Faster-than-light

Faster-than-light (also superluminal or FTL) communication and travel are the conjectural propagation of information or matter faster than the speed of light.

The special theory of relativity implies that only particles with zero rest mass may travel at the speed of light. Tachyons, particles whose speed exceeds that of light, have been hypothesized, but their existence would violate causality, and the consensus of physicists is that they cannot exist. On the other hand, what some physicists refer to as "apparent" or "effective" FTL[1][2][3][4] depends on the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations in less time than light could in normal or undistorted spacetime.

According to the current scientific theories, matter is required to travel at slower-than-light (also subluminal or STL) speed with respect to the locally distorted spacetime region. Apparent FTL is not excluded by general relativity; however, any apparent FTL physical plausibility is speculative. Examples of apparent FTL proposals are the Alcubierre drive and the traversable wormhole.

Superluminal travel of non-information

In the context of this article, FTL is the transmission of information or matter faster than c, a constant equal to the speed of light in a vacuum, which is 299,792,458 m/s (by definition of the meter) or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:

  • Some processes propagate faster than c, but cannot carry information (see examples in the sections immediately following).
  • In some materials where light travels at speed c/n (where n is the refractive index) other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation (see phase velocity below).

Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as FTL as described here.

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

Daily sky motion

For an earth-bound observer, objects in the sky complete one revolution around the Earth in one day. Proxima Centauri, the nearest star outside the Solar System, is about four light-years away.[5] In this frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater than c as the rim speed of an object moving in a circle is a product of the radius and angular speed.[5] It is also possible on a geostatic view, for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000 AU.[6] The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.

Light spots and shadows

If a laser beam is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than c.[7] Similarly, a shadow projected onto a distant object can be made to move across the object faster than c.[7] In neither case does the light travel from the source to the object faster than c, nor does any information travel faster than light.[7][8][9] An analogy can be made to pointing a water hose in one direction and then quickly moving the hose to point the stream of water in another direction. At no point does the water leaving the hose ever increase in velocity, but the endpoint of the stream can be moved faster than the water in the stream itself.

Apparent FTL propagation of static field effects

Since there is no "retardation" (or aberration) of the apparent position of the source of a gravitational or electric static field when the source moves with constant velocity, the static field "effect" may seem at first glance to be "transmitted" faster than the speed of light. However, uniform motion of the static source may be removed with a change in reference frame, causing the direction of the static field to change immediately, at all distances. This is not a change of position which "propagates", and thus this change cannot be used to transmit information from the source. No information or matter can be FTL-transmitted or propagated from source to receiver/observer by an electromagnetic field.

Closing speeds

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of a particle accelerator of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

Special relativity does not prohibit this. It tells us that it is wrong to use Galilean relativity to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correct velocity-addition formula for computing such relative velocity.

It is instructive to compute the relative velocity of particles moving at v and −v in accelerator frame, which corresponds to the closing speed of 2v > c. Expressing the speeds in units of c, β = v/c:

Proper speeds

If a spaceship travels to a planet one light-year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance traveled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a proper velocity. There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. A light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller.

Possible distance away from Earth

Since one might not travel faster than light, one might conclude that a human can never travel further from the Earth than 40 light-years if the traveler is active between the age of 20 and 60. A traveler would then never be able to reach more than the very few star systems which exist within the limit of 20–40 light-years from the Earth. This is a mistaken conclusion: because of time dilation, the traveler can travel thousands of light-years during their 40 active years. If the spaceship accelerates at a constant 1 g (in its own changing frame of reference), it will, after 354 days, reach speeds a little under the speed of light (for an observer on Earth), and time dilation will increase their lifespan to thousands of Earth years, seen from the reference system of the Solar System, but the traveler's subjective lifespan will not thereby change. If the traveler returns to the Earth, she or he will land thousands of years into the Earth's future. Their speed will not be seen as higher than the speed of light by observers on Earth, and the traveler will not measure their speed as being higher than the speed of light, but will see a length contraction of the universe in their direction of travel. And as the traveler turns around to return, the Earth will seem to experience much more time than the traveler does. So, while their (ordinary) coordinate speed cannot exceed c, their proper speed (distance as seen by Earth divided by their proper time) can be much greater than c. This is seen in statistical studies of muons traveling much further than c times their half-life (at rest), if traveling close to c.[10]

