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arxiv: 2604.11830 · v1 · submitted 2026-04-11 · 🪐 quant-ph · gr-qc

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

Hideyasu Yamashita
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:44 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc
keywords quantum statesphysical realityquantum field theory on curved spacetimealgebraic QFTvacuum stateGNS representationdispensability of states
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The pith

Quantum field theory on curved spacetime offers no criterion to separate physically real quantum states from fictional ones.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper contends that the algebraic formulation of quantum field theory on curved spacetime lacks any distinguished vacuum state or associated physical Hilbert space. In ordinary quantum mechanics and Minkowski-space field theory, only density matrices on the GNS representation space of a chosen vacuum count as physically real while others are treated as non-physical fictions. Curved spacetime removes this dividing line because no vacuum can be singled out. The author also challenges pragmatic defenses of state realism by arguing that the notion of quantum state is dispensable already in non-relativistic quantum mechanics and is likely dispensable in field theories as well.

Core claim

In the algebraic approach to QFT on curved spacetime, states are simply positive linear functionals on a C*-algebra with no preferred vacuum to generate a Hilbert space via the GNS construction. Consequently there is no basis for declaring some states physically realizable and others fictional, unlike the situation in non-relativistic QM or QFT in flat spacetime. This absence leads directly to skepticism about whether quantum states carry physical reality at all.

What carries the argument

The GNS representation space built from a vacuum state, which supplies the fixed Hilbert space that normally marks the boundary between physical and fictional states but cannot be chosen uniquely when spacetime is curved.

If this is right

  • Quantum states lose any claim to physical reality in QFTCS because no vacuum selects a preferred representation.
  • The pragmatic argument that states must be real because they are useful collapses if the concept of state can be removed from the theory.
  • Skepticism about state reality applies already to non-relativistic quantum mechanics once states are shown to be dispensable there.
  • Any formulation of QFTM or QFTCS must be checked for whether it can be rewritten without explicit reference to quantum states.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If states are dispensable, measurement outcomes in curved spacetime might be described directly in terms of algebra elements rather than expectation values.
  • The argument suggests examining whether unitary inequivalence of representations in QFTCS carries any observable consequence once no vacuum is fixed.
  • One could attempt to reformulate the Schrödinger equation or field equations as relations among observables alone, testing whether predictions remain unchanged.

Load-bearing premise

Physical states are those that can be written as density matrices on the single Hilbert space obtained from one fixed vacuum via the GNS construction, and this requirement is necessary for any state to count as real.

What would settle it

An explicit construction of a unique, physically preferred vacuum state that works for arbitrary curved spacetimes and restores a consistent distinction between density-matrix states on its GNS space and all other functionals.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents two skeptical arguments concerning the physical reality of quantum states. First, it claims that algebraic QFT on curved spacetime (AQFTCS) implies skepticism because, unlike non-relativistic QM and QFT in Minkowski spacetime where only states expressible as density matrices on the GNS representation space of a fixed vacuum are deemed physically real, QFTCS lacks any distinguished vacuum or physical Hilbert space, rendering the distinction between real and fictional states impossible. Second, it counters 'pragmatic realism' (which justifies states via their indispensability) by arguing that quantum states are dispensable in non-relativistic QM and conjecturing the same for QFTM and QFTCS, with some preliminary considerations.

Significance. If the central claim holds, the paper would highlight a potential interpretive challenge for quantum states in QFTCS arising from the absence of a canonical vacuum. The algebraic approach is clearly outlined, and the distinction between mathematical states on a C*-algebra and physically real ones is usefully drawn. However, the result's significance is constrained by its interpretive nature and the preliminary status of the dispensability conjecture, which lacks formal support.

major comments (1)
  1. [Abstract] Abstract, second paragraph: the inference that 'we cannot distinguish physically real states from fictional states' in QFTCS rests on the premise that physicality requires expressibility as a density matrix on the GNS space of a distinguished vacuum. This premise is not defended against standard representation-independent selection criteria in QFTCS such as the Hadamard condition or microlocal spectrum condition, which can demarcate admissible states without reference to a fixed vacuum. The argument therefore does not establish that the absence of a canonical vacuum entails the absence of any physical/fictional distinction.
minor comments (2)
  1. The conjecture that quantum states are dispensable in QFTM and QFTCS is stated without any detailed supporting argument or explicit preliminary considerations, which weakens the counter to pragmatic realism even if it is not load-bearing for the primary skepticism claim.
  2. Notation for the C*-algebra and GNS construction is introduced without explicit cross-references to standard definitions in the literature, which could aid readers unfamiliar with algebraic QFT.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address the major comment below and will incorporate revisions to clarify and strengthen the relevant sections of the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract, second paragraph: the inference that 'we cannot distinguish physically real states from fictional states' in QFTCS rests on the premise that physicality requires expressibility as a density matrix on the GNS space of a distinguished vacuum. This premise is not defended against standard representation-independent selection criteria in QFTCS such as the Hadamard condition or microlocal spectrum condition, which can demarcate admissible states without reference to a fixed vacuum. The argument therefore does not establish that the absence of a canonical vacuum entails the absence of any physical/fictional distinction.

    Authors: We acknowledge that the argument presented in the abstract relies on the standard premise from non-relativistic QM and QFTM that physically real states are those expressible as density matrices on the GNS Hilbert space of a distinguished vacuum. We have not explicitly contrasted this with representation-independent criteria such as the Hadamard condition or microlocal spectrum condition, which are indeed used in QFTCS to select physically admissible states. This is a valid observation. In revision, we will update the abstract and expand the discussion in the main text to address these criteria directly. Our position is that while such conditions demarcate admissible states, they do not provide a canonical physical Hilbert space in the manner available in flat spacetime, thereby preserving the core of the skeptical argument within the algebraic framework. We will make this clarification explicit. revision: yes

Circularity Check

1 steps flagged

Skepticism on physical states in QFTCS follows by definition from restricting physicality to GNS-vacuum density matrices

specific steps
  1. self definitional [Abstract]
    "Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of 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."

    Physical reality is stipulated to require expressibility on the GNS space of a distinguished vacuum. The claim that no distinction is possible in QFTCS follows immediately by this definition once the vacuum is absent, without separate justification that the GNS-vacuum criterion is exhaustive or required for physicality.

full rationale

The paper's core argument defines physical states as those expressible as density matrices on the fixed GNS representation space of a distinguished vacuum (as in flat-space QM/QFTM), then notes the absence of any such vacuum or Hilbert space in QFTCS and concludes that no distinction between real and fictional states is possible. This inference reduces directly to the definitional premise rather than an independent derivation. The text provides no examination of alternative selection criteria (e.g., Hadamard or microlocal conditions) that could demarcate physical states independently of a fixed vacuum. The second part on dispensability of states in QM is not shown to be circular from the given excerpts. This matches self-definitional circularity with moderate load on the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the philosophical premise that physicality of states requires a distinguished vacuum Hilbert space; this is treated as an axiom imported from standard QM without independent justification supplied for the curved case.

axioms (2)
  • domain assumption Only states expressible as density matrices on the GNS representation space of a fixed vacuum are physically real.
    Invoked to contrast standard QM/QFTM with QFTCS.
  • domain assumption Absence of a distinguished vacuum in QFTCS removes any criterion for physicality.
    Core step of the skepticism.

pith-pipeline@v0.9.0 · 5578 in / 1303 out tokens · 23452 ms · 2026-05-10T15:44:28.171364+00:00 · methodology

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