Quantum Mechanics without Nonlocality

N. L. Chuprikov

REVIEW

Quantum Mechanics without Nonlocality

N. L. Chuprikov

Quantum Physics · Submitted 21 Feb 2006 · 27 references

Pith's verdict: The paper's central claim that Born's rule fails for entangled states rests on an extra postulate that makes a concrete wrong prediction (no interference in 1D scattering), so the nonlocality argument collapses.

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arXiv IDquant-ph/0602173 (version 3)

Pith IDIXCUHTHY, Pith's permanent record of this paper and its review

CitationN. L. Chuprikov. "Quantum Mechanics without Nonlocality." arXiv:quant-ph/0602173 (2006). https://pith.science/paper/IXCUHTHY

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Colleague — this one is a clear reject, but not because the author is sloppy. The paper makes a bold move: define any superposition of macroscopically distinct sub-processes as 'entangled,' then declare Born's rule meaningless for such states, and thereby dissolve Bell-inequality nonlocality. The one genuinely interesting piece is the 1D scattering decomposition in Section 3: the full wave function is split into transmitted and reflected components with the reflected part odd about the barrier midpoint, and the author claims these subensembles evolve without superluminal speeds. That is a real technical claim, and it deserves a careful look in the context of tunneling-time debates.

But the load-bearing step in Section 4 is an extra postulate, not a derivation: 'a particle, as an indivisible object, cannot simultaneously take part in two macroscopically distinct processes.' From that the author concludes observables and Born's rule have no physical sense for entangled states. Fine, if you grant the metaphysics. But the model has a concrete, testable consequence that fails. The paper explicitly says the transmitted and reflected probability fields 'do not influence each other.' In the overlap region left of the barrier, standard QM predicts interference between incident and reflected waves — standing-wave fringes in front of a mirror. The additive picture |ψ_tr|^2+|ψ_ref|^2 without the cross-term is empirically wrong. So the central principle isn't just unorthodox; it makes a false prediction.

Everything else follows from that. The jump from one-particle scattering to Bell states is asserted. No criterion for 'macroscopically distinct' is given. The key decomposition is delegated to a self-cited companion paper, and there is no alternative formalism or experimental prediction offered. Citation pattern is thin but not misleading. The paper is honest in the sense that it states its axiom directly.

Who is this for? Possibly a reader tracking tunneling-time interpretations, where the decomposition might be repurposed. As a resolution of Bell nonlocality, it doesn't hold up. I would desk reject rather than referee. I can't see citing or discussing it in a group.

Referee report

Significance

If the central claim were correct, it would reframe one of the most discussed questions in quantum foundations: Bell violations would no longer be evidence of nonlocality, and the standard application of Born's rule to entangled states would be declared meaningless. That would be a significant result. The paper also deserves credit for identifying a genuine conceptual tension in the 'no-signalling' interpretation of nonlocal correlations and for asking whether the superposition principle is consistent with the particle picture. However, the significance is not realized in the manuscript: the load-bearing premise is an extra postulate rather than a derivation, the argument contradicts well-established interference phenomena, and no replacement formalism or testable prediction is supplied. As it stands, the paper offers a philosophical reinterpretation based on an unsupported assumption rather than a demonstrated correction to quantum mechanics.

Major objections (4)

