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Cited by 18Quantum Mechanics and ApplicationsAlgebraic and Geometric AnalysisQuantum and Classical Electrodynamics

EPR Correlations Using Quaternion Spin

Open access
Sanctuary, Bryan·2024·Quantum Reports
DOI 10.3390/quantum6030026
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Abstract

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 12—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 12, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper presents a quaternion-spin (Q-spin) statistical simulation that reproduces EPR coincidence correlations and Bell inequality violation without non-local entanglement, attributing the violation to spin coherence/helicity. It reports a total simulated CHSH of 2.995, exceeding the quantum singlet value 2.828 and approaching 3.

Key findings

  • Replacing SU(2) spin symmetry with the quaternion group Q8 complexifies the Dirac field, giving structured spin with two orthogonal spin-1/2 magnetic moments that couple in free flight into a spin-1 boson; decoupling in a polarizing field yields measured fermion spin-1/2 and violates Bell inequalities without non-locality.
  • The simulation decomposes EPR correlation into polarization (triangle, CHSH = 2.027) and coherence (mustache, CHSH = 0.968), giving total CHSH = 2.995, close to 3; quantum mechanics gives CHSH = 2√2 = 2.828, while theoretical polarization is 2 and the mustache difference is 0.828.
  • The coherence correlation is fit by E_q = −1/4 sin(2θ_ab) for 0 ≤ θ_ab ≤ π and +1/4 sin(2θ_ab) for π < θ_ab ≤ 2π; the doubling of the angle is attributed to the boson magnetic moment of 2μ.
  • The paper claims Bell’s theorem is disproved by counterexample, with no hidden variables and only the local variable θ; entanglement is replaced by helicity, and a residual polarization correlation of 0.027 makes simulated polarization CHSH = 2.027 exceed the BI value of 2.

Methods

  • A statistical simulation using quaternion spin (Q-spin) with Q8 symmetry; algorithms determine clicks from polarized states and coherent events, with FORTRAN and C code, Gnuplot plotting code, and text outputs provided as supplementary materials.
  • The simulation treats all EPR pairs with no missing coincidences and as statistically independent; the only variable is the angle θ orienting spin on the Bloch sphere, and the Least Action Principle selects axis alignment.
  • Correlation is computed from equal and unequal coincidences as E(a,b) = (N_eq − N_nq)/N_tot; polarization and coherence contributions are separated using Boolean δ_p and δ_c, and CHSH is evaluated from four experiments with Alice and Bob filter settings.

Limitations

  • The paper states that the cross-over in Figure 8 was expected at zero but is shifted lower, and the cause has not been determined; it also states that coincidence EPR experiments are not yet able to distinguish polarization events from coherence events, and that distinguishing polarization from coherence for a single particle and controlling boson decoupling is an experimental challenge.
  • The paper states that no new data were created or analyzed and that data sharing is not applicable; it also states that the simulation is not a quantum simulation but a model suggested by the treatment.
  • Evident from the text: the results rely on assumptions such as the boson resisting decoupling until the field is close to a fermion axis, θ remaining stable in free flight without decoherence, and helicity conservation between separated pairs; no experimental confirmation is reported.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/quantum6030026

Cites

62 of 62 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 37 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning

    A statistical simulation replicates the correlation observed in EPR coincidence experiments without needing non-local connectivity.

    “We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The CHSH correlation for the full mustache is 1.

    “The CHSH correlation for the full mustache is 1.”
    Quote in the paperSubstantial claim
  • Findingown data

    The simulation gives a total CHSH value of 2.995, or almost 3.

    “The simulation gives a total CHSH value of 2.995, or almost 3.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The doubling gives the mustache function two periods over one period of θab.

    “The doubling gives the mustache function two periods over one period of θ ab in Figure 7.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    As the spins approach randomly set filters, the correlation between the two resonance states is -cos θab.

    “= -cos θ ab”
    Quote in the paperSubstantial claim
  • May combine two claims. 65
  • Classified as probably not a substantial claim. 34
  • The quote only partly states this claim. 1

  • May combine two claims.

    Findingown data

    Using a vector gives the triangle with CHSH = 2; using a bivector gives the mustache function with CHSH = 1.

    “Using a vector gives the triangle, Figure 7, with a CHSH = 2. Using a bivector gives the mustache function with CHSH = 1.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The theoretical CHSH value for polarizations is 2, whereas in Figure 7 it is 2.027.