Phase velocities above c

The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies.[11] However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.[12] Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.[13]

Group velocities above c

The group velocity of a wave (e.g., a light beam) may also exceed c in some circumstances.[14][15] In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity above c. However, even this situation does not imply the propagation of signals with a velocity above c,[16] even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than c without this effect.[17] However, group velocity can exceed c in some parts of a Gaussian beam in vacuum (without attenuation). The diffraction causes that the peak of pulse propagates faster, while overall power does not.[18]

Universal expansion

History of the Universe
History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang.[19][20][21]

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if proper distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally.[22] (See Comoving and proper distances for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the inflationary epoch thought to have occurred in a tiny fraction of the second after the Big Bang (models suggest the period would have been from around 10−36 seconds after the Big Bang to around 10−33 seconds), when the universe may have rapidly expanded by a factor of around 1020 to 1030.[23]

There are many galaxies visible in telescopes with red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.[24][25][26]

However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future,[27] because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in Comoving and proper distances#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.[25]

Astronomical observations

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars, and recently also in microquasars. The effect was predicted before it was observed by Martin Rees and can be explained as an optical illusion caused by the object partly moving in the direction of the observer,[28] when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light.[29] Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.

Quantum mechanics

Certain phenomena in quantum mechanics, such as quantum entanglement, might give the superficial impression of allowing communication of information faster than light. According to the no-communication theorem these phenomena do not allow true communication; they only let two observers in different locations see the same system simultaneously, without any way of controlling what either sees. Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment. Since the underlying behavior does not violate local causality or allow FTL communication, it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.

The uncertainty principle implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than c, even in a vacuum; this possibility must be taken into account when enumerating Feynman diagrams for a particle interaction.[30] However, it was shown in 2011 that a single photon may not travel faster than c.[31] In quantum mechanics, virtual particles may travel faster than light, and this phenomenon is related to the fact that static field effects (which are mediated by virtual particles in quantum terms) may travel faster than light (see section on static fields above). However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e., non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.

There have been various reports in the popular press of experiments on faster-than-light transmission in optics — most often in the context of a kind of quantum tunnelling phenomenon. Usually, such reports deal with a phase velocity or group velocity faster than the vacuum velocity of light.[32][33] However, as stated above, a superluminal phase velocity cannot be used for faster-than-light transmission of information.[34][35]

Hartman effect

The Hartman effect is the tunneling effect through a barrier where the tunneling time tends to a constant for large barriers.[36][37] This could, for instance, be the gap between two prisms. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted. There is a non-zero probability that the photon will tunnel across the gap rather than follow the refracted path. For large gaps between the prisms the tunnelling time approaches a constant and thus the photons appear to have crossed with a superluminal speed.[38]

However, the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than c, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate".[39] The evanescent waves in the Hartman effect are due to virtual particles and a non-propagating static field, as mentioned in the sections above for gravity and electromagnetism.

Casimir effect

In physics, the Casimir–Polder force is a physical force exerted between separate objects due to resonance of vacuum energy in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, owing to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Because the effect is due to virtual particles mediating a static field effect, it is subject to the comments about static fields discussed above.

EPR paradox

The EPR paradox refers to a famous thought experiment of Albert Einstein, Boris Podolsky and Nathan Rosen that was realized experimentally for the first time by Alain Aspect in 1981 and 1982 in the Aspect experiment. In this experiment, the measurement of the state of one of the quantum systems of an entangled pair apparently instantaneously forces the other system (which may be distant) to be measured in the complementary state. However, no information can be transmitted this way; the answer to whether or not the measurement actually affects the other quantum system comes down to which interpretation of quantum mechanics one subscribes to.

