On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle

[2608.16762] On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle Skip to main content Search Submit Donate Log in General Relativity and Quantum Cosmology arXiv:2608.16762 (gr-qc) [Submitted on 17 Aug 2026 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle Authors: Kengo Shimada View PDF HTML (experimental) Abstract: We investigate the unitarity of quantum evolution relative to an internal time defined by a local observer's clock. The observer is modeled as a relativistic particle carrying both a clock and a matter-field detector, analyzed first on a fixed curved background and subsequently within a fully diffeomorphism-invariant theory of dynamical gravity. In the former case, we find that evolution with respect to the internal clock time is generally nonunitary, implying a violation of the Einstein equivalence principle at the quantum level. In contrast, in the latter case, diffeomorphism invariance allows us to adopt observer-centric coordinates without loss of generality. On the resulting partially-reduced phase space, one of the diffeomorphism generators becomes linear in the clock Hamiltonian, generating a relational evolution that is consistent with the remaining diffeomorphism constraints. Assuming that an effective quantum field theory exists to be consistent with the diffeomorphism invariance, these features ensure unitary evolution relative to the internal clock, thereby preserving the equivalence principle even in the quantum regime. Our results highlight the fundamental role of diffeomorphism invariance in shaping relational unitary evolution from the perspective of a local observer. Comments: 33 pages, 3 figures; References and discussions added; conclusions unchanged Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph) Report number: YITP-25-198, FQSP-2026-2 Cite as: arXiv:2608.16762 [gr-qc] (or arXiv:2608.16762v2 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2608.16762 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kengo Shimada [ view email ] [v1] Mon, 17 Aug 2026 16:09:09 UTC (458 KB) [v2] Wed, 26 Aug 2026 17:57:20 UTC (460 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-08 Change to browse by: hep-th quant-ph References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• On the (Non)Unitarity with respect to the Clock of a Dynamical Local Observer and the Einstein Equivalence Principle#677744
• Addressing the Conflict Between Relativity and Quantum Theory: Models, Measurement and the Markov Property#702103
• Mathematical Relativity Theory#479912
• Time travel and coincidence-free local dynamical theories#773439
• Einstein's Clocks, Poincare's Maps#413266