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REVIEW 3 major objections 5 minor 55 references

Emergent cosmology and gravity from quantum time?

T0 review · 3 major / 5 minor · reviewed 2026-07-11 · grok-4.5

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Pith's one-line read Interpreting the squared amplitude of a stationary quantum state as the density of intrinsic time produces spacetime curvature and FLRW cosmology without presupposing gravity.

desk verdict Clean, explicit toy that reparametrizes a flat 4D radial wavefunction into closed FLRW via amplitude-uniform τ, but the Lorentzian metric and Einstein equations are still inserted by hand. read the letter →

arxiv 2607.05020 v1 pith:TV5P4YUB submitted 2026-07-06 gr-qc math-phmath.MPphysics.hist-phquant-ph

Ovidiu Cristinel Stoica This is my paper · ORCID
classification gr-qcmath-phmath.MPphysics.hist-phquant-ph
keywords quantumtimeoperatorWheeler-DeWittequationFLRWcosmologyLambda-CDMemergentgravityintrinsicobservables
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 shows that stationary quantum states regain an effective dynamics once time is read from macroscopic pointer observables. Treating the squared amplitude as the probability density for each value of that intrinsic time, and reparametrizing so the density becomes uniform, induces a curved metric component along the time direction. In a concrete toy model, any closed expanding FLRW cosmology—including the standard ΛCDM model—arises from ordinary spherically symmetric zero-energy solutions of the Schrödinger equation on flat four-dimensional Euclidean space, with no gravity present in the original Hamiltonian. When several independent time observables are admitted, the same mechanism can curve all spacetime directions. The result therefore opens a concrete route by which general relativity, or a modification of it, might emerge solely from quantum amplitudes and the choice of time observables.

What carries the argument

The uniform intrinsic time τ(r) obtained by accumulating the radial shell measure I(r) = 2π^{2} |Ψ(r)|^{2} r^{3} so that dP/dτ is constant; the inverse r(τ) then supplies the scale factor of an FLRW line element.

What would settle it

Construct an explicit multi-degree-of-freedom wavefunction in which local clocks and the global amplitude density disagree on the relative duration of two epochs; if no consistent encoding of the amplitude into those clocks exists, the claimed curvature cannot be observed from within.

Watch

Extended reading notes

Core claim

By reading intrinsic time from the squared amplitude of a stationary wavefunction and uniformizing its probability density, the closed Friedmann-Lemaître-Robertson-Walker metric (including any desired expanding cosmology such as ΛCDM) emerges from ordinary spherically symmetric Schrödinger solutions on flat four-dimensional Euclidean space, with no gravity present in the original theory.

Load-bearing premise

The squared amplitude must both set the physical rate at which intrinsic time flows and leave detectable traces in the records available to observers inside the universe.

Editorial extensions

If this is right

  • Closed FLRW cosmologies, including the standard ΛCDM model, can be recovered from free or simple potentials without Einstein equations.
  • The Wheeler-DeWitt constraint arises from positivity of the Hamiltonian alone once time is treated as an intrinsic observable.
  • Multiple independent time observables can induce curvature in all spacetime directions, opening a path to emergent general relativity or modified gravity.
  • Galactic rotation curves might be reinterpreted as local variations in the rate of intrinsic time flow encoded by amplitudes.
  • Intrinsic records must somehow encode the amplitude distribution if observers are to experience the emergent curvature.