    “The theoretical CHSH value for polarizations is 2, whereas in Figure 7, it is 2.027.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Findingnone given

    At zero and π, the correlation is respectively anti-correlated with -1 and correlated with +1.

    “At zero and π, the correlation is respectively anti-correlated with -1 and correlated with +1.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The simulation finds more correlation than from a singlet state, CHSH = 2.828.

    “We find more correlation than from a singlet state, CHSH = 2.828.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Residual correlation remains, with a cross-over close to the horizontal axis.

    “As shown in Figure 8, residual correlation remains.A cross-over occurs close to the horizontal axis.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    The total correlation from polarization and coherence gives CHSH = 3, in contrast to that from an entangled state of 2√2.

    “We note that the total correlation from polarization and coherence gives a total of CHSH = 3, in contrast to that from an entangled state of 2 √ 2.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Findingnone given

    At π/2 and 3π/2, the fermions are orthogonal, and there is no correlation.

    “At π 2 and 3π 2 , the fermions are orthogonal, and there is no correlation.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Subtracting the product state from the coincidence data separates the part responsible for the BI violation, with CHSH = 0.828.

    “Subtracting the two separates the part responsible for the BI violation, with CHSH = 0.828.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The simulated correlation from either polarization axis gives the polarization as the triangle, with CHSH = 2.027.

    “The simulated correlation from either polarization axis gives the polarization as the triangle, with a CHSH = 2.027.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    The computer simulation generates the correlation from polarization and coherence, giving a CHSH correlation of respectively 2 and 1 for a total of 3.

    “The computer simulation generates the correlation from polarization and coherence, giving a CHSH correlation [1] of respectively 2 and 1 for a total of 3.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [1] Clauser, 1969, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. source

      Not checked in the free run.

  • May combine two claims.

    Findingown data

    Quantum theory gives the CHSH value of 2 sqrt 2, which is less than the simulation value of 2.995, which is close to 3.

    “Quantum theory gives the value of 2 √ 2, which is less than that from the simulation of 2.995, which is close to 3.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data

    The residual correlation of 0.027 has the same sign changes as the polarization correlation.

    “We note the residual correlation of 0.027, Figure 8 has the same sign changes.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    Each sine curve gives the correlation between the bosons of Alice and Bob, and this correlation maximizes at multiples of pi/4 where both are bosons.

    “Each sine curve gives the correlation between the bosons of Alice and Bob.This maximizes at multiples of π 4 where both are bosons.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    Dropping the coherent terms leaves only fermion electrons, and the correlation is then the triangle in Figure 7.

    “By dropping the coherent terms, only fermion electrons remain, and the correlation is the triangle in Figure 7.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group Q8, which complexifies the Dirac field.

    “The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q 8 , which complexifies the Dirac field.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Point particle spin becomes structured with two orthogonal magnetic moments, each with spin 1/2, and these moments couple in free flight to create a spin-1 boson.

    “Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 1 2 -these moments couple in free flight to create a spin-1 boson.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    Spin becomes structured and geometrically equivalent to a photon.

    “From this change, spin becomes structured and geometrically equivalent to a photon, Figure 1 [7].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [7] Sanctuary, B. (2024). Quaternion Spin. Mathematics, 12. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The transition from a free-flight boson to a measured fermion causes the observed violation of Bell's Inequalities and resolves the EPR paradox.

    “The transition from a free-flight boson to a measured fermion causes the observed violation of Bell's Inequalities and resolves the EPR paradox.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    The complementary property to measured spin polarization is helicity.

    “The complementary property to the measured spin polarization is the helicity [8].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [8] Sanctuary, B. (2023). Spin helicity. Preprints, 2023010571. source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Spin has two orthogonal spin-1/2 axes, Σ3 and Σ1, which are reflections of each other, and in free flight these couple to give a composite boson spin of magnitude 1, Σ13.

    “It has two orthogonal spins 1 2 axes, Σ 3 and Σ 1 , which are reflections of each other, and in free-flight, these couple to give a composite boson spin of magnitude 1, Σ 13 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [7] Sanctuary, B. (2024). Quaternion Spin. Mathematics, 12. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationnone given

    Depending on its orientation in the field, when a boson encounters a filter, it either decouples into two independent fermion spins of 1/2 or remains a boson and precesses without decoupling.

    “Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 1 2 , or it remains a boson and precedes without decoupling.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    The boson electron exists only in free flight (isotropy) and displays helicity, which spins the axis of linear momentum either L or R.

    “The boson electron, e - B , exists only in free flight (isotropy) and displays helicity, which spins the axis of linear momentum either L or R.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    The complementary attributes of spin, polarization, and coherence simultaneously exist.

