Quantum limits of a space-time reference frame
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914279575257088 |
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| author | Mattei, Davide Castro-Ruiz, Esteban |
| author_facet | Mattei, Davide Castro-Ruiz, Esteban |
| contents | We study the limitations for defining spatial and temporal intervals when the only available reference frame is a single composite quantum system, whose internal degrees of freedom serve as a temporal reference, a clock, and whose center of mass degrees of freedom act as a spatial reference, a rod. By combining quantum speed limits with the mass energy equivalence of special relativity, we show that spatial localizability and temporal resolution are not independent: sharpening one inevitably blurs the other. Specifically, the internal energy coherence needed for precise timekeeping affects the center of mass dynamics, enhancing position spreading during free evolution. As a result, a single composite system cannot act as a perfect quantum reference frame for both space and time, leading to a Heisenberg like uncertainty relation between spatial and temporal intervals. After analyzing this trade off from an external perspective, we formulate it in a purely relational manner, by means of covariant observables relative to the space time quantum reference frame, uncovering an additional intrinsic uncertainty of order the Compton wavelength of the frame. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11407 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum limits of a space-time reference frame Mattei, Davide Castro-Ruiz, Esteban Quantum Physics We study the limitations for defining spatial and temporal intervals when the only available reference frame is a single composite quantum system, whose internal degrees of freedom serve as a temporal reference, a clock, and whose center of mass degrees of freedom act as a spatial reference, a rod. By combining quantum speed limits with the mass energy equivalence of special relativity, we show that spatial localizability and temporal resolution are not independent: sharpening one inevitably blurs the other. Specifically, the internal energy coherence needed for precise timekeeping affects the center of mass dynamics, enhancing position spreading during free evolution. As a result, a single composite system cannot act as a perfect quantum reference frame for both space and time, leading to a Heisenberg like uncertainty relation between spatial and temporal intervals. After analyzing this trade off from an external perspective, we formulate it in a purely relational manner, by means of covariant observables relative to the space time quantum reference frame, uncovering an additional intrinsic uncertainty of order the Compton wavelength of the frame. |
| title | Quantum limits of a space-time reference frame |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.11407 |