Quantum Latent Gauge and Coherence Selective Forces

Abstract: We propose a hidden U(1) gauge interaction that couples exclusively to quantum coherence in massive systems. The central innovation is a conserved coherence current operator constructed from the Noether mass current via operator-level coarse-graining. This current vanishes for classical matter distributions but is nonzero for spatial superpositions and entangled states, yielding a gauge interaction that is dormant in classical regimes but activated by quantum coherence. The framework predicts three distinctive signatures: (i) interferometric phase shifts scaling linearly with fringe visibility, (ii) decoherence rates with characteristic m^2 scaling and spatial dependence distinct from collapse models, and (iii) entanglement-selective forces between distant massive qubits. The theory maintains full gauge invariance, causality, and positive time evolution. We show that state-of-the-art atom interferometers and levitated nanoparticles can place first constraints on this interaction class, complementary to classical fifth-force searches. This approach provides a novel theoretical framework for probing coherence-selective fundamental interactions and their potential role in the quantum-classical transition. To make this more concrete, we also spell out a simple benchmark latent-field model and work out, in detail, how a representative large-momentum-transfer atom interferometer constrains the corresponding coupling strength.