Faster-than-light

Faster-than-light (also supraluminal or FTL) communications and travel are staples of the science fiction genre. However, according to physics as currently understood, these concepts are outright impossible, as well as being well beyond our current technology.

Relativity

Special relativity

Special relativity makes the speed of light (299,792,458 metre per second in vacuum) an absolute speed limit for the transmission of information. All observed particles with mass travel slower. (To be precise, it requires an infinite amount of energy to accelerate a massive object to the speed of light.) The observed speed of a massive particle depends on the observer's frame of reference. Observers in the particle's rest frame (i.e. observers who "move along with" the particle) would say the particle is at rest. Observers in all other equally valid frames of reference may perceive the particle to be traveling at any speed less than the speed of light. Meanwhile, massless particles, such as the photon, are required to travel at exactly the speed of light. (A massless particle can have no rest frame.)

How can the speed of light be a cosmic speed limit? Let's perform a series of thought experiments in special relativity.

Build a rocket that accelerates steadily and has lots of fuel. Set it to accelerating. Sooner or later it will go faster than the speed of light, won't it? In fact it won't; the problem is that as objects travel at speeds close to the speed of light (relative to an observer), their clocks (and all other processes) seem to slow down. So while the rocket was shooting out fuel at a tremendous speed initially, when it nears the speed of light it starts shooting out the fuel ever more slowly, and its acceleration correspondingly decreases so that it can never quite reach the speed of light.

Suppose that we try to help the rocket along by giving it a push. We have a new problem: the rocket's mass has also apparently increased as it nears the speed of light, and it continues to increase as the speed increases. (What's really going on isn't that the mass of the rocket is increasing, rather it's that Newton's second law (<math>F = ma<math>) is not valid at very high speeds. It seems as if the mass "m" is getting bigger, because at greater speeds we must use a bigger force "F" to achieve the same amount of rocket acceleration "a".) Bottom line: we cannot go faster than the speed of light in this way either.

One possibility for overcoming this is to use the force of gravity to pull the ship along. At this point we must leave special relativity and enter the realm of general relativity.

General relativity

The limit is not quite as absolute in general relativity. That theory forbids a massive object to accelerate to the speed of light, just as special relativity does. However, it allows spacetime to be distorted in a fashion which causes an object to move faster than light from the point of view of a distant observer. That object still moves slower than light in its own reference frame. One such arrangement is the Alcubierre drive metric, which can be thought of as producing a traveling wave in spacetime that carries an object along with it. Another possibility is the wormhole, which provides a "short cut" between two distant locations. To date there is no feasible way to construct any such special curvature; they all require unknown exotic matter, enormous (but 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 of causality. Many physicists believe that the above phenomena are in fact impossible, and future theories of gravity will prohibit them.

Astronomy

Superluminal motion in Quasars

In some Radio galaxies, Blazars, Quasars and recently also in some galactic sources called Microquasars apparent velocities faster than light are observed (see Superluminal motion for more details). The effect was predicted before the first observations and explained as an optical illusion caused by a light travel time effect. The astronomical observation contain no physics which would not be compatible with the theory of special relativity. Actual derived velocities, however, are close to the speed of light (relativistic motion). They are the first examples in which a bulk of mass is moving close to the speed of light. In Earth-bound laboratories such large velocities are only seen on the level of a limited number of elementary particles.

Cosmic inflation

The universe on large scales appears homogeneous and isotropic. On second thought, this is rather surprising, since it also holds for those parts that are too far apart to influence each other (for example, seen in opposite direction). Technically, this is expressed by saying they are not within each other's horizon which is limited by the speed of light. Homogeneity and isotropy is explained in the theory of cosmic inflation. The idea is, that objects (such as particles with mass) cannot travel faster than light, but space itself can. In the inflation theory it is assumed that space itself dramatically expands (with velocities much larger than the speed of light) in the first few pico seconds after the big bang.

Quantum mechanics

Certain phenomena in quantum mechanics, such as entanglement, appear to transmit information faster than light. These phenomena do not allow true communication; they only let two observers in different locations know what the other must see. The fact that the laws of physics seem to conspire to prevent superluminal communications via quantum mechanics is very interesting and somewhat poorly understood.

In the context of quantum field theory, in the framework of local quantum physics, this is the requirement that if O is a bounded open subset of spacetime, then the observable algebra of the causal completion of O is the same as the observable algebra over O. Certainly, there are QFT models where this axiom does NOT hold and so, why this axiom holds is an open question.

It has been postulated that there could exist a class of particles (known as tachyons) which must always travel faster than light, but such particles have never been observed. 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.

Non-informative phenomena

Processes which do not transmit information may move faster than light. A good example is a beam of light projected onto a distant surface. The spot where the beam strikes is not a physical object. 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. This effect is believed to be responsible for supernova ejecta appearing to move faster than light as observed from Earth. It could also be demonstrated with a large laser reflecting off the surface of the moon.

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, 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

<math>\beta = v/c \,\!<math>

and

<math>-\beta = -v/c \,\!<math>,

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

<math>\Delta\beta = { \beta + \beta \over 1 + \beta \beta } = { 2\beta \over 1 + \beta^2 }<math>,

which is less than the speed of light.

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.