Local Scale Invariance in Quantum Theory: Experimental Predictions
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Quantum Physics arXiv:2601.07883 (quant-ph) [Submitted on 12 Jan 2026] Title:Local Scale Invariance in Quantum Theory: Experimental Predictions Authors:Indrajit Sen, Matthew Leifer View a PDF of the paper titled Local Scale Invariance in Quantum Theory: Experimental Predictions, by Indrajit Sen and Matthew Leifer View PDF Abstract:We explore the experimental predictions of the local scale invariant, non-Hermitian pilot-wave (de Broglie-Bohm) formulation of quantum theory introduced in arXiv:2601.03567. We use Weyl's definition of gravitational radius of charge to obtain the fine-structure constant for non-integrable scale effects $\alpha_S$. The minuteness of $\alpha_S$ relative to $\alpha$ ($\alpha_S/\alpha \sim 10^{-21}$) effectively hides the effects in usual quantum experiments. In an Aharonov-Bohm double-slit experiment, the theory predicts that the position probability density depends on which slit the particle trajectory crosses, due to a non-integrable scale induced by the magnetic flux. This experimental prediction can be realistically tested for an electrically neutral, heavy molecule with mass $m \sim 10^{-19} \text{g}$ at a $\sim 10^6 \text{ esu}$ flux regime. We analyse the Weyl-Einstein debate on the second-clock effect using the theory and show that spectral frequencies are history-independent. We thereby resolve Einstein's key objection against local scale invariance, and obtain two further experimental predictions. First, spectral intensities turn out to be history-dependent. Second, energy eigenvalues are modified by tiny imaginary corrections that modify spectral linewidths. We argue that the trajectory dependence of the probabilities renders our theory empirically distinguishable from other quantum formulations that do not use pilot-wave trajectories, or their mathematical equivalents, to derive experimental predictions. Comments: Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2601.07883 [quant-ph] (or arXiv:2601.07883v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.07883 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Indrajit Sen [view email] [v1] Mon, 12 Jan 2026 00:23:49 UTC (133 KB) Full-text links: Access Paper: View a PDF of the paper titled Local Scale Invariance in Quantum Theory: Experimental Predictions, by Indrajit Sen and Matthew LeiferView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: gr-qc hep-th 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)