    “The complementary attributes of spin, polarization, and coherence simultaneously exist.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    The correlation from coherence can only be measured when Alice and Bob's spins are oriented within the same 45° wedge.

    “The correlation from coherence can only be measured when Alice and Bob's spins are oriented within the same 45 • wedge as seen in Figure 5.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    The two complementary spin attributes are extreme points in their distinct convex spaces.

    “The two complementary spin attributes are extreme points in their distinct convex spaces.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given

    A product state does not violate BI with a CHSH = 2.

    “In contrast, a product state does not violate BI with a CHSH = 2.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    The filtering processes for Alice and Bob are entirely independent and, therefore, local.

    “The filtering processes for Alice and Bob are entirely independent and, therefore, local.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given

    Polarization belongs to a convex set, a disc with Cl1,2; quaternion space, the S3 hypersphere, is also convex.

    “Polarization belongs to a convex set, a disc with Cℓ 1,2 .Quaternion space, the S 3 hypersphere, is also convex.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The second paper shows that the correlation between an EPR pair is conserved after separation.

    “The second paper [8] shows that the correlation between an EPR pair is conserved after separation.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [8] Sanctuary, B. (2023). Spin helicity. Preprints, 2023010571. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationreasoning

    Since quantum teleportation rests entirely on Bell's Theorem, this and all research based upon quantum teleportation requires reassessment.

    “Since quantum teleportation [14] rests entirely on Bell's Theorem, then this and all research based upon quantum teleportation requires reassessment.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14] Bennett, 1993, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationnone given

    The angle θ is taken as random but can be in the experimenter's control and used, in principle, to distinguish polarization from coherence.

    “In our case, the angle, θ, is taken as random but can be in the experimenter's control and used, in principle, to distinguish polarization from coherence.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    The Dirac equation becomes non-Hermitian, so spin spacetime is complex, giving helicity states as complex conjugates.

    “The Dirac equation becomes non-Hermitian [7], so spin spacetime is complex, giving helicity states as complex conjugates.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [7] Sanctuary, B. (2024). Quaternion Spin. Mathematics, 12. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Study design and conductnone given

    The simulation treats all EPR pairs, with no missing coincidences, and they are statistically independent.

    “The simulation treats all EPR pairs, with no missing coincidences, and they are statistically independent.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    EPR coincidence experiments maintain correlation over space-like separations, from which the authors conclude that helicity maintains a common frequency between Alice and Bob and they do not decohere, i.e., θ remains stable in free flight.

    “However, EPR coincidence experiments maintain correlation over space-like separations, from which we conclude the helicity maintains a common frequency between Alice and Bob, and do not decohere, i.e., θ remains stable in free flight.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Any three filter angles for Bob and any two for Alice can also be used, but as they move from those in Figure 5, the CHSH correlation will decrease.

    “Any three filter angles for Bob and any two for Alice can also be used, but as they move from those in Figure 5, the CHSH correlation will decrease.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationreasoning

    Polarization and coherent states are pure since the paper treats a single EPR pair.

    “Polarization and coherent states are pure since we treat a single EPR pair.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    The two fermionic axes have opposite magnetic moments; the field orientation determines whether the state is plus or minus.

    “Note that the two fermionic axes have opposite magnetic moments; the field orientation determines whether the state is plus or minus.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationcitation

    Q-spin accounts for the violation of Bell's Inequalities without non-locality, thereby disproving Bell's Theorem by counterexample.

    “Here, Q-spin [7], which is on the same mathematical basis as the Dirac approach, accounts for the violation of Bell's Inequalities (BI) [9] without non-locality, thereby disproving Bell's Theorem by counterexample.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [7] Sanctuary, B. (2024). Quaternion Spin. Mathematics, 12. source

      Not checked in the free run.

    • cites [9] Bell, 1964, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    Close to multiples of π/2, the boson has decoupled.

    “Close to multiples of π 2 , the boson has decoupled.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    In free flight, an electron is a boson of odd parity, e-B, with only helicity states of L or R.

    “In free flight, an electron is a boson of odd parity, e - B , with only helicity states of L or R, Figure 1.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Using a singlet state, quantum mechanics gives CHSH = 2√2 = 2.828.

    “Using a singlet state, QM gives CHSH = 2 √ 2 = 2.828.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationreasoning

    The boson resists decoupling until the field is close to a fermion axis and dominates the spin-spin coupling.

