REVIEW 5 major objections 5 minor 14 references
Reanalysis of Everett's relative-state formulation of quantum mechanics
T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read A reanalysis of Everett's original relative-state papers argues that RSQM's definition of a 'good observation' requires the measured object to remain unchanged for the whole observation, making the formulation unable to describe nearly…
desk verdict A close reading of Everett that overreaches: the claimed 'fatal mathematical error' is a misreading of an ideal-measurement model, and the contradiction with experiment collapses. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is Everett's definition of a 'good observation' together with the superposition step in his Eq. (HEA 12). In that definition an interaction in an isolated system transforms $\varphi_i\,\psi_O[\ldots]$ into $\varphi_i\,\psi_O[\ldots\alpha_i]$, with the object eigenstate $\varphi_i$ required to be 'unchanged' and the observer recording $\alpha_i$. The paper's reading of 'unchanged' as 'constant over the entire interaction interval' does the decisive work: it converts a seemingly benign repeatability condition into a restriction that excludes real measurements. The companion mathematical mechanism is the derivative identity showing that Everett's sample solution is only exact for time-independent (zero-energy) object states, so the example that was meant to demonstrate generality actually exposes how narrow the definition is.
What would settle it
A direct calculation would settle the issue: take an object eigenstate that evolves under its own Hamiltonian during the interaction, $\varphi_i(t)$, and ask whether the Schrödinger equation with $H_I=-i\hbar q\,\partial/\partial r$ admits a solution of the form $\varphi_i(t)\,\eta(r-qt)$ outside the special case $\partial\varphi_i/\partial t=0$. If such a solution exists, the paper's claim that Everett's example forces zero-energy object states is wrong; if it does not, the claim that RSQM's example cannot describe changing object states is confirmed.
Extended reading notes
Core claim
On the paper's own terms, the central discovery is that RSQM's internal definition of a good observation makes the theory unable to describe change. Everett requires that an object system initially in an eigenstate $\varphi_i$ be 'unchanged' during the specified period of the observation, while only the observer state changes to record the eigenvalue $\alpha_i$. Read literally, this forbids any interaction in which the object's state evolves, so it forbids transitions, decays, photon absorption and emission, and chemical reactions. The paper further identifies a mathematical slip in Everett's illustrative measurement example: the proposed solution $\psi(q,r-qt)$ satisfies the Schrödinger equation with $H_I=-i\hbar q\,\partial/\partial r$ only if $\partial\varphi/\partial t=0$, meaning the object wavefunction is constant in time and space. From that, the paper concludes that Eq. HEA 12, which writes the final state as $\sum_i a_i \varphi_i \psi_O[\ldots\alpha_i]$, is not justified for arbitrary superpositions and instead only applies to the negligible subset of eigenfunctions that satisfy the good-observation definition.
Load-bearing premise
The entire argument rests on interpreting Everett's phrase 'the system state, if it is an eigenstate, shall be unchanged' as requiring the object state to be identical at every instant during the observation, rather than as a statement that the initial and final object states are the same at the endpoints of an idealized measurement.
Editorial extensions
If this is right
- If the reading is correct, any measurement in which the object system's state changes during the interaction—including radioactive decay, photon emission and absorption, and chemical reactions—lies outside the scope of RSQM's good-observation definition.
- Everett's Eq. 12 cannot be used for an arbitrary initial superposition; it would need a separate derivation for eigenfunctions that do not satisfy the good-observation condition.
- Correcting the von Neumann-style example turns it from a demonstration of generality into a demonstration of the definition's narrowness, since the object wavefunction must be time-independent.
- Real experiments already function as tests of RSQM, and they disagree with it; this contradicts the belief that laboratory tests of RSQM are impossible.
- If no way is found to relax the unchanged-object requirement, the original RSQM cannot serve as a universal wavefunction theory.