An experiment performed in 1997 by Nicolas Gisin has demonstrated non-local quantum correlations between particles separated by over 10 kilometers.[40] But as noted earlier, the non-local correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved. The situation is akin to sharing a synchronized coin flip, where the second person to flip their coin will always see the opposite of what the first person sees, but neither has any way of knowing whether they were the first or second flipper, without communicating classically. See No-communication theorem for further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues has determined that in any hypothetical non-local hidden-variable theory, the speed of the quantum non-local connection (what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light.[41]

Delayed choice quantum eraser

The delayed-choice quantum eraser is a version of the EPR paradox in which the observation (or not) of interference after the passage of a photon through a double slit experiment depends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon,[42] which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it can't be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an FTL or backwards-in-time manner.[43][44]

Superluminal communication

Faster-than-light communication is, according to relativity, equivalent to time travel. What we measure as the speed of light in a vacuum (or near vacuum) is actually the fundamental physical constant c. This means that all inertial observers, regardless of their relative velocity, will always measure zero-mass particles such as photons traveling at c in a vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by Poincaré transformations. These transformations have important implications:

  • The relativistic momentum of a massive particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
  • To accelerate an object of non-zero rest mass to c would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
  • Either way, such acceleration requires infinite energy.
  • Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a space-like interval.[45] In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference,[46] or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale). Therefore, any theory which permits "true" FTL also has to cope with time travel and all its associated paradoxes,[47] or else to assume the Lorentz invariance to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).
  • In special relativity the coordinate speed of light is only guaranteed to be c in an inertial frame; in a non-inertial frame the coordinate speed may be different from c.[48] In general relativity no coordinate system on a large region of curved spacetime is "inertial", so it is permissible to use a global coordinate system where objects travel faster than c, but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" and the local speed of light will be c in this frame,[49] with massive objects moving through this local neighborhood always having a speed less than c in the local inertial frame.

Justifications

Relative permittivity or permeability less than 1

The speed of light

is related to the vacuum permittivity ε0 and the vacuum permeability μ0. Therefore, not only the phase velocity, group velocity, and energy flow velocity of electromagnetic waves but also the velocity of a photon can be faster than c in a special material has the constant permittivity or permeability whose value is less than that in vacuum.[50]

Casimir vacuum and quantum tunnelling

Special relativity postulates that the speed of light in vacuum is invariant in inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of the light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the SI unit of length (the meter) has been defined using the speed of light.

The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called simply the vacuum energy, which could perhaps be altered in certain cases.[51] When vacuum energy is lowered, light itself has been predicted to go faster than the standard value c. This is known as the Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 1036.[52] Accordingly, there has as yet been no experimental verification of the prediction. A recent analysis[53] argued that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative chronology protection conjecture which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze. Other authors argue that Scharnhorst's original analysis, which seemed to show the possibility of faster-than-c signals, involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.[54]

The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Cologne, claim to have violated relativity experimentally by transmitting photons faster than the speed of light.[38] They say they have conducted an experiment in which microwave photons — relatively low-energy packets of light — travelled "instantaneously" between a pair of prisms that had been moved up to 3 ft (1 m) apart. Their experiment involved an optical phenomenon known as "evanescent modes", and they claim that since evanescent modes have an imaginary wave number, they represent a "mathematical analogy" to quantum tunnelling.[38] Nimtz has also claimed that "evanescent modes are not fully describable by the Maxwell equations and quantum mechanics have to be taken into consideration."[55] Other scientists such as Herbert G. Winful and Robert Helling have argued that in fact there is nothing quantum-mechanical about Nimtz's experiments, and that the results can be fully predicted by the equations of classical electromagnetism (Maxwell's equations).[56][57]

Nimtz told New Scientist magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the University of Toronto, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars from the tail at each station along the way, so that the center of the ever-shrinking main train moves forward at each stop; in this way, the speed of the center of the train exceeds the speed of any of the individual cars.[58]

Winful argues that the train analogy is a variant of the "reshaping argument" for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse.[56] Instead, Winful argues that the group delay in tunneling is not actually the transit time for the pulse (whose spatial length must be greater than the barrier length in order for its spectrum to be narrow enough to allow tunneling), but is instead the lifetime of the energy stored in a standing wave which forms inside the barrier. Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.[59][60]

