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

• URL: http://arxiv.org/abs/2604.11830v1
• Date: Sat, 11 Apr 2026 17:26:35 GMT
• Title: A skepticism on the concept of quantum state related to quantum field theory on curved spacetime
• Abstract summary: Some skeptical arguments on the physical reality of quantum states are given.<n>I argue that the algebraic formalism of quantum field theory in curved spacetime leads to such a skepticism.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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