Reading between the lines
- A natural next test would be to search Everett's unpublished drafts and correspondence for any place where 'unchanged' is glossed as 'same initial and final state' rather than 'constant throughout'; finding such a gloss would weaken the paper's central reading.
- Modern many-worlds programs built on decoherence typically drop the literal unchanged-object requirement, so the paper's conclusion about the original formulation does not automatically extend to those successors.
- One could construct a model interaction in which the object state changes during the measurement but the final total state still has the branch structure of Eq. 12; if such a model obeys the Born-rule statistics, it would undercut the claim that branch structure requires an unchanged object.
- The paper's approach suggests a general methodological criterion for judging interpretations: an interpretation should be assessed by the fraction of experimentally realized interactions it can describe, not merely by its internal logical consistency.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims to demonstrate that Everett's relative-state formulation of quantum mechanics (RSQM) contradicts an overwhelming body of experimental physics. The author argues that the definition of a 'good observation' in HEA/HET requires the object system eigenstate to remain unchanged throughout the interaction, which he interprets as requiring the object wavefunction to be constant in time and space (a 'zero-energy state'). On this basis he claims that RSQM can describe only a negligible subset of physical observations, that the von Neumann measurement example in HET contains a 'fatal mathematical error', and that Eq. (HEA 12) is 'logically indefensible' when applied to arbitrary superpositions. The paper concludes that experimental tests of RSQM have already been completed and universally reject it.
Significance. If the paper's claims were correct, they would overturn a widely studied interpretation of quantum mechanics. However, the central argument is based on a misinterpretation of the standard non-demolition (repeatability) condition for ideal quantum measurements. The paper does not engage with the established literature on Everett's formulation, in which 'good observation' is an idealized measurement model, not a description of all physical interactions. The paper provides no new calculations or experimental data; its claimed falsification rests on a non-standard reading of Everett's definition and a misapplication of the chain rule in the von Neumann example. The topic is of historical and philosophical interest, but the paper's technical argument does not support its sweeping conclusion.
major comments (5)
- [Section 2.6.2, Eq. (3)] The author's claim that HEA 5 and HEA 6 are false in general is based on an incorrect application of the chain rule. For the Hamiltonian H_I = -iℏ q ∂/∂r, the state ψ = φ(q)η(r−qt) with time-independent φ(q) is an exact solution of the Schrödinger equation iℏ ∂ψ/∂t = H_I ψ. The extra term iℏ (∂φ(q,t)/∂t) η(r−qt) in the author's Eq. (3) vanishes identically when φ is time-independent, which is precisely the situation in Everett's example: during the interaction interval the total Hamiltonian contains no free object-system evolution, so the object wavefunction is not evolving under its own Hamiltonian. The author's conclusion that φ must be a 'zero-energy state' conflates 'no evolution during the measurement interval' with 'zero energy'. The standard reading is that φ is the initial eigenstate, left unchanged by the measurement up to a phase—the non-demolition condition—and the example is error-free.
- [Sections 2.8 and 2.9] The author's interpretation of the phrase 'the [object] system state, if it is an eigenstate, shall be unchanged' (HEA p. 458, HET p. 65) as requiring the object wavefunction to be constant in space and time throughout the observation is not supported by the text or by standard quantum measurement theory. The requirement is that an eigenstate of the measured observable be left unaltered (up to a phase) by the measurement interaction, ensuring repeatability of the measurement. This does not imply that the object system cannot evolve at other times or in other processes. The inference that RSQM rules out all experiments in which the final state differs from the initial state (e.g., radioactive decay, chemical reactions, electronic transitions) is a non sequitur, because those processes are not 'good observations' in Everett's sense; the definition is an idealized model for measurement, not a claim about all physical interactions.
