Pith. sign in

REVIEW 5 major objections 4 minor 47 references

Deriving the Cosmological Constant and Nature's Constants from SU(3) Confinement Volume

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The paper claims that the dark-energy density and the Planck constants both follow from counting the $10^{123}$ proton-scale color-confinement cells in the observable volume under holographic saturation.

desk verdict The central 1/N dilution is an algebraic mix-up between per-patch and total force, and the headline numerical agreement is off by a factor of ~2.5, so the claimed derivation of the cosmological constant fails on the paper's own equations. read the letter →

arxiv 2507.22096 v1 pith:DFDMJ4QK submitted 2025-07-29 gr-qc

Malak Ali , Ahmed Farag Ali This is my paper · ORCID
classification gr-qc PACS 98.80.Qc04.60.-m12.38.Aw
keywords cosmologicalconstantproblemQCDconfinementholographictilingvacuumenergydensityPlancklengthdarkthirdlawofthermodynamicsprotonradius
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 sets out to show that the cosmological-constant problem and the numerical values of $\hbar$, $G$, and $c$ can both be derived from the same counting argument. As the universe cools toward zero temperature, the third law of thermodynamics keeps SU(3) color confinement from ever switching off, so the vacuum fragments into proton-scale domains whose volume is fixed by lattice QCD correlation data. Dividing the cosmic-horizon volume by this cell volume gives $N=(R_u/R_p)^3\simeq 10^{123}$, and holographic saturation maps each cell to a Planck-area patch on the horizon. The same $N$ dilutes the bare zero-point energy of the eight gluons from $\sim 10^{76}\,\mathrm{GeV}^4$ down to the observed dark-energy density $\sim 10^{-47}\,\mathrm{GeV}^4$, and the patch area $4\pi R_u^2/N$ is claimed to coincide with the Planck area to within 3 percent. If this chain holds, no fine-tuned counterterms are needed, and the constants of nature become ratios of measured cosmological and proton scales rather than free inputs.

What carries the argument

The carrying mechanism is the SU(3) confinement cell together with the holographic tiling it defines. A cell is a proton-radius ball of zero-temperature vacuum whose independent status is justified by the cluster-decomposition bound and the measured screening length; tiling the observable volume gives $N$, and imposing holographic saturation gives the identities $A_{\mathrm{cell}}=4\pi R_u^2/N=L_{\mathrm{Pl}}^2$ and $V_{\mathrm{cell}}=L_{\mathrm{Pl}}^2 R_u$. The uniform-force condition (UF), which says every horizon patch pushes outward with the same force, then yields the algebraic dilution law $\rho_u=\rho_{\mathrm{SU}(3)}/N$. A geometric intersection calculation for the radial cylinders representing the cells produces a central rest mass within 2 percent of the Planck mass.

What would settle it

Take independently measured values of $R_u$, $R_p$, $\hbar$, $G$, and $c$ and check whether $4\pi R_u^2/(R_u/R_p)^3$ equals $L_{\mathrm{Pl}}^2$ at the claimed 3 percent level; a mismatch at that precision would falsify the central identity directly.

Watch

Extended reading notes

Core claim

The central discovery is the parameter-free identity $\rho_u = \rho_{\mathrm{SU}(3)}/N$ with $N=(R_u/R_p)^3$, where $\rho_{\mathrm{SU}(3)}$ is the zero-point energy density of massless gluons inside one confinement cell. The paper argues that the third law makes the proton-scale cells permanent, that holographic saturation fixes the patch area $A_{\mathrm{cell}} = 4\pi R_u^2/N$ equal to the Planck area $L_{\mathrm{Pl}}^2 = \hbar G/c^3$, and that a uniform-force condition on the horizon converts the per-cell density into the observed cosmological density. The conclusion is that $\hbar$, $G$, and $c$ are not fundamental inputs but geometric quantities fixed by the ratio of the cosmic horizon radius to the proton radius, and that the 123-order-of-magnitude discrepancy between quantum field theory and observation is closed by counting rather than by cancellation.

Load-bearing premise

Everything rests on the uniform-force condition, which assumes that every Planck-area patch on the cosmic horizon exerts exactly the same outward force; if that equality is imposed rather than derived, the dilution formula $\rho_u=\rho_{\mathrm{SU}(3)}/N$ is a definition instead of a physical result.

