Pith. sign in

REVIEW 5 major objections 5 minor 49 references

This paper argues that quantum mechanics, gravity, and classical physics are three phases of one pre-geometric quantum field theory, linked by the value of the inverse Planck constant.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-02 23:23 UTC pith:TTKOA7KV

load-bearing objection A clear synthesis of Volovik's idea that ℏ is an emergent metric element, but the QFT–QM–CM bridge is asserted rather than derived because the order-parameter dynamics are absent. the 5 major comments →

arxiv 2602.21243 v2 pith:TTKOA7KV submitted 2026-02-14 physics.gen-ph

Quantum and Classical mechanics vs QFT

G.E. Volovik This is my paper
classification physics.gen-ph
keywords emergent quantum mechanicsPlanck constant order parameterpre-geometric quantum field theorysymmetry breakingtetradsemergent gravitypath integralcoherence length
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that quantum mechanics is not a fundamental layer of nature but an emergent one, arising from a phase transition in a pre-geometric quantum field theory. In that transition, the inverse Planck constant 1/ℏ (and 1/(ℏc)) changes from zero to a nonzero value and serves as the order parameter; the same event produces the spacetime metric. The result is a single continuum: pure quantum field theory for 1/ℏ→0, quantum mechanics in between, and classical mechanics for ℏ→0. If true, this dissolves the usual assumption that ℏ is a fixed constant and reframes wave-function collapse and nonlocality as consequences of deep pre-geometric randomness. It also explains why Newtonian gravity and the Coulomb force look classical even though they are quantum effects that vanish in the strictly classical limit.

Core claim

The central claim is that the inverse Planck constant 1/ℏ (and its companion 1/(ℏc)) are elements of the emergent Minkowski metric rather than fundamental constants. In the symmetric pre-geometric phase, these inverse constants vanish, so there are no distances and no QM; at the symmetry-breaking transition they acquire nonzero values as order parameters, generating both the metric/tetrads and the quantum-mechanical regime with masses, wave functions, and particle trajectories. With this Ansatz, all physical actions become dimensionless, and the integration over field variables in the QFT phase goes over into the path integral of QM, which in turn reduces to classical mechanics in the limit

What carries the argument

The central object is the metric Ansatz of Eq. (7), GMink = diag(-1/ℏ², 1/(ℏc)², ...), which gives the inverse Planck constants the role of order parameters for a symmetry-breaking transition between a pre-geometric QFT phase and the QM phase. The determinant of the tetrad, E = -1/ℏ⁴, quantifies the broken-symmetry phase, and ℏ (or ℏc) acts as a coherence length lying between the microscopic UV scale and macroscopic scale. This machinery provides the two small parameters, a/ξ for the QFT limit and ξ/l for the classical limit, and redefines all dimensions: masses become dimensionless and the action acquires the dimension of length.

Load-bearing premise

The load-bearing premise is that a pre-geometric phase exists in which 1/ℏ is strictly zero and that a phase transition makes it nonzero as an order parameter; the paper does not provide a dynamics for that order parameter.