A number of authors have published papers disputing Nimtz's claim that Einstein causality is violated by his experiments, and there are many other papers in the literature discussing why quantum tunneling is not thought to violate causality.[61]

It was later claimed by Eckle et al. that particle tunneling does indeed occur in zero real time.[62] Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500–600 attoseconds (an attosecond is one quintillionth (10−18) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.[59][60][63]

Give up (absolute) relativity

Because of the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is doubly special relativity, which posits that the Planck length is also the same in all reference frames, and is associated with the work of Giovanni Amelino-Camelia and João Magueijo.

There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g., Mach's principle), which implies that the rest frame of the universe might be preferred by conventional measurements of natural law. If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the observable universe, it is difficult to imagine (much less construct) experiments to test this hypothesis.

Spacetime distortion

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.[64] Miguel Alcubierre theorized that it would be possible to create a warp drive, in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally traveling faster than light.[65] However, several objections raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the traversable wormhole, which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not locally move faster than light travelling through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.

Gerald Cleaver and Richard Obousy, a professor and student of Baylor University, theorized that manipulating the extra spatial dimensions of string theory around a spaceship with an extremely large amount of energy would create a "bubble" that could cause the ship to travel faster than the speed of light. To create this bubble, the physicists believe manipulating the 10th spatial dimension would alter the dark energy in three large spatial dimensions: height, width and length. Cleaver said positive dark energy is currently responsible for speeding up the expansion rate of our universe as time moves on.[66]

Heim theory

In 1977, a paper on Heim theory theorized that it may be possible to travel faster than light by using magnetic fields to enter a higher-dimensional space.[67]

Lorentz symmetry violation

The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called Standard-Model Extension.[68][69][70] This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments[71] and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.[72] The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including Lorentz-violating neutrino oscillations and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.

In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that spontaneous symmetry breaking of Lorentz invariance[73] shortly after the Big Bang could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field;[74] however, there are also some models where Lorentz symmetry is broken in a more fundamental way. If Lorentz symmetry can cease to be a fundamental symmetry at Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.

In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,[75][76] existing low-energy bounds cannot be applied to high-energy phenomena; however, many searches for Lorentz violation at high energies have been carried out using the Standard-Model Extension.[72] Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.

Superfluid theories of physical vacuum

In this approach the physical vacuum is viewed as the quantum superfluid which is essentially non-relativistic whereas the Lorentz symmetry is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.[77] Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be the quantum Bose liquid whose ground-state wavefunction is described by the logarithmic Schrödinger equation. It was shown that the relativistic gravitational interaction arises as the small-amplitude collective excitation mode[78] whereas relativistic elementary particles can be described by the particle-like modes in the limit of low momenta.[79] The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the relativistic one - they can reach the speed of light limit at finite energy; also, faster-than-light propagation is possible without requiring moving objects to have imaginary mass.[80][81]

Time of flight of neutrinos

MINOS experiment

In 2007 the MINOS collaboration reported results measuring the flight-time of 3 GeV neutrinos yielding a speed exceeding that of light by 1.8-sigma significance.[82] However, those measurements were considered to be statistically consistent with neutrinos traveling at the speed of light.[83] After the detectors for the project were upgraded in 2012, MINOS corrected their initial result and found agreement with the speed of light. Further measurements are going to be conducted.[84]

OPERA neutrino anomaly

On September 22, 2011, a preprint[85] from the OPERA Collaboration indicated detection of 17 and 28 GeV muon neutrinos, sent 730 kilometers (454 miles) from CERN near Geneva, Switzerland to the Gran Sasso National Laboratory in Italy, traveling faster than light by a relative amount of 2.48×10−5 (approximately 1 in 40,000), a statistic with 6.0-sigma significance.[86] On 17 November 2011, a second follow-up experiment by OPERA scientists confirmed their initial results.[87][88] However, scientists were skeptical about the results of these experiments, the significance of which was disputed.[89] In March 2012, the ICARUS collaboration failed to reproduce the OPERA results with their equipment, detecting neutrino travel time from CERN to the Gran Sasso National Laboratory indistinguishable from the speed of light.[90] Later the OPERA team reported two flaws in their equipment set-up that had caused errors far outside their original confidence interval: a fiber optic cable attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast.[91]

