On the Physical Untenability of the Standard Notion of Quantum State

Christian de Ronde

REVIEW 5 major objections 4 minor 1 cited by

On the Physical Untenability of the Standard Notion of Quantum State

T0 review · 5 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The standard notion of a quantum state is physically untenable because the same vector cannot be both certain and uncertain.

desk verdict The central claim that the standard notion of quantum state is internally inconsistent dissolves once certainty is recognized as basis-relative. read the letter →

arxiv 2505.23989 v1 pith:KZ3RMIQ3 submitted 2025-05-29 quant-ph physics.hist-ph

Christian de Ronde This is my paper

classification quant-phphysics.hist-ph

keywords quantumstatepuritystandardmechanicssuperpositionbasisdependenceKochen-Speckertheoremcontextualitymeasurementproblem

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

The paper argues that the standard, textbook notion of a quantum state is physically untenable because it rests on at least four mutually incompatible definitions. These are: the abstract vector in Hilbert space, the operational 'pure' state that gives a certain outcome in one basis, the superposition that gives uncertain outcomes, and the post-measurement empirical state. The central contradiction is that the same abstract vector can be represented as a certain state in one basis and an uncertain superposition in another, yet the formalism treats both as 'the same state'. The paper concludes that a rational physical theory must abandon this inconsistent notion and replace it with a coherent, basis-invariant account.

What carries the argument

The central mechanism is the identification of two mutually inconsistent senses of 'the same' behind the term 'quantum state': a purely mathematical abstract-invariance of vectors under basis change, and an operational notion of certainty that is basis-dependent. The argument turns on the explicit example in Table 1, where Ψ, |↑x⟩, and a|↑y⟩+b|↓y⟩ are different representations of the same vector but carry incompatible physical interpretations (certain vs. uncertain). The Kochen-Specker theorem is invoked to rule out a global, basis-independent valuation of physical properties, so that the mathematical equivalence cannot be translated into physical equivalence. This gap between mathematical and physical equivalence is what the paper says makes the standard notion untenable.

What would settle it

Prepare a spin-1/2 system in the state |↑x⟩ and compute the probabilities for measurements of σ_x and σ_y from the same state vector: σ_x returns +1 with probability 1, while σ_y returns +1 and −1 each with probability 1/2. Standard quantum mechanics derives both results from the single state without logical conflict. If the paper's claim that the same state cannot be both certain and uncertain is correct, this calculation must contain a hidden inconsistency; identifying where it fails would settle the claim.

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Extended reading notes

Core claim

The paper's central claim is that the standard formulation of quantum mechanics defines the quantum state in at least four different ways that are not equivalent: as an abstract, basis-independent vector; as a pure state that yields a measurement outcome with probability 1 in a particular basis; as a superposition that yields probabilistic outcomes; and as the actual outcome observed after a measurement. These definitions conflate mathematical equivalence with physical equivalence. In particular, the same abstract vector Ψ can be written as |↑x⟩ in one basis, which is certain, and as a|↑y⟩+b|↓y⟩ in another, which is uncertain; the paper asserts that the same state cannot be both certain and uncertain at the same time. Because the formalism lacks an operational-invariant link between basis representations, a fact the paper connects to the Kochen-Specker theorem, the standard notion of state refers to different, incompatible states of affairs while claiming to refer to one. The conclusion is that the notion of quantum state is physically untenable and obstructs a rational understanding of quantum phenomena.

Load-bearing premise

The argument assumes that 'certainty' (probability = 1) is an intrinsic property of the quantum state itself, rather than a relation between a state and a chosen observable; if certainty is relative to a basis, the alleged contradiction does not arise.

Editorial extensions

If this is right

If the standard notion of quantum state is untenable, then every interpretation that treats the state as a fundamental physical entity inherits the same inconsistency.
The measurement problem and the collapse postulate are not auxiliary difficulties but direct consequences of using incompatible definitions of state.
A replacement account of quantum states must provide an operational-invariant formalism that connects to objective, basis-independent concepts.
The distinction between 'pure' states and superpositions cannot be drawn consistently within the standard account, so any argument built on that distinction is unsound.