What would settle it

A lattice simulation of the pre-geometric action that finds no symmetry-breaking transition producing a nonzero tetrad expectation value (equivalently 1/ℏ) for any coupling would falsify the GUT route. Alternatively, a measurement showing that the effective ℏ in an emergent-gravity analog system can never be tuned to zero or infinity would contradict the claimed QFT and classical limits.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Quantum mechanics and spacetime geometry emerge together from a single phase transition, with 1/ℏ as the order parameter; neither is more fundamental than the other.
  • In the QFT limit 1/ℏ→0, gravity and electric charge vanish, and the wave function becomes constant in space (if αMe is held fixed), so QM ceases to exist as a separate layer.
  • In the classical limit ℏ→0, the path integral of QM yields classical mechanics, and the Newton and Coulomb interactions, being proportional to ℏ, disappear.
  • The wave function is not a physical object; only correlations are physical in the underlying QFT, so the collapse of the wave function reflects the randomness of the pre-geometric world rather than a deterministic process.
  • Because the symmetric phase has no notion of distance, it may support action at a distance, which carries over to QM as nonlocal correlations and implies that no material system is truly closed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the paper is right, the program of quantizing gravity is backwards: gravity and QM are twin byproducts of one deeper transition, so a theory of quantum gravity should be sought in the pre-geometric QFT phase, not by quantizing the metric.
  • The coherence-length picture suggests a concrete analog test: in condensed-matter systems with emergent gravity (e.g., superfluid 3He–B), one may tune an effective 1/ℏ and look for the predicted disappearance of QM at high energy or emergence at low temperature.
  • The claim that only correlations are physical could be extended to quantum information: entanglement and the density matrix would be emergent, which may bear on the black-hole information problem.
  • One could try to detect the predicted four-fermion-family structure or the relation between the UV cutoff and family number through cosmological dark-matter searches, since the paper connects a fourth generation of neutrinos with asymmetric dark matter.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper extends the Akama-Diakonov-Wetterich (ADW) pre-geometric gravity program by proposing that the Planck constants ℏ and /h = ℏc are elements of the emergent Minkowski metric, Eq. (7), with the inverse Planck constants 1/ℏ and 1//h serving as order parameters. It claims that a phase transition from a symmetric pre-geometric state (1/ℏ = 0, no metric, no distances) to a broken-symmetry state produces quantum mechanics and spacetime geometry simultaneously; the classical limit is ℏ → 0, while the QFT limit is 1/ℏ → 0. The paper provides dimensional analyses, rewrites known quantum-gravitational corrections in the new units (appendices B–E), and speculates about wave-function collapse, the nature of the quantum vacuum, and the number of fermion generations. The central claim is that QM is a bridge between QFT and CM, but the phase transition and the conversion of QFT path integrals into QM path integrals are asserted rather than derived.

Significance. If the proposed construction were realized by a concrete dynamical model, it would constitute a major conceptual shift: quantum mechanics would be emergent from a pre-geometric QFT, with ℏ as a vacuum expectation value, and gravity would arise from the same ordering phenomenon. The appendices are a genuine strength: they show that a number of known quantum-gravitational corrections (Reissner-Nordström metric, Newton potential, deflection angle, gravitational potential) can be consistently rewritten in the proposed dimensionless scheme, which demonstrates internal dimensional consistency for those expressions. However, the central emergence claim is not established. The paper offers no potential, no kinetic term, and no microscopic mechanism for the order parameter 1/ℏ; the phase transition is an ansatz, and the QFT–QM–CM bridge is therefore a restatement of the chosen variables rather than an independent derivation. The contribution is best viewed as a speculative research program pointer, not a result.

