In 1899 Planck introduced units of length, mass, and time formed from the physical constants. We examine a Measurement Quantization (MQ) count-geometry description of these measures and the associated Informativity differential, a model-specific normalization of realized lengths arising from discrete counts. The count-resolved factor approaches unity in the asymptotic large-count limit and differs from unity at the electromagnetic demarcation, the model’s fixed electromagnetic interaction scale. Using fixed 2022 inputs from the Committee on Data for Science and Technology (CODATA), we calculate MQ fundamental measures and distinguish finite-count and upper-count descriptions of the gravitational coupling and reduced Planck constant. Consistent MQ upper-count substitutions give the same gravitational coupling across the Planck-unit identities. Comparisons with historical CODATA editions are retained as comparisons, rather than digit-for-digit experimental confirmation. A representative solar calculation illustrates the small additional divergence obtained when a finite-count coupling is substituted into a common weak-field deflection benchmark.

Keywords: Gravitational Constant, Reduced Planck Constant, Planck Units, Length Contraction, Discrete Measure, Measure

We discuss the Informativity differential introduced above. This count-dependent normalization is distinct from velocity-dependent Lorentz contraction [1] and from curvature in the MQ description. We examine how this factor enters MQ versions of Planck’s unit expressions [2], and compare the resulting constants with published CODATA values [3–6]. G denotes the gravitational coupling in m³ kg⁻¹ s⁻², and ℏ denotes the finite-count reduced Planck relation in J s. Upright G and ħ indicate upper-count values. Current MQ calculations use the 2022 fine-structure input throughout. An algebraic identity among quantities sharing these inputs is distinguished from independent agreement with an experiment.

MQ [7–13] describes measure using counts n_L, n_M, and n_T of the fundamental length l_f, mass m_f, and time t_f, respectively. The counts are dimensionless, while the measures carry metres, kilograms, and seconds. The Internal Frame is the model’s discrete configuration domain, with relational structure encoded by integer counts. The System Frame is the continuous relational realization of that structure under the Frames mapping, rather than a domain with independent fundamental measures (Appx. B). The relations between the fundamental measures and conventional Planck units involve the Informativity differential ([13], Appx. X), and the derivation of Planck’s unit expressions is given in [13], Appx. BN. The numerical consequences of these relations are evaluated below without treating definitional agreement as independent physical validation.

The two-frame description and its realization relation are adopted from the MQ construction ([13], Appx. I–K; local Appx. B). These are model definitions used to describe classical expressions, rather than an experimental demonstration that space itself is discrete.

These frames serve a different purpose from inertial or gravitational descriptions in relativity. MQ uses them to investigate how length, mass, and time may arise from count structure. Rewriting escape-velocity and uncertainty relations in MQ nomenclature tests the consistency of that construction; those rewritings alone do not establish physical discreteness.

The Planck units tension considered here concerns comparisons between count-resolved MQ calculations and conventional Planck-unit values. Historical CODATA recommendations for G were 6.67384(80), 6.67408(31), and 6.67430(15), in units of 10⁻¹¹ m³ kg⁻¹ s⁻², for 2010, 2014, and 2018 [3–5]. The 2022 recommendation remains 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻² [6]. The current MQ upper-count result is 6.6740779383(10) × 10⁻¹¹ m³ kg⁻¹ s⁻², about 1.48 of the 2022 recommended standard uncertainties below its central value. Thus it is within two, but outside one, recommended standard uncertainty. This comparison does not establish a CODATA calculation error or a distance-dependent experimental origin for the spread.

MQ distinguishes the electromagnetic demarcation from macroscopic measurements ([13], Appx. AB, AE, AN). The current 2022-input calculation gives the demarcation count n_L=84.6005456716(65). For macroscopic distances the normalized count factor 2Q_Ln_L approaches one. Here Q_L is the positive fractional realization residual of a count of l_f, and n_L denotes the relevant dimensionless distance count in either geometric context. Equations (1) and (2) show the algebraic lower boundary and upper-count limit; the physical electromagnetic demarcation is not n_L=1.

