Abstract
The conventionalist thesis asserts that all internal clock synchronization procedures are equivalent to Einstein’s, making the one-way speed of light conventional and the Lorentz transformations (LT) and Lorentz transformations with absolute simultaneity (LTA) empirically equivalent. This paper investigates these claims through a novel canonical phase-space analysis of Sagnac-type optical effects. Using the Poisson bracket as a consistency check, we show that treating the Mansouri-Sexl synchronization parameter \(\epsilon\) as a free gauge variable is incompatible with a phase-space description of light propagation on non-simply connected topologies. The bracket \(\{{2L},c'\}\) vanishes—restoring commutativity between loop geometry and local light speed—only if the conventional parameter is fixed and vanishes (\(\epsilon = 0\)), corresponding to the LTA; for the LT (\(\epsilon = v\)), the bracket is nonzero, indicating that \(2L\) and \(c'\) are not independent observables and that spacetime continuity is breached. The promotion of \(\epsilon\) to a conjugate momentum is introduced here as a test hypothesis to examine the internal consistency of the conventionalist framework; it is not assumed to be an established Hamiltonian result. This does not mean that nature "forces" \(\epsilon = 0\), but rather that the conventionalist assumption that \(\epsilon\) is a free parameter is internally inconsistent for Sagnac-type effects. The inconsistency is resolved by adopting a synchronization procedure not equivalent to Einstein’s—such as the classical entanglement synchronization described in Ref. [1]—which naturally corresponds to \(\epsilon = 0\) and renders the one-way speed of light observable in principle. We also present a heuristic extension to the Arnowitt-Deser-Misner (ADM) formulation of general relativity, suggesting that the shift vector field—the GR analog of \(\epsilon\)—may lose its gauge freedom on non-simply connected topologies. A speculative quantization of the phase-space commutator yields an uncertainty relation \({{{\Delta{({2L})}} \cdot \Delta}c'} \gtrsim {{({\hslash/2})}{|{c/{({c + v})}}|}}\), implying that imposing an invariant coordinate light speed (\({\Delta c'}\rightarrow 0\)) forces divergent spatial fluctuations (\({\Delta{({2L})}}\rightarrow\infty\)). Tentative remarks on topological vacuum anomalies in quantum field theory suggest that the LTA may eliminate the coordinate time dislocation on closed loops. We further examine Faraday induction from moving electrified bodies and equilibrium paradoxes in relativistic electromagnetism, showing that the LTA resolve these paradoxes naturally. Our analysis indicates that the claimed LT-LTA equivalence is not general, and that experimental investigations of the one-way speed of light may be feasible.