Reading between the lines

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

  • If the mechanism is correct, laboratory systems with controllable time-pointer amplitudes could exhibit measurable rate-of-time anomalies that mimic weak gravitational effects.
  • The Monday/Friday thought experiment suggests a deeper link between Born-rule self-location probabilities and the thermodynamic arrow that may unify the two open problems.
  • The construction may supply a concrete realization of how a preferred foliation and Lorentzian signature arise from a Euclidean configuration space.
  • Failure of the amplitude to leave records would falsify the claim that emergent curvature is observationally distinct from a pure coordinate artifact.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper argues that interpreting the squared amplitude of a stationary quantum state as a probability density over an intrinsic time observable induces an effective curvature in the time direction. In the main construction (§II), a spherically symmetric zero-energy solution of the four-dimensional Schrödinger equation is reparametrized by a uniform intrinsic time τ defined via the cumulative shell measure of |Ψ|^{2} (eqs. 33–42). The author then writes a Lorentzian FLRW line element ds^{2} = −c^{2} dτ^{2} + (r(τ)/L)^{2} dΣ^{2} and extracts ḣ/r and r̈/r, which are inserted into the classical Friedmann equations to obtain effective ρ and p. Explicit examples include the free particle, the isotropic harmonic oscillator, and a reverse-engineered potential that recovers closed ΛCDM. Section III sketches a possible extension to four independent timelike coordinates that might generate full spacetime curvature; §IV raises the open problem of whether |Ψ(τ)|^{2} is encoded in intrinsic records so that the reparametrization is observationally meaningful.

Significance. If the construction could be shown to produce the Einstein equations (or a controlled modification) rather than merely to reparametrize a flat Euclidean wavefunction into an FLRW form, it would constitute a novel route from quantum theory without gravity to emergent spacetime curvature. The algebraic reductions (radial Schrödinger equation, shell measure I(r), extraction of Hubble and acceleration parameters) are clean and free of fitting for the free and harmonic cases. The paper is explicit about its open questions (§IV) and presents itself as a proof-of-concept rather than a completed derivation of GR. These strengths make the toy models worth recording, but the gap between reparametrization and dynamical gravity limits the immediate impact.

major comments (3)
  1. §II.C, eqs. (44)–(47): After defining the uniform τ, the Lorentzian FLRW metric is postulated by hand (“we can naturally define a Lorentzian metric”). The subsequent extraction of ρ and p simply inserts the kinematic quantities ṙ/r and r̈/r into the classical Friedmann equations imported from GR. Nothing in the quantum construction generates the Einstein tensor or stress-energy conservation; those are assumed. The claim that FLRW “emerges au without presupposing gravity” therefore overstates what is shown: a coordinate reparametrization of a flat Euclidean solution is dressed as FLRW by an external metric ansatz.
  2. §II.G, eqs. (76)–(88): For the closed ΛCDM recovery the desired expansion history r(τ) is inverted to obtain |Ψ(r)| and then V(r). The potential is therefore reverse-engineered so that the “emergent” cosmology is an input rather than an output. While the free and harmonic examples avoid this circularity, the abstract and introduction present the ΛCDM recovery as a central illustration of emergence; that illustration does not support the stronger claim.
  3. §IV (esp. the Monday/Friday thought experiment and the remark that records alone cannot reveal |Ψ|^{2}): The paper correctly identifies that the physical content of the reparametrization hinges on |Ψ(τ)|^{2} being both the rate of time flow and encoded in intrinsic records. Without a mechanism that correlates the two, the uniform τ is observationally indistinguishable from a mere coordinate choice. This is load-bearing for any claim that the construction yields observable curvature rather than a mathematical re-labeling; the section leaves the issue open without a concrete resolution path.
minor comments (5)
  1. Abstract and §I: the phrase “without presupposing gravity” appears repeatedly; given that the Friedmann equations are used, a more precise formulation (“without an a-priori curved spacetime metric”) would avoid overstatement.
  2. Eq. (42) and surrounding text: the normalization of the generalized eigenvectors |τ⟩ via the Dirac delta scaling is stated but not fully derived; a short appendix or reference would help.
  3. Figure 1 caption: “Big Rip” singularity at τ → T is clear, but the units of the vertical axis (r in units of a) should be stated explicitly.
  4. §III.B: the Klein-Gordon example notes the lack of a positive-definite probability density and points to Feshbach-Villars/Krein-space fixes, but does not carry any of them through; either a concrete calculation or a clearer disclaimer that the section is only schematic would improve clarity.
  5. References [9] and [40] are listed as preprints by the same author; if they contain essential technical steps used here, brief self-contained summaries would make the present manuscript more autonomous.

