From Newton to Einstein Towards All-Embracing Asymptotic Lorentz Relativity: Beyond the Mathematical Truncation of Boost Factors

AbstractIn the foundational paper on the new Asymptotic Lorentz Relativity (ALR) [8], we pre-sented a self-contained, mathematically rigorous extension of standard relativistic kinemat-ics that resolves the longstanding singularities of Einstein's relativity and naturally explainsboth the Hubble Tension and a non-zero photon mass. The ALR framework coincides withthe Einsteinian for up to the intermediate velocities. In this note, we refer to all notationsused in that foundational ALR paper.The aim of this note is not to demand immediate acceptance of the ALR theoryweprefer its rigorous mathematics to speak for itself. Rather, we provide the physics communitywith a clear opportunity to resolve classical relativities of singularities at the light limit,while keeping the established Newtonian and Einsteinian mechanicsIndeed, in [8] all three theories are hierarchically positioned, each assigned to its specicvelocity domain in which it remains a well-functioning, non-singular, and highly successfultheorysuch as Einsteinian relativity up to the range of intermediate velocities [8].Historically speaking, Einsteinian relativity extends Newtonian mechanics, just as thenew ALR framework is demonstrated to extend the Einsteinian paradigm. From a mathe-matical point of view, ALR is based on the full boost information of the un-truncated innitegeometric series [8]. Conversely, the Einsteinian boost factor (Lorentz) emerges as a severetruncation of this full series to its rst two terms. The Newtonian boost factor is, in turn, atruncation of the Einsteinian, retaining merely the rst term of the same geometric series.From this perspective, it is evident that in each case, the structural loss of kinematic infor-mation creates the explicit physical limits of the respective relativity, whether Einsteinianor Newtonian.