Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation
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Quantum Physics arXiv:2603.28983 (quant-ph) [Submitted on 30 Mar 2026] Title:Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation Authors:Simon Friederich, Mritunjay Tyagi View a PDF of the paper titled Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation, by Simon Friederich and Mritunjay Tyagi View PDF HTML (experimental) Abstract:In a companion paper we derived a unique time-reversal-invariant stochastic generalization of the Liouville equation and showed that it coincides with the evolution equation for the Husimi $Q$-function in a broad class of bosonic quantum field theories. Here we investigate the prospects for interpreting that evolution equation in terms of underlying stochastic trajectories. Drawing on Drummond's time-symmetric stochastic action formalism, we show that the traceless diffusion Fokker-Planck equation defines a natural measure over stochastic trajectories conditional on mixed-time boundary conditions. However, we identify a significant gap: it has not been established that every $Q$-function can be represented as a weighted average of these conditional probabilities over boundary values. The trajectory interpretation holds for ensembles with fixed boundary conditions but does not straightforwardly extend to arbitrary quantum states. Despite this limitation, we show that Drummond's trajectory dynamics are fundamentally non-Markovian -- a natural consequence of combining stochasticity with time-reversal invariance. This non-Markovianity places the dynamics outside the scope of the ontological models framework and thereby explains why the major no-go theorems for hidden-variable theories do not rule out the approach. These results clarify both the achievements and the remaining challenges in the project of understanding quantum field theory as the statistical mechanics of time-symmetric stochastic processes. Comments: Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2603.28983 [quant-ph] (or arXiv:2603.28983v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.28983 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Simon Friederich [view email] [v1] Mon, 30 Mar 2026 20:31:35 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Can Quantum Field Theory be Recovered from Time-Symmetric Stochastic Mechanics? Part II: Prospects for a Trajectory Interpretation, by Simon Friederich and Mritunjay TyagiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?) 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?)