Tachyons

In special relativity, it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light. However, it might be possible for an object to exist which always moves faster than light. The hypothetical elementary particles with this property are called tachyonic particles. Attempts to quantize them failed to produce faster-than-light particles, and instead illustrated that their presence leads to an instability.[92][93]

Various theorists have suggested that the neutrino might have a tachyonic nature,[94][95][96][97] while others have disputed the possibility.[98]

Exotic matter

Mechanical equations to describe hypothetical exotic matter which possesses a negative mass, negative momentum, negative pressure, and negative kinetic energy are[99]

,

Considering and , the energy-momentum relation of the particle is corresponding to the following dispersion relation

,

of a wave that can propagate in the negative-index metamaterial. The pressure of radiation pressure in the metamaterial is negative[100] and negative refraction, inverse Doppler effect and reverse Cherenkov effect imply that the momentum is also negative. So the wave in a negative-index metamaterial can be applied to test the theory of exotic matter and negative mass. For example, the velocity equals

,
,

That is to say, such a wave can break the light barrier under certain conditions.

General relativity

General relativity was developed after special relativity to include concepts like gravity. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer. One such distortion is the Alcubierre drive, which can be thought of as producing a ripple in spacetime that carries an object along with it. Another possible system is the wormhole, which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypothetical exotic matter or negative energy.

General relativity also recognizes that any means of faster-than-light travel could also be used for time travel. This raises problems with causality. Many physicists believe that the above phenomena are impossible and that future theories of gravity will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In string theory, Eric G. Gimon and Petr Hořava have argued[101] that in a supersymmetric five-dimensional Gödel universe, quantum corrections to general relativity effectively cut off regions of spacetime with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.

Variable speed of light

In physics, the speed of light in a vacuum is assumed to be a constant. However, hypotheses exist that the speed of light is variable.

The speed of light is a dimensional quantity and so cannot be measured.[102] Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when the height of a mountain is measured, what is really measured is the ratio of its height to the length of a meter stick. The conventional SI system of units is based on seven basic dimensional quantities, namely distance, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.[103] These units are defined to be independent and so cannot be described in terms of each other. As an alternative to using a particular system of units, one can reduce all measurements to dimensionless quantities expressed in terms of ratios between the quantities being measured and various fundamental constants such as Newton's constant, the speed of light and Planck's constant; physicists can define at least 26 dimensionless constants which can be expressed in terms of these sorts of ratios and which are currently thought to be independent of one another.[104] By manipulating the basic dimensional constants one can also construct the Planck time, Planck length, and Planck energy which make a good system of units for expressing dimensional measurements, known as Planck units.

João Magueijo proposed a different set of units, a choice which he justifies with the claim that some equations will be simpler in these new units. In the new units he fixes the fine structure constant, a quantity which some people, using units in which the speed of light is fixed, have claimed is time-dependent. Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.

See also

Faster-than-light technologies in science fiction

Notes

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References

External links

Alcubierre drive

The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space without breaking any physical laws.Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful, in which case a drive will not be possible. Even if it is physically meaningful, its possibility would not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties can not exist, then the drive could not be constructed. However, at the close of his original article Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes) that the Casimir vacuum between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive.

Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backwards time travel (see the chronology protection conjecture) and thus make the Alcubierre drive invalid.

Ansible

An ansible is a category of fictional device or technology capable of near-instantaneous or superluminal communication. It can send and receive messages to and from a corresponding device over any distance or obstacle whatsoever with no delay, even between star systems. As a name for such a device, the word "ansible" first appeared in a 1966 novel by Ursula K. Le Guin. Since that time, the term has been broadly used in the works of numerous science fiction authors, across a variety of settings and continuities.

