What does this research mean for the field?

Objective wavefunction collapse for massive spatial superpositions is driven by a discrete computational buffer overload at the Planck scale, yielding a specific collapse time of τ = ħ / (8π E_G) that recovers the Penrose-Diósi scaling with a falsifiable prefactor. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

This work aims to derive the collapse time of a wavefunction from first principles of the Universal Processing Law.

March 28, 2026Open Access

Universal Processing Law (UPL) Track 5: Objective Wavefunction Collapse from Computational Buffer Overload: A Discrete Derivation of the Penrose-Diosi Time via the Universal Processing Law

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Key Points

This work aims to derive the collapse time of a wavefunction from first principles of the Universal Processing Law.
Derived the master equation for computational capacity at the Planck scale.
Explored gravitational effects on quantum superpositions using specific mass values.
Predicted collapse times for different masses based on the processing debt accumulation.
Collapse time derived as tau = hbar / (8pi E_G).
Predicted collapse time of approximately 7 days for a 10^-14 kg silica microsphere.
Predicted collapse time of approximately 0.63 seconds for a 10^-12 kg tungsten microsphere.

Abstract

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 Superposition 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 EG / EP, 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. Collapse Time & Falsifiable Predictions The resulting collapse time is = / (8 EG), recovering the Penrose-Diósi scaling with a specific numerical prefactor of 1/ (8) derived entirely from first principles. This prefactor is a falsifiable prediction testable by current-generation optomechanical experiments. For example: 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. Conclusion The derivation uses no continuous time, no classical Hamiltonian, and no interpretive postulates. This is the fourth quantitative result derived strictly from the UPL master equation, following the cosmological constant (97. 3% accuracy), the Bekenstein-Hawking entropy (S = A/ (4lP²) ), and the standard Kerr quasinormal mode (QNM) spectrum recovery. All theoretical concepts, derivations, and original ideas are the sole intellectual work of Ahmed Lahmidi. Contact: ahmed. lahmidi. contact@gmail. com

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Universal Processing Law (UPL) Track 5: Objective Wavefunction Collapse from Computational Buffer Overload: A Discrete Derivation of the Penrose-Diosi Time via the Universal Processing Law

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