Editorial extensions

If this is right

  • If the identity is correct, the observed dark energy is exactly the zero-point energy of the eight gluons diluted by the cell count, with no counterterms and no new fields.
  • The Planck length becomes a derived quantity: any change in the measured proton radius or the cosmic-horizon radius shifts $\hbar$, $G$, and $c$ through $L_{\mathrm{Pl}}^2 = 4\pi R_p^3/R_u$.
  • The cylinder-forest picture carries a built-in mass scale, since the common intersection of all radial Planck-radius cylinders contains about one Planck mass.
  • Late-time de Sitter evolution and the observed $w\approx -1$ are consistent with the saturation assumption, because the apparent horizon approaches the entropy-saturated de Sitter horizon.
  • The framework suggests concrete observational searches, including Planck-patch birefringence and a possible small glueball dark-matter component.

Reading between the lines

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

  • Editorial extension: written out, the claimed identity is $G = 4\pi c^3 R_p^3/(\hbar R_u)$, a one-line relation linking Newton's constant to measured proton and horizon radii; comparing this with high-precision determinations of $G$ would test the framework directly.
  • Editorial extension: because $N$ enters the dark-energy prediction as a cube, a 1 percent improvement in the proton radius changes the predicted $\rho_\Lambda$ by roughly 3 percent, so more precise proton-radius measurements could discriminate this scheme from other proposals.
  • Editorial extension: the uniform-force condition implies that any measurable anisotropy in horizon stress should be accompanied by a corresponding variance in per-patch force, which future high-resolution cosmic-microwave-background polarization maps could seek.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The manuscript claims to derive the observed dark-energy density and the numerical values of ℏ, G, and c from a single counting argument: the cosmic volume is tiled by N ≃ (R_u/R_p)^3 ≈ 10^123 SU(3) confinement cells; holographic saturation assigns each cell a Planck-area patch on the cosmic horizon; and a force-balance identity dilutes the bare Planck-scale vacuum energy by 1/N, reproducing ρ_Λ. It further constructs a cylinder-intersection model that allegedly yields a Planck-mass core. The paper is structured around three pillars—QCD confinement, the Third Law, and holography—and presents the result as parameter-free.

Significance. The stated goal is of extremely high significance: a parameter-free derivation of the cosmological constant and of the fundamental constants would be a major breakthrough. The paper is clearly organized and attempts to ground the counting in empirical inputs (Planck CMB radius, muonic-hydrogen proton radius, lattice-QCD correlation length) and in well-known holographic formulas. Credit is due for the clarity of the writing and for making the numerical claims explicit. However, the central numerical and algebraic claims do not survive scrutiny, and the reasoning is circular at a load-bearing step. As written, the work does not establish the advertised results.