Examples of how the Informativity differential affect measure, for instance that of G ([13], Appx. M) and ℏ ([13], Appx. L), are also provided. Here p_si denotes the MQ momentum realization, with units kg m s⁻¹, and c denotes the exact vacuum speed of light, 299792458 m s⁻¹ [6].

We next derive the consequences of the adopted count geometry and evaluate their numerical scale.

Measurement Quantization [13] provides the model assumptions and derivations used here. The adopted count structure is applied to gravitational coupling, the speed of light, escape velocity, and uncertainty relations. Heisenberg’s uncertainty relation [14] concerns conjugate quantities; its use in this construction does not independently prove a fundamental spatial count.

The MQ derivations and the reported evidence for countable measure are presented in Measurement Quantization [13]. References to its appendices now identify published external targets; the unique local term, framework, and fundamental-expression material is retained in Appendices A, F, and J. These sources establish the model context for the present calculation and do not replace the independent input ledger.

The accompanying calculation and revision records identify the inputs, dependencies, uncertainty assumptions, and current numerical results used in this manuscript. They support reproducibility of the calculations, rather than supply an independent observation of countable measure. Reported model uncertainties propagate the stated input errors and do not quantify uncertainty in the MQ assumptions.

The normalized factor 2Q_Ln_L describes the count dependence used below (Fig. 1). In the local right-triangle construction, a, b, and c are side lengths in metres; the geometric c is distinct from the vacuum speed of light. The dimensionless counts n_L,a, n_L,b, and n_L,c denote the respective side lengths divided by l_f. The comma separates the length-count label from the local side index. A, B, and C label the diagram vertices; AB, BC, and AC denote their connecting segments.

Such that the Pythagorean Theorem is used to describe these counts, then side c of a right-angle triangle is the sum of a whole unit count equal to side b plus a fractional count Q_L of a more precise calculation (i.e., ).

The reference side has unit count. The adjacent side has count n_L, and the hypotenuse has count n_L+Q_L. Thus Q_L is the positive remainder in the precise geometric calculation. For adjacent count 3, the hypotenuse is and Q_L=−3, which rounds to 0.162278. Equations (7)–(10) express this count geometry.

This can be reduced.

Where the first term, Q_L², quickly approaches zero with increasing distance, we recognize that,

For macroscopic measurements the normalized factor 2Q_Ln_L is indistinguishable from one at ordinary measurement precision. The following gravitational and reduced Planck relations retain its exact count dependence ([13], Appx. L, M).

Using the MQ fundamental measures ([13], Appx. W), the upper-count forms of these relations reduce to the momentum relation (20), also derived in Appendix C. The limit must be stated explicitly when a finite-count expression is substituted into an upper-count identity.

The next three reductions are evaluated at the upper count limit.

The fundamental reference relation (20) is evaluated at the upper count limit, where 2Q_Ln_L tends to one. Its momentum realization is , numerically 3.26239030504(25) kg m s⁻¹ for the current inputs. This dimensional momentum is distinct from the invariant dimensionless coefficient θ_si, despite their common numerical coefficient in the stated SI realization.

Table 1 evaluates the fractional difference between finite-count G and its upper-count value as 100Q_L² percent. This is an exact consequence of (13) and (3). Here a₀ denotes the conventional Bohr radius used as a representative atomic distance. The small values at macroscopic distances are computed rather than reported as zero. They are model calculations; their presence below measurement resolution does not establish an observed change in G. The distance label Gly denotes 10⁹ light-years, using a Julian year of 31557600 s in these calculations.

Table 1. Calculated percentage deficit of finite-count G relative to upright upper-count G. Count dependence follows [13], Appx. M; current numerical entries use the 2022 input ledger.

a The Bohr radius a₀=5.29177210544(82) × 10⁻¹¹ m is used as the representative atomic distance [6].

b Nonzero count-geometry values are shown even when they are far below experimental resolution. The 13.794 Gly column is a representative distance, not a newly measured cosmological value.

In this manuscript, upright G and ħ denote MQ values at the upper count limit; the finite-count symbols retain mathematical italics. Macroscopic quantities use the upper-count convention when the residual is negligible at the stated precision. This convention labels the model realization. It does not establish that an experimental apparatus samples the electromagnetic demarcation or measures a different gravitational coupling.

