# Faster than light

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 v • d • e
 Millennium Falcon cockpit view of hyperspace

Faster than light

Faster than light travel or communication is a common SF theme, plot device, and SF trope. The science behind FTL is non-trivial and includes such conundrums as causality violations. Contrast with slower than light. (e)

## Taxonomy of FTL Mechanisms

1. [1.0] Discontinuous Drives ("teleport-like"). Discontinuous drives are ones in which the traveler does not traverse the space between origin and destination.
1. [1.1] Flash gates. Devices in which the object transported disappears from point X and reappears at point Y.
1. [1.1.1] Transmitter to receiver. Teleport in which a discrete transmitter and a receiver are needed. May require a ship, or may not.
2. [1.1.2] Transmitter to anywhere.Teleport in which a transmitter is needed, but a receiver is not; the transporter can select the target location ("Beam me down" is the most well-known example)
1. [1.1.2.1] Transmitter to anywhere /variant. Transmitter can be transported with the teleportation. See also [1.4.1.1] "Single jump/variant".
3. [1.1.3] Anywhere to receiverTeleport in which a receiving unit is needed, but a transmitter is not. ("Beam me up" is an example of this.)
4. [1.1.4] Distant transmitterA teleport system in which a fixed unit is needed, but this unit can teleport you from a place to another place. (The "point to point" use of the transporter in Trek is an example.)
2. [1.2] "Door" gates. Gates in which an opening is made between point X and point Y which exists for some finite time; the object transported then moves though the gate.
1. [1.2.1] Portal to portal. A transmitting device to act as the "out" door and a receiving device to act as the "in" door are both required. (e.g., Poul Anderson, The Enemy Stars.)
2. [1.2.2] Portal to anywhere. Here the transmitting door opens a receiving door without requirement for any device at the receiving end. ('Tak Halus' (pseud. of Steven Robinette) did a series of stories in Analog in early 70s with this premise)
3. [1.2.3] Anywhere to portal. The same as [1.2.2] "Portal to anywhere", but traveling in the opposite direction.
4. [1.2.4] Distant portal. Anywhere to anywhere, device located elsewhere. Here "door" opens from X to Y by use of a device at a third location C. The 'door' equivalent of [1.1.4] "Distant transmitter".
3. [1.3] "Permanent" gates (Wormholes). "Permanent" here means that these stay open without the requirement of a device, that is, they are a path from X to Y without being energized. There are a wide variety of subsets of this. Recently the most talked-about are Lorentzian wormholes, which are apparently allowed by the general theory of relativity if the presence of negative matter is permitted. General relativity variants include Morris-Thorne spherical wormholes, Visser portals, Kerr ring-wormholes, Einstein-Rosen bridges (nb: which actually collapse before allowing you to traverse them), Tippler rotating cylinders (nb: which don't actually serve as bridges, but at least one SF writer, Poul Anderson, wrote a book which assumed that they did). A non-relativity version is the "mirrors" used in Wolfe's New Sun series of books.
4. [1.4] Teleportation (aka "jump"). Here I use "teleportation" to imply something that can transport itself without a fixed transmitter or receiver. Reference to quantum "tunneling" is often made. Some books imply that humans can do this unassisted (Tyger, Tyger/The Stars My Destination). Many more use ships which can "jump" with some device. Here I use 'jump' or 'teleportation' only for the case that physical travel is not required in some alternate version of space, in distinction to some SF writers who use the term or a variant for cases where a ship 'jumps' to some 'hyperspace' (jumpspace, subspace, etc) where it can travel FTL.
1. [1.4.1] Single jump. A ship (or person) who can jump from place to destination in a single step, and can select the target.
1. [1.4.1.1] Single jump/variant. In the variant, this only works at selected places, and takes you only to selected spaces (The Mote in God's Eye). This type of variant in general can be considered a version of the [1.1] "Flash-gate" discussed above.
2. [1.4.2] Multiple-connection. The ship can engage a "jump" drive, which will connect your location in space-time with another location in space-time that is fixed by the universe (may depend on your state of motion in some variants). The connection will vary from place to place, so to go to a given destination you need a "map" of where to go in space to find the place that jumps to the right spot. The analogy is of the universe to a crumpled sheet of paper. An ant can cross from one place on the paper to another where the paper touches itself. (Heinlein, Starman Jones). For some locations, a long trip moving from one place to another to take multiple jumps may be necessary.
3. [1.4.3] Multi-jump (Stutter). A ship can jump from place to place, but not far enough to travel in a single jump. Thus, the ship travels by a series of short jumps. In the limit of very short jumps, the ship "appears" to be traveling through space at a "pseudo" velocity without actually having any momentum. (This shades into [1.4.1] "Single jump" as the length of jump gets longer).
