Indefinite probabilities in quantum spacetime: A deepening of unpredictability
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918529403453440 |
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| author | D'Esposito, Vittorio Fabiano, Giuseppe Frattulillo, Domenico |
| author_facet | D'Esposito, Vittorio Fabiano, Giuseppe Frattulillo, Domenico |
| contents | Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group to describe rotational symmetry for spin-$\frac{1}{2}$ systems and Stern-Gerlach apparatuses leads to the description of probabilities of outcomes of spin measurements in terms of non-commuting operators. As a result, we obtain an uncertainty principle between different probability operators, realizing a notion of indefinite probabilities. This is then reflected in the non-commutativity of the entries of the rotation matrix relating the reference frames of two observers, hence fundamentally preventing them from sharply measuring their relative orientation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23862 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Indefinite probabilities in quantum spacetime: A deepening of unpredictability D'Esposito, Vittorio Fabiano, Giuseppe Frattulillo, Domenico Quantum Physics General Relativity and Quantum Cosmology Non-commutative spacetime and quantum groups have been argued to capture non-classical features of spacetime and its symmetries in the low-energy limit of quantum gravity. In this letter, we show that employing the $SU_q(2)$ quantum group to describe rotational symmetry for spin-$\frac{1}{2}$ systems and Stern-Gerlach apparatuses leads to the description of probabilities of outcomes of spin measurements in terms of non-commuting operators. As a result, we obtain an uncertainty principle between different probability operators, realizing a notion of indefinite probabilities. This is then reflected in the non-commutativity of the entries of the rotation matrix relating the reference frames of two observers, hence fundamentally preventing them from sharply measuring their relative orientation. |
| title | Indefinite probabilities in quantum spacetime: A deepening of unpredictability |
| topic | Quantum Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.23862 |