Reading between the lines

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

One could test the argument by checking whether the alleged contradiction dissolves if 'certainty' is treated as a relation between a state and a chosen observable rather than an intrinsic property of the state; the paper does not consider this relativization.
The same reasoning could be applied to classical mechanics to see whether the standard account truly differs from classical reference-frame relativity in the way the paper claims, or whether the claimed contradiction is a general feature of any state notion.
If the conclusion is accepted, a natural next step would be to search for formulations of quantum mechanics that use only basis-invariant, intensive quantities and do not rely on the basis-dependent pure-state concept.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear [Colleague],

The punchline: this paper's central argument—that the standard notion of quantum state is physically untenable because the same vector can be both certain and uncertain—does not survive contact with the formalism. The alleged contradiction in Section 4 rests on treating certainty as an intrinsic property of the state. In quantum mechanics, probability-1 is always relative to a chosen observable/basis. |↑x⟩ has P=1 for σx and |a|² for σy; those are different conditional probabilities, not conflicting assignments to the same event. The paper's own Definitions 1.2 and 1.3 already quantify over bases: 'there exists a basis where certain' and 'there exist many bases where not' are compatible statements. No inconsistency follows.

What the paper does well: it usefully isolates four different textbook definitions of 'quantum state'—abstract vector, operational pure state, superposition, post-measurement state—and it documents real terminological sloppiness. The historical discussion about Dirac and Born is engaging, and the point that 'pure state' and 'superposition' are often used inconsistently is fair. If the paper had stopped at 'textbooks are sloppy,' I would have been sympathetic.

Soft spots: the load-bearing step in Table 1 is invalid, as above. The paper also misreads Kochen-Specker: KS rules out noncontextual hidden-variable valuations, not the existence of well-defined basis-relative Born probabilities. The claim that a 'global intensive valuation' exists, from the author's own prior papers, is asserted rather than argued, and it carries a lot of weight. The conclusion of untenability is far beyond what the evidence supports.

Who is this for? Philosophers of physics and anyone interested in how textbook language can mislead. But as a research contribution to the foundations of QM, the central argument fails. I would not cite it in my own work. I would, however, send it to a referee rather than desk-reject: the paper is clearly argued, engages a live debate, and the flaw is instructive—a good referee can show exactly why certainty is basis-relative. For a reading group, it's a useful case study in contextuality and relational properties.

Recommendation: if it comes to you, invite a revision that either retracts the untenability claim or actually engages with the basis-relative nature of probability. As it stands, reject.

Referee Report

5 major / 4 minor

Summary. The paper claims that the standard Dirac–von Neumann notion of quantum state is physically untenable because it is defined in several incompatible ways. Section 1 lists four definitions: the abstract Hilbert-space vector (Definition 1.1), the basis-dependent pure state that yields a certain outcome (Definition 1.2), the basis-dependent superposition state with uncertain outcomes (Definition 1.3), and the empirical post-measurement state (Definition 1.4). Section 4 and Table 1 present the central 'clear inconsistency': the same vector Ψ can be written as |↑x⟩ in one basis and as a|↑y⟩+b|↓y⟩ in another, so the same state would be both certain and uncertain. The paper concludes that the standard concept must be replaced by an operationally invariant intensive formalism, and it invokes the Kochen–Specker theorem and the collapse postulate as additional evidence.

Significance. If the central argument were valid, it would be a significant challenge to a foundational concept of quantum theory. However, the paper does not provide a valid derivation of any internal contradiction. The alleged contradiction arises only if certainty is treated as an intrinsic property of the state rather than a relation between a state and a measurement basis, which is not part of the standard formalism and is even inconsistent with the paper's own Definitions 1.2 and 1.3. The Kochen–Specker theorem is misapplied, and the collapse postulate is not a formal contradiction of the axioms. The paper's positive alternative is referenced only to the author's prior work. The clear taxonomy of textbook usages is useful, but the main conclusion is unsupported.

major comments (5)