4. [1.4.4] Hopscotch drive. Use of any version of a gate or portal to accomplish self-motivated teleportation by having a transmitter transmit a transmitter, so that a ship "bootstraps" across space by continuously beaming itself incremental distances. (Such a drive is somewhere in the fuzzy region between a [2.0] "Continuous" and a [1.0] "Discontinuous drive").
5. [1.4.5] FTL by time travel. In FTL by time travel, faster than light travel is achieved by traveling to the destination at ordinary slower-than-light speed, then teleporting backward in time to arrive at the same time you started (e.g., Roger MacBride Allen, The Depths of Time).
5. [1.5] "Fold" drive ( Telportation/variant ). A "fold" drive appeals to the "folded space" concept of [1.4.2] "Multiple-connection", but now assumes that the ship can intentionally "fold" space to produce the direct connection between point X and point Y required. Since this categorization is by how the drive appears, and not how it functions, "fold" variants are identical to actual teleport (or "portal") variants, cf. [1.2] "Door gates")
2. [2.0] Continuous Drives. Continuous drives are ones in which the traveler does traverse the space between start and finish. A ship gets from point X to point Y by traveling rather than by an instant "jump", although the travel is not necessarily in "real" space. The word "ship-like" is a little fuzzy, since many SF writers use 'ships' to accomplish what is actually teleportation-like travel. This is, I think, because ships are such a great story device
1. [2.1.1] Fixed trail. A "railroad" drive is one in which it is assumed that some physical structure connects two points, and that FTL travel is possible, but only traveling along this structure (as railroad travel is only possible along a railroad). One might appeal to the concept of a cosmic string, or some other astrophysical object. The railroad is in some ways a conceptual link between wormhole-like drives and ship-like drives. If the travel is actually instantaneous, with an object leaving one end appearing at the same time at the other end, the railroad drive becomes a variant of [1.3] "Permanent gate". (e.g., Glen Cook, The Dragon Never Sleeps.)
2. [2.1.2] Consumable trail. In a consumable trail, some structure must be put in place between a and b, and the drive consumes this material as it travels in order to produce FTL. Some versions of the Alcubierre drive, for example, require that a structure of negative energy be put in place along the path from x to y, and the ship can then travel between the two points, but destroys the structure as it travels.
2. [2.2] "Non-railroad" drives. This section covers continuous drives (that is, drives where the ship traverses space to get to the place desired) which do not require a structure in place in space.
1. [2.2.1] Real space drives. Real space drives assume that faster than light travel is possible in physical space. In terms of appearance, all of these drives apparently operate the same way (you go faster than light), and so if I were to keep to my strict classification, these would all be in the same category. The main difference between the drives is how they talk around relativity.
1. [2.2.1.1] Newtonian space drives (EMF classification: fakedrive). This version of a FTL drive simply ignores relativity. The ship goes faster than light merely by speeding up to a velocity which is faster than light. (e.g., E.E."Doc" Smith, The Skylark of Space.)
2. [2.2.1.2] Post-relativistic space drives (EMF classification: fakedrive). This is a minor variant [2.2.1.1] "Newtonian space drive"; the drive assumes that there is some (yet unknown) "correction" to relativity such that the speed of light is not, in fact, a barrier. Often this correction will be some added term which applies only very close to the speed of light.
3. [2.2.1.3] Tachyonic travel. Tachyonic travel notes that faster than light speeds are in fact permitted by relativity for bodies of imaginary rest mass, and assumes that there is some way to reach the faster than light state (often invoking "tunneling") from slower than light states without leaving "real" spacetime. (nb: tachyonic FTL travel still has causality paradoxes in special relativity).
4. [2.2.1.4] Modified local speed of light. Drive assumes that the speed of light in the vicinity of the ship can be modified by the drive system in some way, so that although the ship does not exceed the speed of light, it nevertheless can travel faster than 300,000 kilometers per second.
5. [2.2.1.5] Modified regional speed of light. Assumes that the speed of light is greater than 300,000 kilometers per second in some places in the universe. Faster speeds can be achieved in other places in the universe .
6. [2.2.1.6] Modified universal speed of light. A scientist discovers a way to change the speed of light in the entire universe, and does so. Now any ship can go faster than (what used to be) the speed of light.
7. [2.2.1.7] Tachyonic teleportation. The ship and/or person is converted into a stream of tachyons and beamed across space, then reconstituted at the receiver. Actually a variant of [2.2.1.2] "Tachyonic travel" and/or [2.2.2.1.1] "Hyperspace with transmitter and receiver"; listed separately because it is significant that the ship does not travel as a cohesive unit. Other variant names can be used for the particles, which can travel either through real space or some alternative space.