Dilithium (Star Trek)

In the Star Trek fictional universe, dilithium is an invented material which serves as a controlling agent in the faster-than-light warp drive. In the original series, dilithium crystals were rare and could not be replicated, making the search for them a recurring plot element. According to a periodic table shown during a Next Generation episode, it has the chemical symbol Dt and the atomic number 87, which in reality belongs to francium.In the real world, dilithium (Li2) is a molecule composed of two covalently bonded lithium atoms.

Faster-than-light communication

Superluminal communication is a hypothetical process in which information is sent at faster-than-light (FTL) speeds. The current scientific consensus is that faster-than-light communication is not possible, and to date it has not been achieved in any experiment.

Under present knowledge superluminal communication is impossible because, in a Lorentz-invariant theory, it could be used to transmit information into the past. This contradicts causality and leads to logical paradoxes.A number of theories and phenomena related to superluminal communication have been proposed or studied, including tachyons, quantum nonlocality, and wormholes.

Faster-than-light neutrino anomaly

In 2011, the OPERA experiment mistakenly observed neutrinos appearing to travel faster than light. Even before the mistake was discovered, the result was considered anomalous because speeds higher than that of light in a vacuum are generally thought to violate special relativity, a cornerstone of the modern understanding of physics for over a century.OPERA scientists announced the results of the experiment in September 2011 with the stated intent of promoting further inquiry and debate. Later the team reported two flaws in their equipment set-up that had caused errors far outside their original confidence interval: a fiber optic cable attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast. The errors were first confirmed by OPERA after a ScienceInsider report; accounting for these two sources of error eliminated the faster-than-light results.In March 2012, the collocated ICARUS experiment reported neutrino velocities consistent with the speed of light in the same short-pulse beam OPERA had measured in November 2011. ICARUS used a partly different timing system from OPERA and measured seven different neutrinos. In addition, the Gran Sasso experiments BOREXINO, ICARUS, LVD and OPERA all measured neutrino velocity with a short-pulsed beam in May, and obtained agreement with the speed of light.On June 8, 2012 CERN research director Sergio Bertolucci declared on behalf of the four Gran Sasso teams, including OPERA, that the speed of neutrinos is consistent with that of light. The press release, made from the 25th International Conference on Neutrino Physics and Astrophysics in Kyoto, states that the original OPERA results were wrong, due to equipment failures.On July 12, 2012 OPERA updated their paper by including the new sources of errors in their calculations. They found agreement of neutrino speed with the speed of light.Neutrino speeds "consistent" with the speed of light are expected given the limited accuracy of experiments to date. Neutrinos have small but nonzero mass, and so special relativity predicts that they must propagate at speeds slower than light. Nonetheless, known neutrino production processes impart energies far higher than the neutrino mass scale, and so almost all neutrinos are ultrarelativistic, propagating at speeds very close to that of light.

Heim theory

Heim theory, first proposed by German physicist Burkhard Heim publicly in 1957, is an attempt to develop a theory of everything in theoretical physics. The theory has received little attention in the scientific literature and is regarded as being outside mainstream science but has attracted some interest in popular and fringe media.Heim attempted to resolve incompatibilities between quantum theory and general relativity. To meet that goal, he developed a mathematical approach based on quantizing spacetime. Others have attempted to apply Heim theory to nonconventional space propulsion and faster than light concepts, as well as the origin of dark matter.Heim claimed that his theory yields particle masses directly from fundamental physical constants and that the resulting masses are in agreement with experiment, but this claim has not been confirmed.Heim theory is formulated mathematically in six or more dimensions and uses Heim's own version of difference equations.

Geoffrey A. Landis has compared the story behind the creation of Heim theory with the plot of a science fiction story.

Hyperdrive

Hyperdrive is a name given to certain methods of traveling faster-than-light (FTL) in science fiction. Related concepts are jump drive and warp drive.

