Superluminal -- from Eric Weisstein's World of Physics

A superluminal phenomenon is a frame of reference traveling with a speed greater than the speed of light c. There is a putative class of particles dubbed tachyons which are able to travel faster than light. Faster-than-light phenomena violate the usual understanding of the "flow" of time, a state of affairs which is known as the causality problem (and also called the "Shalimar Treaty").

It should be noted that while Einstein's theory of special relativity prevents (real) mass, energy, or information from traveling faster than the speed of light c (Lorentz et al. 1952, Brillouin and Sommerfeld 1960, Born and Wolf 1999, Landau and Lifschitz 1997), there is nothing preventing "apparent" motion faster than c (or, in fact, with negative speeds, implying arrival at a destination before leaving the origin). For example, the phase velocity and group velocity of a wave may exceed the speed of light, but in such cases, no energy or information actually travels faster than c. Experiments showing group velocities greater than c include that of Wang et al. (2000), who produced a laser pulse in atomic cesium gas with a group velocity of

. In each case, the observed superluminal propagation is not at odds with causality, and is instead a consequence of classical interference between its constituent frequency components in a region of anomalous dispersion (Wang et al. 2000).

It turns out that all relativistic wave equations possesses infinity families of formal solutions with arbitrary speeds raging from zero to infinity, called undistorted progressive waves (UPWs) by Rodrigues and Lu (1997). However, like the arbitrary-speed plane wave solutions, UPWs have infinite energy and therefore cannot be produced in the physical world. However, approximations to these waves with finite energy, called finite aperture approximations (FAA), can be produced and observed experimentally (Maiorino and Rodrigues 1999). Among the infinite family of exact superluminal solutions of the homogeneous wave equation and Maxwell equations are waves known as X-waves. X-waves do not violate special relativity because all superluminal X-waves have wavefronts that travel with the speed parameter c (the speed of light) that appears in the corresponding wave equation. The superluminal motion of the peak is therefore a transitory phenomenon similar to the reshaping phenomenon that occurs (under very special conditions) for waves in dispersive media with absorption or gain and which is in this case responsible for superluminal (or even negative) group velocities (Maiorino and Rodrigues 1999).

Several authors have published theories claiming that the speed-of-light barrier imposed by relativity is illusionary. While these "theories" continue to be rejected by the physics community as ill-informed speculation, their proponents continue to promulgate them in rather obscure journals. An example of this kind is the Smarandache hypothesis, which states that there is no such thing as a speed limit in the universe

(Smarandache 1998). Similarly Shan (1999ab) has concluded that the superluminal communication must exist in the universe

and that they do not result in the casual loop paradox.

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