Generalized Lorentzian Adjustment of Reference Frames and Waves of Transformation of Spacetime

Abstract

It is demonstrated that any two reference frames (RFs), which are uniformly and rectilinearly moving relative to each other, can be adjusted via (possibly anisotropic) rescaling and re-synchronization so that the resulting pair of RFs is Lorentzian; this statement remains true if the word "Lorentzian" is replaced by "Galilean" or "Riemannian", i.e., if a finite positive value of $c^2$ is replaced by $\infty$ or by a negative real number. In this particular sense, the Lorentzian, as well as Galilean or Riemannian, phenomenon turns out to be merely a matter of an arbitrary choice of appropriate rescaling and re-synchronization of any given pair of RFs. Generalizations and refinements of this result are obtained, including universal generalized Lorentzian adjustment via rescaling and re-synchronization of arbitrarily large families of RFs. Alternatively, the generalized Lorentzian property of a pair of RFs is shown to be a consequence of reciprocity and isotropy, with no adjustment needed in this case. The universality of light and of the corresponding Lorentzian property of the spacetime is questioned. Waves of transformation of spacetime are introduced, which have in a certain sense a more universal character than electromagnetic or gravitational waves.