Intergalactic travel

Intergalactic travel is the term used for hypothetical manned or unmanned travel between galaxies. Due to the enormous distances between our own galaxy the Milky Way and even its closest neighbors—hundreds of thousands to millions of light-years—any such venture would be far more technologically demanding than even interstellar travel. Intergalactic distances are roughly a hundred-thousandfold (five orders of magnitude) greater than their interstellar counterparts.The technology required to travel between galaxies is far beyond humanity's present capabilities, and currently only the subject of speculation, hypothesis, and science fiction.

However, theoretically speaking, there is nothing to conclusively indicate that intergalactic travel is impossible. There are several hypothesized methods of carrying out such a journey, and to date several academics have studied intergalactic travel in a serious manner.

Jump drive

A jump drive is a speculative method of traveling faster than light (FTL) in science fiction.

Related superluminal concepts are hyperdrive, warp drive and interstellar teleporter. The key characteristic of a jump drive (as the term is usually used) is that it allows a starship to be instantaneously teleported between two points. A jump drive is supposed to make a spaceship (or any matter) go from one point in space to another point, which may be several light years away, in a single instant. Like time travel, a jump drive is often taken for granted in science fiction, but very few science fiction works talk about the mechanics behind a jump drive. There are vague indications of the involvement of tachyons and the space-time continuum in some works.

Macross

Macross (マクロス, Makurosu, English: ) is a Japanese science fiction mecha anime media franchise, created by Shōji Kawamori of Studio Nue in 1982. The franchise features a fictional history of Earth and the human race after the year 1999. It consists of four TV series, four movies, six OVAs, one light novel, and five manga series, all sponsored by Big West Advertising, in addition to 40 video games set in the Macross universe, 2 crossover games, and a wide variety of physical merchandise.

Within the series, the term Macross is used to denote the main capital ship. This theme began in the original Macross, the SDF-1 Macross.

Overtechnology refers to the scientific advances discovered in an alien starship ASS-1 (Alien Star Ship - One later renamed Super Dimension Fortress - One Macross) that crashed on South Ataria island. Humans were able to reverse engineer the technology to create the mecha (variable fighters and destroids), faster-than-light space fold drive for starships and other advanced technologies that the series features. The first TV series was adapted into the first season of Robotech in 1985, with edited content and a revised script.

Slipstream (science fiction)

"Slipstream" is a science fiction term for a fictional method of faster-than-light space travel, similar to hyperspace travel, warp drive, or "transfer points" from David Brin's Uplift series.

Starship

A starship, starcraft or interstellar spacecraft is a theoretical spacecraft designed for traveling between planetary systems, as opposed to an aerospace-vehicle designed for orbital spaceflight or interplanetary travel.

The term is mostly found in science fiction, because such craft is not known to have ever been constructed. Reference to a "star-ship" appears as early as 1882 in Oahspe: A New Bible (1882).Whilst the Voyager and Pioneer probes have travelled into local interstellar space, the purpose of these unmanned craft was specifically interplanetary and they are not predicted to reach another star system (although Voyager 1 will travel to within 1.7 light years of Gliese 445 in approximately 40,000 years). Several preliminary designs for starships have been undertaken through exploratory engineering, using feasibility studies with modern technology or technology thought likely to be available in the near future.

In April 2016, scientists announced Breakthrough Starshot, a Breakthrough Initiatives program, to develop a proof-of-concept fleet of small centimeter-sized light sail spacecraft, named StarChip, capable of making the journey to Alpha Centauri, the nearest extrasolar star system, at speeds of 20% and 15% of the speed of light, taking between 20 and 30 years to reach the star system, respectively, and about 4 years to notify Earth of a successful arrival.

On November 8, 2018, Elon Musk announced that SpaceX was renaming the Big Falcon Rocket, a fully reusable launch vehicle and spacecraft system, to Starship. Though the spacecraft will not possess any reasonable interstellar capability, Musk defended the name by claiming that "later versions will."

Tachyon

A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Most physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality. No experimental evidence for the existence of such particles has been found.