Circularity Check

3 steps flagged · score 6.0 of 10

ΛCDM (and any target FLRW) is recovered by inverting the desired r(τ) to define |Ψ| then V(r); the FLRW line element itself is imposed by hand after τ-uniformization, so the claimed emergence is by construction for the observationally relevant case.

  1. fitted input called prediction [§II.F–G, eqs. (75)–(88)]
    "we can find suitable potentials and stationary solutions for any closed and expanding FLRW geometry, i.e. for any positive monotone function r=r(τ) o I(r)=1/(Tṙ(τ(r))) o |Ψ(r)|^{2}=1/(2π^{2} T r^{3} ṙ) o V(r)=ℏ^{2}/2m (Ψ''+3/r Ψ')/Ψ. o To find the potential V and the stationary solution Ψ giving this model [ΛCDM], we apply equation (49), obtaining |Ψ(r)|= o Computing V(r) gives a rational function in r o"

    The target scale-factor history of closed ΛCDM is inverted to define |Ψ(r)| and then V(r) so that the radial Schrödinger equation is satisfied by construction. The “emergent” cosmology is therefore an input that has been reverse-engineered into the potential; the subsequent derivation simply recovers the same history that was fed in.

  2. self definitional [§II.C, eq. (44)]
    "Even if the wavefunction Ψ is defined on a Euclidean space, since the spherical symmetry allowed a preferred foliation by the intrinsic time, we can naturally define a Lorentzian metric by the line element ds^{2}=−c^{2}dτ^{2} + r^{2}(τ)/L^{2} dΣ^{2}, obtaining a FLRW model like (7)."

    After τ is defined so that the probability density is uniform, the FLRW line element is simply postulated. The curvature in the time direction and the identification with a closed expanding universe therefore hold by the choice of metric ansatz, not by any dynamical derivation from the stationary wavefunction or from Einstein’s equations.

1 more flagged steps
  1. self definitional [§II.C, eqs. (46)–(54) and surrounding text]
    "Using the dot notation for the derivatives with respect to τ, the Friedmann equations (10) become o To solve for ρ and p, we plug the expressions of ṙ/r and r̈/r in the Friedmann equations (46)."

    The classical Friedmann equations (which presuppose the Einstein tensor and a perfect-fluid stress-energy) are imported after the metric has already been written in FLRW form. The extracted ρ and p are therefore not outputs of the quantum construction; they are the unique fluid that would source the already-imposed geometry inside GR.

full rationale

The free and harmonic-oscillator examples are non-circular calculations: a fixed V yields a stationary Ψ, τ is defined as the cumulative shell measure of |Ψ|^{2}, and the resulting r(τ) is an output. The central observational claim, however, is that closed FLRW cosmologies including ΛCDM emerge without presupposing gravity. That claim is realized by the explicit inversion of §II.F–G: any desired monotone r(τ) is used to set I(r) = 1/(T ṙ) and therefore |Ψ(r)|, after which V(r) is solved from the radial Schrödinger equation so that this Ψ is a zero-energy eigenfunction. The target expansion history is therefore an input, not a prediction. Independently, once τ is chosen the paper simply writes the Lorentzian FLRW line element (eq. 44) by definition; the Einstein/Friedmann equations are then imported to read off ρ and p. Nothing in the quantum construction produces the Einstein tensor or stress-energy conservation. The result is a legitimate reparametrization that can be dressed as FLRW, but the strongest “emergence” statements reduce to these two constructive steps. Self-citations to the author’s concurrent arXiv:2607.01296 supply the timeless constraint but are not load-bearing for the curvature claim itself. Score 6 reflects partial circularity concentrated on the ΛCDM recovery and the metric ansatz, while the free/harmonic cases remain genuine outputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The central claim rests on (i) the interpretive axiom that |Ψ|^{2} supplies a physical probability density over intrinsic time whose non-uniformity can be absorbed into a reparametrization that is then promoted to a metric component, (ii) the geometric choice to define a Lorentzian line element from that reparametrized radial coordinate, and (iii) the freedom to choose any radial potential V(r) (or to reverse-engineer it). No new particles or forces are introduced, but the uniform-time operator and the four independent time observables are novel entities whose independent evidence is currently zero.