major comments (5)
  1. [Sec. III.A, Eq. (7)] The order parameters 1/ℏ and 1//h are introduced by postulate: Eq. (7) sets G_Mink = diag(−1/ℏ², 1//h², 1//h², 1//h²), and Sec. III.A states that these inverse Planck constants are order parameters of a symmetry-breaking phase transition. No free-energy functional, potential, kinetic term, or coupling to the ADW fermionic fields is provided that would make these fields dynamical or produce a transition from the symmetric value zero. The abstract's central claim that QM emerges from this symmetry breaking is therefore a restatement of the Ansatz, not a derivation. This is load-bearing for the entire paper.
  2. [Sec. IV.A and Sec. VIII.F] There is an internal contradiction in the dimensional scheme. Sec. IV.A states: 'Any action, including that in Eq. (10), has the dimension of length (or time)', whereas Sec. VIII.F states: 'Any action in ADM scenario must be dimensionless' and Eq. (48) explicitly writes S_ADW = M ∫ dt/ℏ, which is dimensionless for [ℏ] = [time]. This contradiction directly affects the use of e^{iS} as a phase, the interpretation of the action, and the claimed classical limit. The reader cannot determine which dimensional convention is intended, and the framework's main tool—dimensional bookkeeping—is rendered inconsistent.
  3. [Sec. V, Eq. (26)] The symmetric-phase correlator D(r) = D(0) = D(∞) is asserted on the basis that no length scale exists in that phase. However, no microscopic action realizing 1/ℏ = 0 with such correlations is presented, and the limit ordering in Eqs. (18)–(19) is uncontrolled. The statement that the QFT phase exhibits action at a distance, which is later used for the collapse discussion in Sec. VII, is therefore unsupported. Without a concrete realization of the symmetric phase, the claimed 'clue' to the pre-geometric state remains a stipulation.
  4. [Sec. VII] The sentence 'The integration over field variables in the QFT phase leads to a path integral formulation of QM' is a central postulate of the paper, but no mapping from the QFT partition function to the QM path integral is shown. No expression is given for the relevant partition function, no coarse-graining procedure is defined, and no derivation connects the pre-geometric correlators to the Schrödinger equation. This is the bridge announced in the title, and its absence means the QFT–QM–CM connection is not demonstrated.
  5. [Secs. I and III.A] The abstract and introduction claim that the inverse Planck constants emerge 'in both scenarios: GUT and anti-GUT'. In the body, the GUT scenario is only a verbal symmetry-breaking picture, and the anti-GUT scenario is merely a cited lattice model of Diakonov. No explicit construction is given for either scheme that would realize the order parameter 1/ℏ from the ADW action (1) or from the Wilczek action (20). The claim that QM emerges in both scenarios is thus not substantiated.
minor comments (5)
  1. [Abstract, Secs. III–V] The notation for ℏc is inconsistent: the abstract uses '// h' and '1/{\!\!h}', while later sections mostly use '/ h'. Please unify the symbol.
  2. [Sec. VIII.F] The text says 'dimensionless action for the classical dynamics of a point particle in Minkowski spacetime in ADM approach'. Given the context and Eq. (48) (S_ADW), this should be 'ADW approach', not 'ADM'.
  3. [Eqs. (32)–(34)] Expressions such as 'M/K / h/r' are difficult to parse. Use explicit parentheses, e.g., (M/K)·( /h /r), or define r̃ = r/ /h consistently before presenting the expansions.
  4. [Sec. V] The statement 'In conventional approach this corresponds to α = e²/ℏc → 0 as ℏ → ∞' may mislead readers, since ℏ → ∞ is not the standard classical-field limit. The paper should explicitly state that this is a convention in which ℏ is a metric element, not the standard limit.
  5. [Sec. IV.B, Eq. (11)] The relation l_P = √(ℏG) ≡ ℏ is presented as a natural assumption, but the direction of the identification is ambiguous. Specify whether G = ℏ is an independent assumption or a consequence of the metric Ansatz.

Circularity Check

3 steps flagged

The QFT–QM–CM bridge is the Eq. (7) ansatz restated: 1/ℏ is declared the order parameter, so the QFT state (1/ℏ=0) and QM state (1/ℏ≠0) are definitions, and the claimed limits are read off from the chosen coordinates; the core premise is imported from the author's own refs. 10–11.

specific steps
  1. self definitional [Sec. III.A, Eq. (7)]
    "Here we extend the ADW theory by considering the Planck constants ℏ and /h=ℏc as the elements of the metric of emergent Minkowski spacetime: 10 GMink μν = diag(−1/ℏ2, 1//h2, 1//h2, 1//h2).(7) In the symmetric state, the Planck constants are absent, 1/ℏ=1//h=0. These inverse Planck constants, 1/ℏ and 1//h, play the role of the order parameters of the symmetry breaking phase transition."

    The symmetric pre-geometric/QFT phase is defined by 1/ℏ=0 and the broken-symmetry 'QM state' by 1/ℏ≠0, because the metric is diag(−1/ℏ²,...). Therefore the statement that QM emerges when 1/ℏ becomes nonzero is the definition of the order parameter, not a consequence of a dynamical model. No free energy, potential, or microscopic mechanism with stationary points at 1/ℏ=0 and 1/ℏ≠0 is supplied, so the claimed phase transition is exactly the chosen variable change.

