Gravitational Phase Interferometry to Test Planck Discreteness and Objective Reduction

The hypothesis that spacetime possesses a discrete structure at the Planck scale - potentially composed of quantized tetrahedral or simplicial building blocks - arises naturally in background-independent approaches to quantum gravity such as Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT). In these frameworks, spatial geometry emerges from spin networks of quantum tetrahedra with discrete area and volume spectra, while spacetime evolution proceeds via spin foams or summed triangulations. Roger Penrose’s Objective Reduction (OR) mechanism further posits that quantum superpositions of massive states generate incompatible spacetime curvatures whose gravitational self-energy difference triggers an objective collapse when the associated energy uncertainty reaches ħ/τ, implicitly requiring a non-continuous spacetime geometry. This article presents an exhaustive theoretical foundation and proposes a hybrid tabletop experiment - the Planck Geometry Interferometer - designed to simultaneously measure gravitational phase shifts arising from proper-time differences and spontaneous collapse lifetimes. By placing mesoscopic masses in spatial superpositions and monitoring quantized deviations in phase or collapse time, the experiment can distinguish discrete tetrahedral geometries (LQG-style) from continuous spacetime or pure Penrose foam. Building directly on existing proposals, the setup is shown to be within reach of current optomechanical, cryogenic, and interferometric technologies. Detailed protocols, expected signatures of discreteness, feasibility assessments, and implications for falsifying or confirming Planck-scale discreteness are provided. A negative result would constrain or refute these models; a positive detection of quantization would constitute direct empirical evidence for discrete spacetime.