What question did this study set out to answer?

This research aims to formulate a five-dimensional extension of special relativity incorporating a constrained internal state.

February 23, 2026Open Access

Extended Lorentz Symmetry with a Constrained Internal State Coordinate: A Ghost-Free SO(4,1) Framework, a New Noether Charge, and Precision Tests of Temporal–Informational Coupling

Key Points

This research aims to formulate a five-dimensional extension of special relativity incorporating a constrained internal state.
Developed a ghost-free framework using SO(4,1) dynamics.
Defined a new conserved quantity linking time evolution to internal state evolution.
Established modular thermal suppression related to measured temperatures.
Introduced a superselection mechanism to stabilize mass while allowing controlled sector preparation.
Outlined an experimental program focusing on differential frequency effects in coherence switching.
Introduced a new conserved quantity that influences energetic and internal evolution.
Demonstrated coherence control through an internal state coordinate and gauge sector.
Provided a basis for precision tests of dynamics related to information flow.

Abstract

This preprint formulates a constrained five-dimensional extension of special relativity in an SO (4, 1) embedding space with signature (+----), where the extra coordinate is treated as an internal state coordinate τ governing coherence/information flow rather than a macroscopic spatial direction. Ghost and ill-posed evolution pathologies are avoided by Dirac constrained dynamics (worldline) and distributional support on a regulated hypersurface (field theory). A new conserved Noether charge, Σ, associated with the SO (4, 1) generator in the (0, 4) plane, couples ordinary energetic evolution to internal state evolution and yields falsifiable signatures in precision platforms. Core claims and results: • Ghost-free constrained dynamics: physical motion is defined on a constrained phase space; bulk propagation is suppressed via hypersurface-supported field theory. • New conserved quantity: Σ = t E_τ − τ E (notation as defined in the manuscript) links coordinate-time evolution to internal-sector evolution. • Modular/thermal suppression: tracing over inaccessible degrees of freedom induces a KMS-weighting of internal modes with an effective modular temperature Tₑff; Tₑff is defined operationally and anchored to measured laboratory bath temperatures, with a conservative nonzero floor from the cosmic microwave background when other sources are minimized. • Superselection mechanism: a compact internal U (1) _τ gauge sector yields a Gauss-law constraint that forbids local interference between distinct total P4 sectors, stabilizing observed 3+1 masses while allowing controlled preparation within a fixed sector. • Fifth-force avoidance: the associated U (1) _τ gauge boson is taken to be a dark massive vector (Stückelberg or secluded Higgs mechanism) with ultra-weak coupling and/or finite range, consistent with existing constraints. • Experimental program: the main near-term signal is a protocol-correlated differential frequency effect (coherence switching / clock-comparison), including preparation transients, rather than an uncontrolled “drift” of a single clock. How to cite: Rački, I. (2026). Extended Lorentz Symmetry with a Constrained Internal State Coordinate: A Ghost-Free SO (4, 1) Framework, a New Noether Charge, and Precision Tests of Temporal–Informational Coupling (v1). Zenodo. DOI: Zenodo will insert after publishing

Extended Lorentz Symmetry with a Constrained Internal State Coordinate: A Ghost-Free SO(4,1) Framework, a New Noether Charge, and Precision Tests of Temporal–Informational Coupling

Key Points

Abstract

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