  2. ansatz smuggled in via citation [Sec. I (Introduction); Sec. III.A]
    "We make attempt to combine the ADW theory and the approach in which the inverse Planck constants, 1/ℏ and 1//h≡1/(ℏc), correspond to the time and space components of the emergent Minkowski tetrads.10,11"

    Refs. 10 and 11 are the author's own prior papers; the load-bearing premise that 1/ℏ is a metric element and order parameter is taken from them rather than re-derived here. The present text gives no microscopic action for ℏ and does not show that the cited work is independently verified, so the central bridge rests on a self-citation chain for the core ansatz.

  3. other [Sec. VII (Open questions)]
    "The integration over field variables in the QFT phase leads to a path integral formulation of QM, which in turn yields the laws of classical mechanics in the limit ℏ→0."

    The phases were defined in Sec. III.A solely by the order parameter 1/ℏ going from 0 (QFT) to finite (QM). The assertion that integration over QFT field variables 'leads to' the QM path integral is the claimed emergence restated; no transformation of the ADW functional integral into a QM path integral is exhibited. Thus the 'prediction' is the definition of the phases.

full rationale

The paper's central bridge QFT → QM → CM is not derived from a microscopic action; it is written into the Ansatz (7). There, the Minkowski metric is defined to be diag(−1/ℏ², ...), and the symmetric phase is defined by 1/ℏ = 1//h = 0; these same quantities are then declared to be order parameters. Consequently, the statement that a phase transition from the 'QFT state' (1/ℏ = 0) to the 'QM state' (1/ℏ ≠ 0) produces quantum mechanics is a restatement of the Ansatz: 'QM state' is, by construction, the state in which ℏ is finite. The QFT and CM limits (1/ℏ → 0 and ℏ → 0) are likewise read off from the chosen coordinates, not obtained from a Hamiltonian or free energy. No potential, kinetic term, or microscopic mechanism for the order parameter 1/ℏ is given, so the claimed 'emergence' cannot be distinguished from a change of units/variables. The core premise is imported from the author's own refs. 10 and 11, which are themselves proposals rather than externally verified derivations; here the citation carries the load. The appendix does contain standard external results (Donoghue, Khriplovich–Kirilin) rewritten in the new variables, but those are peripheral consistency checks, not the claimed QFT–QM–CM bridge. Hence the central claim reduces by construction to the input metric Ansatz and to the self-cited premise, warranting a score of 8.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 2 invented entities

The paper's central mechanism rests on treating the inverse Planck constants as order-parameter fields in an emergent metric. This is not derived from a more basic model; it is an Ansatz imported from the author's earlier work. The other ingredients (ADW pregeometry, unimodularity, standard path-integral limit) are background assumptions. There are no fitted constants in the usual sense, but the assumed value of ℏ at T=0 and the arbitrary mass scale M0 are free choices needed to make the dimensional story explicit.

