A preprint posted to arXiv in April 2026 by independent researcher Hideyasu Yamashita delivers a sharp philosophical critique of one of quantum theory’s most basic building blocks: the quantum state. Rather than presenting new calculations or simulations, the work is a purely conceptual analysis grounded in the algebraic formulation of quantum field theory on curved spacetime (AQFTCS). It argues that without a distinguished vacuum or preferred Hilbert space, the usual distinction between “physically real” states and mathematically allowed but fictitious ones evaporates. The paper remains a preprint and has not undergone peer review; its methodology is philosophical argumentation rather than empirical testing, and its limitations are openly acknowledged by the author, who offers only preliminary remarks on how physics might proceed without invoking states at all.

Yamashita begins by contrasting non-relativistic quantum mechanics and flat-space quantum field theory, where the GNS construction relative to a fixed vacuum lets physicists separate density operators on a concrete Hilbert space (deemed physically realizable) from the vastly larger set of abstract states on the C*-algebra of observables. In curved spacetime, general covariance and the lack of a global timelike Killing vector rob us of any unique vacuum. Different observers can disagree on what “empty” space looks like—an effect made famous by the Unruh radiation seen by accelerated detectors and Hawking radiation near black-hole horizons. Consequently, the algebraic framework treats every algebraic state on equal mathematical footing, leaving no principled way to declare some real and others fictional.

This observation is not entirely new; textbooks such as Birrell and Davies’ Quantum Fields in Curved Space (1982) and Robert Wald’s 1994 monograph have long emphasized the ambiguity of vacuum choice. What Yamashita adds is the explicit claim that this ambiguity renders the very notion of a quantum state physically meaningless rather than merely observer-dependent. He then counters “pragmatic realism”—the attitude that quantum states must be real because they are indispensable—by sketching how even ordinary quantum mechanics can be reformulated in terms of transition amplitudes or consistent-histories without ever assigning a state vector or density matrix to the system itself. The conjecture is that a similar state-free approach could extend to both flat-space QFT and QFTCS, though the technical details are left for future work.

Going deeper, this skepticism intersects with three domains the preprint touches only lightly. First, the black-hole information paradox. Hawking’s original calculation relies on tracing out degrees of freedom behind the horizon, producing a mixed state for the outgoing radiation. If those entangled “states” are not physically real, the very setup of the paradox becomes suspect. Work by Almheiri, Marolf, Polchinski and Sully (the AMPS firewall argument, arXiv:1207.3123) already exposed tensions in semiclassical state counting; Yamashita’s lens suggests the tension may originate in an over-reification of the state concept rather than a failure of unitarity. Second, the quantum-to-classical transition. Decoherence theory depends on reduced density matrices obtained by partial trace. If no fundamental density matrix exists, explanations of why macroscopic objects appear classical must be recast in purely algebraic terms—perhaps through the dynamics of expectation-value functionals alone. This resonates with relational interpretations championed by Carlo Rovelli, in which quantum reality is always relative to an observer and never absolute.

Third, quantum gravity itself. Loop quantum gravity defines kinematical states on spin networks; string theory uses Hilbert spaces of excitations on background geometries. A thoroughgoing algebraic reformulation might eliminate the need for a background Hilbert space altogether, aligning instead with holographic ideas in which the algebra of boundary operators determines everything. Wald’s review (arXiv:gr-qc/9509050) already shows how Hadamard states can serve as a surrogate for “physically reasonable” states in curved space; Yamashita’s critique implies even these are provisional, chosen for mathematical convenience rather than ontological priority.

Conventional coverage of algebraic QFTCS has largely celebrated its background-independence and mathematical rigor while quietly retaining state language for practical calculations. The preprint reveals this as an inconsistency: the formalism is sold as more general precisely because it drops the fixed Hilbert space, yet most physicists continue to treat states as real entities. What it misses, however, is any concrete proposal for rewriting textbook predictions—Hawking radiation spectra, inflationary perturbations, entanglement entropy—without ever mentioning states. Until such a translation exists, practitioners will likely continue using the “fictional” machinery that demonstrably works.

Nevertheless, the work performs a valuable service by forcing a re-examination of which parts of quantum theory are truly fundamental and which are scaffolding. If states turn out to be dispensable, the path toward a background-independent theory of quantum gravity may be shorter than expected—shifting emphasis from wave functions to algebras of observables and their flows. The quantum-classical interface, the fate of information behind horizons, and even the measurement problem take on new guises when stripped of state realism. Yamashita’s skepticism may ultimately prove too radical for most physicists, yet it illuminates a crack in the foundation that deserves serious attention as we attempt to unify quantum theory with gravity.