free parameters (4)
  • scale factor T of the intrinsic-time measure
    Chosen by hand so that the conditional states |ψ(τ) angle are normalized; sets the unit of τ and appears in every expression for ḣ/r and r̈/r.
  • length unit L relating r to the dimensionless scale factor a
    Introduced to convert the Euclidean radial coordinate into the FLRW scale factor; free overall scale.
  • radial potential V(r) (or equivalently the target expansion history r(τ))
    For the free and harmonic cases V is fixed a priori; for ΛCDM it is reverse-engineered from the desired densities ho_r0, ho_m0, Λ so that the emergent cosmology matches observation by construction.
  • mass m and oscillator frequency ω (harmonic example)
    Set the oscillator length a=√(ℏ/mω) that controls the location of the Big-Rip singularity; free parameters of the toy model.
assumptions (4)
  • ad hoc to paper The squared amplitude of a stationary state may be interpreted as an unnormalized probability density over the spectrum of an intrinsic time operator, and non-uniformity of that density can be removed by a monotonic reparametrization that is physically meaningful.
    Stated in the abstract and §I–II; not a standard postulate of quantum mechanics or of the Page-Wootters formalism, which normally conditions on clock readings without reinterpreting the amplitude as a time-flow rate.
  • ad hoc to paper Once τ is uniform, the line element ds^{2}=-c^{2}d au^{2}+(r(τ)/L)^{2} dΣ^{2} may be ‘naturally defined’ and identified with a physical FLRW metric.
    §II.C; the Euclidean geometry supplies the spatial slices, but the promotion of the reparametrized radial coordinate into a Lorentzian metric component is an additional geometric postulate.
  • domain assumption The Hamiltonian is bounded from below and admits a zero-energy eigenstate (Wheeler-DeWitt-type constraint).
    Inherited from the author’s prior work [9] and standard in quantum cosmology; used to justify the existence of the timeless wavefunction Ψ.
  • domain assumption Spherical symmetry in four Euclidean dimensions is an adequate minisuperspace for homogeneous isotropic cosmology.
    §II.A; standard symmetry reduction, but here the ambient space is flat Euclidean rather than a curved superspace.
invented entities (2)
  • Uniform intrinsic-time operator T obtained by reparametrizing the radial coordinate so that the shell probability is constant in τ
    purpose: Converts the amplitude density into a uniform time coordinate whose non-linear relation to r produces the FLRW scale factor.
    Defined in §II.B (eqs. 36–42); no independent experimental handle is given beyond the cosmological models it is used to generate.
  • Four independent future-directed timelike intrinsic-time observables (τ_{0},τ_{1},τ_{2},σ_{3})
    purpose: To generate curvature in all four spacetime directions rather than only the time direction.
    Introduced in §III.A–B; the construction remains schematic and supplies no concrete metric or Einstein-equation derivation.

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Cite this review

Pith. "Pith review of Emergent cosmology and gravity from quantum time?." pith.science (2026). https://pith.science/paper/TV5P4YUB

@misc{pith2026260705020,
  author       = {Pith},
  title        = {Pith review of: Emergent cosmology and gravity from quantum time?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TV5P4YUB}},
  note         = {Machine review of arXiv:2607.05020}
}
read the original abstract

Macroscopic observables allow the recovery of intrinsic dynamics from stationary quantum states. I show that, by interpreting the squared amplitude as the probability density for each definite value of intrinsic time, a curvature emerges in the time direction. For example, from the perspective of intrinsic quantum time, the Friedmann-Lema\^itre-Robertson-Walker cosmological model emerges from spherically symmetric stationary solutions in four-dimensional Euclidean space, without presupposing gravity. If there is no unique direction of time, curvature emerges in all spacetime dimensions, without presupposing gravity, from the variable amplitude of the stationary wavefunction alone. This opens a new possibility that general relativity or some modification of it emerges from intrinsic time observables.