    “we surmise the boson resists decoupling until the field is close to a fermion axis and also dominates the spin-spin coupling.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    If one or the other has decoupled into a fermion, only a product state is possible.

    “If one or the other has decoupled into a fermion, only a product state is possible.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    If one spin is polarized, there is no helicity, and only the scalar part of the quaternion is present.

    “If one spin is polarized, there is no helicity, and only the scalar part of the quaternion is present,”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    To obtain the full correlation, both the spins of Alice and Bob must be complex.

    “However, to get this result, both the spins of Alice and Bob must be complex.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    How the resonant spin decouples depends upon the filter strength and its orientation relative to the resonant spin.

    “How the resonant spin decouples depends upon the filter strength and its orientation relative to the resonant spin.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Adding the helicity contribution to the product of cosines recovers the full singlet correlation, -cos θab, suggesting the observed violation of BI results from helicity.

    “Adding this to the product of cosines recovers the full singlet correlation, -cos θ ab , suggesting the observed violation of BI results from helicity.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning

    The larger magnitude will align.

    “and the larger magnitude will align.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    The missing correlation is attributed to quantum coherence, which until this work had not been formulated.

    “In contrast, here, we attribute the missing correlation to quantum coherence, which until this work had not been formulated.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Using Q-spin, the coincidence events are complementary; sometimes an event gives a boson correlation, other times a polarization correlation.

    “Using Q-spin, the coincidence events are complementary.Sometimes, an event gives a boson correlation; other times, it gives a polarization correlation.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    Q-spin is one particle with four states, whereas Dirac's equation gives two particles with two states each.

    “Q-spin is one particle with four states, whereas Dirac's equation gives two particles with two states each.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Introducing a magnetic field causes the vector with the greatest attraction to align and the others to lie orthogonal to it.

    “Introducing a magnetic field causes the vector with the greatest attraction to align and, hence, the others to lie orthogonal to it.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    If confirmed, the classical polarization exceeds BI by a small amount and violates the theorem again.

    “If confirmed, the classical polarization exceeds BI [9] by a small amount and violates the theorem again [11].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [9] Bell, 1964, On the Einstein Podolsky Rosen paradox, Phys. Phys. Fiz.

      Not checked in the free run.

    • cites [11] Bell, J.S. (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge University Press. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    Q-spin has three axes of angular momentum: two fermions each with magnetic moment μ, and one bivector boson with magnetic moment 2μ.

    “Q-spin has three axes of angular momentum: the two fermions, each with a vector magnetic moment of µ, and the one bivector boson, with a magnetic moment of 2µ.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    Decoherence occurs when θ for Alice and Bob differ.

    “Decoherence occurs when θ for Alice and Bob differ.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    When a boson encounters a field, the indistinguishability is broken; depending on orientation, it either precesses uncoupled or decouples into a fermion.

    “When encountering a field, illustrated by the longer arrow, the indistinguishable is broken.Then, depending on its orientation relative to the boson spin, either the boson preceeses uncoupled, lower middle panel, or if the field is closer to one of the two fermionic axes, the boson decouples into a fermion, as shown in the left and right panels.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premiseown data

    The coincidence data give a cosine similarity, which violates BI.

    “The coincidence data give a cosine similarity, which violates BI.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationnone given

    The simulation determines the correlation between classical axes; it is not a quantum simulation but a model suggested by the treatment.

    “The simulation determines the correlation between classical axes.It is not a quantum simulation; instead, it is a model that the treatment here suggests.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    Spin makes an angle of cos χ = m/√S(S+1) with a field direction; χ = 45° for spin-1 bosons and 54.74° for spin-1/2.

    “Spin makes an angle of cos χ = m √ S(S+1) with a field direction.That is χ = 45 • for spin-1 bosons, as shown in Figure 6.A spin 1 2 has χ = 54.74• , supporting the assertion that the bosons remain intact within the cone.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Only 1/4 of the coincidences lead to coherence, which is the origin of the 1/4 factor in Equation (22).

    “Therefore, only 1 4 of the coincidences lead to coherence, which is the origin of that factor in Equation (22).”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationnone given

    With no mixed states, one must only distinguish between polarized (pol) and coherent (coh) states.

    “With no mixed states, we must only distinguish between polarized (pol) and coherent (coh) states.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationnone given

    The spinor spins the polarization, and the indistinguishable two polarization axes create the mirror states for the helicity to know which way to spin.

    “The spinor spins the polarization; the indistinguishable two polarization axes create the mirror states for the helicity to know which way to spin.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The value of 2 quantifies the Infamous Boundary between polarization and coherence.

