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REVIEW 3 major objections 5 minor 28 references

Does the quantum mechanical wave function exist?

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The wave function exists as a real feature of Nature, this paper argues.

desk verdict Kiefer's paper is a lucid synthesis of standard arguments that concludes the wave function is ontic, but the conclusion is assumed rather than derived, as the paper itself concedes. read the letter →

arxiv 1908.04607 v1 pith:U37S4SPH submitted 2019-08-13 quant-ph gr-qc

Claus Kiefer This is my paper · ORCID
classification quant-phgr-qc MSC 81P0581P1583C45 PACS 03.65.-w03.65.Ta04.60.-m
keywords wavefunctionrealityquantumontologysuperpositionprincipledecoherencemeasurementproblemgravitycosmologyWheeler-DeWittequation
topics The Measurement ProblemQuantum Gravity
open problems Quantum Gravity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper takes on the old dispute over whether the quantum wave function is a real physical entity or merely a summary of what we know. Its answer is that the wave function definitely exists, with the same kind of reality as an electric field. The case rests on three pillars: the superposition principle is experimentally secure and central to all quantum physics; decoherence explains why macroscopic superpositions are not seen without ever abandoning unitary Schrödinger evolution; and quantum cosmology removes the classical observer that epistemic readings require. If the paper is right, everyday classical space-time and observers are approximate, decohered features of a high-dimensional wave function, not primitive ingredients.

What carries the argument

The load-bearing machinery is the superposition principle, the linearity that makes a sum of two physical states again a physical state, combined with environment-induced decoherence and the timeless Wheeler–DeWitt equation of canonical quantum gravity. The superposition principle supplies the universal linear dynamics; decoherence shows why interference terms vanish in the reduced density matrix of a subsystem, so classicality emerges without collapse; and the Wheeler–DeWitt equation with its semiclassical limit supplies the cosmological context in which no classical observer pre-exists and time itself is approximate. These three mechanisms together let the paper conclude that the wave function cannot be reduced to an information catalogue.

What would settle it

A tabletop experiment in which a millimetre-scale mass is prepared in a spatial superposition and a second mass acts as a gravitational probe would settle the key premise: gravitationally induced entanglement between the two would confirm the superposition is real, while a purely classical gravitational response would show the linear formalism breaks down for gravity.

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Extended reading notes

Core claim

On its own terms, the central claim is that the wave function is an ontic quantity: it exists whether or not anyone looks, in the same way an electric field exists. The paper reaches this by taking the superposition principle as the irreducible core of quantum theory, showing through decoherence that the apparent collapse is only a transfer of correlations to inaccessible environmental degrees of freedom, and then extending the linear formalism to gravity. In quantum cosmology the Wheeler–DeWitt equation has no external time and no measurement agency, so the wave functional of the Universe must be the fundamental reality; classical time, the classical metric, and observers emerge through a semiclassical limit with decoherence. Consequently, dead-and-alive superpositions and multiple versions of observers are not artefacts but real branches of the universal wave function.

Load-bearing premise

The whole argument leans on the premise that the standard linear, unitary quantum formalism can be extrapolated without modification to gravitational fields and to the Universe as a whole.

Editorial extensions

If this is right

  • If the wave function is ontic, the universal state never collapses: apparent measurement outcomes are branching correlations, and macroscopic objects in superposition are genuinely present in all branches at once.
  • Epistemic readings that require a classical observer from the outset lose their footing, because quantum cosmology has no external observer to supply measurement outcomes.
  • Explicit collapse models and pilot-wave theories, which modify or supplement the Schrödinger equation, likewise presuppose an ontic wave function, so the paper's conclusion is compatible with them as well as with purely unitary theories.
  • Gravitational superpositions of massive bodies become a real prediction of the linear formalism, so tabletop tests of gravitationally induced entanglement bear directly on the wave function's reality.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Going beyond the paper: if the wave function is fundamental, then the configuration space it lives on is more fundamental than the three-dimensional space we perceive, a form of configuration-space realism the paper does not spell out.
  • A testable extension the paper leaves implicit is to treat direct weak-measurement reconstructions of wave functions for increasingly large composite systems as a diagnostic of onticity, with successful reconstruction supporting the paper's conclusion.
  • If future experiments observe gravitationally induced entanglement between superposed masses, the most economical explanation is that the superposition, and hence the wave function, is real; conversely, a gravity-induced collapse signal would undercut the paper's central claim.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper asks whether the quantum mechanical wave function (or wave functional) exists as an ontic entity. The author reviews the superposition principle, the measurement problem, decoherence, and quantum geometrodynamics, and argues that these considerations jointly favor the conclusion that the wave function is a real feature of Nature. The discussion is a concise synthesis of standard material, with the final section appealing to the timelessness of the Wheeler–DeWitt equation to argue that the Copenhagen interpretation is inapplicable at the fundamental level and that an ontic reading is therefore preferred.

