# Faster-than-light

(Redirected from FTL)

Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. However, according to physics as currently understood, these concepts require exotic conditions that are certainly well beyond our current technology to establish, and that may be directly forbidden by more complete models of the universe's physical laws. Should FTL travel or communication be possible, problems with causality will occur.

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## Relativity

Main article: Theory of Relativity

According to Einstein's theory of Relativity, the linear speed of any normal object can only be measured relative to other objects. To explain, examine the case of two observers passing each other in an otherwise empty universe. To each observer, the other observer would seem to be moving, while the observer himself remains stationary. Relativity states that neither of these views is "correct" - they are both perfectly valid. Each observer's motion can only be defined in a given 'frame of reference'.

Massless particles follow different rules, however. They are required to travel at exactly the speed of light, and that speed is (necessarily) independent of the frame of reference of the observer. This leads to some interesting consequences, explained below.

The fundamental obstacle to travelling faster than light in relativity comes from the Lorentz transformations. When relativity is taken into account, the concept of simultaneity becomes relative. In other words, if I observe two events that are not at the same location and conclude that they occurred at the same time, another observer (moving relative to me) may perfectly correctly conclude that one occurred before the other. A third observer might disagree on which came first. If one of the events caused the other, this would be a distressing situation: to some observers, the cause would happen after the event. Nothing is wrong with these observers; their point of view is as correct as anyone else's. Fortunately (in special relativity), if one can get from one event to the other by travelling slower than light, all observers will agree on the order. However, any two events that would require you to travel faster than light to get from one to the other will appear in different orders to different observers. So if ever someone travels faster than light, some observers will see them travelling back in time. So, in both special and general relativity, faster-than-light travel is the same thing as time travel. (Faster-than-light communication poses exactly the same problems, and in fact is much easier to analyze).

This fact does not rule out the possibility of faster-than-light travel; in fact, general relativity seems to permit it. But while faster-than-light travel does not appear to lead to any obvious paradoxes or violate any fundamental principles of physics, time travel certainly does: it leads to the grandfather paradox (among many others) and it violates the principle of causality.

In a sense, when people assert that relativity forbids faster-than-light travel, what they mean is that relativity says that faster-than-light travel leads to all kinds of problems, so we hope that something forbids faster-than-light travel. Fortunately, in special relativity, it seems to be possible to find problems with any proposed scheme for faster-than-light travel. In general relativity, this is much more difficult, and solutions to the equations producing closed timelike cycles do exist; in this case we hope that quantum gravity will forbid time travel (and, consequently, faster-than-light travel).

### Special relativity

Special relativity states that there is an absolute speed limit for the transmission of information through conventional space: the speed of light in a vacuum, roughly 300 million metres per second. Note that there are some processes which do propagate faster than light, but which don't carry any information faster than light (See the section on existing FTL motion in this article). Although it seems counter-intuitive, light will be seen to move at the speed of light regardless of the frame of reference of the observer. A flashlight in a moving train will not produce light with a speed in excess of the speed of light. Both an observer in the train and one on the stationary platform will measure the same speed of light, in reference to their own reference points. This results in the Lorentz transformations; observers moving with respect to one another do not agree on the size of an object nor on simultaneity. Despite this apparent disagreement, all points of reference are fundamentally equally valid.

Relativity also shows that no object with a rest mass of greater than zero can be accelerated to light speed or above. Furthermore, accelerating an object to relativistic speeds (speeds at which relativity becomes important) requires an increasing amount of energy as an object approaches the speed of light. An infinite amount of energy would be necessary to accelerate the object to light speed. In a non-accelerating observer's frame of reference, the accelerating object would appear to be getting shorter and moving more slowly through time (see Time dilation), in accordance with the Lorentz transformations, as well as gaining mass. However, from the accelerating object's point of view, it would merely appear to be accelerating normally while the speed of the light ahead remained constant and unattainable.

At relativistic speeds, velocities add in an unusual way. An observer A, moving away from Earth at a cruising speed of half the speed of light can be stationary from his point of view. Accelerating to a speed of half the speed of light would seem perfectly possible, and indeed, it is. But from the perspective of an observer on Earth B, observer A would be moving at just 0.613 times the speed of light. See the addition of velocities formula:

[itex]\frac{v+u}{1+\left ( \frac{vu}{c^2} \right)}[itex]

which adds speeds v and u together, while [itex]c[itex] represents the speed of light.