[Section 4] The central premise that 'a particle, as an indivisible object, cannot simultaneously take part in two (or several) macroscopically distinct processes' is asserted as a postulate, not derived from quantum mechanics or from any broader physical principle. The entire conclusion that observables and Born's rule are meaningless for entangled states depends on this premise, and no argument is given for why standard quantum mechanics, which does apply Born's rule to superpositions, must be replaced by this corpuscular indivisibility constraint. If this premise is false, the argument collapses, and the paper provides no independent evidence for it.
[Section 3] The assertion that 'the probability fields for transmission and reflection, being superimposed, do not influence each other' is a concrete physical claim that directly contradicts standard quantum mechanics. In the overlap region in front of the barrier, the standard probability density is |ψ_ref + ψ_tr|^2, which contains the interference cross-term 2Re(ψ_ref^* ψ_tr), and this cross-term is observable, for example as standing-wave fringes in front of a mirror or in electron interference experiments. The paper's alternative, |ψ_tr|^2 + |ψ_ref|^2, would eliminate these fringes. Since the paper does not account for the extensive experimental evidence for such interference, this is not merely a metaphysical gloss but an empirically falsifiable prediction that fails.
[Section 4] The generalization from the one-particle scattering case to compound Bell states is asserted rather than derived. The sentence 'The same concerns the entangled states of compound quantum systems' appears without a proof that all Bell-type entangled states involve macroscopically distinct alternative sub-processes in the sense required by the paper's postulate, nor is a criterion given for what counts as 'macroscopically distinct.' Without such a criterion and a derivation for the multipartite case, the paper's central claim about Bell inequalities and Bell experiments is unsupported.
[Section 3] The key decomposition ψ_full = ψ_ref + ψ_tr and the claim that the truncated functions ψ̃_ref and ψ̃_tr evolve with constant norms are deferred to the self-cited companion paper [14], which is not reproduced or summarized here. As a result, the reader cannot verify the uniqueness of the decomposition, the claimed continuity at the midpoint xc, or the absence of superluminal evolution. These properties are load-bearing for the argument that the decomposed sub-processes are free of nonlocality, so the present manuscript is not self-contained at its technically crucial step.

Minor objections (5)

[Abstract] There are typographical errors in the abstract, including 'incon sistency' and 'reﬂected,' which should be corrected.
[Section 3] The definition of the truncated functions ψ̃_ref and ψ̃_tr in Eqs. (1) and (2) introduces a spatial cut at xc; the paper asserts continuity and norm conservation but does not show that the time-dependent Schrödinger equation is satisfied in a neighborhood of the cut, which would be needed to justify the claim that these functions describe physically allowed sub-processes.
[Section 4] The term 'macroscopically distinct' is used as a central classificatory notion but is never defined quantitatively; it is unclear whether the criterion depends on particle mass, separation scale, detector resolution, or some other physical quantity.
[References] Reference [14] is a self-citation to quant-ph/0602172, and reference [10] is incompletely formatted ('Cambridge' is split by a line break ending the citation); both should be completed and the dependence on [14] made explicit.
[Section 2] The criticism of Bohmian mechanics, that the fate of the particle depends on the coordinate of its starting point, is stated too briefly; the alleged contradiction with quantum-mechanical principles is not demonstrated, and the passage reads as a summary of a longer argument rather than a self-contained objection.

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The paper

The paper claims

This paper argues that quantum nonlocality is an artifact of misapplying Born's rule to entangled states.

The reading

This paper argues that quantum nonlocality of entangled states is not a real phenomenon but an artifact of standard quantum mechanics. The cause, it says, is the superposition principle's failure to distinguish between an unentangled state and a superposition of macroscopically distinct alternatives. Because a particle cannot take part in two or more such alternatives at once, observables and Born's formula cannot be applied to entangled states. Bell's inequalities, which average over an entangled state, therefore have no clear physical interpretation, and experimental violations of them do not demonstrate nonlocality—they only show that the correlations built into the existing theory contradict special relativity. The argument is anchored in a model of one-dimensional scattering where the full wave function is decomposed into transmitted and reflected sub-waves.

What carries the argument

The central object is the decomposition $\psi_{full}(x;E)=\psi_{ref}(x;E)+\psi_{tr}(x;E)$ of the stationary scattering solution into reflected and transmitted parts, together with the trimmed packets $\tilde{\psi}_{ref}$ and $\tilde{\psi}_{tr}$ that belong to opposite sides of the barrier's midpoint. These packets obey the time-dependent Schrödinger equation everywhere except at the midpoint, where the continuity equation is still satisfied. They serve as the unentangled, 'non-dendritic' states for which observables are defined; the original full state, being their superposition, is called entangled and is declared inaccessible to one-particle observables. This decomposition is what lets the paper locate nonlocality in the misapplication of the superposition principle rather than in any actual faster-than-light influence.

