The Geometric Part of Decoherence: Quasi-Orthogonality in High-Dimensional Hilbert Spaces

• URL: http://arxiv.org/abs/2605.03807v1
• Date: Tue, 05 May 2026 14:31:58 GMT
• Title: The Geometric Part of Decoherence: Quasi-Orthogonality in High-Dimensional Hilbert Spaces
• Abstract summary: In a high-dimensional Hilbert space, almost all state vectors are nearly interpretive, accommodating an exponentially large reservoir of mutually quasi-orthogonal environmental records.<n>This geometry explains why macroscopic alternatives fail to exhibit visible interference once such records are populated.<n>The argument is conditional and finite-dimensional, and it leaves the core of quantum mechanics untouched.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of mutually quasi-orthogonal environmental records. This geometry explains why macroscopic alternatives fail to exhibit visible interference once such records are populated. The argument is conditional and finite-dimensional, and it leaves the interpretive core of quantum mechanics untouched: geometry alone does not select a pointer basis, does not guarantee that a given Hamiltonian drives the system into typical regions of the accessible subspace, and does not turn an improper mixture into a proper one. It merely supplies the vast Hilbert-space capacity that makes decoherence so overwhelmingly effective for all practical purposes.

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