free parameters (3)
  • M0 (arbitrary mass scale) = arbitrary, not fitted
    Introduced in Eqs (34), (38), (42), (45) to normalize Planck constant to length/time dimensions; the paper claims invariance under M0, making it a bookkeeping scale rather than a fitted parameter.
  • ℏ at T=0 = ~Planck length l_P (assumed)
    Sec IV.B assumes ℏ(T=0) is on the order of the Planck length, or equivalently l_P = √(ℏG) ≡ ℏ; this fixes the relation between ℏ and G and sets Planck mass to 1.
  • C_b (bending coefficient) = not specified (contains ln(r0/b))
    In Eq (40) the cubic bending coefficient C_b is left undetermined and depends on an IR cutoff r0; no value or derivation is given.
axioms (5)
  • domain assumption Tetrads emerge as vacuum expectation values of fermion bilinears, E^a_μ = ⟨Ê^a_μ⟩ (Eq 4).
    The ADW pregeometry premise underpins the entire paper; it is taken from Diakonov/Akama/Wetterich.
  • ad hoc to paper The emergent Minkowski metric is G_Mink = diag(−1/ℏ²,1/⧸h²,1/⧸h²,1/⧸h²) (Eq 7).
    This is the central postulate; no derivation from the ADW action is given. It encodes the later conclusions about dimensions and limits.
  • ad hoc to paper In the symmetric pre-geometric phase 1/ℏ = 1/⧸h = 0 and there is no metric/distances (Sec III.A, Sec V).
    The existence and properties of this phase are assumed; no order-parameter potential or dynamics is provided.
  • domain assumption The tetrad determinant E is constant (unimodular gravity), giving E = −1/ℏ⁴ (Sec III.A).
    Unimodularity is invoked to connect the order parameter to ℏ; it is a modeling choice.
  • standard math Standard quantum-mechanical limit: path integral yields classical mechanics as ℏ→0.
    Relied on in Sec VII and abstract to close the QFT→QM→CM ladder.
invented entities (2)
  • Pre-geometric symmetric QFT phase no independent evidence
    purpose: A state with no metric, no distances, and 1/ℏ=0, from which QM and gravity emerge by symmetry breaking.
    Postulated in Sec III.A and V; no falsifiable handle is given other than qualitative claims about action at a distance.
  • 1/ℏ and 1/⧸h as order-parameter fields no independent evidence
    purpose: To act as the order parameters whose vanishing marks the QFT phase and whose nonzero value produces QM and the metric.
    Introduced in Sec III.A; the fields are not given a Lagrangian, kinetic term, or potential.

pith-pipeline@v1.3.0-alltime-deepseek · 12832 in / 13084 out tokens · 107001 ms · 2026-08-02T23:23:54.987245+00:00 · methodology

0 comments
read the original abstract

15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical quantities. In particular, particle masses are dimensionless. We are trying to extend the Akama-Diakonov-Wetterich theory by introducing the Planck constants $\hbar$ and ${/\!\!h}=\hbar c$ as elements of the emergent metric. The inverse Planck constant $1/\hbar$ has the dimension of frequency, and, therefore, the mass $M$ of a particle, which has the dimension $\hbar\omega$, is dimensionless. In this extension, quantum mechanics emerges from the intrinsic quantum fields either in the symmetry breaking mechanism (GUT), or in the opposite mechanism of emergent symmetry in the low-energy corner (anti-GUT). In both cases, quantum mechanics (QM) serves as a bridge between the area of quantum fields (QFT) in the limit $1/\hbar \rightarrow 0$, and the area of classical physics (CM) in the limit $\hbar \rightarrow 0$. In the GUT scheme the inverse Planck constants, $1/\hbar$ and $1/{\\!\!h}$, play the role of the order parameter of the symmetry breaking phase transition from the pre-geometric QFT state to the QM state, in which the quantum mechanics emerges together with the space-time metric. In this phase transition, the integration over field variables in the QFT phase transforms to a path integral formulation of QM, which in turn yields the laws of classical mechanics in the limit $1/\hbar \rightarrow \infty$.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 23 linked inside Pith

  1. [1]

    Diakonov, Towards lattice-regularized Quantum Gravity, arXiv:1109.0091

    D. Diakonov, Towards lattice-regularized Quantum Gravity, arXiv:1109.0091

    Pith/arXiv arXiv

  2. [2]

    Vladimirov and D

    A.A. Vladimirov and D. Diakonov, Phase transitions in spinor quantum gravity on a lattice, Phys. Rev. D 86 , 104019 (2012)

    2012

  3. [3]

    Wetterich, Fundamental scale invariance, Nuclear Physics B 964 , 115326 (2021)

    C. Wetterich, Fundamental scale invariance, Nuclear Physics B 964 , 115326 (2021)

    2021

  4. [4]

    Wetterich, Pregeometry and spontaneous time-space asymmetry, JHEP 06 (2022) 069

    C. Wetterich, Pregeometry and spontaneous time-space asymmetry, JHEP 06 (2022) 069

    2022

  5. [5]