- [Section 3, Eqs. (5)-(10)] The comparison between CQM and RSQM for tritium decay and for sodium D-line superpositions mischaracterizes both theories. Equation (5) is not the quantum state of an individual tritium nucleus; it describes the ensemble average of a decaying population, as the author himself partially acknowledges later. More importantly, the claim that RSQM 'precludes spontaneous transitions' is false: RSQM does not assert that all systems remain in eigenstates; it provides a relative-state description of entangled systems, which for a decay process would yield a superposition of the undecayed atom correlated with the environment and the decay products correlated with the environment. The author's 'RSQM equivalent' in Eq. (7) with a(t)=1 is a straw man, because Eq. HEA 12 applies to observations, not to all dynamical processes.
- [Abstract and Section 1.1] The paper's central claim that 'the set of good observations is a minuscule and completely negligible subset of physical observations' is trivially true but irrelevant. Everett's definition of a good observation is an idealization for measurement, not a claim about all physical interactions. The paper provides no evidence that Everett intended the definition to apply to every interaction; indeed, HET explicitly discusses approximate measurements and general correlations (HET pp. 53-54). The conclusion that RSQM contradicts 'an overwhelming body of experimental physics' is therefore not established.
- [Section 3.1 Synopsis] The concluding claim that 'RSQM is a failed program' is not supported by the analysis. The paper's argument rests entirely on the misinterpretation of the non-demolition condition and on a straw-man account of the von Neumann example. In particular, the paper never addresses the standard derivation of the Born rule in Everett's formulation, nor does it engage with the large literature on Everettian quantum mechanics that treats 'good observation' as an idealized special case.
minor comments (5)
- [Abstract] There is a typo in the first sentence: 'RSQ M' should be 'RSQM'.
- [Section 2.8] The quotation from HEA about approximate measurement is cited as 'HEA 101', but HEA (Rev. Mod. Phys. 29, 454-462) spans pages 454-462; the page number appears to be an error.
- [Section 3, Eq. (6)] The factor √2 in Eq. (6) appears to be a typo; it should probably be 1/√2 or the expression should be re-derived.
- [Throughout] The paper uses the abbreviation 'CQM' for 'conventional quantum mechanics' and 'HE' for the combined HET/HEA works; these abbreviations should be defined at first use.
- [Section 3] The word 'exqample' is a typo for 'example'.
Circularity Check
No significant circularity: the paper's case rests on textual interpretation and independent quantum-mechanical and experimental checks, not on fitted inputs or self-citations.
full rationale
The paper does not fit a parameter and then rename it as a prediction, and it does not rely on a self-citation chain. Its central claims are exegetical and deductive: it argues that Everett's definition of a good observation requires the object eigenstate to remain unchanged throughout the interaction, and that under that reading HEA 12 cannot give the final state for arbitrary initial superpositions nor describe decay or other state-changing processes. These claims are checked directly against the quoted HEA/HET text and against standard quantum-mechanical examples such as tritium decay and sodium D-line superpositions. The disputed step is the interpretation of 'shall be unchanged' as time-independence for the whole observation period; that is a substantive interpretive disagreement about what Everett meant, not a circular derivation. Even if that interpretation is wrong, the error would be one of exegesis or physics, not a reduction of the conclusion to its own premises. No load-bearing self-citation appears, and no result is defined into existence. The absence of circularity is therefore the appropriate finding.
Assumptions & free parameters
assumptions (3)
- standard math The Schrödinger equation and linearity of quantum mechanics are used to derive Eq. 3 and to argue about superposition.
- domain assumption Everett's 'good observation' definition is interpreted as applying to all physical interactions, not just idealized measurements.
- domain assumption The phrase 'shall be unchanged' is taken to require the object eigenstate to be constant during the entire observation period.
