The repercussions of the Theories of Relativity can be very interesting, when examined carefully, because while information cannot be conveyed faster than the speed of light, not everything carries information. The phase of light, for example, does not carry any information and now researchers have gotten it to reach an infinite speed within a special device, as reported by Science.
The key to this achievement was making a device with an index of refraction of 0. The index of refraction of a material is a ratio between the phase speed of light within a material and in a vacuum. That means a material with an index of refraction greater than 1 slows light but those with an index less than one actually speeds light up. Such materials are not possible in Nature but with the careful construction of nanostructures, it is possible to create such 'impossible' materials. In this case it was accomplished by create a cavity the light reflects back and forth in, but at a specific wavelength, instead of have the usual alternation between light and dark areas, becomes all lit up. This is only possible if the peaks of the light wave, the phase of the wave, are moving infinitely fast.
Now, this still obeys relativity, so superluminal communication is not going to be possible with these devices. However, its affects on the phase front of the light could be utilized for optical circuitry including antennas.