Quantum Mechanics from First Principles: Unifying Mechanics via an Expanded Theory of Relativity
Year: 2025
Type: preprint
Abstract: We propose a geometric extension of spacetime in which time is a three–vector whose local orientation is encoded by a quaternionic rotor \(R(x)=\exp(Q(x))\). Within a six–dimensional Clifford framework, block–boost consistency fixes the temporal signature and projects to the standard Lorentz interval when the rotor sector is frozen (\(Q=0\)). Demanding advection of the rotor along worldlines yields a universal first–order, Dirac–like field equation \[ i \epsilon^\mu \,\Sigma^\mu\partial_\mu\Psi - A^Q\,\rho^{Q\prime}(\Psi^\dagger\Psi)\,\Psi=0, \] valid for arbitrary spin in a basis \(\Sigma^\mu\in\{\mathbf{1},S_1,S_2,S_3\}\) with $S_k$ the basis of any irreducible representation of $\mathfrak{su}(2)$. A zeroth–order matching to the Planck–Einstein relation fixes the rotor–matter coupling to \(A^Q=m^2c^3/\hbar\). Two complementary realizations then follow: (i) with on–shell energy–momentum, the radial Coulomb reproduces the Dirac–Coulomb spectrum; (ii) with the canonical map \(\varepsilon^\mu\!\rightarrow i\hbar c\,\partial^\mu\), the framework yields second–order inhomogeneous wave equations that reduce to Klein–Gordon for \(\Sigma^\mu=\mathbf{1}\) and to Maxwell–type equations for the spin-1 basis. At one loop, a Pauli–algebra computation of the vertex correction gives the anomalous magnetic form factor \(F_2(0)=\alpha/(2\pi)\). The rotor sector predicts testable signatures—spatially varying clock-rate shifts and anomalous spin precession—providing direct constraints on \(A^Q\) and on the form of the temporal potential \(V^Q\). Our results unify the kinematics of relativity and the dynamics of quantum waves within a single geometric mechanism and open a route to falsifiable departures from the standard paradigm.
Authors: J. Manuel Oliveira, J Manuel Oliveira
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4415123963
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