The Space-Time Membrane Model: Unifying Quantum Mechanics and General Relativity through Elastic Membrane Dynamics

We propose a Space-Time Membrane (STM) model that treats four-dimensional spacetime as an elastic membrane paired with a hypothetical “mirror” universe on its opposite side. Energy external to the membrane deforms it, producing gravitational curvature akin to General Relativity (GR), while energy distributed uniformly within the membrane remains curvature-neutral. Localised particle excitations manifest as oscillatory modes on one face, partnered with mirror antiparticles on the other. Although the STM model does not claim to replace established quantum field theory (QFT), it offers a complementary route to reconciling gravity and quantum phenomena: deterministic wave interactions can reproduce quantum-like interference and “entanglement analogues,” potentially seeded by small, persistent waves at sub-Planck scales. A modified elastic wave equation—incorporating tension, bending stiffness, and spatially varying membrane properties—captures weak-field gravitational effects reminiscent of GR. Simultaneously, it supports stable standing waves analogous to quantum interference. Within this picture, photons emerge as “wave-plus-anti-wave” oscillations that remain massless, exhibit correct polarisation states, and respect U(1) gauge symmetry and Lorentz invariance. By tuning intrinsic coupling constants, time-averaged stiffness shifts can align with observed vacuum energy, offering insight into the cosmological constant. Despite these promising features, the STM model remains speculative. Further theoretical and observational work is needed to clarify its relationship to standard physics and evaluate its quantitative predictions. As a geometric, deterministic perspective, it complements but does not supersede GR or QFT, suggesting pathways for future theoretical investigations and possible analogue experiments.