to the increase in distances as a result of the expansion of the universe , not to the Doppler effect. In the context of relativistic cosmology, Hubble's law is valid for any distance if it is interpreted as a physical distance (distance to a fixed point in time) and as the change in this distance over time. can be greater than the speed of light, which is sometimes seen as a contradiction to the theory of relativity and used as a counter-argument to the big bang theory. Conceptually, however, the rate of change in distance must not be confused with a speed. Velocities are local quantities that are subject to the restrictions of the special theory of relativity. As global variables, changes in distance are not subject to these restrictions and can be of any size. Real faster than light velocities are therefore not available even in distant galaxies. ${\ displaystyle d}$${\ displaystyle v}$${\ displaystyle v = {\ dot {d}}}$${\ displaystyle {\ dot {d}}}$

### Cosmological theories with variable speed of light

Various cosmological theories with a variable speed of light (VSL) have been proposed. In particular, a proposal by João Magueijo and Andreas Albrecht from 1999 became known, in which the horizon problem and the problem of the flatness of the universe, which are usually explained today in the context of the inflationary model of cosmology, are instead represented by a speed of light that is up to 60 orders of magnitude higher in the early universe to be explained. In this theory, the speed of light is a dynamic variable, i.e. it changes over time, but in a special way that does not modify the form of the field equations of general relativity too much. The Lorentz invariance of the theory is broken explicitly, there is an excellent reference system (which is given by the cosmological expansion). According to Magueijo and Albrecht, the problem of the cosmological constant is also solved in this way. Magueijo also wrote a popular science book about it. The Canadian physicist John Moffat made a similar proposal in 1992 , also with the intention of solving cosmological problems. The idea of ​​the variable speed of light was taken up by Köhn and combined with the concept of several time dimensions. He showed that the speed of light in such spacetime depends on time. However, this time dependence is negligible for the observable universe, so that the speed of light appears constant in the current universe, whereas it was variable in the early universe, as originally proposed by Albrecht and Magueijo.

The theory stands in the tradition of time-changing fundamental (dimensionless) physical quantities that have been discussed since Dirac . It makes sense to only discuss the variability of dimensionless quantities, since the variability of dimensional quantities in physics depends on the units of measurement used and therefore has no fundamental significance. In the case of the VSL theories, the fine structure constant is variable, which in principle should be observable as a function of the redshift for distant objects.

### Wormholes

A related effect is the crossing of so-called wormholes , which is often used in science fiction novels. A spaceship does not move faster than the speed of light locally, but it takes a shortcut in curved space so that in the end it arrives at its destination faster than the light. As a two-dimensional analogy, one can look at the path over a folded sheet of paper. Instead of staying on the paper, a traveler can simply drill a hole in the paper and use it to reach the other side that has been folded over. Time machines would also be conceivable with this technology. While such wormholes can be constructed theoretically in the theory of relativity, it appears that in practice they would be very unstable, so that not even information could be passed through them.

### Hyperspace

The idea of ​​an abbreviation through hyperspace , in which our spacetime could be embedded, would have a comparable effect, which is also often used in science fiction . The idea is as follows: To shorten the path from the North Pole to the South Pole, travel across the earth instead of along the surface. The way through the earth (via the third dimension) is shorter than the way on the (two-dimensional) earth's surface. In the same way, one could imagine that our spacetime is also embedded in a higher-dimensional hyperspace (like the earth's surface in space), and could therefore be shortened through hyperspace. Here, too, you would not have to fly faster than the speed of light (in hyperspace) to arrive at the destination faster than light in normal space.

## Others

The use of the English term FTL (for faster than light) goes back to the 1950s. In Breakthrough Propulsion Physics Program of NASA concepts and theories were evaluated for superluminal.

