Proposal for a contextual test of Lorentz invariance

The conceptual tension between nonlocality and relativistic causality motivates scenarios in which Lorentz invariance emerges as an effective low-energy symmetry rather than a fundamental property. We present a phenomenological framework inspired by Bohmian dynamics and analogue gravity, where collective excitations of a superfluid-like medium exhibit emergent Lorentzian propagation with an effective light speed. Beyond conventional dispersion tests, we predict a novel low-energy signature: contextual sensitivity of propagation to quantum coherence in nearby control systems, inducing small fluctuations of the effective light cone. We propose a feasible Mach–Zehnder interferometric protocol to probe these effects via precision differential measurements, opening a new experimental route to explore spacetime symmetries.