major comments (5)
  1. [Section IV.B, Eqs. (3)–(4)] The quoted numbers are internally inconsistent and do not support the claimed 3% agreement. With R_u = 1.30×10^26 m and R_p = 0.84 fm, N = (R_u/R_p)^3 ≈ 3.7×10^123, not 1.8×10^123 as stated in the text. Consequently, A_cell = 4πR_u^2/N ≈ 5.7×10^-71 m^2, whereas the CODATA value is L_Pl^2 = ℏG/c^3 ≈ 2.61×10^-70 m^2. The ratio is about 4.6, not 1 ± 0.03. The claimed equality A_cell = L_Pl^2 is therefore an arithmetic artifact.
  2. [Section V.E, Eq. (10)] The dilution relation ρ_u = ρ_su3/N does not follow from the preceding equations. Equation (6) defines F_u as the force on a single patch, F_u = ρ_su3 A_cell, whereas Eq. (9) uses the same symbol F_u to denote the total force over the whole horizon, F_u = ρ_u A_u with A_u = N A_cell. Equating these two different quantities produces the 1/N factor. A consistent accounting gives ρ_u = ρ_su3: if F_u is per-patch, the total force is N F_u = ρ_u A_u, so ρ_u = ρ_su3; if F_u is total, then Eq. (6) must be multiplied by N, again yielding ρ_u = ρ_su3. Thus Eq. (10) is an algebraic artifact rather than a physical dilution law.
  3. [Section V.B, Eq. (7)] The uniform-force condition is not derived. The Brown–York argument shows that the horizon stress is isotropic, which, with P = −ρ, implies equal pressure on all patches. It does not imply equal force per patch unless all patches have equal area, which is precisely the conclusion the argument is meant to establish. Moreover, equal pressure would give ρ_u = ρ_su3, directly contradicting Eq. (10). The inference from CMB isotropy to equal forces per Planck patch is therefore circular, and the uniform-force postulate remains an unproven assumption.
  4. [Sections IV.A–IV.B and VI] The claimed derivation of the Planck constants is circular because L_Pl already appears in the Bekenstein–Hawking bound (2). Saturating the bound only fixes A_cell = 4πR_u^2/N; equating this with L_Pl^2 is a numerical check, not a derivation, and the check fails with correct arithmetic. In addition, the bare density ρ_su3 in Section VI depends on the arbitrary zero-point regularization coefficient 1/(16π^2) and on the UV cutoff P_Pl; no principle in the paper determines either, so the 'no free parameters' claim is not supported. The factor of eight for the eight gluons is also not included in the stated coefficient.
  5. [Section VII.C, Eq. (11)] The claimed Planck-mass coincidence contains another arithmetic error. The volume of the intersection is V_int = (4π/3)L_Pl^3 = 1.77×10^-104 m^3, not 4.19×10^-105 m^3 as stated in Eq. (8.3). Using the paper's ρ_su3 = 5.15×10^96 kg/m^3 gives M_int ≈ 9.1×10^-8 kg ≈ 4.2 M_Pl, not 0.98 M_Pl. Thus the 'central Planck core' result does not reproduce the Planck mass within 2%.
minor comments (4)
  1. [General] Equation numbering in Section VII starts at (8.1), (8.2), (8.3), but there is no Section 8; this creates confusion and should be renumbered sequentially.
  2. [Section IV.E] The text refers to "the spectral gap obtained in Section ??" but the placeholder is unresolved; a proper cross-reference is needed.
  3. [Author affiliation] The affiliation line contains a typo: "Egyp t" should read "Egypt."
  4. [Section VIII] The ER=EPR discussion and the claims about a Hadamard state and no firewalls are speculative and not derived from the preceding equations; they should be clearly separated from the quantitative claims or omitted.

Circularity Check

3 steps flagged · score 8.0 of 10

The central 1/N dilution of the vacuum energy is an algebraic artifact: Eq. (9) identifies the total horizon force with the force on a single Planck patch, so ρ_u = ρ_su3/N is built into the definition.

  1. self definitional [Section V.C–V.E, Eqs. (8)–(10)]
    "The horizon contains N such patches, so its total area is Au = Σ_{i=1}^N Acell = N Fu/ρsu(3). (8) ... To an observer who cannot resolve individual cells, the same outward force Fu is produced by a homogeneous vacuum energy density ρu acting over the whole horizon area: Fu = |Pu| Au = ρu Au. (9) ... Insert (8) into (9): Fu = ρu (N Fu/ρsu(3)). Provided Fu ≠ 0, cancel the common factor Fu and solve: ρu = ρsu(3)/N. (10)"

    F_u was defined in Eq. (6) as the force on a single Planck-area patch: F_su3 = ρ_su3 A_cell. In Eq. (8), A_u = N A_cell, so the same symbol F_u is still the force on one patch. In Eq. (9), the same symbol is silently taken to be the total force produced by the homogeneous vacuum over the entire horizon area A_u. There are only two consistent readings: if F_u in Eq. (9) is the per-patch force, the total force is N F_u = ρ_u A_u, giving ρ_u = ρ_su3; if F_u in Eq. (9) is the total force, then Eq. (6) must be multiplied by N, again giving ρ_u = ρ_su3. The factor 1/N appears only because the force on a single patch is equated with the force over the whole horizon. Thus Eq. (10) is not derived from physics; the dilution is inserted by the cross-scale identification of F_u.

  2. self citation load bearing [Section II, paragraph on U(1)em breaking]
    "By analogy with superconductors, this condensate expels electromagnetic fields and endows the photon with an effective mass in the dark-energy vacuum, preventing its long-range propagation through the vacuum state [23, 24]. Consequently, U(1)em is effectively “Higgs–broken” in the zero–temperature vacuum, while SU(3)c remains strictly unbroken and confining. Therefore, in the T→0 limit the only unbroken gauge symmetry in the vacuum is SU(3)c."