Figures

Figures reproduced from arXiv: 2607.05020 by the authors.

Figure 1
Figure 1. FIG. 1. Plot of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Plot of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. System of timelike coordinates ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

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Works this paper leans on

55 extracted references · 4 linked inside Pith

  1. [1]

    B.S. DeWitt. Quantum theory of gravity. I. The canoni- cal theory.Phys. Rev., 160(5):1113, 1967

    1967

  2. [2]

    B.S. DeWitt. Quantum theory of gravity. II. The mani- festly covariant theory.Phys. Rev., 162(5):1195, 1967

    1967

  3. [3]

    Introductory lectures on quantum cosmol- ogy

    JJ Halliwell. Introductory lectures on quantum cosmol- ogy. In S Coleman, JB Hartle, I Piran, and S Wein- berg, editors,Quantum cosmology and baby universes, volume 7, pages 159–243. World Scientific, 1991

    1991

  4. [4]

    An introduction to quantum cosmology

    DL Wiltshire. An introduction to quantum cosmology. In B Robson, N Visvanathan, and WS Woolcock, editors, Cosmology: the Physics of the Universe, pages 473–531. World Scientific, 1996

    1996

  5. [5]

    Kiefer.Quantum gravity

    C. Kiefer.Quantum gravity. Oxford University Press, Oxford, UK, 3rd ed. edition, 2012

    2012

  6. [6]

    Kiefer and B

    C. Kiefer and B. Sandh¨ ofer. Quantum cosmology. Zeitschrift f¨ ur Naturforschung A, 77(6):543–559, 2022

    2022

  7. [7]

    Page and W.K

    D.N. Page and W.K. Wootters. Evolution without evo- lution: Dynamics described by stationary observables. Phys. Rev. D, 27(12):2885, 1983

    1983

  8. [8]

    Wick, A.S

    G.C. Wick, A.S. Wightman, and E.P. Wigner. The intrin- sic parity of elementary particles.Phys. Rev., 88(1):101, 1952

    1952

Show all 55 references
  1. [9]

    O.C. Stoica. Quantum time without negative energy. Preprint arXiv:2607.01296, 2026

    2026 arXiv

  2. [10]

    Unruh and R.M

    W.G. Unruh and R.M. Wald. Time and the interpre- tation of canonical quantum gravity.Phys. Rev. D, 40(8):2598, 1989

    1989

  3. [11]

    Hegerfeldt and S.N.M

    G.C. Hegerfeldt and S.N.M. Ruijsenaars. Remarks on causality, localization, and spreading of wave packets. Phys. Rev. D, 22(2):377, 1980

    1980

  4. [12]

    O.C. Stoica. Can we accurately read or write quantum data?Physica Scripta, 100(8):085108, 2025

    2025

  5. [13]

    “time” replaced by quantum cor- relations.IJTP, 23(8):701–711, 1984

    William K Wootters. “time” replaced by quantum cor- relations.IJTP, 23(8):701–711, 1984

    1984

  6. [14]

    D.N. Page. Density matrix of the universe.Phys. Rev. D, 34(8):2267, 1986

    1986

  7. [15]

    D.N. Page. Time as an inaccessible observable. Report nsf -itp-89-18, University of California at Santa Barbara, February 1989

    1989

  8. [16]

    D.N. Page. Clock time and entropy. InPhysical origins of time asymmetry, pages 147–159, Cambridge, UK, 1994. Cambridge Univ. Press

    1994

  9. [17]

    Quantum time.Phys

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum time.Phys. Rev. D, 92(4):045033, 2015

    2015

  10. [18]

    Loveridge and T

    L. Loveridge and T. Miyadera. Relative quantum time. Found. Phys., 49(6):549–560, 2019. 12

    2019

  11. [19]

