# Fasterthanlight

Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. There are two alternative ways of interpreting the speed limit of lightspeed for information transfer. It could be taken to mean literally what it says - no information can travel faster than light in a vacuum, even though the speed of light itself could change depending on the nature of the vacuum. Current physics strongly suggests this is the case. As such, it imposes no speed limit on information transfer, since the maximum speed posited, the speed of light, can be increased. Or we could take it to mean that no information can travel faster than 'c', roughly 300 million metres per second.

## Terminology

In the context of this article, FTL actually refers to the transmission of information or matter faster than c, a constant equal to the speed of light in a vacuum, roughly 300 million metres per second. This is not quite the same as travelling faster than light, since:

• There are some processes which do propagate faster than c, but which can't actually carry information (See the Apparent FTL section in this article).
• Light itself will travel slower than c when not in a vacuum (causing refraction), and in certain materials other particles can travel faster than it (but still slower than c), leading to Cherenkov radiation.

Neither of these phenomena violate special relativity or create problems with causality, and thus do not qualify as FTL as described here.

## Possibility of FTL

Faster-Than-Light travel or communication is problematic in a universe that is consistent with Einstein's Theory of Relativity. In a hypothetical universe where Newton's laws of motion and the Galilean transformations are exact, rather than approximate, the following would be true:

However, 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 acceleration or relative velocity, will always measure zero-mass particles (e.g., gravitons as well as photons) naturally traveling at c. This result means that measurements of space, time, and velocity are not consistent between different reference frames, but are instead related by the Lorentz transformations. These transformations have important implications:

• 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
• Equivalently, 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 a sensible notion.

Because of this, there appear to be only four ways to justify Faster-Than-Light behavior:

### Option A: ignore special relativity

This is the simplest solution, and is particularly popular in science fiction. Alas, empirical evidence unanimously affirms that the universe obeys Einstein's laws rather than Newton's where they disagree. And while physicists consider General Relativity only an approximation (due to its incompatibility with quantum mechanics), virtually all consider special relativity exact, and there appear to be no serious theoretical challenges to its supremacy.

### Option B: get light to go faster

Einstein's equations of special relativity posit 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 itself. That is an experimentally determined quantity.

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 be changed in certain cases. When vacuum energy is lowered, light itself can go faster than the standard value 'c'. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at millimeter/micrometer spacing. It is called a Casimir vacuum. Calculations show light will go faster in such a vacuum. However, there has been no experimental verification, since the technology to detect the change isn't here yet.

Einstein's equations of special relativity have an implicit assumption of homogeneity. Space is assumed to be the same everywhere. In the case of the Casimir vacuum, this assumption is clearly violated. Inside the Casimir vacuum, we have homogenous space, and outside it, we have homogenous space as well. Inside the Casimir vacuum, the equations of special relativity will apply with the increased value of the speed of light. Outside it, the equations of special relativity will apply with the normal 'c'. However, when considering two frames of reference, one inside the vacuum, and one outside, the equations of special relativity can no longer be applied, since the assumption of homogeneity has been broken. In other words, the Casimir effect breaks up space into distinct homogenous regions, each of which obey the special relativity laws separately.

### Option C: give up causality

The other 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 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. An alternative is to conjecture that, while time travel is possible, it somehow never leads to paradoxes; this is the Novikov self-consistency principle.

Note that causality is often misunderstood in this context. Just seeing time in another frame pass in reverse does not violate causality. In a sense, this is equivalent to recording an event and playing it in reverse. It is the ability to send a signal back to the past that violates causality. Moving faster than the speed of light will enable a person to view events in another frame in reverse time. But just motion faster than light alone does not allow the sending of signals back into the past of the other frame. Many cases of faster than light travel do allow such signalling, and hence are considered unviable. But it is not a must that causality violation result from faster than light travel.

### Option D: give up (absolute) relativity

Due to the strong empirical support for special relativity, any modifications to it must necessarily be quite subtle and difficult to measure. The most well-known attempt is double 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 evidence casts doubt on this theory, some physicists still consider it viable. However, even if this theory is true, it is still very unclear that 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.

## 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.

Tachyons are not structurally stable. The equations of relativity do allow faster than light travel, since the equations are symmetric about the velocity 'c', the speed of light. However, any particle which is moving faster and faster, at velocities less than 'c', ends up with more and more kinetic energy. This is true even in the classical model, but with special relativity, as the velocity approaches 'c', the energy goes to infinity.

Once the velocity crosses 'c', the energy has no place to go but down. In other words, a particle with mass moving at any speed above 'c' will lose energy when its velocity goes up even further. Put another way, such a particle will speed up when it loses energy.

Everything that moves causes a change in the structure of the fabric of space. This change in the structure of the fabric of space causes the formation of gravitational ripples (waves), which carry away energy. In most cases, the change is so minor, it is ignorable. However, for a particle with mass moving above 'c', even a tiny loss of energy is troublesome. As mentioned above, it actually increases the velocity, causing more energy loss, which increases the velocity further. This positive feedback loop causes the particle to soon reach infinite velocity. In effect, the particle vanishes.

This structural instability of tachyons is a significant limitation to their practical value, if they do indeed exist.

## 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 its own reference frame. However, it permits distortions in spacetime that allow an object to move faster than light from the point of view of a distant observer, even though it always moved slower than light in its own reference frame. 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. To date there is no feasible way to construct any such special distortion; they all require unknown exotic matter, enormous (though finite) amounts of energy, or both.

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.

## 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 which 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.

### Relative motion

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 $\displaystyle \beta$ and $\displaystyle -\beta$

$\displaystyle \beta = v/c \,\!$

and

$\displaystyle -\beta = -v/c \,\!$ ,

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

$\displaystyle \Delta\beta = { \beta - -\beta \over 1 + \beta ^2 } = { 2\beta \over 1 + \beta^2 }$ ,

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.

### 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, 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.

### 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 is completely consistent with special relativity, and doesn't allow for faster-than-light communication.