We derive the objective wavefunction collapse time for a massive spatial superposition from the first principles of the Universal Processing Law (UPL), a Planck-scale discrete computational geometry governed by the master equation N₋₎₂₀₋ = C_ Lg Lᵥ. The Hardware Mechanism of Collapse In UPL, a quantum superposition of mass M at two locations is a parallel computation: the hardware must simultaneously render two contradictory gravitational fields. The extra Click demand per hardware cycle is: ₂ₘ₂₋₄ = 8\, EGEP where EG is the gravitational self-energy of the superposition and EP is the Planck energy. The processing debt accumulates over discrete hardware cycles until it reaches the critical threshold of one Click (the irreducible quantum of computational action). At this point, the hardware executes a Decisive Click, collapsing the superposition to a single branch. The Collapse Time The resulting collapse time is: = 8\, EG This recovers the Penrose-Diosi scaling with a specific numerical prefactor of 1/ (8) derived entirely from first principles. Falsifiable Predictions This prefactor is a falsifiable prediction testable by current-generation optomechanical experiments: - For a silica microsphere (M = 10^-14 kg), the predicted collapse time is approximately 7 days. - For a tungsten microsphere (M = 10^-12 kg), it is approximately 0. 63 seconds. The derivation uses no continuous time, no classical Hamiltonian, and no interpretive postulates. This is the fourth quantitative result from the UPL master equation, following the cosmological constant (97. 3% accuracy), the Bekenstein-Hawking entropy S = A/ (4lP²), and the Kerr QNM spectrum recovery. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed. lahmidi. contact@gmail. com
Ahmed Lahmidi (Thu,) studied this question.