Extended reading notes

Core claim

The central claim is that quantum nonlocality is not an actual phenomenon. In the paper's view, it appears in quantum mechanics because the superposition principle does not conceptually separate unentangled states from superpositions of macroscopically distinct alternatives. For a particle completing a one-dimensional scattering, the full wave function can be uniquely written as $\psi_{full}=\psi_{ref}+\psi_{tr}$, and the two parts can be trimmed into wave packets that describe the reflected and transmitted sub-processes separately. Since these sub-processes are macroscopically distinct at the final stage, the one-particle state is an entangled one, and a particle, being indivisible, cannot be in two such alternatives simultaneously. Hence no observable exists for the entangled state, Born's rule does not apply to it, and Bell inequalities—which require averaging over an entangled state—have no clear physical sense. Their observed violation is therefore not evidence of nonlocality but only evidence that the correlations in the existing theory conflict with special relativity.

Load-bearing premise

The load-bearing premise, asserted in Section 4, is that a particle is an indivisible object that cannot take part in two or more alternative macroscopically distinct sub-processes, so that no observable can be defined for an entangled state.

Editorial extensions

If this is right

Bell inequality violation experiments no longer count as evidence for nonlocality; on this view they show only that the correlations used in standard entangled-state calculations are incompatible with special relativity.
Born's rule should be restricted to unentangled time-dependent states; expectation values computed on an entangled state are physically meaningless.
For one-particle scattering, the only meaningful time is the dwell time, measurable with a non-demolishing clock; group and other characteristic times for the entangled state have no physical sense.
For compound systems, correlation calculations are legitimate only when both events lie on a single 'non-dendritic' multi-particle trajectory, i.e., only for unentangled states.
The superposition principle must be revised to distinguish macroscopically distinct states from their superpositions and to force any entangled state into a decomposition into unentangled states.

Reading between the lines

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

If the paper is right, entanglement-based technologies that treat Bell-inequality violation as a resource—such as device-independent randomness expansion or quantum key distribution—would be relying on averages that are not physically defined, so their security analysis would need a local reinterpretation.
The argument leaves the notion 'macroscopically distinct' unquantified; a general criterion would be needed before the no-observables rule could be applied beyond the scattering example, so the paper's proposal is best read as a challenge to define such a boundary.
A direct test of the model is to check numerically whether the trimmed wave packets remain good solutions of the Schrödinger equation away from the midpoint for realistic potentials; if the equation is appreciably violated, the decomposition cannot be physically legitimate.
If accepted, the decomposition suggests that single-particle entanglement and multiparticle entanglement may need different treatments, since the indivisibility premise applies literally only to a single particle; extending the rule to compound systems is an extrapolation the paper makes but does not prove.

Original abstract

We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,488 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.33 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We argue that quantum nonlocality of entangled states is not an actual phenomenon.	contribution 0.48	0.53	0.95	asserted 0.93
s1	It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle.	interpretation 0.82	0.20	0.16	asserted 0.87
s2	In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state.	background 0.62	0.07	0.05	asserted 0.99
s3	However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes.	background 0.34	0.10	0.06	asserted 1.00
s4	Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states.	interpretation 0.53	0.26	0.16	asserted 1.00
s5	The same concerns the entangled states of compound quantum systems.	result 0.49	0.17	0.04	asserted 0.99
s6	In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal.	background 0.98	0.05	0.03	asserted 1.00
s7	However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation.	interpretation 0.87	0.14	0.08	asserted 1.00
s8	Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm.	interpretation 0.93	0.07	0.27	asserted 1.00
s9	They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.	interpretation 0.98	0.10	0.26	asserted 1.00

What kind of paper the classifier reports this is: position or commentary 1.00 · evidence from argument 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (27)