8. [2.2.1.8] Other real drives. This covers other ways of dealing with relativity problems without leaving real space. (Usually this involves employing doubletalk and bafflegab.)
9. [2.2.1.9] "Bubble" drives (EMF classification: warpdrive). "A bubble of different space is projected around the ship so that the ship can travel faster-than-light while still in realspace." This is listed last, since it is an intermediate step between "real space" drives and alternative space drives, with some nature of both. (This seems to be the FTL system used on Star Trek.)
2. [2.2.2] Alternative space (non-real space drives). In SF parlance, often called hyperspace, hyper, jumpspace, FTL space, and other such words. EMF classification: "Type I; hyperdrive: The ships enters some different space during the trip, whether or not time passes for the crew while in this space."
1. [2.2.2.1] Alternative space with fixed nodes. Like teleport systems, a alternative space drive may require a fixed station.
1. [2.2.2.1.1] Hyperspace with transmitter and receiver. A fixed station boosts the ship into hyperspace; another station is needed to retrieve the ship out of hyperspace. In some variants, only specific locations are nodes which can be used to access hyperspace.
2. [2.2.2.1.2] Hyperspace with transmitter. A fixed station boosts the ship into hyperspace. (Babylon-5?)
3. [2.2.2.1.3] Hyperspace with receiver. A ship can enter hyperspace on its own, but needs a receiver to get back into real space. Another one I've never seen in SF.
4. [2.2.2.1.4] Hyperspace with distant transmitter. In this variant, a fixed machine is needed to access hyperspace, but the machine need not be at either the original location or the destination. I've never seen this in SF; included for completeness.
2. [2.2.2.2] Alternative space without fixed nodes.These are the variants of the classic SF hyperdrive. There are probably more examples of this in SF than all other of the drive types combined, and hence it is possible to make very fine divisions within the type. EMF classification: "Type I; hyperdrive: The ships enters some different space during the trip, whether or not time passes for the crew while in this space." The space is often explained away as being a dimension different from the four dimensions we currently can perceive (this explanation typically advanced by people who seem to have only a foggy idea what a "dimension" is). There are many variants based on the supposed "theory" of how the drive works, including entering a space where the speed of light is faster, entering a space which maps onto real space with a mapping such that points far apart in real space are closer in the alternative space, entering a space where the ship expands and then contracts to a different place, entering a space where everything moves at the same FTL speed, etc. Likewise, there are a long list of "conditions" which hyperspace drives are imagined to require. A common one is that the FTL space cannot be entered when "in the gravitational well of a massive body," (Niven, Ringworld series) or that your ship must have a high velocity in real space before you can enter FTL space (Niven, World of Ptavvs, O'Donnell, Fire on the Border) These two are convenient for sf writers, because they explain why spaceships are required. Important questions for hyperspace concepts are whether ships can see and/or dock with each other in hyperspace, whether all ships travel the same speed, and whether a ship can navigate while in hyperspace. These questions can also be asked of [2.2.2.1] "Hyperspace with fixed nodes". I will take this last to be the question used for subdivisions.
1. [2.2.2.2.1] "Jump" hyperspace. The destination is fixed when the ship enters the alternative space, either as a function of its position and velocity entering, or else by some settings in the drive. After a ship enters the alternative space, there is no way for it to change the destination. (e.g., GDW's "Traveller" RPG)
2. [2.2.2.2.2] Direction hyperspace. A ship's direction is fixed when the ship enters hyperspace (often, but not always, fixed by the direction the ship was traveling when it entered). How far it travels, however, is a variable that can be changed. Usually the distance is proportional to time spent in hyperspace, but may be a more complicated function. The ship may or may not be able to calculate its position in real space while in hyperspace.
3. [2.2.2.2.3] Navigable hyperspace. The ship is able to completely navigate in hyperspace. It may or may not be able to calculate its position in real space while in hyperspace. Sometimes the hyperspace may have geography or dangers which must be navigated around.
3. [3.0] Modifying the Universe. A final category of FTL, not precisely fitting in elsewhere, requires modifying the universe. Some items in this category also could be made to fit other categories.
1. [3.1] Modify distance in space. Remove or shrink the space between two points.
2. [3.2] Modify the speed of light. Change the value of the speed of light in the region where travel is desired (see [2.2.1.6] "Modified universal speed of light")
3. [3.3] Universal parameter change. Gain access to the parameters that describe the universe, possibly by hacking into the operating system that the universe runs. Find the parameters which describe your location. Rewrite these parameters to put you in the place you want to be. (e.g., Greg Bear, Moving Mars)