The possibility of particles moving faster-than-light was first proposed by O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan in 1962, although the term they used for it was "meta-particle". In the 1967 paper that coined the term, Gerald Feinberg proposed that tachyonic particles could be quanta of a quantum field with imaginary mass. However, it was soon realized that excitations of such imaginary mass fields do not under any circumstances propagate faster than light, and instead the imaginary mass gives rise to an instability known as tachyon condensation. Nevertheless, in modern physics the term "tachyon" often refers to imaginary mass fields rather than to faster-than-light particles. Such fields have come to play a significant role in modern physics.

The term comes from the Greek: ταχύ, tachy, meaning "rapid". The complementary particle types are called luxons (which always move at the speed of light) and bradyons (which always move slower than light); both of these particle types are known to exist.

Tachyonic antitelephone

A tachyonic antitelephone is a hypothetical device in theoretical physics that could be used to send signals into one's own past. Albert Einstein in 1907

presented a thought experiment of how faster-than-light signals can lead to a paradox of causality, which was described by Einstein and Arnold Sommerfeld in 1910 as a means "to telegraph into the past". The same thought experiment was described by Richard Chace Tolman in 1917; thus, it is also known as Tolman's paradox.

A device capable of "telegraphing into the past" was later also called a "tachyonic antitelephone" by Gregory Benford et al. According to the current understanding of physics, no such faster-than-light transfer of information is actually possible. For instance, the hypothetical tachyon particles which give the device its name do not exist even theoretically in the standard model of particle physics, due to tachyon condensation, and there is no experimental evidence that suggests that they might exist. The problem of detecting tachyons via causal contradictions was treated but without scientific verification.

Technology in Star Trek

The technology in Star Trek has borrowed freely from the scientific world to provide storylines. Episodes are replete with references to tachyon beams, baryon sweeps, quantum fluctuations and event horizons. Many of the technologies created for the Star Trek universe were done so out of simple financial necessity—the transporter was created because the limited budget of the original series in the 1960s did not allow expensive shots of spaceships landing on planets.Discovery Channel Magazine stated that cloaking devices, faster-than-light travel and dematerialized transport were only dreams at the time the original series was made, but physicist Michio Kaku believes all these things are possible. William Shatner, who portrayed James T. Kirk in the original Star Trek series, believed this as well, and went on to cowrite the book I'm Working on That, in which he investigated how Star Trek technology was becoming feasible.

The Dosadi Experiment

The Dosadi Experiment is a 1977 science fiction novel by American writer Frank Herbert. It is the second full-length novel set in the ConSentiency universe established by Herbert in his novelette The Tactful Saboteur and continued in Whipping Star. It was first published as a four-part serial in Galaxy Science Fiction magazine from May to August, 1977.

Warp drive

A warp drive is a fictitious superluminal spacecraft propulsion system in many science fiction works, most notably Star Trek. A spacecraft equipped with a warp drive may travel at speeds greater than that of light by many orders of magnitude. In contrast to some other fictitious FTL technologies such as a jump drive, the warp drive does not permit instantaneous travel between two points, but rather involves a measurable passage of time which is pertinent to the concept. In contrast to hyperdrive, spacecraft at warp velocity would continue to interact with objects in "normal space." The general concept of "warp drive" was introduced by John W. Campbell in his 1931 novel Islands of Space.Einstein's theory of special relativity states that energy and mass are interchangeable, and speed of light travel is impossible for material objects that weigh more than photons. The problem of a material object exceeding light speed is that an infinite amount of kinetic energy would be required to travel at exactly the speed of light. This can theoretically be solved by warping space to move an object instead of increasing the kinetic energy of the object to do so. Such a solution to the faster than light travel problem leads to two directly opposite approaches to light-speed travel in science fiction: in the first, spaceships themselves are brought to light speed and beyond; in the second, not-yet-local space itself is made to come to the ship while the ship moves at sub-light speeds.

Wormhole

A wormhole (or Einstein–Rosen bridge) is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime (i.e., different locations or different points of time). More precisely it is a transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in Anti-de Sitter space.

Wormholes are consistent with the general theory of relativity, but whether wormholes actually exist remains to be seen.

A wormhole could connect extremely long distances such as a billion light years or more, short distances such as a few meters, different universes, or different points in time.

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