June 13, 2020
special relativity, pole in the barn paradox, inconsistency, double relativity
This article introduces a variant of the celebrated relativity paradox The Pole in the Barn. The proposed variant replaces with two laser beams the observers that report contradictory observations on whether or not the whole pole enters in the barn. The new version of the old paradox leads almost immediately to a true contradiction that puts to the test the consistency of the theory of special relativity, although the theory could be inconsistent not by itself but as a consequence of an underlying inconsistent hypothesis: the hypothesis of the actual infinity from which the mathematical concept of the (spacetime) continuum is derived. If that were the case, space and time could only be of a discrete nature, and the experimental support of special relativity could be explained in terms of a coincidence: Lorentz factor has the same algebraic form as the factor for converting continuous in discrete geometries.