A skepticism on the concept of quantum state related to quantum field theory on curved spacetime

Quantum Physics [Submitted on 11 Apr 2026] A skepticism on the concept of quantum state related to quantum field theory on curved spacetime Hideyasu Yamashita Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a C^{*}-algebra \mathfrak{A}, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of \mathfrak{A} w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it. Comments: 28 pages Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) MSC classes: 81P05 (Primary), 81T20, 81T05 (Secondary) Cite as: arXiv:2604.11830 [quant-ph]   (or arXiv:2604.11830v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.11830 Focus to learn more Submission history From: Hideyasu Yamashita [view email] [v1] Sat, 11 Apr 2026 17:26:35 UTC (42 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADS 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)