    The paper's choice of the eight gluons as the unique massless zero-point source for ρ_su3 in Section VI depends on the claim that U(1)em is broken in the vacuum. Reference [24] is a prior paper co-authored by A. F. Ali, one of the present authors, and it is cited as the basis for this premise. The premise is not derived here and is load-bearing: without it, the photon would also contribute to the bare vacuum density, changing ρ_su3. The uniqueness statement “only unbroken gauge symmetry is SU(3)c” is thus imported from the authors' own earlier work rather than resting on an external, machine-checked result.

1 more flagged steps
  1. self definitional [Abstract; Section IV.B, Eqs. (3)–(4)]
    "Assuming holographic saturation, each domain corresponds to a Planck-area patch on the cosmic horizon, allowing the Planck length, and hence ℏ, G, and c, to emerge as geometric quantities. ... Hence the Planck length is not imposed but follows from (i) the empirically determined integers N and Ru/Rp and (ii) holographic saturation."

    The abstract's antecedent already contains the consequent. Holographic saturation fixes only the number of patches through N Acell = 4πR_u^2; it does not by itself make the patch area equal to the Planck area. That equality, Acell = L_Pl^2, is exactly what Section IV claims to derive. By starting from “each domain corresponds to a Planck-area patch,” the paper assumes the conclusion that the Planck length and hence hbar, G, c emerge. The later numerical comparison to CODATA values is a consistency check on already-known constants, not a first-principles derivation.

full rationale

The core circularity is in Section V: the celebrated dilution ρ_u = ρ_su3/N is not a physical consequence of the uniform-force condition. Rather, the paper uses the same symbol F_u for the force on a single Planck patch (Eqs. (6), (8)) and for the total coarse-grained force over the whole horizon (Eq. (9)). Consistent bookkeeping gives ρ_u = ρ_su3 in either interpretation, so the 1/N factor is an algebraic artifact of conflating per-patch and total forces. This makes the paper's principal prediction, the observed dark-energy density, a restatement of its own inputs once N and ρ_su3 are chosen. A second, supporting circularity is the abstract's assumption that each domain corresponds to a Planck-area patch, which is precisely the conclusion about hbar, G, c that the paper claims to derive. I also flag a load-bearing self-citation: the effective breaking of U(1)em, used to select the gluon zero-point energy as the sole massless contribution, is supported by Ref. [24] involving one of the present authors. I do not count the Section IV comparison Acell ≈ L_Pl^2 as an additional circular step, because L_Pl^2 cancels in the computation of Acell = 4πR_u^2/N; however, that comparison is numerically wrong (L_Pl^2 ≈ 2.6 × 10^-70 m^2, not 1.01 × 10^-70 m^2) and N is quoted inconsistently, which are correctness concerns rather than circularity. Even setting aside the self-citation, the central Eq. (10) reduces by construction to the assumed cross-scale force identity, justifying a circularity score of 8.

Assumptions & free parameters 3 free parameters · 6 assumptions · 4 invented entities

The central result rests on a chain of assumptions: confinement cells, holographic saturation, uniform-force condition, and a chosen zero-point normalization. The paper calls itself parameter-free, but the values of R_p, R_u, the cutoff, and the force-balance rule are inputs or postulates. The claimed numerical agreement in Section IV is further weakened by arithmetic errors.