## literature

• Kirk T. McDonald: Radiation from a Superluminal Source . Princeton University, Princeton. NJ 08544, November 26, 1986, arxiv : physics / 0003053 .
• Ernst Udo Wallenborn: What is the Nimtz experiment? theorie.gsi.de, June 23, 1999.
• Rüdiger Vaas: Tunnel through space and time , Franckh-Kosmos, Stuttgart 2006 (2nd edition), ISBN 3-440-09360-3 .
• João Magueijo: Faster than the speed of light - the draft of a new cosmology. Bertelsmann, Munich 2003, ISBN 3-570-00580-1 .
• Günter Nimtz (et al.): Zero time space - how quantum tunneling broke the light speed barrier. Wiley-VCH, Weinheim 2008, ISBN 978-3-527-40735-4 .
• Michio Kaku : Faster than Light; in Physics of the Impossible. Pp. 197-215, Allen Lane, London 2008, ISBN 978-0-7139-9992-1 . German: The physics of the impossible. Rowohlt, Reinbek 2008, ISBN 978-3-498-03540-2 .
• John G. Cramer: Faster-than-Light Implications of Quantum Entanglement and Nonlocality. S 509-529, in Marc G. Millis (et al.): Frontiers of Propulsion Science. American Inst. Of Aeronautics & Astronautics, Reston 2009, ISBN 1-56347-956-7 .
• Moses Fayngold: Special relativity and motions faster than light. Wiley-VCH, Weinheim 2002, ISBN 3-527-40344-2 .
• Nick Herbert Faster than light- superluminal loopholes in physics , New American Library, 1988.
• Barak Shoshany: Lectures on Faster-than-Light Travel and Time Travel , SciPost Physics Lecture Notes, 10, 2019, Arxiv

Wiktionary: faster than light speed  - explanations of meanings, word origins, synonyms, translations
Videos

## Individual evidence

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2. Matt oysters on tachyons ( Memento from February 18, 2014 in the Internet Archive ), also in quantum mechanical treatment (English)
3. Nature , Volume 211, p. 468
4. Wissenschaft.de: Will Einstein's dogma fall? August 1, 1997, accessed September 7, 2019 . , with a description of the experiments by Günter Nimtz
5. Peak and the rising edge of a frequency band limited wave packet , according to W. Heitmann, G. Nimtz: On causality proofs of superluminal barrier traversal of frequency band limited wave packets , Phys. Lett. A, Vol. 196, 1994, p. 154
6. Ernst-Udo Wallenborn: And Mozart? ( Memento of the original from April 5, 2009 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Wallenborn 1999 on the experiment by Nimtz
7. Ernst-Udo Wallenborn: But isn't that faster than light? ( Memento of the original from April 5, 2009 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Wallenborn in a discussion of the Nimtz experiment, 1999
8. G. Privitera, G. Salesi, VS Olkhovsky, E. Recami: Tunneling times: An elementary introduction. In: Rivista del Nuovo Cimento vol. 26, n.4 , 2003. arxiv : quant-ph / 0412146
9. Ernst-Udo Wallenborn: Superluminal Tunneln ( Memento of the original from August 4, 2003 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Arguments against an interpretation of the tunnel effect as faster than light information propagation, 23 June 1999
10. Discussion of the speed definitions, Duke University ( Memento of June 10, 2010 in the Internet Archive )
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18. ^ John Barrow: Cosmologies with varying light speed , 1998. arxiv : astro-ph / 9811022 .
19. Magueijo: Faster Than the Speed ​​of Light: The Story of a Scientific Speculation . Massachusetts: Perseus Books Group, 2003.
20. ^ Moffat: Superluminary Universe: A Possible Solution to the Initial Value Problem in Cosmology , International Journal Modern Physics D, Vol. 2, 2003, p. 351, Moffat Reinventing Gravity , Collins 2008
21. and before that in 1988 the French Jean-Pierre Petit, with him the gravitational constant also changed over time, so that Einstein's field equations remain invariant overall
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23. 1999, observations by JK Webb and others seemed to show such variability, see: Webb, Churchill, Drinkwater, Flambaum, Barrow: Physical Review Letters , Vol. 82, 1999, p. 884

25. G. Nimtz and W. Heitmann, Prog. Quant. Electr. 21 , 81 (1997)