# From Wikipedia

Faster-than-light (also superluminal or FTL) communications and travel refer to the propagation of information or matter faster than the speed of light. Under the special theory of relativity, a particle (that has mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons).

On the other hand, what some physicists refer to as "apparent" or "effective" FTL[1][2][3][4] is the hypothesis that unusually distorted regions of spacetime might permit matter to reach distant locations faster than what it would take light in the "normal" route (though still moving subluminally through the distorted region).

Apparent FTL is not excluded by general relativity. Examples of apparent FTL proposals are the Alcubierre drive and the traversable wormhole, although the physical plausibility of these solutions is uncertain.

Outside of mainstream physics, others (often without physics training) have speculated on mechanisms that might allow FTL travel to be achieved, often relying on new conjectures of physics of their own invention, but their ideas have not gained significant acceptance in the physics research community. Fictional depictions of superluminal travel and the mechanisms of achieving it are also a staple of the science fiction genre.

## Travel

In the context of this article, FTL is transmitting information or matter faster than c, a constant equal to the speed of light in a vacuum, 299,792,458 meters per second, or about 186,282 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 below).
• Light travels at speed c/n when not in a vacuum but traveling through a medium with refractive index = n (causing refraction), and in some materials other particles can travel faster than c/n (but still slower than c), leading to Cherenkov radiation

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

## Possibility

Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. According to Einstein's theory of special relativity, what we measure as the speed of light in a vacuum is actually the fundamental physical constant c. This means that all 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. Going beyond the speed of light in a homogeneous space would hence require more than infinite energy, which is not generally considered to be a sensible notion.
• 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.[5] 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, 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,[6] or else to assume the Lorentz invariance to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).

## Justifications

Despite the established conclusion that relativity precludes FTL travel, some have proposed ways to justify FTL behaviour:

### Ignore special relativity

This option is popular particularly in science fiction. However, empirical and theoretical evidence strongly supports Einstein's theory of special relativity as the correct description of high-speed motion,[7] which generalizes the more familiar Galilean relativity, which is actually an approximation at conventional (much less than c) speeds. Similarly, general relativity is an overwhelmingly supported and experimentally verified theory of gravitation, except in the regime of very high energy densities over very short distances, where an as-yet-undeveloped theory of quantum gravity is necessary. Special relativity, however, is incorporated easily into quantum field theories. Therefore, even in the broader contexts of general relativity and quantum mechanics, conventional acceleration from subluminal to superluminal speeds is not possible.