[14]

N. L. Chuprikov, e-prints quant-ph/0602172

View on Pith Pith review arXiv
[1]

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)

View on Pith 1935
[2]

J. S. Bell, Physics 1, 195 (1964)

View on Pith 1964
[3]

A. Aspect, Nature (London) 398, 189 (1999)

View on Pith 1999
[4]

R. A. Bertlmann and A. Zeilinger (eds.), Quantum [Un]spe akables, from Bell to Quantum Information, Springer Verlag, Heidelberg, (200 2)

View on Pith
[5]

T. Norsen, e-prints quant-ph/0404016v2

View on Pith Pith review arXiv
[6]

T. Norsen, e-prints quant-ph/0408105v3

View on Pith Pith review arXiv
[7]

T. Norsen, e-prints quant-ph/0408178

View on Pith Pith review arXiv
[8]

H. M. Wiseman, e-prints quant-ph/0509061

View on Pith Pith review arXiv
[9]

Werner Heisenberg, The Physical Principles of the Quant um Theory (Dover Publications, 1949), p. 39

View on Pith 1949
[10]

J. S. Bell, Speakable and Unspeakable in Quantum Mechan ics, (Cambridge University

View on Pith
[11]

Ll. Masanes, A. Acin, and N. Gisin, Phys. Rev. A 73, 01211 2 (2006)

View on Pith 2006
[12]

A. Shimony, Controllable and uncontrollable non-loca lity, in S. Kamefuchi et al. (eds.), Foundations of Quantum Mechanics in the Light of New Technology (Physical Society of Japan, Tokyo, 1984), pp. 225-230. 7

View on Pith 1984
[13]

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim , A. Sen(De), U. Sen, and B. Synak-Radtke, Phys. Rev. A 71, 062307 (2005). Press, C ambridge, 1987)

View on Pith 2005
[15]

Charles H. Bennett, David P. DiVincenzo, Christopher A . Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, William K. Wootter s, e-prints quant-ph/9804053v4

View on Pith Pith review arXiv
[16]

E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989)

View on Pith 1989
[17]

R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994)

View on Pith 1994
[18]

V.S. Olkhovsky and E. Recami, Phys. Repts. 214, 339 (1992)

View on Pith 1992
[19]

A.M. Steinberg, Phys. Rev. Let. 74, 2405 (1995)

View on Pith 1995
[20]

J.G. Muga, C.R. Leavens, Phys. Repts. 338, 353 (2000)

View on Pith 2000
[21]

C.A.A. Carvalho, H.M. Nussenzveig, Phys. Repts. 364, 83 (2002)

View on Pith 2002
[22]

V. S. Olkhovsky, E. Recami, J. Jakiel, Phys. Repts. 398, 133 (2004)

View on Pith 2004
[23]

E.H. Hauge, J.P. Falck and T.A. Fjeldly, Phys. Rev. B 36, 4203 (1987)

View on Pith 1987
[24]

W. Jaworski and D.M. Wardlaw, Phys. Rev. A 37, 2843 (1988)

View on Pith 1988
[25]

C.R. Leavens and G.C. Aers, Phys. Rev. B 39, 1202 (1989)

View on Pith 1989
[26]

M. Buttiker, Phys. Rev. B 27, 6178 (1983)

View on Pith 1983
[27]

W.R. McKinnon and C.R. Leavens, Phys. Rev. A 51, 2748 (1995). 8

View on Pith 1995

How the literature uses it

Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 2 papers

Consequently, there is no nonlocal influence between entangled particles in measurements.

Locality of quantum entanglement · 0.96
Here I discuss an experiment involving particles entangled in energy and time variables that shows that there is no nonlocal state reduction during measurements on entangled particles.

An experiment that proves the absence of nonlocality in quantum mechanics · 0.93

States a conflicting result 1 paper

We show that the observed phenomenon of quantum nonlocality cannot be incorporated in a class of $\psi$-epistemic models.