Significance. Taken as a review essay, the paper is a clear and accurate exposition of the measurement problem, decoherence, and the conceptual consequences of quantum gravity. The author correctly emphasizes that decoherence alone does not solve the measurement problem and that both the Everett and collapse-model approaches assign an ontic role to the wave function. The paper also highlights the tension between the Copenhagen interpretation and quantum cosmology. However, the paper does not provide a new technical argument; its conclusion depends on an extrapolation of unitary quantum theory to full quantum gravity and on a prior commitment to an ontic reading, both of which are acknowledged in the text. The significance of the paper lies in framing the debate, not in settling it.

major comments (3)
  1. [Section 3, final paragraph] The sentence 'In all these considerations, the wave function is assumed to be real (ontic)' exposes that the quantum-cosmology argument presupposes the ontic status rather than deriving it. The inapplicability of the Copenhagen interpretation at the most fundamental level does not rule out non-ontic alternatives (e.g., relational or epistemic readings) that also do not require classical observers. The conclusion 'the wave function really exists' is therefore not entailed by the premises presented, and the argument needs either to rule out such alternatives or to be stated in explicitly conditional form.
  2. [Section 3, paragraph on Hilbert-space extrapolation and final paragraph] The author concedes that 'it is thus not at all obvious whether the standard notion of Hilbert space need, or even can, be extrapolated to the level of full quantum gravity' and names the fundamental configuration space as 'the perhaps most important open question.' Since the ontic existence claim concerns a wave functional in a fundamental configuration space, the conclusion rests on an extrapolation whose validity the author himself flags as uncertain. A conditional claim of the form 'if canonical unitary quantum geometrodynamics is correct at the fundamental level, then the wave function exists' would be defensible, but the unconditional statement in the abstract goes beyond what the text supports.
  3. [Section 2, paragraph on collapse models] The statement that collapse models 'only make sense if the wave function acquires a real (ontic) status' establishes the coherence of ontic interpretations, not their truth. The paper does not engage with contemporary epistemic or relational interpretations beyond the label 'Copenhagen' that attempt to explain quantum phenomena without treating the wave function as ontic. The argument from the existence of ontic interpretations to the existence of the wave function is therefore a non sequitur; the author should either address such alternatives directly or temper the conclusion to reflect that the paper argues for the viability, rather than the necessity, of an ontic reading.
minor comments (5)
  1. [Section 3, Feynman quotation] The phrase 'In order words' appears in the quotation from Feynman; it should be 'In other words'.
  2. [Last paragraph] The sentence 'The perhaps most important open question is: what is the configuration state for the wave functional at the most fundamental level?' should read 'what is the configuration space for the wave functional at the most fundamental level?'
  3. [Section 1, paragraph on superposition principle] The text says 'An importance consequence of the superposition principle'; this should be 'An important consequence'.
  4. [Footnote 12] The phrase 'the possibility to directly measuring the wave function' should be 'the possibility of directly measuring the wave function'.
  5. [General] The author's own monographs (Kiefer 2012a, 2015a) are used as authoritative references for several load-bearing claims; independent references would strengthen the argument and give readers a more balanced set of sources for the standard results cited.

Circularity Check

1 steps flagged · score 4.0 of 10

The quantum-cosmology branch assumes the ontic conclusion; other supporting arguments are independent, so circularity is partial, not total.