### Faster light (Casimir vacuum and quantum tunnelling)

Einstein's equations of special relativity postulate that the speed of light 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 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 the vacuum energy. This vacuum energy can perhaps be changed in certain casesThe truth.. 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.[8] Accordingly there has as yet been no experimental verification of the prediction. A recent analysis[9] argued out 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 (with the hope that such a theory would guarantee the impossibility of a true time machine ever forming). 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.[10]

The physicists Günter Nimtz and Alfons Stahlhofen, of the University of Koblenz, claim to have violated relativity experimentally by transmitting photons faster than the speed of light.[11] 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 apart, using a phenomenon known as quantum tunnelling. 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 at each station along the way, so that the center of the train moves forward at each stop; in this way, the center of the train exceeds the speed of any of the individual cars.[12]

### Give up causality

Another approach is to accept special relativity, but to posit that mechanisms allowed by general relativity (e.g., wormholes) will allow traveling between two points without going through the intervening space. While this gets around the infinite acceleration problem, it still would lead to closed timelike curves (i.e., time travel) and causality violations. Causality is not required by special or general relativity, but is nonetheless generally considered a basic property of the universe that should not be abandoned. Because of this, most physicists expect (or perhaps hope) that quantum gravity effects will preclude this option.The truth. An alternative is to conjecture that, while time travel is possible, it never leads to paradoxes; this is the Novikov self-consistency principle.

An important point to note is that in general relativity it is possible for objects to be moving apart faster than light because of the expansion of the universe, in some reasonable choice of cosmological coordinates. This is understood to be due to the expansion of the space between the objects, and general relativity still reduces to special relativity in a "local" sense, meaning that two objects passing each other in a small local region of spacetime cannot have a relative velocity greater than c, and will move more slowly than a light beam passing through the region. (See Option F below)

### 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. One consequence of this theory is a variable speed of light, where photon speed would vary with energy, and some zero-mass particles might possibly travel faster than c. While recent evidenceThe truth. casts doubt on this theory, some physicists still consider it viable.The truth. However, even if this theory is accurate, it is still very unclear whether it would allow information to be communicated, and appears not in any case to allow massive particles to exceed c.

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.

### Non-physical realms

A very popular option in space opera is to assume the existence of some other realm (typically called hyperspace, subspace, or slipspace) which is accessible from this universe, in which the laws of relativity are usually distorted, bent, or nonexistent, facilitating rapid transport between distant points in this universe, sometimes with acceleration differences - that is, not requiring as much energy or thrust to go faster. To accomplish rapid transport between points in hyperspace/subspace, special relativity is often assumed not to apply in this other realm, or that the speed of light is higher. Another solution is to posit that distant points in the mundane universe correspond to points that are close together in hyperspace.

This method of faster-than-light travel does not correspond to anything seriously proposed by mainstream science.

### Space-time 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.[13] Miguel Alcubierre theorized that it would be possible to create an Alcubierre 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. 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 which travels 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.

Dr. Gerald Cleaver, associate professor of physics at Baylor University, and Richard Obousy, a Baylor graduate student, theorize that by manipulating the extra spatial dimensions of string theory around a spaceship with an extremely large amount of energy, it 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, just like it did after the Big Bang, when the universe expanded much faster than the speed of light for a very brief time.[14]

### Quantized space and time

As given by the planck length, there is a minimum amount of 'space' that can exist in this universe (1.616×10−35 meters). This limit can be used to determine a minimum time quantisation of 5.391×10−44 seconds, which corresponds to a beam of light with a wavelength approaching the planck length. This means that there is a physical limit to how much blue shift a beam of light can endure. According to general relativity there is no limit to this shift, and an infinitesimally small space can exist, but according to well accepted quantum theory these limits do exist.

This is precisely what happens towards the center of a black holeThe truth.; the incoming light becomes blue shifted past the planck length as it approaches the region of discontinuity within our universe. The argument is: if a black hole with finite mass can create such a discontinuity in the fabric of space and time, why would people be unable to do the same thing using a finite amount of energy and acceleration? (According to general relativity, the space-time distortions caused by gravity are fundamentally identical to space-time distortions caused simply by accelerating your reference frame).