[Section 4, Table 1] The claimed 'clear inconsistency' does not follow from the standard formalism. Certainty is always relative to a chosen observable: for the vector Ψ, P(↑x|σx measurement)=1 and P(↑y|σy measurement)=|a|^2 are different conditional probabilities for different measurement contexts, not competing assignments to the same event. The unitary transformation between the {|↑x⟩,|↓x⟩} and {|↑y⟩,|↓y⟩} bases is exactly the translation between the two descriptions, so the paper's assertion 'a state that is certain cannot be uncertain' is true only if 'certain' is treated as an intrinsic property of the vector, which Definition 1.2 and Definition 1.3 do not assert. The contradiction is an artifact of the paper's own nonstandard reading.
[Section 1, Kochen–Specker remark] The paper invokes the Kochen–Specker theorem to conclude that there is 'no invariant global valuation' across bases and that different basis representations of the same vector correspond to different physical states. This is a misreading: the theorem rules out noncontextual two-valued assignments to a set of projection operators, but it does not forbid basis-relative Born probabilities, and it does not imply that a vector in two different bases is a different state. The theorem therefore cannot support the paper's central claim that the standard notion of quantum state is inconsistent.
[Section 2, collapse postulate] The paper characterizes the projection postulate as 'a non-linear evolution within a linear mathematical formalism' and calls this 'another serious inconsistency.' In the standard axioms the projection postulate is an additional rule for updating the state after a measurement, not a dynamical law competing with the Schrödinger equation. The measurement problem is a genuine conceptual puzzle, but it is not a formal contradiction within the Dirac–von Neumann formulation, so this passage cannot serve as independent evidence for the paper's conclusion.
[Section 3, pure states] The question 'Are quantum superpositions pure states?' is presented as exposing an inconsistency because it can be answered both yes and no. The two answers correspond to two different meanings of the word 'pure': under Definition 1.1 every unit vector, including a superposition, is a pure state, while under Definition 1.2 'pure' means 'certain outcome in a particular basis.' These are distinct concepts, and the standard literature has no difficulty distinguishing them; the paper has identified a terminological ambiguity in some textbooks, not a contradiction in the quantum state notion.
[Section 4, support for the claimed inconsistency] The central claim is asserted rather than demonstrated: Section 4 says the inconsistency 'should already be clear to the attentive reader' and refers to [10] for a 'more detailed analysis,' while the only explicit argument is the invalid certainty inference discussed above. Similarly, the existence of a 'global intensive valuation' is stated on the authority of [9] with no derivation in this manuscript. Since the paper's conclusion is a strong one about the untenability of a standard concept, it needs a self-contained argument; citations to the author's own prior work do not supply the missing support.

minor comments (4)

[Abstract] There is a typo in the abstract: 'notion ofquantum state' should read 'notion of quantum state'; similar spacing and formatting issues appear throughout the text.
[Table 1] The coefficients a and b in the superposition a|↑y⟩+b|↓y⟩ are never defined; the paper should state that they are complex coefficients with |a|^2+|b|^2=1 and should specify the relation between the two bases.
[Section 1] The term 'global intensive valuation' is used without definition; a reader who is not familiar with [9] cannot evaluate the claim that such a valuation exists.
[Section 1] The paper uses 'reference frame' to mean a Hilbert-space basis, which is potentially misleading; a unitary change of basis is not a change of reference frame in the sense of Galilean or relativistic physics.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a conceptual critique of the standard notion of quantum state, not a derivation or prediction from fitted inputs.

full rationale

The paper's argument is a philosophical critique, not a derivation of predictions from fitted parameters. It proceeds by isolating four distinct definitions of 'quantum state' found in standard textbooks (Dirac, Peres, Nielsen and Chuang) and then arguing that these definitions are incompatible. The load-bearing step is the Table 1 discussion in Section 4: the same abstract vector Ψ is represented as |↑x⟩ in one basis and as a|↑y⟩ + b|↓y⟩ in another, and the paper concludes that a state that is certain cannot also be uncertain. This is an interpretive claim about what 'same state' should mean; it can be challenged on the ground that certainty is basis-relative, but that challenge is a matter of correctness or philosophical adequacy, not circularity. The paper does not fit any parameter and then rename the fit as a prediction, nor does it define its conclusion into existence by construction. The self-citations to de Ronde and Massri (2021, 2022) are used only as pointers to an alternative 'global intensive valuation' and to further analysis; the alleged inconsistency of the standard definitions is established independently of those citations, so the self-citations are not load-bearing. The central argument rests on textbook definitions, the superposition principle, and the Kochen–Specker theorem, all of which are external sources. No circular step of the kind enumerated in the analysis patterns is present.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No numerical free parameters. The paper is a conceptual critique; its central claim depends on the four axioms listed above. The most fragile is Axiom 4, which is not stated or defended.

