Exact quantum time compatible with positive energy

Quantum Physics arXiv:2607.01296 (quant-ph) [Submitted on 1 Jul 2026] Title:Exact quantum time compatible with positive energy Authors:Ovidiu Cristinel Stoica View a PDF of the paper titled Exact quantum time compatible with positive energy, by Ovidiu Cristinel Stoica View PDF HTML (experimental) Abstract:What would it be like to be in a superposition of yesterday, today, and tomorrow? This question may seem at best entertaining, but it is necessary, and exploring it allows us to understand how exact irreversible clocks and change are possible, despite the Unruh-Wald and Hegerfeldt-Ruijsenaars no-go theorems forbidding them. Unruh and Wald (1989) proved that if energy is bounded from below, no observable can increase monotonically with the Schrödinger time parameter t. Perfectly monotonic clocks and irreversible observable changes (Hegerfeldt-Ruijsenaars, 1980) seem impossible. From the perspective of the Schrödinger time, the world appears in a superposition of different intrinsic clock states indicating different times and opposite time directions. This seems to directly contradict our daily experiences of time and change. I show that there is no contradiction: from an intrinsic perspective of the world, sharp irreversible changes do happen, because the macroscopic pointer states resolve the superposition of different times. Large-scale time-reversing or discontinuous transitions are not internally observable in the records. From the intrinsic perspective, an unbounded intrinsic-time translation generator plays the role of the Hamiltonian, generating only forward time evolution with respect to the intrinsic time, but not to the Schrödinger parameter t, which is thus not justified to play the role of time. This allows sharp time observables even if the external Hamiltonian is bounded from below. In addition, this leads to a stationary wavefunction of the universe satisfying a Wheeler-DeWitt-type equation, without assuming gravity. Comments: Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2607.01296 [quant-ph] (or arXiv:2607.01296v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.01296 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ovidiu Cristinel Stoica [view email] [v1] Wed, 1 Jul 2026 13:43:32 UTC (17 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact quantum time compatible with positive energy, by Ovidiu Cristinel StoicaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: physics physics.hist-ph References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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?) 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?)