    “The value of 2 quantifies the Infamous Boundary [49] between polarization and coherence.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [49] Wick, D. (2012). The Infamous Boundary: Seven Decades of Heresy in Quantum Physics, Springer Science and Business Media.

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    Bell's theorem does not apply to quantum systems, and no conclusions concerning non-locality and quantum theory can be drawn from any of his works.

    “Bell's theorem does not apply to quantum systems, and no conclusions concerning non-locality and quantum theory can be drawn from any of his works [11].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [11] Bell, J.S. (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy, Cambridge University Press. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Interpretationnone given

    In free flight, Q-spin acts like a boson with odd parity, and in a perturbing field it acts like a fermion with even parity.

    “In free flight, Q-spin acts like a boson with odd parity, and in a perturbing field, it acts like a fermion with even parity.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Entanglement is a fundamental property of quantum theory but not of Nature.

    “Entanglement is a fundamental property of quantum theory but not of Nature.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationcitation

    Only one property can be realized simultaneously, which supports Bohr's notion of complementarity.

    “However, only one property can be realized simultaneously, supporting Bohr's notion of complementarity [48].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [48] Bohr, 1935, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. source

      Not checked in the free run.

  • May combine two claims.

    Premisereasoning

    In this treatment, helicity replaces non-local entanglement and Q-spin replaces Dirac spin.

    “In this treatment, helicity replaces non-local entanglement.Q-spin replaces Dirac spin.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductreasoning

    In calculating expectation values, the state operator includes only the polarization and not the bivector for helicity, which is justified because a bivector is not physically observable in our spacetime.

    “In calculating expectation values, the state operator includes only the polarization, and not the bivector for helicity.This is justified because a bivector is not physically observable in our spacetime.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    The violation of Bell's inequalities is not evidence for non-locality but evidence for the existence of helicity and other properties of Nature that constitute local realism.

    “The violation of Bell's inequalities is not evidence for non-locality, an impossible concept to grasp, but rather evidence for the existence of helicity and other properties of Nature that constitute local realism.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    The value of 3 results from modeling the three axes of Q-spin, suggesting a CHSH = 1 for each axis.

    “The value of 3 results from modeling the three axes of Q-spin, suggesting a CHSH = 1 for each axis.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based). May combine two claims.

    Premisenone given

    To obtain correlation from coherence, Alice and Bob must be bosons and both in coherent states (coh-coh).

    “However, recall that to obtain correlation from coherence, Alice and Bob must be bosons, and both in coherent states, coh-coh.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    When the Dirac equation is changed to include Q-spin, the two resulting mirror states have no parity, only reflection, but they combine into states of even parity polarization and odd parity coherence.

    “When the Dirac equation is changed to include Q-spin, the two resulting mirror states have no parity, only reflection, but they combine into states of even parity polarization and odd parity coherence.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisenone given

    In this work there are no hidden variables; the only variable is local, theta, relating spin and Minkowski spaces.

    “In this work, there are no Hidden Variables.The only variable is local, θ, relating spin and Minkowski spaces.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationcitation

    The existence of Q-spin requires accepting that Nature has a reality beyond our spacetime, that there is information lost, and that there are properties in Nature we cannot observe.

    “The existence of Q-spin requires accepting that Nature has a reality beyond our spacetime, that there is information lost [54], and that there are properties in Nature we cannot observe.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [54] Braunstein, 2007, Quantum information cannot be completely hidden in correlations: Implications for the black-hole information paradox, Phys. Rev. Lett. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The doubling of the filter angles gives credence to a boson spin-1 with magnetic moment 2 mu, and not a fermion spin-1/2 with magnetic moment mu, being responsible for the mustache.

    “This doubling gives credence to the presence of a boson spin-1, with a magnetic moment of 2µ, being responsible for the mustache, and not a fermion, spin- 1 2 , with the magnetic moment of µ.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    When Bell's inequality is violated, non-locality is not the cause; the violation is evidence of local realism.

    “When BI is violated [53], non-locality is not the cause.Instead, the opposite follows, as shown here: the violation is evidence of local realism.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [53] Abellán, C., Acín, A., Alarcón, A., Alibart, O., Andersen, C.K., Andreoli, F., Beckert, A., Beduini, F.A., Bendersky, A., and Bentivegna, M. (2018). Challenging local realism with human choices. arXiv.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationreasoning

    Quantum mechanics is a theory of measurement but not of Nature.