Cite this review
Pith. "Pith review of Reanalysis of Everett's relative-state formulation of quantum mechanics." pith.science (2026). https://pith.science/paper/2UZ4JPYO
@misc{pith2026241117757,
author = {Pith},
title = {Pith review of: Reanalysis of Everett's relative-state formulation of quantum mechanics},
year = {2026},
howpublished = {\url{https://pith.science/paper/2UZ4JPYO}},
note = {Machine review of arXiv:2411.17757}
}
read the original abstract
Everett's "Relative State Formulation of Quantum Mechanics" (RSQM), which appeared in Reviews of Modern Physics, is based on his thesis "The Theory of the Universal Wavefunction". The most noteworthy property of these works is the claim by other authors that these works are the seminal contribution to Many Worlds theories of branching realities and the claim that practical laboratory experimental tests of RSQM are not possible. This report shows that Everett's two works describe a formulation of quantum mechanics that contradicts an overwhelming body of experimental physics.
Reference graph
Works this paper leans on
-
[1]
H. Everett III, “Relative State” Formulation of Quantum Mechanics, Rev. Mod. Phys. 29, 454-462 (1957)
work page 1957
-
[2]
H. Everett III, The Theory of the Universal Wave Function (unpublished version of 1956 thesis in The Many-Worlds Interpretation of Quantum Mechanics, A Fun - damental Exposition , B. S. DeWitt and Neill Graham (eds.), Princeton Series in Physics, Princeton University Press, Princeton (1973)
work page 1973
-
[3]
E. B. Shikhovtsev, Biographical Sketch of Hugh Everett, III K . W. Ford (ed.) (2003) https://space.mit.edu/home/tegmark/everett/everettbio.pdf 26
work page 2003
-
[4]
Schlosshauer, Decoherence, the measurement problem, and interpretations of quantum mechanics, Rev
M. Schlosshauer, Decoherence, the measurement problem, and interpretations of quantum mechanics, Rev. Mod. Phys. 76, 1267-1305 (2004)
work page 2004
-
[5]
H. W. Kirby, The Early History of Radiochemistry, MLM-1960 AEC Research and Development Report, U.S. Atomic Energy Commission (1972)
work page 1972
-
[6]
P. Byrne, Everett and Wheller: the Untold Story, in Many Worlds? Everett, Quan- tum Theory, and Reality , S. Saunders, J. Barrett, A. Kent, and D. Wallace (eds.), Oxford University Press, 521-541, Oxford (2010)
work page 2010
-
[7]
L. E. Ballentine, The statistical interpretation of quantum mechanics, Rev. Mod. Phys. textbf42, 358 (1970)
work page 1970
-
[8]
B. S. DeWitt, Quantum mechanics and reality, Phys. Today 23 54-73 (1970)
work page 1970
Show all 14 references
-
[9]
Schroedinger, The present situation in quantum mechanics: A translation of Schroedinger’s”cat paradox” paper (by J
E. Schroedinger, The present situation in quantum mechanics: A translation of Schroedinger’s”cat paradox” paper (by J. D. Trimmer), Proceedings of the American Philosophical Society 124, 323-338 (1980)
1980
-
[10]
P. A. Kent, One World Versus Many: The Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation, in Many Worlds? Everett, Quan- tum Theory, and Reality , S. Saunders, J. Barrett, A. Kent, and D. Wallace (eds.), Oxford University Press, Oxford 307-...
2010
-
[11]
W. M. Jones, The Half-Life of Tritium by Absolute Counting, Phys . Rev. 83, 537-539 (1951)
1951
-
[12]
M. P. Unterweger and L. L. Lucas, Calibration of the National Institute of Standards and Technology tritiated-water standards, Appl. Radiat. Isot. 52, 527-531 (2000)
2000
-
[13]
Yu. A. Akulov and Boris A Mamyrin, Helium-isotope mass-spectrometric method for studying tritium beta decay (idea, experiment, nuclear and molecular physics applications), Phys.-Usp. 46 1153-1162 (2003)
2003
-
[14]
Carlsson, Accurate time-resolved laser spectroscopy on sodium and bismuth atoms, Z
J. Carlsson, Accurate time-resolved laser spectroscopy on sodium and bismuth atoms, Z. Phys. D - Atoms, Molecules and Clusters 9 147-151 (1988) 27
1988
Reviewed August 12, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.