"Uncertainty Is Not Uncertain: The Robertson Bound as Geometric Projection Cost"
Year: 2026
Type: preprint
Abstract: The Heisenberg uncertainty relation (Robertson bound) is a valid theorem about non-commuting operators in Hilbert space. Its standard interpretation — that nature is fundamentally indeterminate — is not. We demonstrate that the bound quantifies the information cost of geometric projection, not an ontological property of reality. The factor 1/2 appearing in the bound is identified as k_arc = 4.5/9 = 0.5, the universal projection coefficient of the discrete digit topology {1,...,9} under inversion symmetry phi(x) = 9 − x. This same coefficient governs fermion spin (s = 1/2), kinetic energy ((1/2)mv²), and the Born rule — all instances of a single mechanism: dimensional reduction from a complete relational state (S²) to a binary observable ({+1, −1}). Quantum tunneling requires no energy borrowing: effective topological distance through a coherent barrier is identically zero. The particle does not cross the wall; the wall was never closed in all dimensions. Three falsifiable predictions are provided. Heisenberg discovered the geometry of observation and mistook it for the nature of reality.
Author: Bastos, Filipe
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130939010