Abstract ABLE TO TRAVEL FASTER THAN LIGHT

The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a relativistic space-time even if the actual space-time had a quite different geometry (f.i. a galilean space-time). A typical example is provided by sine-Gordon solitons in a galilean world. A " sub-world " restricted to such solitons would be " relativistic " , with the critical speed of solitons playing the role of the speed of light. Only the study of the deep structure of matter will unravel the actual geometry of space and time, which we expect to be scale-dependent and determined by the properties of matter itself. If Lorentz invariance is a property of equations describing a sector of matter at a given scale, an absolute frame (the " vacuum rest frame ") may exist without contradicting the minkowskian structure of the space-time felt by ordinary particles. But c , the speed of light, will not necessarily be the only critical speed in vacuum: for instance, a superluminal sector of matter may exist related to new degrees of freedom not yet discovered experimentally. Such particles would not be tachyons: they may feel a different minkowskian space-time with a critical speed c 1 > c and behave kinematically like ordinary particles apart from the difference in critical speed. At v (speed) > c , they are expected to release " Cherenkov " radiation (ordinary particles) in vacuum. We present a discussion of possible physical (theoretical and experimental) and cosmological implications of such a scenario, assuming that the superluminal sector couples weakly to ordinary matter.