    Maccone and K

    L. Maccone and K. Sacha. Quantum measurements of time.Phys. Rev. Lett, 124(11):110402, 2020

    2020

  12. [20]

    Castro-Ruiz, F

    E. Castro-Ruiz, F. Giacomini, A. Belenchia, and ˇC. Brukner. Quantum clocks and the temporal local- isability of events in the presence of gravitating quantum systems.Nature communications, 11(1):2672, 2020

    2020

  13. [21]

    C. Foti, A. Coppo, G. Barni, A. Cuccoli, and P. Verruc- chi. Time and classical equations of motion from quan- tum entanglement via the Page and Wootters mecha- nism with generalized coherent states.Nature Comm., 12(1):1787, 2021

    2021

  14. [22]

    H¨ ohn, A.R.H

    P.A. H¨ ohn, A.R.H. Smith, and M.P.E. Lock. Trin- ity of relational quantum dynamics.Phys. Rev. D, 104(6):066001, 2021

    2021

  15. [23]

    Gambini and J

    R. Gambini and J. Pullin. The solution to the problem of time in quantum gravity also solves the time of arrival problem in quantum mechanics.New Journal of Physics, 24(5):053011, 2022

    2022

  16. [24]

    Altaie, D

    M.B. Altaie, D. Hodgson, and A. Beige. Time and quan- tum clocks: A review of recent developments.Frontiers in Physics, 10, 2022

    2022

  17. [25]

    Watching the clocks: Interpreting the Page–Wootters formalism and the internal quantum ref- erence frame programme.Found

    Emily Adlam. Watching the clocks: Interpreting the Page–Wootters formalism and the internal quantum ref- erence frame programme.Found. Phys., 52(5):99, 2022

    2022

  18. [26]

    S. Rijavec. Heisenberg-picture evolution without evolu- tion.Preprint arXiv:2204.11740, 2022

    2022 arXiv

  19. [27]

    Robustness of the page-wootters con- struction across different pictures, states of the uni- verse, and system-clock interactions.Phys

    Simone Rijavec. Robustness of the page-wootters con- struction across different pictures, states of the uni- verse, and system-clock interactions.Phys. Rev. D, 108(6):063507, 2023

    2023

  20. [28]

    Suleymanov and E

    M. Suleymanov and E. Cohen. Quantum frames of refer- ence and the relational flow of time.Eur. Phys. J. Special Topics, pages 1–13, 2023

    2023

  21. [29]

    Ridley and E

    M. Ridley and E. Cohen. Two times or none?Preprint arXiv:2509.22264, 2025

    2025

  22. [30]

    A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis.Astrophysical Journal, 270:365–370, 1983

    Mordehai Milgrom. A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis.Astrophysical Journal, 270:365–370, 1983

    1983

  23. [31]

    Relativistic gravitation theory for the MOND paradigm.Phys

    JD Bekenstein. Relativistic gravitation theory for the MOND paradigm.Phys. Rev. D, 70:083509, 2004

    2004

  24. [32]

    Benoit Famaey and Stacy S. McGaugh. Modified newto- nian dynamics (MOND): Observational phenomenology and relativistic extensions.Living Reviews in Relativity, 15:10, 2012

    2012

  25. [33]

    Wave function of the uni- verse.Phys

    JB Hartle and SW Hawking. Wave function of the uni- verse.Phys. Rev. D, 28(12):2960, 1983

    1983

  26. [34]

    Vilenkin

    A. Vilenkin. Quantum creation of universes.Phys. Rev. D, 30(2):509, 1984

    1984

  27. [35]

    A. Linde. Quantum creation of an open inflationary uni- verse.Phys. Rev. D, 58(8):083514, 1998

    1998

  28. [36]

    Ashtekar and P

    A. Ashtekar and P. Singh. Loop quantum cosmology: a status report.Class. Quant. Grav., 28(21):213001, 2011

    2011

  29. [37]

    Deruelle and J-P Uzan.Relativity in modern physics

    N. Deruelle and J-P Uzan.Relativity in modern physics. Oxford University Press, Oxford, UK, 2018

    2018

  30. [38]