## Tachyons

In special relativity, while it is impossible to accelerate an object to the speed of light, or for a massive object to move at the speed of light, it is not impossible for an object to exist which always moves faster than light. The hypothetical elementary particles that have this property are called tachyons. Their existence has neither been proven nor disproven, but even so, attempts to quantise them show that they may not be used for faster-than-light communication.[15] Physicists sometimes regard the existence of mathematical structures similar to Tachyons arising from theoretical models and theories as signs of an inconsistency or that the theory needs further refining.[16]

## 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 agrees that any technique for faster-than-light travel could also be used for time travel. This raises problems with causality. Many physicists believe that the above phenomena are in fact 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 Gimon and Petr Hořava have argued[17] that in a supersymmetric five-dimensional Gödel universe quantum corrections to general relativity effectively cut off regions of spacetimes 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.

## FTL phenomena

In these 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.

If a laser is swept across a distant object, the spot of light can easily be made to move at a speed greater than c.[18] Similarly, a shadow projected onto a distant object can be made to move faster than c.[19] In neither case does any matter or information travel faster than light.

### Closing speeds

An observer may conclude that two objects are moving faster than the speed of light relative to each other, by adding their velocities according to the principle of Galilean relativity.

For example, two fast-moving particles approaching each other from opposite sides of a particle accelerator will appear to be moving at slightly less than twice the speed of light, relative to each other, from the point of view of an observer standing at rest relative to the accelerator. This correctly reflects the rate at which the distance between the two particles is decreasing, from the observer's point of view and is called the closing speed. However, it is not the same as the velocity of one of the particles as would be measured by a hypothetical fast-moving observer traveling alongside the other particle. To obtain this, the calculation must be done according to the principle of special relativity. If the two particles are moving at velocities v and -v, or expressed in units of c, $\beta$ and $-\beta$, where

$\beta \equiv v/c \,\!$

then this relative velocity (again in units of the speed of light c) is

$\beta_{rel} = { \beta - (-\beta) \over 1 + \beta ^2 } = { 2\beta \over 1 + \beta^2 }$,

which is less than the speed of light.

### 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 travelled, 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.

### 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[20]. 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[21]. Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.

### Group velocities above c

The group velocity of a wave (e.g. a light beam) may also exceed c in some circumstances. 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, even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, basically 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, the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than without this effect.

### Universal expansion

The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving 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] 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 – 1030.[23]

### 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,[24] when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, 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.[25] 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, appear to transmit 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 event 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 behaviour doesn't violate local causality or allow FTL 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. To quote Richard Feynman:

… there is also an amplitude for light to go faster (or slower) than the conventional speed of light. You found out in the last lecture that light doesn't go only in straight lines; now, you find out that it doesn't go only at the speed of light! It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, c.[26]

Richard Feynman

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 tunneling phenomenon. Usually, such reports deal with a phase velocity or group velocity faster than the vacuum velocity of light. But, recall from above, that a superluminal phase velocity cannot be used for faster-than-light transmission of information. There has sometimes been confusion concerning the latter point.

Quantum teleportation transmits quantum information at whatever speed is used to transmit the same amount of classical information, likely the speed of light. This quantum information may theoretically be used in ways that classical information can not, such as in quantum computations involving quantum information only available to the recipient. In science fiction, quantum teleportation is either used as a basis for teleportation of physical objects at the speed of light, presumably preserving some important aspect of the entanglement between the particles of the object, or else is misrepresented as allowing faster-than-light communication.

#### Hartman effect

The Hartman effect is the tunnelling effect through a barrier where the tunnelling time tends to a constant for large barriers.[27] This was first described by Thomas Hartman in 1962.[28] 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 finite 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.[29]

However, an analysis by Herbert Winful from the University of Michigan suggests that 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".[30] Winful means by this that the photons crossing the barrier are virtual photons only existing in the interaction and could not be propagated into the outside world.

#### Casimir effect

In physics, the Casimir effect or 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, due 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. Energy appears suddenly as if it came from the vacuum. See Option B above for a discussion of whether or not this effect could actually be used to send signals faster than c or violate causality.

We can also quote the spectacular case of the thought experiment of Einstein, Podolski and Rosen (EPR paradox) which could be realized in experiments for the first time by Alain Aspect in 1981 and 1982. In this case, the measurement of the state on one of the quantum systems of an entangled pair forces the other system to be measured in the complementary state. Thus functions quantum teleportation.

An experiment performed in 1997 by Nicolas Gisin at the University of Geneva has demonstrated nonlocal quantum correlations between particles separated by over 10 kilometers.[31] But as noted earlier, the nonlocal correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved; see no-communication theorem for further information.

