Expanded theory of relativity: Demonstrating wave-particle duality as an integral part of relativity theory

Expanded theory of relativity: Demonstrating wave-particle duality as an integral part of relativity theory | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 26 August 2025 V9 View latest version Share on Expanded theory of relativity: Demonstrating wave-particle duality as an integral part of relativity theory Authors : J. Manuel Oliveira 0009-0003-3977-3852 [email protected] and J Manuel Oliveira Authors Info & Affiliations https://doi.org/10.22541/au.174197384.43987988/v9 509 views 236 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We present a geometric framework that promotes time from a scalar parameter to a genuine three-dimensional temporal vector whose local orientation is encoded by a quaternionic rotor field \[ R(x)=\exp\big(Q(x)\big),\qquad Q(x)\in\mathfrak{su}(2). \] Starting from block-boost consistency in a six-dimensional Clifford space, the effective projection onto physical coordinates reproduces the standard Lorentz interval while introducing a new dynamical sector (the \emph{flag}) that coexists with the usual particle worldline (the \emph{pole}). Requiring the rotor to be Lie-dragged along particle worldlines yields a universal first-order wave equation for a flag field \(\Psi\), \[ i \varepsilon^\mu \Sigma^\mu\partial_\mu\Psi - A^{Q} \rho^{Q\prime}(\Psi^\dagger\Psi) \Psi = 0, \] valid across spin representations via \(\Sigma^\mu\in\{\mathbf{1},S_1,S_2,S_3\}\). In appropriate representations and limits the formalism reproduces Dirac-, Klein–Gordon- and Maxwell-type dynamics. Separation of variables in the spin-\(\tfrac12\) flag equation reduces to Kummer’s confluent hypergeometric form and reproduces the Dirac–Coulomb hydrogenic spectrum. The rotor sector generically produces falsifiable signatures — notably small spatially varying clock shifts and anomalous spin-precession terms — which can be constrained by precision atomic clocks and spin-interferometry. We close by outlining paths to determine the temporal potential \(V^{Q}\), couple the rotor to gravity, and quantize the flag sector. We propose a unified six-dimensional spacetime framework in which time is elevated to a three-vector, enforcing maximal symmetry between spatial and temporal dimensions. Imposing invariance under generalized Lorentz transformations fixes the metric to that of a Clifford algebra $Cl(3,3)$ and naturally recovers the emergent four-dimensional Minkowski subspace. Concurrently, a novel multicomponent field (vecPsi) arises, whose conservation laws yield a continuous family of wave–particle equations encompassing all irreducible spin representations. This construction resolves the classical normalization paradox by producing exponentially localized resting-particle wavefunctions. Finally, coupling (vecPsi) dynamics to spacetime curvature opens new geometric pathways for quantum–gravity interplay and potential dark-matter–like phenomena. We outline prospects for deriving explicit dynamical laws for (vecPsi), computing curvature corrections, and identifying experimental signatures in both quantum-optical and cosmological settings. Supplementary Material File (exptheoryrel_20250826.pdf) Download 451.76 KB File (qmfirstprinciples_2-4.pdf) Download 404.51 KB File (qmfirstprinciples_2-6.pdf) Download 359.47 KB File (qmfirstprinciples_20250706.pdf) Download 357.31 KB File (qmfirstprinciples_2025_08_02.pdf) Download 373.74 KB File (qmfirstprinciples_250501.pdf) Download 425.07 KB File (qmfirstprinciples_4-5.pdf) Download 391.89 KB File (qmfirstprinciples_6-1.pdf) Download 349.68 KB File (relativityqm_4.pdf) Download 313.87 KB Information & Authors Information Version history V1 Version 1 14 March 2025 V2 Version 2 28 April 2025 V3 Version 3 02 May 2025 V4 Version 4 22 May 2025 V5 Version 5 27 May 2025 V6 Version 6 02 June 2025 V7 Version 7 07 July 2025 V8 Version 8 04 August 2025 V9 Version 9 26 August 2025 V10 Version 10 08 September 2025 V11 Version 11 13 October 2025 V12 Version 12 21 November 2025 V13 Version 13 08 December 2025 V14 Version 14 12 December 2025 V15 Version 15 15 December 2025 V16 Version 16 08 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords general relativity lorentz transformations quantum gravity quantum mechanics unified theory Authors Affiliations J. Manuel Oliveira 0009-0003-3977-3852 [email protected] View all articles by this author J Manuel Oliveira Clínica Girassol Commandant Gika avenue Physics Department, Clínica Girassol View all articles by this author Metrics & Citations Metrics Article Usage 509 views 236 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation J. Manuel Oliveira, J Manuel Oliveira. Expanded theory of relativity: Demonstrating wave-particle duality as an integral part of relativity theory. Authorea . 26 August 2025. DOI: https://doi.org/10.22541/au.174197384.43987988/v9 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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