Bell Nonlocality and the Reality of Quantum Wavefunction · 0.92

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [14]

N. L. Chuprikov, e-prints quant-ph/0602172

View on Pith Pith review arXiv

[2] [1]

A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935)

View on Pith 1935

[3] [2]

J. S. Bell, Physics 1, 195 (1964)

View on Pith 1964

[4] [3]

A. Aspect, Nature (London) 398, 189 (1999)

View on Pith 1999

[5] [4]

R. A. Bertlmann and A. Zeilinger (eds.), Quantum [Un]spe akables, from Bell to Quantum Information, Springer Verlag, Heidelberg, (200 2)

View on Pith

[6] [5]

T. Norsen, e-prints quant-ph/0404016v2

View on Pith Pith review arXiv

[7] [6]

T. Norsen, e-prints quant-ph/0408105v3

View on Pith Pith review arXiv

[8] [7]

T. Norsen, e-prints quant-ph/0408178

View on Pith Pith review arXiv

[9] [8]

H. M. Wiseman, e-prints quant-ph/0509061

View on Pith Pith review arXiv

[10] [9]

Werner Heisenberg, The Physical Principles of the Quant um Theory (Dover Publications, 1949), p. 39

View on Pith 1949

[11] [10]

J. S. Bell, Speakable and Unspeakable in Quantum Mechan ics, (Cambridge University

View on Pith

[12] [11]

Ll. Masanes, A. Acin, and N. Gisin, Phys. Rev. A 73, 01211 2 (2006)

View on Pith 2006

[13] [12]

A. Shimony, Controllable and uncontrollable non-loca lity, in S. Kamefuchi et al. (eds.), Foundations of Quantum Mechanics in the Light of New Technology (Physical Society of Japan, Tokyo, 1984), pp. 225-230. 7

View on Pith 1984

[14] [13]

M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim , A. Sen(De), U. Sen, and B. Synak-Radtke, Phys. Rev. A 71, 062307 (2005). Press, C ambridge, 1987)

View on Pith 2005

[15] [15]

Charles H. Bennett, David P. DiVincenzo, Christopher A . Fuchs, Tal Mor, Eric Rains, Peter W. Shor, John A. Smolin, William K. Wootter s, e-prints quant-ph/9804053v4

View on Pith Pith review arXiv

[16] [16]

E.H. Hauge and J.A. Støvneng, Rev. Mod. Phys. 61, 917 (1989)

View on Pith 1989

[17] [17]

R. Landauer and Th. Martin, Rev. Mod. Phys. 66, 217 (1994)

View on Pith 1994

[18] [18]

V.S. Olkhovsky and E. Recami, Phys. Repts. 214, 339 (1992)

View on Pith 1992

[19] [19]

A.M. Steinberg, Phys. Rev. Let. 74, 2405 (1995)

View on Pith 1995

[20] [20]

J.G. Muga, C.R. Leavens, Phys. Repts. 338, 353 (2000)

View on Pith 2000

[21] [21]

C.A.A. Carvalho, H.M. Nussenzveig, Phys. Repts. 364, 83 (2002)

View on Pith 2002

[22] [22]

V. S. Olkhovsky, E. Recami, J. Jakiel, Phys. Repts. 398, 133 (2004)

View on Pith 2004

[23] [23]

E.H. Hauge, J.P. Falck and T.A. Fjeldly, Phys. Rev. B 36, 4203 (1987)

View on Pith 1987

[24] [24]

W. Jaworski and D.M. Wardlaw, Phys. Rev. A 37, 2843 (1988)

View on Pith 1988

[25] [25]

C.R. Leavens and G.C. Aers, Phys. Rev. B 39, 1202 (1989)

View on Pith 1989

[26] [26]

M. Buttiker, Phys. Rev. B 27, 6178 (1983)

View on Pith 1983

[27] [27]

W.R. McKinnon and C.R. Leavens, Phys. Rev. A 51, 2748 (1995). 8

View on Pith 1995