#### Delayed choice quantum eraser

Delayed choice quantum eraser (The experiment of Marlan Scully) is an alternative 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, [32] 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 (see the delayed choice quantum eraser article for further information).

## Variable speed of light

In conventional physics, the speed of light in a vacuum is assumed to be a constant. There exist theories which postulate that the speed of light is not a constant. The interpretation of this statement is as follows.

The speed of light is a dimensional quantity and so, as has been emphasized in this context by João Magueijo, it cannot be measured.[33] Measurable quantities in physics are, without exception, dimensionless, although they are often constructed as ratios of dimensional quantities. For example, when you measure the height of a mountain you really measure the ratio of its height to the length of a meterstick. 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[34]. 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.[35] 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.

Magueijo's proposal used 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.

While it may be mathematically possible to construct such a system, it is not clear what additional explanatory power or physical insight such a system would provide, assuming that it does indeed accord with existing empirical data.

## Notes

1. Gonzalez-Diaz, Pedro F. (2000). "Warp drive space-time" (PDF). Physical Review D 62: 044005–1–044005–7. DOI:10.1103/PhysRevD.62.044005.  Template:Arxiv
2. http://arxiv.org/pdf/gr-qc/0107097
3. PDF for gr-qc/9810026
4. PDF for gr-qc/9908023
5. Einstein, A, Relativity:the special and the general theory, pp25-27, Methuen & Co, 1927.
6. Gott, J. Richard (2002). Time Travel in Einstein's Universe.  pp82-83
7. What is the experimental basis of Special Relativity?
8. http://www.nat.vu.nl/~scharnh/m16scine.htm Science News: Secret of the vacuum: Speedier light
9. S. Liberati, S. Sonego and M. Visser, Faster-than-c signals, special relativity, and causality, Annals Phys. 298, 167-185 (2002) preprint.
10. [0706.0553] Can Light Signals Travel Faster than c in Nontrivial Vacuua in Flat space-time? Relativistic Causality II
11. Macroscopic experiments with virtual photons
12. Charles H. Lineweaver and Tamara M. Davis (March 2005). "Misconceptions about the Big Bang". Scientific American.
13. Traveling Faster Than the Speed of Light: A New Idea That Could Make It Happen Newswise, Retrieved on August 24, 2008.
14. Feinberg, Gerald (1967). "Possibility of Faster-Than-Light Particles". Physical Review 159: 1089–1105. DOI:10.1103/PhysRev.159.1089.
15. Gates, S. James. Superstring Theory: The DNA of Reality.
16. Gimon, Eric G.; Petr Horava (May 2004). Over-rotating black holes, Gödel holography and the hypertube. Retrieved on 2006-06-05.
17. Hecht, Eugene (1987). Optics, 2nd ed., Addison Wesley, 62. ISBN 0-201-11609-X.
18. MathPages - Phase, Group, and Signal Velocity. Retrieved on 2007-04-30.
19. Cosmology Tutorial - Part 2
20. Inflationary Period from HyperPhysics
21. Rees, M. J., "Appearance of relativistically expanding radio sources", Nature 211, 468, 1966.
22. R. D. Blandford, C. F. McKee and M. J. Rees, "Super-luminal expansion in extragalactic radio sources", Nature 267, 211, 1977.
23. Feynman. "Chapter 3", QED, 89.
24. J.C. Martinez, and E. Polatdemir, "Origin of the Hartman effect", Physics Letters A, Vol 351, Iss 1-2, 20 February 2006, pp31-36.
25. T. E. Hartman, "Tunneling of a wave packet", J. Appl. Phys. 33, 3427 (1962).
26. G. Nimtz, A. A. Stahlhofen, "Macroscopic violation of special relativity", 5 August 2007 available as eprint [1]
27. Winful, H, "Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox", Physics Reports, Vol 436, Iss 1-2, December 2006, pp1-69.
28. History
29. Delayed Choice Quantum Eraser
30. Magueijo, João (1999). A time varying speed of light as a solution to cosmological puzzles. Retrieved on 2006-06-05.

## References

• D F Falla and M J Floyd, "Superluminal motion in astronomy", Eur. J. Phys. 23 69-81, 2002