A Fundamental Lagrangian for a Timeless Universe: Derivation of Gravitation and Quantum Mechanics

This work proposes a new framework to reconcile general relativity and quantum mechanics. Spacetime is not fundamental but emerges from a dimensionful scalar information field vm(x)v_m(x)vm(x). Matter couples to the conformal effective metric generated by vmv_mvm, yielding gravity and geodesic motion while reproducing GR in the classical limit. The quantum fluctuations of vmv_mvm provide a universal environment, offering a physical mechanism for decoherence. The Einstein–Hilbert term is not inserted by hand but induced at one loop. Key prediction: quantum coherence times depend on the local gravitational potential, producing measurable differences between identical systems at different altitudes.