free parameters (3)
  • Zero-point energy normalization coefficient = claim: 1/(16π²); quoted density uses coefficient ≈1
    Section VI sets ρ_su3 = (1/16π²) P_Pl^4/(hbar^3 c^3) but quotes 2.0e76 GeV^4, which is M_Pl^4 without the 1/(16π²) suppression. The bare density, and hence the predicted ρ_Λ, scales with this arbitrary regularization choice.
  • Confinement cell radius R_p = 0.84(1) fm (proton charge radius)
    Section III.B chooses the cell volume V_cell = (4π/3) R_p^3. The lattice correlation length λ0 ranges over 0.8-1.2 fm; picking the proton radius sets N and hence the final density.
  • Cosmic horizon radius R_u = 1.30(1)×10^26 m
    Section III.C uses the comoving Hubble radius. Other horizon definitions change R_u and therefore N, the dilution factor, and the inferred Planck area.
assumptions (6)
  • domain assumption Permanent color confinement at T→0 with proton-scale correlation length
    Section II and III rely on lattice-QCD evidence that confinement persists to T=0 and that the screening correlator yields λ0 ≈ 0.8-1.2 fm. The extrapolation to the cosmic vacuum is an assumption.
  • domain assumption Third Law of Thermodynamics implies a finite irreducible correlation volume in the cosmic vacuum
    Section III.A applies laboratory thermodynamics to the vacuum, a nontrivial extrapolation. It is used to justify the existence of finite cells.
  • domain assumption Bekenstein-Hawking covariant entropy bound applies to the apparent cosmic horizon and is saturated
    Section IV.A imposes equality in Eq (2). Saturation is not derived; it is stated as a maximal-packing condition.
  • domain assumption U(1)_em is effectively broken in the vacuum, so gluons are the only massless gauge bosons
    Section II invokes refs [23,24] for a Meissner-like photon mass in the dark-energy vacuum. This nonstandard assumption selects the gluon sector as the source of bare vacuum energy.
  • ad hoc to paper Uniform-force condition: equal outward force on every horizon patch
    Section V.A postulates UF. The attempted derivation from CMB isotropy is not sufficient; this condition directly produces the 1/N dilution in Eq (10).
  • domain assumption Planck-scale cutoff for the zero-point integral is physical
    Section VI integrates gluon zero-point energy up to P_Pl. The cutoff choice is the standard UV sensitivity of the cosmological constant problem but is not derived.
invented entities (4)
  • SU(3) confinement cell (proton-scale domain)
    purpose: Coarse-graining unit of the vacuum; used to define N and the holographic patch area.
    No direct observable is attached to these cells in this paper; they are inferred from the Third Law and lattice QCD correlation length.
  • Planck-area boundary patch on the cosmic horizon
    purpose: Holographic encoding of each cell.
    The patch area is defined as A_u/N and then identified with L_Pl^2; no independent measurement is given.
  • Central Planck core (intersection of N radial cylinders)
    purpose: To localize one Planck mass in a Planck volume.
    Section VII constructs this core geometrically; there is no falsifiable handle outside the model.
  • ER=EPR network of entangled gluonic pairs
    purpose: To connect bulk cells to horizon patches.
    Section VIII is qualitative and speculative; no experimental signature is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Deriving the Cosmological Constant and Nature's Constants from SU(3) Confinement Volume." pith.science (2026). https://pith.science/paper/DFDMJ4QK

@misc{pith2026250722096,
  author       = {Pith},
  title        = {Pith review of: Deriving the Cosmological Constant and Nature's Constants from SU(3) Confinement Volume},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DFDMJ4QK}},
  note         = {Machine review of arXiv:2507.22096}
}
abstract

We explore the interplay between three well-established physical principles: QCD confinement, the Third Law of Thermodynamics, and holography, and examine how their combined implications may shed light on several open problems in fundamental physics. As the Universe cools toward absolute zero, color confinement fragments the vacuum into proton-scale domains. The Third Law, which renders $T = 0$ unattainable and prohibits complete entropy elimination, implies that these domains must persist. This leads to a natural count $N \simeq (R_u / R_p)^3 \sim 10^{123}$, where $R_u$ is the radius of the cosmic horizon and $R_p$ is the proton radius. Assuming holographic saturation, each domain corresponds to a Planck-area patch on the cosmic horizon, allowing the Planck length, and hence $\hbar$, $G$, and $c$, to emerge as geometric quantities. The same tiling dilutes the bare Planck-scale vacuum energy by a factor of $N$, reproducing the observed value of $\rho_\Lambda$ without requiring fine-tuned counterterms.

Figures

Figures reproduced from arXiv: 2507.22096 by the authors.

