Synchronization Horizon
A quantum foundations research project proposing that wave-function collapse is a deterministic data-compression artifact — analogous to a read-write conflict in a distributed database — rather than requiring a collapse postulate, many-worlds branching, or conscious observation.
Every analytical result is backed by Python numerical verification and, where applicable, formal proofs in Lean 4.
Core Insight
Textbook quantum mechanics assumes measurement is instantaneous. But the universe has no global clock. Due to the Heisenberg uncertainty principle and the micro black hole limit, measurement must take finite time. During that window, if the fine-structure constant drifts, the measurement operator accumulates phase uncertainty — producing decoherence as a natural averaging effect.
Key Ideas
Finite-Time Measurement
Attempting instantaneous measurement (Δt → 0) requires infinite energy concentration, forming a micro black hole. Physics forbids instantaneous reads — setting a floor at the Schwarzschild timescale.
Time-Averaged POVM Channel
A finite-duration measurement averages over drifting phase, producing a dephasing channel. Populations are invariant; coherences contract by a factor |g(T)| ≤ 1. This is a standard completely-positive trace-preserving map.
Decoherence Rate
Under Ornstein–Uhlenbeck α(t) fluctuations, the dephasing rate scales quadratically with energy splitting, quadratically with fluctuation amplitude, and linearly with correlation time.
Research Topics
- Quantum Foundations — measurement problem, decoherence, the “stop-the-world” fallacy of instantaneous projection
- Quantum Information Theory — CPTP channels, entropy dynamics, Bell concurrence under dephasing
- Micro Black Hole Limits — Schwarzschild timing bounds, Bekenstein information capacity
- Zeno and Anti-Zeno Effects — continuous measurement limits under finite-time constraints
- Quantum Darwinism — pointer-state selection and redundancy under α-drift
Verification Approach
Results are verified through two complementary methods:
- Python numerical simulations — Ornstein–Uhlenbeck process simulation, ensemble averaging, parameter sweeps confirming scaling laws across 3 orders of magnitude, using NumPy and SciPy.
- Lean 4 formal proofs — Machine-checked proofs covering diagonal invariance, off-diagonal contraction, Hermiticity preservation, entropy increase, asymptotic convergence, repeated-window contraction, Bell concurrence bounds, and quadratic energy scaling.
Every claim is tagged with its epistemic status: established, derived, reiteration, assumption, numerically verified, Lean-proved, or open question.
Status
The Synchronization Horizon framework includes a full technical paper and a popular-level treatment (“The Blurry Universe”). The papers are not yet published.