Mathematically, while is impossible to accelerate an object to the speed of light, or for an object to move at the speed of light, it is not impossible for an object to exist at a speed greater than the speed of light. Particles that would use this mathematical loop hole are called tachyons, though their existence has neither been proven nor disproven. If they exist and can interact with normal matter, they would also allow causality violations. If they exist but cannot interact with normal matter, their existence cannot be proven, so they might as well not exist.

Mathematically, it is also possible for an object to travel at speeds greater than the speed of light, by not accelerating. Theoretically, warping the space around an object could move an object, without accelerating it. At this point we leave special relativity, and enter the realm of general relativity.

### General relativity

General relativity was developed after special relativity, to include concepts like gravity. While it still maintains that no object can move faster than light, it allows for spacetime to be distorted. An object could move faster than light from the point of view of a distant observer, while moving at sublight speed from its own reference frame. One such arrangement 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. To date there is no feasible way to construct any such special curvature; they all require unknown exotic matter, enormous (though finite) amounts of energy, or both.

General relativity predicts 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.

### Disputing claims

All of the above is based on Einstein's theory of relativity. Some theorists have proposed that, like Newton's theories on motion, Einstein's theory of relativity might be replaced by a newer theory. Such alternative theories exist. However, the overwhelming majority of physicists are still convinced that so far no sufficient evidence exists which could support the withdrawal of relativity in the favour of an alternative theory.

Some calculations show that it should be mathematically possible to transmit information faster than light. But as a basis, these calculations use theories that exclude faster than light transmission. Obviously, there is a logical flaw, somewhere.

Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed, and can be explained as an optical illusion caused by the object moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these object 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. In Earth-bound laboratories, we've been able to accelerate just elemental particles to such speeds.

The possibility of faster-than-light propagation of information appears quite unlikely to the best of our current knowledge.

## Quantum mechanics

Certain phenomena in quantum mechanics, such as quantum entanglement, appear to transmit information faster than light. 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. The fact that the laws of physics seem to conspire to prevent superluminal communications via quantum mechanics is very interesting and somewhat poorly understood.

The speed of light can have any value within the limits of the uncertainty principle as demonstrated in any Feynman diagram that draws a photon at any angle other than 45 degrees. 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" (Chapter 3, page 89 of Feynman's book QED). However, this does not imply the possibility of superluminal information transmission, as no photon can have an average speed in excess of the speed of light.

There have been various experimentally based reports of 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 above the vacuum velocity of light, but not with faster-than-light transmission of information, although there has sometimes been a degree of confusion concerning the latter point.

As it is currently understood, quantum mechanics doesn't allow for faster-than-light communication.

## Apparent FTL

### Moving spot of light

Processes which do not transmit information may move faster than light. A good example is a beam of light projected onto a distant surface, such as the Moon. The spot where the beam strikes is not a physical object, just a point of light. Moving it (by reorienting the beam) does not carry information between locations on the surface. To put it another way, the beam can be considered as a stream of photons; where each photon strikes the surface is determined only by the orientation of the beam (assuming that the surface is stationary). If the distance between the beam projector and the surface is sufficiently far, a small change of angle could cause successive photons to strike at widely separated locations, and the spot would appear to move faster than light. If the surface is at the distance of the moon, a light source mounted on a phonograph is changing angle rapidly enough to create this effect. This effect is believed to be responsible for supernova ejecta appearing to move faster than light as observed from Earth. See the section in this article.

It is also possible for two objects to move faster than light relative to each other, but only from the point of view of an observer in a third frame of reference, who naively adds velocities according to galilean relativity. An observer on either object will see the other object moving slower than light.

For example, fast-moving particles on opposite sides of a circular 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, and who naively adds velocities according to galilean relativity. However, if the observer has a good intuition of special relativity, and makes a correct calculation, and the two particles are moving, for example, at velocities [itex]\beta[itex] and [itex]-\beta[itex]

[itex]\beta = v/c \,\![itex]

and

[itex]-\beta = -v/c \,\![itex],

then from the observer's point of view, the relative velocity Δβ (again in units of the speed of light c) is

[itex]\Delta\beta = { \beta - -\beta \over 1 + \beta ^2 } = { 2\beta \over 1 + \beta^2 }[itex],

which is less than the speed of light.

### Phase velocities above c

The phase velocity of a wave can easily exceed c, the vacuum velocity of light. In principle, this can occur even for simple mechanical waves, even without any object moving with velocities close to or above c. However, this does not imply the propagation of signals with a velocity above c.

### Group velocities above c

Under certain circumstances, even the group velocity of a wave (e.g. a light beam) can exceed c. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum 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.

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