Faster-than-light

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 almost certainly occur.

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 Cerenkov 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:

• space and time measurements always give the same results in every 'frame of reference'
• velocities add linearly
• there is nothing fundamental about the wave velocity of light
• Simultaneity is a well-defined concept

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 surprising 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 two 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 non-zero amount time

• transmitting information faster than c can violate causality; more precisely, doing this produces situations where observers in different reference frames will disagree on the order of causally-linked events.

Because of this, there appear to be only three 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: 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). 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.

Option C: Modify special 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.

Tachyons

Mathematically, 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 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 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 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.

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 $\beta$ and $-\beta$

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

and

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

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

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

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.

External links

• Encyclopedia of laser physics and technology on "superluminal transmission", with more details on phase and group velocity, and on causality
• July 22, 1997, The New York Times Company: Signal Travels Farther and Faster Than Light Quote: "..."We find," Chiao said, "that a barrier placed in the path of a tunneling particle does not slow it down. In fact, we detect particles on the other side of the barrier that have made the trip in less time than it would take the particle to traverse an equal distance without a barrier -- in other words, the tunneling speed apparently greatly exceeds the speed of light. Moreover, if you increase the thickness of the barrier the tunneling speed increases, as high as you please..."
• Markus Pössel: Faster-than-light (FTL) speeds in tunneling experiments: an annotated bibliography Quote: "...An experiment of theirs, where a single photon tunnelled through a barrier and its tunneling speed (not a signal speed!) was 1.7 times light speed, is described in Steinberg, A.M., Kwiat, P.G. & R.Y. Chiao 1993: "Measurement of the Single-Photon Tunneling Time" in Physical Review Letter 71, S. 708--711..."
• Relativity and FTL (=Superluminal motion) Travel Homepage
• The Warp Drive: Hyper-Fast Travel Within General Relativity, Miguel Alcubierre Class. Quantum Grav. 11 (1994), L73-L77 Quote: "...It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed..."
• NASA: Status of "Warp Drive" Maturity - speculation
• Usenet Physics FAQ: is FTL travel or communication Possible?
• Critique of Geometro-Stochastic Theory
• Superluminal
• The Speed of Light: How Fast Can We Go?
• Smarandache Hypothesis
• Light Speed