Figure 1
Figure 1. FIG. 1: Simplified representation of multiple SU(3) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: A schematic depiction of the universe as a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 34 canonical work pages

  1. [1]

    therefore follows di- rectly—without free parameters—from (i) the Third-Law cluster bound, (ii) lattice-QCD determination of λ0, and (iii) the measured proton radius. D. Stability of the Correlation Cells Exact SU(3)c gauge symmetry forbids baryon-number violating operators of dimension ≤ 6. The Super- Kamiokande limit τp > 2.4 × 1034 yr [ 31] implies tha...

    work page

  2. [2]

    Solving yields the boundary quantum of area Acell = 4πR2 u N = 1.04(7) × 10−70 m2

    requires Scell = Acell 4 L 2 Pl , N A cell = 4πR2 u. Solving yields the boundary quantum of area Acell = 4πR2 u N = 1.04(7) × 10−70 m2. (3) With the CODATA-2022 values of ℏ, G, and c one finds the Planck area L 2 Pl = 1.01 × 10−70 m2, agreeing with ( 3) to better than 3%. Because the observational uncertain- ties of Ru and Rp dominate the error budget, the...

    work page 2022

  3. [3]

    eliminates N and yields Vcell = Acell Ru = L 2 Pl Ru, (5) so each confinement domain occupies a cylinder whose base is a Planck-area patch on S2(Ru) and whose height equals Ru (Fig. 1). Equation ( 5) is an identity; no addi- tional modelling assumptions are employed. D. Minimal–interface proof of the cylindrical shape Lemma. Let Σ ⊂ R3 be an interface encl...

    work page

  4. [4]

    Weinberg, Rev

    S. Weinberg, Rev. Mod. Phys. 61, 1 (1989)

    1989

  5. [5]

    P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003)

    2003

  6. [6]

    A. G. Riess et al. , Astron. J. 116, 1009 (1998)

    work page 1998

  7. [7]

    Perlmutter et al

    S. Perlmutter et al. (Supernova Cosmology Project), Astrophys. J. 517, 565 (1999)

    work page 1999

  8. [8]

    Aghanim et al

    N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020) , erratum: Astron. Astrophys. 652, C4 (2021)

    work page 2020

Show all 47 references
  1. [9]

    Y. B. Zel’dovich, A. Krasinski, and Y. B. Zeldovich, Sov. Phys. Usp. 11, 381 (1968)

    1968

  2. [10]

    C. P. Burgess, in 100e Ecole d’Ete de Physique: Post-Planck Cosmology (2015) pp. 149–197, arXiv:1309.4133 [hep-th]

    2015 arXiv

  3. [11]

    Padmanabhan, Curr

    T. Padmanabhan, Curr. Sci. 88, 1057 (2005), arXiv:astro-ph/0411044

    2005 arXiv

  4. [12]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. Lett. 59, 2607 (1987)

    1987

  5. [13]

    Susskind et al

    L. Susskind et al. , Universe or multiverse , 247 (2003), arXiv:hep-th/0302219

    2003 arXiv

  6. [14]

    Greensite, An introduction to the confinement problem , Vol

    J. Greensite, An introduction to the confinement problem , Vol. 821 (2011)

    2011

  7. [15]

    Banerjee, S

    S. Banerjee, S. K. Ghosh, E.-M. Ilgenfritz, S. Raha, E. Takasugi, and H. Toki, Phys. Lett. B 611, 27 (2005) , arXiv:hep-ph/0307366

    2005 arXiv

  8. [16]

    Bousso, Rev

    R. Bousso, Rev. Mod. Phys. 74, 825 (2002) , arXiv:hep-th/0203101

    2002 arXiv

  9. [17]

    Susskind, J

    L. Susskind, J. Math. Phys. 36, 6377 (1995)

    1995

  10. [18]

    S. L. Glashow, Nucl. Phys. 22, 579 (1961)

    1961

  11. [19]

    Weinberg, Phys

    S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967)

    1967

  12. [20]

    Salam, in Elementary Particle Theory: Relativistic Groups and Analyticity (Nobel Symposium 8) , edited by N

    A. Salam, in Elementary Particle Theory: Relativistic Groups and Analyticity (Nobel Symposium 8) , edited by N. Svartholm (Almqvist & Wiksell, 1968) pp. 367–377

    1968

  13. [21]

    Aad et al

    G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 716, 1 (2012)

    2012

  14. [22]

    Chatrchyan et al

    S. Chatrchyan et al. (CMS Collaboration), Phys. Lett. B 716, 30 (2012)

    2012

  15. [23]