Table 2 compares the finite-count reduced Planck relation (4) with its value at the current electromagnetic demarcation. The electromagnetic value reproduces the conventional International System of Units (SI) reduced Planck input because the conventional Bohr-radius product is used in the fundamental-length construction. That equality is an input identity, not independent confirmation.

Table 2. Calculated percentage difference of the reduced Planck relation from its electromagnetic-demarcation value at n_L=84.6005456716(65). The count relation follows [13], Appx. L; entries are current 2022-input calculations.

A mixed finite-count and upper-count substitution can change a Planck-unit calculation. Here l_p, t_p, and m_p denote the conventional Planck-form expressions , , and , respectively, with units m, s, and kg. Each form uses the paired constants specified for its table row. Table 3 preserves the historical calculations reproduced from [13] using rounded published inputs from the 2010, 2014, and 2018 CODATA editions. They are historical comparisons, not new current estimates. Correlations among conventional Planck units and their defining constants prevent treating these rearrangements as independent measurements of G. With unrounded conventional inputs, these inversions return the defining G identically [6], Table XXXIII. Differences introduced by rounded tabulated values are not a physical inconsistency in the conventional definitions.

Table 3. Calculations of G using Planck’s Unit Expressions. Reprinted from [13], Table 1.

^a Planck’s Unit expressions are resolved using those values provided in CODATA publications for 2010, 2014 and 2018 [3–5].

With the current MQ upper-count reduced Planck relation ([13], Appx. L) and consistent fundamental measures ([13], Appx. W), all three Planck-unit rearrangements give upright G=6.6740779383(10) × 10⁻¹¹ m³ kg⁻¹ s⁻². This agreement follows from the shared MQ definitions. The result is within one recommended standard uncertainty of the 2014 G and within two of the 2022 G [4,6]. These comparisons do not demonstrate digit-for-digit experimental agreement or identify the 2018 recommendation as a miscalculation.

Table 4 retains the 2010, 2014, and 2018 CODATA recommendations [3–5] as historical rows and recalculates its four MQ rows with the fixed 2022 inputs. Each MQ row combines either electromagnetic-demarcation G or upper-count G with either electromagnetic-demarcation ℏ or upper-count ħ ([13], Appx. L, M). The demarcation count is n_L=84.6005456716(65) ([13], Appx. AB, AE, AN). Planck-form length, time, and mass are calculated from each pair and are not all identified with the same fundamental measures. Their uncertainties are propagated together through the shared fine-structure input. In the table labels, EM abbreviates electromagnetic demarcation, and Upper denotes the upper-count limit.

Table 4. Historical CODATA values and current 2022-input MQ Planck-form calculations. Historical source rows are retained from [13], Table N.2; MQ numerical rows are recalculated here.

^a CODATA publications for 2010, 2014 and 2018 [3–5].

^b Finite-count symbols are italicized; upright G and ħ denote the upper-count values. The electromagnetic reduced Planck value is the exact SI input identity in this construction. Parenthetical digits give propagated standard uncertainties; exact values have no measurement uncertainty. The Planck-form expressions defined before Table 3 are evaluated with each specified pair.

The historical rows and current model rows have different input provenance. Rounded central-value proximity in a column is not an independent validation. In particular, the 2018 and 2022 conventional reduced Planck constant is exact in SI, while the MQ upper-count reduced Planck relation is a calculated quantity. The two must not be assigned the same uncertainty or interpreted as competing CODATA measurements.

The current model bounds are 6.6738448317(10) and 6.6740779383(10), in units of 10⁻¹¹ m³ kg⁻¹ s⁻². The 2018 and 2022 recommended central G lies above the upper bound by about 1.48 recommended standard uncertainties [5–6]. A central value outside this model interval does not by itself establish an experimental inconsistency or an error caused by mixed phenomena.