    Akama, An Attempt at Pregeometry: Gravity with Composite Metric, Progress of Theoretical Physics, 60 , 1900--1909 (1978)

    K. Akama, An Attempt at Pregeometry: Gravity with Composite Metric, Progress of Theoretical Physics, 60 , 1900--1909 (1978)

    1900

  6. [6]

    Vergeles, Unitarity of 4D Lattice Theory of Gravity, Phys

    S.N. Vergeles, Unitarity of 4D Lattice Theory of Gravity, Phys. Rev. D 112 , 054509 (2025)

    2025

  7. [7]

    Froggatt and H.B

    C.D. Froggatt and H.B. Nielsen, Origin of Symmetry , World Scientific, Singapore (1991)

    1991

  8. [8]

    Volovik, The Universe in a Helium Droplet , Clarendon Press, Oxford (2003)

    G.E. Volovik, The Universe in a Helium Droplet , Clarendon Press, Oxford (2003)

    2003

  9. [9]

    Klinkhamer and G.E

    F.R. Klinkhamer and G.E. Volovik, Tetrads and q -theory, Pis'ma ZhETF 109 , 369--370 (2019), JETP Lett. 109 , 364--367 (2019), arXiv:1812.07046

    Pith/arXiv arXiv 2019

  10. [10]

    Volovik, Dimensionless physics: Planck constant as an element of Minkowski metric, Pis’ma v ZhETF 117 , (2023), JETP Lett

    G.E. Volovik, Dimensionless physics: Planck constant as an element of Minkowski metric, Pis’ma v ZhETF 117 , (2023), JETP Lett. 117 , (2023), arXiv:2209.15426 [gr-qc]

    Pith/arXiv arXiv 2023

  11. [11]

    Volovik, Planck constants in the symmetry breaking quantum gravity, Symmetry 15 , 991 (2023), arXiv:2304.04235

    G.E. Volovik, Planck constants in the symmetry breaking quantum gravity, Symmetry 15 , 991 (2023), arXiv:2304.04235

    Pith/arXiv arXiv 2023

  12. [12]

    Volovik, Superfluid 3He-B and gravity, Physica B 162 , 222--230 (1990)

    G.E. Volovik, Superfluid 3He-B and gravity, Physica B 162 , 222--230 (1990)

    1990

  13. [13]

    Ralston, Quantum Theory without Planck's Constant, arXiv:1203.5557 [hep-ph]

    John P. Ralston, Quantum Theory without Planck's Constant, arXiv:1203.5557 [hep-ph]

    Pith/arXiv arXiv

  14. [14]

    Klinkhamer and G.E

    F.R. Klinkhamer and G.E. Volovik, Dynamic vacuum variable and equilibrium approach in cosmology, Phys. Rev. D 78 , 063528 (2008); arXiv:0806.2805 [gr-qc]

    Pith/arXiv arXiv 2008

  15. [15]

    Klinkhamer and G.E

    F.R. Klinkhamer and G.E. Volovik, Merging gauge coupling constants without Grand Unification, Pisma ZhETF 81 , 683--687 (2005); JETP Lett. 81 , 551--555 (2005); hep-ph/0505033

    Pith/arXiv arXiv 2005

  16. [16]

    Frank Wilczek, Riemann-Einstein Structure from Volume and Gauge Symmetry, Phys. Rev. Lett. 80 4851--4854 (1998), arXiv:hep-th/9801184

    Pith/arXiv arXiv 1998

  17. [17]

    Addazi, S

    A. Addazi, S. Capozziello, A. Marciano and G. Meluccio, Gravity from Pre-geometry, Class. Quantum Grav. 42 , 045012 (2025), https://doi.org/10.1088/1361-6382/ada767

    doi:10.1088/1361-6382/ada767 2025

  18. [18]

    Andrea Addazi, Salvatore Capozziello and Giuseppe Meluccio, Holographic Naturalness and Pre-Geometric Gravity, Physics 8 , 2 (2025)

    2025

  19. [19]

