A Refined Near-Tautological Derivation of the Principle of Relativity: From Strict Locality and Indistinguishability

A Refined Near-Tautological Derivation of the Principle of Relativity: From Strict Locality and Indistinguishability PhysicsV.com Credentials: MPhil (Engineering), MSc (Physics)∗ Contact: [email protected] Affiliation: Independent Researcher December 17, 2025 Version 1.0 Note: This document is not a research paper in the conventional sense, as it advances no new scientific knowledge for humanity. It offers a refined pedagogical presentation and clarification of existing ideas regarding the principle of relativity. Abstract This note presents a conceptual argument demonstrating why the principle of relativity can be regarded as near-tautological. By combining the indistinguishability of uniformly moving closed systems—including co-moving light sources—with the requirement of strict locality (no instantaneous action-at-a-distance), the invariance of the laws of physics across inertial frames follows analytically from physically well-motivated premises. The discussion clarifies why the principle, traditionally treated as a postulate or empirical fact, emerges as nearly inevitable when demanding a spacetime with meaningful causal structure. Keywords: special relativity, principle of relativity, tautological argument, strict locality, physics education, indistinguishability of inertial frames 1 Introduction The principle of relativity—that the laws of physics are the same in all inertial frames—is foundational to special relativity. In most textbooks, it is introduced either as an empirical generalization (supported by experiments such as Michelson–Morley) or as a postulate (Einstein, 1905). However, a more operational perspective reveals that the principle has a strong analytic character: once certain natural assumptions about physical systems and causality are accepted, it follows with near inevitability. This note refines a classic thought-experiment argument (the “closed system” or “train” analogy) to show this near-tautological status. Particular attention is paid to including comoving light sources, closing historical concerns from classical ether theory, and incorporating strict locality as the key bridging premise. ∗Degrees awarded by The Chinese University of Hong Kong. 1 2 The Closed-System Argument and Indistinguishability Consider a closed physical system (e.g., a train containing observers, apparatus, air, and including any points of the light sources within the train) where every point moves with the exact same constant velocity vrelative to some external reference frame. By definition of uniform velocity: •The relative velocity between any two points inside the system is zero. •Therefore, the relative positions, distances, and motions of all internal objects—including any points of the light sources within the train—remain identical to the case where the entire system has velocity v= 0. Any internal physical process depends only on the relative configurations and motions of the components involved. The explicit inclusion of co-moving light sources is crucial: it ensures the argument applies fully to electromagnetism—classical “ether wind” effects would require detectable asymmetries in light propagation, which cannot arise internally without breaking the indistinguishability described above. 3 Incorporating Strict Locality If we further require strict locality—that causal influences are local (propagate through space with finite domains of influence, preventing instantaneous action-at-a-distance, which would make spatial separation causally meaningless)—then, since these relative configurations are unchanged (indistinguishability from the v= 0 case), no internal experiment can detect the overall velocity v, and the outcomes of all internal experiments and observations must be identical, regardless of the overall uniform velocity v. A detectable difference under this condition would require either: •Non-local influences (violating strict locality), or •Some absolute-velocity dependence accessible internally (impossible without breaking indistinguishability, as no internal mechanism can access or detect this absolute v—all parts, including light sources, share it exactly). Such a dependence would contradict the uniformity and isolation of the system (and the requirement of strict locality). 4 Conclusion Thus, if we require strict locality, the laws of physics are necessarily the same in all inertial frames. The conditional implication itself is strictly tautological (analytic by construction), while the premise of strict locality is physically well-motivated and nearly self-evident (essential for preserving the causal distinctness of spatially separated points). Therefore, the principle of relativity as a whole is near-tautological. 2 This perspective complements traditional presentations by highlighting the principle’s deep roots in operational indistinguishability and causal structure, making it valuable for pedagogical purposes. References [1] Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der Physik, 322(10), 891–921. https://doi.org/10.1002/andp.19053221004 [2] Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol. I. Addison-Wesley. (Available online: https://www.feynmanlectures.caltech.edu/) 3