  1. other [Section 3 (Quantum gravity), paragraph on quantum cosmology and decoherence, after Eq. (8)]
    "In all these considerations, the wave function is assumed to be real (ontic); this is also the case if one applies collapse models to quantum cosmology."

    The paper presents quantum cosmology and decoherence in the early Universe as part of the case for the abstract's conclusion that 'the wave function really exists, that is, it is a real (ontic) feature of Nature.' But in this very section the ontic status is not derived; it is explicitly taken as an assumption ('the wave function is assumed to be real (ontic)'). The quantum-cosmology argument therefore reduces to asserting the target conclusion as a premise. The earlier superposition/decoherence discussion and the WKB-time equations are independent and give the paper substantive content, so the circularity is confined to this supporting branch rather than the entire derivation.

full rationale

The paper is an interpretive essay rather than a first-principles derivation, so most construction-based circularity patterns do not apply. The superposition principle and decoherence are supported by external experiments and standard theory, and the WKB/Born-Oppenheimer limit in quantum cosmology is sketched from the Wheeler-DeWitt equation (Eqs. (6)-(8)) rather than imported as an unexamined ansatz. Repeated self-citations (Kiefer 2012a, 2012b, 2015a, 2015b) provide background details but are not the sole support for any load-bearing step. The concession that the fundamental configuration space is unknown weakens the argument but is a conditionality or completeness issue, not itself a circular step. The one genuinely circular move is the quantum-cosmology section, where the paper states that the wave function 'is assumed to be real (ontic)' while using that section as support for the conclusion that the wave function really exists; that branch presupposes the answer. Because the rest of the argument has independent content, the overall circularity is partial, not total.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper rests on several domain assumptions that are standard in quantum foundations but not proven. Most critically, it assumes the universal validity of unitary quantum mechanics (including gravity), the Born rule, the applicability of decoherence to macroscopic systems, and the correctness of the Wheeler-DeWitt equation. No free parameters or invented entities are introduced.

assumptions (6)
  • domain assumption Superposition principle is universally valid, including for macroscopic objects and gravitational fields.
    Invoked in Sec. 1 and Sec. 3; the upward extrapolation to gravity is acknowledged by the author as an assumption shared by most researchers.
  • domain assumption Born rule and the probabilistic interpretation are valid.
    Sec. 2: the density matrix formalism and the suppression of interference rely on the Born rule; the paper does not derive it, merely notes its foundational role.
  • domain assumption Environment states are approximately orthogonal, so decoherence yields classicality.
    Sec. 2, Eq. (4): assumes ⟨En|Em⟩≈δnm for macroscopic apparatus, a physical assumption about the environment.
  • domain assumption The Wheeler-DeWitt equation correctly describes quantum gravity at the fundamental level.
    Sec. 3: the paper uses quantum geometrodynamics as the 'simplest and most conservative' approach and draws ontological conclusions from it.
  • domain assumption The Born-Oppenheimer/WKB approximation is applicable to the universe.
    Sec. 3, Eq. (7)-(8): derivation of WKB time assumes a semiclassical background ψ0≈C exp(iS0/ℏ) with slowly varying prefactor.
  • domain assumption Copenhagen interpretation fails in quantum cosmology due to lack of external classical observers.
    Sec. 3: argued by the author; this interpretive premise excludes the main epistemic alternative.

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Cite this review

Pith. "Pith review of Does the quantum mechanical wave function exist?." pith.science (2026). https://pith.science/paper/U37S4SPH

@misc{pith2026190804607,
  author       = {Pith},
  title        = {Pith review of: Does the quantum mechanical wave function exist?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U37S4SPH}},
  note         = {Machine review of arXiv:1908.04607}
}
read the original abstract

I address the question whether the wave function in quantum theory exists as a real (ontic) quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle. I then explain the measurement problem and discuss the process of decoherence. Finally, I address the special features that the quantization of gravity brings into the game. From all of this I conclude that the wave function really exists, that is, it is a real (ontic) feature of Nature.

Figures

Figures reproduced from arXiv: 1908.04607 by the authors.

Figure 1
Figure 1. Feynman’s gedanken experiment in which a microscopic superposition [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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