Recently it has been shown that all relativistic wave equations possess families of undistorted progressive w aves @UPWsA which can travel with arbitrary speeds H v < I.In this paper we present the theory of how to generate UPW solutions of the Maxwell equation and discuss the particular case of the superluminal electromagnetic X -wave @ SEXW AD clarifying its extraordinary properties. The theory of how it is possible to launch nite aperture approximations for the SEXW in free space is also discussed in detail. The theory is illustrated by computer simulations showing the birth of a nite aperture approximation for a SEXW and its superluminal propagation without appreciable distortion up to a IHH km. We discuss also the experimental evidence available and discuss if SEXWs can be used to transmit information.

By using the spacetime algebra, we explain the hehcal motion of the electron (tatterbe~,egung) and its Coulomb field b) introducing a mechamsm that breaks Iotally the cleclromagnehe gauge m~,anancc We show thal this ~auge mvananc¢ is broken ,n all po,nts of spacetime, except for those that corr~pond to thai ¢shndncal hehx which ~s the electron's world hne. and that it give.~ n~ to an o~dlatmg Coulomb-hke field v, lth frequen~ equal to the/,tterbe~,egung one Th,s field ts found to sansf,, the so-called Maxwell-London equations. This oscdlatm8 field, when a~ eragcd over a zltterbev, egun8 period. ~s the usual Coulomb field of the electron.

Recently it has been shown that all relativistic wave equations possess families of undistorted progressive waves (UPWs) which can travel with arbitrary speeds 0 ≤ v < ∞. In this paper we present the theory of how to generate UPW solutions of the Maxwell equation and discuss the particular case of the superluminal electromagnetic X‐wave (SEXW), clarifying its extraordinary properties. The theory of how it is possible to launch finite aperture approximations for the SEXW in free space is also discussed in detail. The theory is illustrated by computer simulations showing the birth of a finite aperture approximation for a SEXW and its superluminal propagation without appreciable distortion up to a 100 km. We discuss also the experimental evidence available and discuss if SEXWs can be used to transmit information.