On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915530358652928 |
|---|---|
| author | Fabiano, Nicola |
| author_facet | Fabiano, Nicola |
| contents | We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase insensitivity. Second, we prove there is no distance-preserving embedding from quantum state space into any fuzzy metric space. Third, we establish that fuzzy logic cannot distinguish symmetric from antisymmetric concept combinations -- a fundamental limitation for modeling structured knowledge. These theorems collectively show that fuzzy frameworks are structurally incapable of representing intrinsic uncertainty, where quantum mechanics provides a superior, geometrically coherent alternative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems Fabiano, Nicola Quantum Physics Functional Analysis 46C99, 03E72, 81P45 We prove three structural impossibility results demonstrating that fuzzy metric spaces cannot capture essential features of quantum state geometry. First, we show they cannot model destructive interference between concepts due to phase insensitivity. Second, we prove there is no distance-preserving embedding from quantum state space into any fuzzy metric space. Third, we establish that fuzzy logic cannot distinguish symmetric from antisymmetric concept combinations -- a fundamental limitation for modeling structured knowledge. These theorems collectively show that fuzzy frameworks are structurally incapable of representing intrinsic uncertainty, where quantum mechanics provides a superior, geometrically coherent alternative. |
| title | On the Incompatibility of Quantum State Geometry and Fuzzy Metric Spaces: Three No-Go Theorems |
| topic | Quantum Physics Functional Analysis 46C99, 03E72, 81P45 |
| url | https://arxiv.org/abs/2509.22364 |