A counter-example to Bell's theorem with a softened singularity and a critical remark to the implicit demand that physical signals may not travel faster than light

Abstract

In the present paper a counter-example to Bell's theorem is given which is based on common probability densities as standard normal (Gaussian) and uniform probability densities. The reason for violating the Bell inequalities lies in the 'softening' of functions similar to the Dirac delta such that they can be 'hidden' inside a sign function. In addtition, the related demand that that physical signals may not travel faster than light is discussed with the FitzGerald-Lorentz contraction factor.