    Albrecht

    A. Albrecht. The theory of everything vs the theory of anything. InBirth of the Universe and Fundamental Physics, pages 321–332. Springer, 1995

    1995

  31. [39]

    Marletto and V

    C. Marletto and V. Vedral. Evolution without evolu- tion and without ambiguities.Phy. Rev. D, 95(4):043510, 2017

    2017

  32. [40]

    O.C. Stoica. The clock ambiguity problem: extended or extinguished?Preprint arXiv:2604.21805, 2026

    2026 arXiv

  33. [41]

    Elementary relativistic wave mechanics of spin 0 and spin 1/2 particles.Rev

    H Feshbach and F Villars. Elementary relativistic wave mechanics of spin 0 and spin 1/2 particles.Rev. Mod. Phys., 30:24–45, 1958

    1958

  34. [42]

    Spectral theory of the klein-gordon equation in krein spaces.Proc

    H Langer, B Najman, and Ch Tretter. Spectral theory of the klein-gordon equation in krein spaces.Proc. Edinb. Math. Soc., 51(3):711–750, 2008

    2008

  35. [43]

    Localized states for elemen- tary systems.Rev

    TD Newton and EP Wigner. Localized states for elemen- tary systems.Rev. Mod. Phys., 21(3):400, 1949

    1949

  36. [44]

    R. Penrose. Singularities and time-asymmetry. In S.W. Hawking and W. Israel, editors,General relativity: an Einstein centenary survey, pages 581–638, Cambridge, UK, 1979. Cambridge Univ. Press

    1979

  37. [45]

    O’Neill.Semi-Riemannian Geometry with Applica- tions to Relativity

    B. O’Neill.Semi-Riemannian Geometry with Applica- tions to Relativity. Number 103 in Pure Appl. Math. Academic Press, New York-London, 1983

    1983

  38. [46]

    Combining rotation curves and gravitational lensing: How to measure the equation of state of dark matter in the galactic halo.MNRAS, 372:136–142, 2006

    T Faber and M Visser. Combining rotation curves and gravitational lensing: How to measure the equation of state of dark matter in the galactic halo.MNRAS, 372:136–142, 2006

    2006

  39. [47]

    Modi- fied gravity and cosmology.Phys

    T Clifton, PG Ferreira, A Padilla, and C Skordis. Modi- fied gravity and cosmology.Phys. Rep., 513:1–189, 2012

    2012

  40. [48]

    Large scale structure as a probe of gravitational slip

    SF Daniel, RR Caldwell, A Cooray, and A Melchiorri. Large scale structure as a probe of gravitational slip. Phys. Rev. D, 77:103513, 2008

    2008

  41. [49]

    Relative state

    H. Everett. “Relative state” formulation of quantum me- chanics.Rev. Mod. Phys., 29(3):454–462, Jul 1957

    1957

  42. [50]

    Wallace.The emergent multiverse: Quantum theory according to the Everett interpretation

    D. Wallace.The emergent multiverse: Quantum theory according to the Everett interpretation. Oxford University Press, Oxford, UK, 2012

    2012

  43. [51]

    L. Vaidman. Probability in the many-worlds interpre- tation of quantum mechanics. In Y. Ben-Menahem and M. Hemmo, editors,Probability in physics, volume XII, pages 299–311. Springer, 2012

    2012

  44. [52]

    Saunders

    S. Saunders. Finite frequentism explains quantum prob- ability.to appear in Brit. J. Philos. Sci., 2024

    2024

  45. [53]

    O.C. Stoica. The relation between wavefunction and 3D space implies many worlds with local beables and prob- abilities.Quantum Reports, 5(1):102–115, 2023

    2023

  46. [54]

    O.C. Stoica. Classical many-worlds interpretation. Preprint arXiv:2407.16774, 2024

    2024 arXiv

  47. [55]

    O.C. Stoica. Born rule: quantum probability as classical probability.Int. J. Theor. Phys., 64(117), 2025

    2025

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