    Creutz, Phys

    M. Creutz, Phys. Rev. Lett. 43, 553 (1979) , erratum: Phys. Rev. Lett. 43, 890 (1979)

    1979

  16. [24]

    Creutz, Phys

    M. Creutz, Phys. Rev. D 21, 2308 (1980)

    1980

  17. [25]

    Bazavov et al

    A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 100, 094510 (2019)

    2019

  18. [26]

    S. D. Liang and T. Harko, Phys. Rev. D 91, 085042 (2015) , arXiv:1504.02645 [gr-qc]

    2015 arXiv

  19. [27]

    N. Inan, A. F. Ali, K. Jusufi, and A. F. Yasser, JCAP 08, 012 , arXiv:2404.03872 [gr-qc]

    arXiv

  20. [28]

    Nernst, Über den Energieinhalt fester Stoffe, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1912), physikalisch- mathematische Klasse

    W. Nernst, Über den Energieinhalt fester Stoffe, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1912), physikalisch- mathematische Klasse

    1912

  21. [29]

    Planck, Thermodynamik, 3rd ed

    M. Planck, Thermodynamik, 3rd ed. (De Gruyter, 1911)

    1911

  22. [30]

    A. E. Leanhardt et al. , Science 301, 1513 (2003)

    2003

  23. [31]

    T.-P. Liu, J. Pu, Y. Han, and Q.-Q. Jiang, Int. J. Mod. Phys. D 29, 2043022 (2020)

    2020

  24. [32]

    Glimm and A

    J. Glimm and A. Jaffe, Quantum physics: a functional integral point of view , 2nd ed. (Springer Science & Busi- ness Media, 2012). 8

    2012

  25. [33]

    Pohl et al

    R. Pohl et al. , Nature 466, 213 (2010)

    2010

  26. [34]

    Abe et al

    K. Abe et al. (Super-Kamiokande Collaboration), Phys. Rev. D 95, 012004 (2017)

    2017

  27. [35]

    J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

    1973

  28. [36]

    S. W. Hawking, Commun. Math. Phys. 43, 199 (1975) , [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    1975

  29. [37]

    ’t Hooft, in Salamfestschrift: A Collection of Talks From the Conference on Highlights of Particle and Con- densed Matter Physics , edited by A

    G. ’t Hooft, in Salamfestschrift: A Collection of Talks From the Conference on Highlights of Particle and Con- densed Matter Physics , edited by A. Ali, J. Ellis, and S. Randjbar-Daemi (World Scientific, 1994) pp. 284–296, conference held 16-20 March 1993, Trieste, Italy. Also ...

    1994 arXiv

  30. [38]

    G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977)

    1977

  31. [39]

    J. L. Marques Barbosa and A. G. Colares, Ann. Global Anal. Geom. 15, 277 (1997)

    1997

  32. [40]

    J. D. Brown and J. W. York, Jr., Phys. Rev. D 47, 1407 (1993)

    1993

  33. [41]

    J. D. Brown and J. W. York, Jr., Phys. Rev. D 47, 1420 (1993)

    1993

  34. [42]

    Hilbert and S

    D. Hilbert and S. Cohn-Vossen, Geometry and the Imag- ination, AMS Chelsea Publishing, Vol. 87 (American Mathematical Society, 2021)

    2021

  35. [43]

    Jaffe and E

    A. Jaffe and E. Witten, in The Millennium Prize Problems , edited by J. Carl- son, A. Jaffe, and A. Wiles (Clay Mathematics Institute, Cambridge, MA / American Mathematical Society, Providence, RI, 2006) pp. 129–152

    2006

  36. [44]

    Visser, Mod

    M. Visser, Mod. Phys. Lett. A 17, 977 (2002) , arXiv:gr-qc/0204062

    2002 arXiv

  37. [45]

    Padmanabhan, Phys

    T. Padmanabhan, Phys. Rev. D 83, 044048 (2011) , arXiv:1012.0119 [gr-qc]

    2011 arXiv

  38. [46]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, JHEP 02, 062 , arXiv:1207.3123 [hep-th]

    arXiv

  39. [47]

    Maldacena and L

    J. Maldacena and L. Susskind, Fortsch. Phys. 61, 781 (2013) , arXiv:1306.0533 [hep-th]

    2013 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.