The Geometric Part of Decoherence: Quasi-Orthogonality in High-Dimensional Hilbert Spaces
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918484919713792 |
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| author | Svozil, Karl |
| author_facet | Svozil, Karl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03807 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Geometric Part of Decoherence: Quasi-Orthogonality in High-Dimensional Hilbert Spaces Svozil, Karl Quantum Physics 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. |
| title | The Geometric Part of Decoherence: Quasi-Orthogonality in High-Dimensional Hilbert Spaces |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.03807 |