Equation (21) rearranges the MQ atomic relation ([13], Appx. BL). Here α_p denotes the dimensionless Planck-like fine-structure factor in the System Frame, and m_e is the electron mass in kilograms. α_c denotes the dimensionless conventional fine-structure constant in the System Frame, using the fixed 2022 input. ℏ_SI denotes the exact conventional SI reduced Planck constant in J s; its SI subscript identifies this input, rather than an additional MQ realization. The previously defined a₀ and l_f retain their meanings. The length l_f is reconstructed from the same input chain rather than treated as an independent measurement. The conventional identity eliminates double counting of correlated atomic inputs [6].

The numerical value in (21) is an MQ calculation based on the 2022 CODATA fine-structure input [6]. It is not an independent measurement. Parenthetical digits give the standard uncertainty in the last displayed digits.

Equation (22) uses the Planck-resolved mass in (21), while (23) uses the MQ fundamental mass. In the present calculation these are the same quantity. Both calculations use the same fundamental time t_f and the macroscopic, upper-count value of G. The manuscript-local labels f(α_p) and f(α_c) name these two evaluations of G, with units m³ kg⁻¹ s⁻²; they are not an additional independently defined MQ function.

We next calculate a representative weak-field deflection for light grazing the Sun. Here M is the manuscript-local solar mass in kilograms, and r denotes radial separation in metres, used here as the grazing distance. θ is the general relativity (GR) benchmark angle in radians. Δθ denotes the positive deficit θ_GR−θ_MQ; the subscripts GR and MQ identify the benchmark and comparison angles. G is the upright MQ upper-count coupling used for the common benchmark. The finite-count MQ comparison replaces this coupling by its count-resolved expression in (3); this scalar substitution is an assumption of the example. We use the published solar mass parameter 1.32712442099(10) × 10²⁰ m³ s⁻² [15], divided by the conventional 2022 CODATA G=6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻² [6], giving M=1.988410(45) × 10³⁰ kg. The photospheric grazing distance is r=6.95658 × 10⁸ m with reported uncertainty 1.40 × 10⁵ m [16]. These are representative source choices rather than a unique definition of an observed solar limb.

In (25), Δθ is defined as the positive deficit θ_GR−θ_MQ, with n_L=r/l_f. Thus the MQ angle in this example is smaller than the common GR benchmark by Δθ. The upper-count G is used as the reference throughout; a one-metre reference is not used. The uncertainty budget treats the reported radius error as a standard uncertainty and assumes independence of the radius, astronomical mass parameter, and terrestrial CODATA G estimates. Correlations among all MQ outputs are retained through their shared fine-structure input. The quoted uncertainties describe these source inputs and assumptions and exclude unknown model uncertainty. This calculation is a representative possibility, not an observed additional solar deflection. The International Astronomical Union (IAU) nominal radius and mass parameter [17] are exact conversion constants and are not substituted for measured properties with zero measurement uncertainty.

For this comparison, γ denotes the dimensionless ratio θ_MQ/θ_GR, and Δγ=1−γ denotes its departure from the GR benchmark. GR alone has γ=1 and Δγ=0 under this normalization. The additional MQ divergence is the positive deficit Δγ. These are manuscript-local comparison quantities, distinct from the standard parametrized post-Newtonian (PPN) γ and the historical MQ electromagnetic transformation parameter. The following reductions use the same upper-count reference G as (24).

The representative solar calculation gives a relative deficit of 1.34939(54) × 10⁻⁸⁸. Accordingly, γ=1−Δγ remains extremely close to unity. The deficit is evaluated directly as Q_L², using the rationalized form of (9), to avoid subtracting nearly equal finite-precision numbers. It is a model-conditional difference from GR under the stated scalar-coupling comparison, not a measurement of the standard PPN parameter.

The solar examples show the scale of the count-geometry deficit under the stated assumptions, far below the input uncertainty of the representative benchmark angle. Cassini radio-link measurements test solar gravitational delay and agree with GR [18]. Their standard parametrized post-Newtonian parameter is distinct from the local ratio used here; applying that test to this MQ construction would require a derivation of the radio-link observable. The present calculation provides no independent experimental confirmation of the Informativity differential.