assumptions (4)

standard math The Kochen-Specker theorem is valid and establishes that there is no invariant global valuation of projection operators for a quantum state across different bases.
Invoked in sections 1 and 4 as the basis for the claim that different reference-frame representations of the same abstract state are not operationally equivalent.
ad hoc to paper A physical state must be invariant under reference-frame transformations in the same way the classical (Galilean) notion of state is.
Introduced in section 1 through the classical rabbit example; this benchmark is used to declare the quantum notion of state inconsistent.
domain assumption The four definitions of quantum state found in textbooks (Defs 1.1-1.4) are implicitly assumed by the standard account to be equivalent and refer to the same concept.
Stated in the introduction: 'there are at least four different definitions that are implicitly considered to be equivalent, consistent and meaningful.'
ad hoc to paper Certainty (probability = 1) is a property of the quantum state itself, not a relation between the state and a chosen measurement basis.
Used in section 4: 'the same state cannot be certain and uncertain at the same time.' Without this assumption the alleged contradiction disappears.

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Cite this review

Pith. "Pith review of On the Physical Untenability of the Standard Notion of Quantum State." pith.science (2026). https://pith.science/paper/KZ3RMIQ3

@misc{pith2026250523989,
  author       = {Pith},
  title        = {Pith review of: On the Physical Untenability of the Standard Notion of Quantum State},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KZ3RMIQ3}},
  note         = {Machine review of arXiv:2505.23989}
}

read the original abstract

The notion of quantum state plays a fundamental role within the Standard account of Quantum Mechanics (SQM) as established by Dirac and von Neumann during 1930s and up to the present. In this work we expose the deep inconsistencies that exist within the multiple definitions of the notion of quantum state that are provided within this axiomatic formulation. As we will argue, these different inconsistent definitions continue to be -- even today -- uncritically confused within the mainstream physical and philosophical literature leading to self-contradictory statements and wrong conclusions. We end with a discussion regarding the untenability of this concept for any rational understanding of theoretical physics.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Realist Approach to Quantum Individuality: Against the "Received" and "Alternative" Views
quant-ph 2025-09 conditional novelty 6.0 of 10

The paper argues that the Received and Alternative views on quantum individuality are two sides of the same anti-realist, particle-presupposing coin, and promotes a relational 'Logos' account of quantum individuals.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [10]

Against the Tyranny of Pure States in Quantum Theory

de Ronde, C.& Massri, C., 2022, “Against the Tyranny of Pure States in Quantum Theory”,Foundations of Science, 27, 27-41

work page 2022

[2] [9]

The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations

de Ronde, C.& Massri, C., 2021, “The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations.”,International Journal of Theoretical Physics, 60, 429-456. 9

work page 2021

[3] [1]

& Byrne, P., (Eds.), 2012,The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980, Princeton University Press, Princeton

Barrett, J. & Byrne, P., (Eds.), 2012,The Everett Interpretation of Quantum Mechanics: Collected Works 1955-1980, Princeton University Press, Princeton

work page 2012

[4] [2]

Preferred Basis, Decoherence and the Quantum State of the Universe

Barvinsky, A.O. & Kamenshchik, A.Y., 2022, “Preferred Basis, Decoherence and the Quantum State of the Universe”, inFrom Quantum to Classical. Fundamental Theories of Physics, Kiefer, C. (Eds), Springer, Cham

work page 2022

[5] [3]

& Życzkowski, K., 2017,Geometry of Quantum States: An Introduction to Quantum Entangle- ment, Cambridge University Press, Cambridge

Bengtsson, I. & Życzkowski, K., 2017,Geometry of Quantum States: An Introduction to Quantum Entangle- ment, Cambridge University Press, Cambridge

work page 2017

[6] [4]

Can Quantum Mechanical Description of Physical Reality be Considered Complete?

Bohr, N., 1935, “Can Quantum Mechanical Description of Physical Reality be Considered Complete?”,Physical Review, 48, 696-702

work page 1935

[7] [5]

Zur Quantemechanik der Stossvorgange

Born, M., 1926, “Zur Quantemechanik der Stossvorgange”,Zeitschrift für Physik37 (1926) 863-867, English translation “On the Quantum Mechanics of Collision Processes” in [32]

work page 1926

[8] [6]

Interpretations of quantum theory: A map of madness

Cabello, A., 2017, “Interpretations of quantum theory: A map of madness”, inWhat is Quantum Information?, pp. 138-143, O. Lombardi, S. Fortin, F. Holik and C. López (Eds.), Cambridge University Press, Cambridge

work page 2017