    Giuseppe Meluccio, Pre-geometric Einstein–Cartan Field Equations and Emergent Cosmology, arXiv:2505.02925

    Pith/arXiv arXiv

  20. [20]

    Nissinen and G.E

    J. Nissinen and G.E. Volovik, Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions, ZhETF 154 , 1051--1056 (2018), JETP 127 , 948--957 (2018), arXiv:1803.09234

    Pith/arXiv arXiv 2018

  21. [21]

    Obukhov and G.E

    Yuri N. Obukhov and G.E. Volovik, Spacetime geometry from Dirac spinor theory, Phys. Rev. D 109 , 064076 (2024), arXiv:2402.11593

    Pith/arXiv arXiv 2024

  22. [22]

    Steven Weinberg, Quantum mechanics without state vectors, Phys. Rev. A 90 , 042102 (2014), arXiv:1405.3483 [quant-ph]

    Pith/arXiv arXiv 2014

  23. [23]

    R. D. Hazeltine, Primer on quantum weirdness, arXiv:2408.08329 [quant-ph]

    Pith/arXiv arXiv

  24. [24]

    Raizen, New tests of quantum mechanics with unstable nuclei, Physics Letters B 865 , 139480 (2025)

    Mark G. Raizen, New tests of quantum mechanics with unstable nuclei, Physics Letters B 865 , 139480 (2025)

    2025

  25. [25]

    Volovik, Thermodynamics and decay of de Sitter vacuum, Symmetry 16 , 763 (2024), https://doi.org/10.3390/sym16060763

    G.E. Volovik, Thermodynamics and decay of de Sitter vacuum, Symmetry 16 , 763 (2024), https://doi.org/10.3390/sym16060763

    doi:10.3390/sym16060763 2024

  26. [26]

    Landau and E.M

    L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Volume 5, Statistical Physics, Elsevier, 1980

    1980

  27. [27]

    Bengochea, Gabriel Leon and Alejandro Perez, Emergence of cosmic structure from Planckian discreteness arXiv:2506.15413

    Gabriel R. Bengochea, Gabriel Leon and Alejandro Perez, Emergence of cosmic structure from Planckian discreteness arXiv:2506.15413

    arXiv

  28. [28]

    Zel'dovich, The equation of state at ultrahigh densities and its relativistic limitations, JETP 14 , 1143 (1962)

    Ya.B. Zel'dovich, The equation of state at ultrahigh densities and its relativistic limitations, JETP 14 , 1143 (1962)

    1962

  29. [29]

    Megumi Ishida, Hiroshi Ohki and Shohei Uemura, Unified Origin of Dirac Neutrino and Asymmetric Dark Matter Masses via a Dirac-Type Leptogenesis, arXiv:2510.13723

    arXiv

  30. [30]

    Volovik, Dark matter from SU(4) model, JETP Lett

    G.E. Volovik, Dark matter from SU(4) model, JETP Lett. 78 , 691--694 (2003); hep-ph/0310006

    Pith/arXiv arXiv 2003

  31. [31]

    Volovik and M.A

    G.E. Volovik and M.A. Zubkov, Emergent Weyl spinors in multi-fermion systems, Nuclear Physics B 881 , 514--538 (2014), arXiv:1402.5700

    Pith/arXiv arXiv 2014

  32. [32]

    Volovik and M.A

    G.E. Volovik and M.A. Zubkov, Emergent Weyl fermions and the origin of i= -1 in quantum mechanics, Pis'ma ZhETF 99 , 552--557 (2014); JETP Lett. 99 , 481--486 (2014), arXiv:1404.4084

    Pith/arXiv arXiv 2014

  33. [33]

    Ho r ava, Stability of Fermi surfaces and K -theory, Phys

    P. Ho r ava, Stability of Fermi surfaces and K -theory, Phys. Rev. Lett. 95 , 016405 (2005)

    2005

  34. [34]

    Donoghue, Quantum General Relativity and Effective Field Theory, arXiv:2211.09902v2 [hep-th]

