Superluminal Neutrinos

Faster-than-light (superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light in vacuum (). The special theory of relativity implies that only particles with zero rest mass (i.e., photons) may travel ''at'' the speed of light, and that nothing may travel faster.

Particles whose speed exceeds that of light (tachyons) have been hypothesized, but their existence would violate causality and would imply time travel. The scientific consensus is that they do not exist.

According to all observations and current scientific theories, matter travels at slower-than-light (subluminal) speed with respect to the locally distorted spacetime region. Speculative faster-than-light concepts include the Alcubierre drive, Krasnikov tubes, traversable wormholes, and quantum tunneling. Some of these proposals find loopholes around general relativity, such as by expanding or contracting space to make the object appear to be travelling greater than ''c''. Such proposals are still widely believed to be impossible as they still violate current understandings of causality, and they all require fanciful mechanisms to work (such as requiring exotic matter).

Superluminal travel of non-information

In the context of this article, "faster-than-light" means the transmission of information or matter faster than ''c'', a constant equal to the speed of light in vacuum, which is 299,792,458 m/s (by definition of the metre) or about 186,282.397 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 examples in the sections immediately following).
*In some materials where light travels at speed ''c/n'' (where ''n'' is the refractive index) other particles can travel faster than ''c/n'' (but still slower than ''c''), leading to Cherenkov radiation (see phase velocity below).
Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as faster-than-light as described here.

In the following 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.

Daily sky motion

For an earth-bound observer, objects in the sky complete one revolution around the Earth in one day. Proxima Centauri, the nearest star outside the Solar System, is about four and a half light-years away.
In this frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater than ''c'' as the rim speed of an object moving in a circle is a product of the radius and angular speed. It is also possible on a geostatic view, for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000 AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.

Light spots and shadows

If a laser beam is swept across a distant object, the spot of laser light can seem to move across the object at a speed greater than ''c''. Similarly, a shadow projected onto a distant object seems to move across the object faster than ''c''.
In neither case does the light travel from the source to the object faster than ''c'', nor does any information travel faster than light. No object is moving in these examples. For comparison, consider water squirting out of a garden hose as it is swung side to side: water does not instantly follow the direction of the hose.

Closing speeds

The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.

Imagine two fast-moving particles approaching each other from opposite sides of a particle accelerator of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.

Special relativity does not prohibit this. It tells us that it is wrong to use Galilean relativity to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correct velocity-addition formula for computing such relative velocity.

It is instructive to compute the relative velocity of particles moving at ''v'' and −''v'' in accelerator frame, which corresponds to the closing speed of 2''v'' > ''c''. Expressing the speeds in units of ''c'', ''β'' = ''v''/''c'':
:$\beta_\text = \frac = \frac \leq 1.$

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 traveled, 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 would.

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. 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.
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 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, 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 (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than ''c'' without this effect. However, group velocity can exceed ''c'' in some parts of a Gaussian beam in vacuum (without attenuation). The diffraction causes the peak of the pulse to propagate faster, while overall power does not.

Cosmic expansion

According to Hubble's law, the expansion of the universe causes distant galaxies to appear to recede from us faster than the speed of light. However, the recession speed associated with Hubble's law, defined as the rate of increase in proper distance per interval of cosmological time, is not a velocity in a relativistic sense. Moreover, in general relativity, velocity is a local notion, and there is not even a unique definition for the relative velocity of a cosmologically distant object. Faster-than-light cosmological recession speeds are entirely a coordinate effect.

There are many galaxies visible in telescopes with redshift numbers of 1.4 or higher. All of these have cosmological recession speeds greater than the speed of light. Because the Hubble parameter is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.

However, because the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological event horizon where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in ). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.

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

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