    “Quantum mechanics is a theory of measurement but not of Nature.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Some limitations of quantum mechanics can be addressed by replacing Dirac spin with Q-spin and entanglement with helicity.

    “Some limitations of quantum mechanics can be addressed by replacing Dirac spin with Q-spin and entanglement with helicity.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given

    Both the replacement of entanglement by helicity and of Dirac spin by Q-spin come from changing the symmetry from SU(2) to Q8.

    “Both these features come from changing the symmetry from SU(2) to Q 8 .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    Coherence and polarization influence each other.

    “Coherence and polarization are incompatible elements of reality.They influence each other.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation

    The 2D structure of Q-spin admits anyons, consistent with a boson and a fermion on one particle, which is not possible in 3D or for a point particle.

    “The 2D structure of Q-spin admits anyons [51], consistent with a boson and a fermion on one particle.This is not possible in 3D or for a point particle.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [51] Wilczek, 1982, Quantum mechanics of fractional-spin particles, Phys. Rev. Lett. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The CHSH values suggest a convergence to 3/4, i.e. 1/4 correlation per axis, leading to a CHSH value of 3 and supporting equal contributions from each axis.

    “This suggests a convergence to 3 4 , which is 1 4 correlation per axis.This leads to a CHSH value of 3, which supports equal contributions from each axis.”
    Quote in the paperSubstantial claim
83 of 83

  • The authors state this as an assumption.

    No non-local entanglement persists after separation, so the EPR pair forms a product state.

    “In that process, we assume no non-local entanglement persists, so the pair forms a product state.”

  • The authors state this as an assumption.

    Non-locality is nonphysical.

    “This work is motivated by rejecting as nonphysical the notion of non-locality as asserted by Bell's Theorem [11].”

  • The paper relies on this without support.

    Spin is a stable property of many particles and its helicity does not decohere over spacetime.

    “Spin is a stable property of many particles and its helicity does not decohere over spacetime.”

  • The authors state this as an assumption.

    A single particle is in a pure state and remains so after leaving the source until encountering a field.

    “By definition, a single particle is in a pure state and remains so after leaving the source until encountering a field.”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • EPR correlations arise naturally when both the vector and bivector dynamics are taken into account.

    “EPR correlations [42,43] arise naturally when both the vector and bivector dynamics are taken into account.”

    From The Zitterbewegung in the Bivector Standard Model (2026) · cites this paper as [43]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Data-availability statement conflicts with reported simulation outputs

    Minor

    The data-availability statement says no new data were created or analyzed, while the paper reports simulated results and provides text files containing the simulation's outputs.

1 of 1

Cites

Flagged first, then by citations

3 of the 65 references couldn’t be matched to a known paper.

Research works printed but not linked: 5

  1. Bohm, D. (1951). Quantum Theory, Prentice-Hall. Chapter 5 Section 3, and Chapter 22 Section 19.
  2. Turnbull, H.W. (1961). Newton to Bentley, February 25 1692/3, The Correspondence of Isaac Newton, Cambridge University Press.
  3. Einstein, A. (2014). Born-Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, Palgrave Macmillan.
  4. Peskin, M.E., and Schroeder, D.V. (1995). An Introduction to Quantum Field Theory (Frontiers in Physics), Westview Press.
  5. Dirac, P.A.M. (1981). The Principles of Quantum Mechanics, Oxford University Press. No. 27.

Cited by

Sorted by citations

Related

Authors
Sanctuary, B.
Affiliations
McGill University (CA)
Corresponding author
Sanctuary, Bryan
ORCID
Sanctuary, Bryan
Venue
Quantum Reports
Publisher
MDPI AG
Published
2024-08-13
Volume
6
Issue
3
Pages
409-425
ISSN
2624-960X (ISSN-L)
DOI
10.3390/quantum6030026
OpenAlex
W4401580565
Semantic Scholar
7ef972309acb7650a353f91f7802ecab89d08d98
Cited by
18
References
65
Citations by year
2026: 4 · 2025: 2 · 2024: 10 · 2023: 2
FWCI
2.55
Type
journal article
Language
en
Open access
Licence
Locations
  • Quantum Reports (publishedVersion, cc-by)
  • Preprints.org (acceptedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
Universiteit Leiden
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Mathematics › Applied Mathematics › Algebraic and Geometric Analysis
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
Keywords
EPR paradox, quaternion group Q8, spin coherence, Bell inequality violation, spin-1 bosons, Bloch sphere, hidden variables, spin symmetry, Dirac field, helicity

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-07.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-07.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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