    John F. Donoghue, Quantum General Relativity and Effective Field Theory, arXiv:2211.09902v2 [hep-th]

    Pith/arXiv arXiv

  35. [35]

    Effective Field Theories,

    A. A. Petrov and A. E. Blechman, “Effective Field Theories,” World Scientific Press, 2016, ISBN 978-981-4434-92-8, 978-981-4434-94-2 doi:10.1142/8619

    doi:10.1142/8619 2016

  36. [36]

    J. F. Donoghue, B. R. Holstein, B. Garbrecht and T. Konstandin, Quantum corrections to the Reissner-Nordstr\"om and Kerr-Newman metrics, Phys. Lett. B 529 , 132--142 (2002) [erratum: Phys. Lett. B 612 , 311--312 (2005)] doi:10.1016/S0370-2693(02)01246-7 arXiv:hep-th/0112237 [hep-th]

    Pith/arXiv arXiv 2002

  37. [37]

    Khriplovich and G.G

    I.B. Khriplovich and G.G. Kirilin, Quantum Long-Range Interactions in General Relativity, J. Exp. Theor. Phys. 98 , 1063 (2004)

    2004

  38. [38]

    de Paula Netto, L

    T. de Paula Netto, L. Modesto, I.L. Shapiro, Universal leading quantum correction to the Newton potential. Eur. Phys. J. C 82 , 60 (2022)

    2022

  39. [39]

    Fr\"ob, C

    M.B. Fr\"ob, C. Rein and R. Verch, Graviton corrections to the Newtonian potential using invariant observables, JHEP 01 (2022) 180

    2022

  40. [40]

    Volovik and A.I

    G.E. Volovik and A.I. Zelnikov, Universal temperature corrections to the free energy for the gravitational field, Pisma ZhETF 78 , 1271--1276 (2003), JETP Lett. 78 , 751--756 (2003); gr-qc/0309066

    Pith/arXiv arXiv 2003

  41. [41]

    Ted Jacobson, Black Hole Entropy and Induced Gravity, arXiv:gr-qc/9404039

    Pith/arXiv arXiv

  42. [42]

    Huan-Hang Chi, Graviton bending in quantum gravity from one-loop amplitudes, Phys. Rev. D 99 , 126008 (2019)

    2019

  43. [43]

    G. G. Kirilin and I. B. Khriplovich, Quantum Power Correction to the Newton Law, JETP 95 , 981--986 (2002)

    2002

  44. [44]

    Volovik, Gravity from symmetry breaking phase transition, J

    G.E. Volovik, Gravity from symmetry breaking phase transition, J. Low Temp. Phys. 207 , 127--137 (2022), arXiv:2111.07817

    Pith/arXiv arXiv 2022

  45. [45]

    G. G. Kirilin, Quantum corrections to the Schwarzschild metric and reparametrization transformations, Phys. Rev. D 75 , 108501 (2007)

    2007

  46. [46]

    Dmitrii Diakonov, De Sitter entropy: on-shell versus off-shell, Physics Letters B 871 , 139967 (2025), arXiv:2504.01942 [hep-th]

    arXiv 2025

  47. [47]

    Kenichi Konishi, Quantum fluctuations, particles and entanglement: a discussion towards the solution of the quantum measurement problems, International Journal of Modern Physics A 37 , 2250113 (2022), arXiv:2111.14723

    Pith/arXiv arXiv 2022

  48. [48]

    Phys.: Conf

    Kenichi Konishi, Quantum fluctuations, particles and entanglement: solving the quantum measurement problems, J. Phys.: Conf. Ser. 2533 , 012009 (2023)

    2023

  49. [50]

    Aidala, The unphysicality of Hilbert spaces, Quantum Stud.: Math

    Gabriele Carcassi, Francisco Calderon, Christine A. Aidala, The unphysicality of Hilbert spaces, Quantum Stud.: Math. Found. 12 , 13 (2025), arXiv:2308.06669

    Pith/arXiv arXiv 2025