Within the adopted MQ count geometry, the normalized factor tends to unity and its positive deficit is Q_L². The fixed 2022-input calculation gives consistent fundamental measures and a common upper-count G. The historical CODATA rows preserve the input-edition comparison; the dependence of those comparisons and the current MQ identities is described with Tables 3 and 4.

The construction in [13], Appx. BN derives Planck-form expressions from the adopted MQ relations. Agreement among expressions derived from the same quantities is an internal consistency result. It must be distinguished from independent support for the physical interpretation. The solar calculation illustrates the size of an additional count-resolved deficit under a scalar-coupling assumption; a full relativistic derivation and an observational test are needed before interpreting it as a validated additional light-deflection effect.

The geometric derivation here concerns spatial length counts in a right triangle with a unit-count reference side. Mass and time enter the subsequent constitutive relations through the fundamental measures. This construction does not prove a contraction for every quantity with two or more dimensions, or prove that length is the only quantity that can be affected.

Definitions used in the paper are summarized below; the wider term catalog is provided in Measurement Quantization [13].

θ_si is the invariant dimensionless coefficient. Its SI momentum realization p_si has numerical value 3.26239030504(25) kg m s⁻¹ in the present calculation, while the MQ angular realization Θ_si carries radians. In [19], Table I, 3.26239 rad is a calculated signal/idler angle for diamond (111) phase matching with a 25 kiloelectronvolt (keV) pump and degenerate 12.5 keV photons, not a measured MQ coefficient with a reported ±2 μrad uncertainty. The experiments in [20] and [21] concern X-ray down-conversion and X-ray/optical wave mixing, respectively. They do not independently establish the MQ identification of this coefficient. The conserved quantities at null infinity in [22], Secs. 4.3–4.4, do not identify an angle and a linear momentum as the same physical quantity.

c is the exact vacuum speed of light, 299792458 m s⁻¹ [6]. The MQ relation uses n_L=n_T=1 as the adopted unit-count normalization. That choice is an internal construction, not an independent observation of the fundamental length or time.

For the gravitational coupling, upright G=6.6740779383(10) × 10⁻¹¹ m³ kg⁻¹ s⁻² denotes the current upper-count calculation. Italic G=6.6738448317(10) × 10⁻¹¹ m³ kg⁻¹ s⁻² denotes its electromagnetic-demarcation calculation. These are MQ outputs based on 2022 inputs, not CODATA recommendations or independent measurements.

The fundamental measures l_f, m_f, and t_f are defined in the Introduction. Current values are l_f=1.61619991148(12) × 10⁻³⁵ m, m_f=2.17643254057(17) × 10⁻⁸ kg, and t_f=5.39106261131(41) × 10⁻⁴⁴ s. Their errors are correlated through the same fine-structure input.

l_p, m_p, and t_p retain the Planck-form meanings given before Table 3, with units m, kg, and s. Their values depend on the pair of constants specified for each row.

n_L, n_M, and n_T are dimensionless counts of l_f, m_f, and t_f in the adopted MQ description. Their physical interpretation depends on the model assumptions.

n_L describes the count of l_f representative of a change in position of an observable measured with respect to the observer’s frame of reference.

The geometric side counts retain the definitions given before (5). They do not introduce separate light-propagation quantities; the solar comparison uses n_L as its distance count.

n_θ denotes the dimensionless System Frame count of θ_si associated with the Internal Frame demarcation and the metric differential, the representation mismatch when integer count structure is realized continuously. This term describes the mismatch itself rather than a physical deformation; it is distinct from the Informativity differential. The evaluated nearest-whole-unit count is . The mixed left-floor/right-ceiling brackets denote the nearest whole unit in this manuscript; this argument is not a half-unit tie.

The mixed bracket convention is the nearest-whole-unit operation defined in the preceding entry; it is distinct from the standard floor or ceiling operation alone.

Q_L retains the positive fractional realization-residual meaning introduced above for a count of l_f in the unit-reference geometry. It is not a generic measurement error or an arbitrary fractional remainder.

The normalized Informativity differential factor is 2Q_Ln_L, as used in (3); its upper-count value is one. The corresponding positive deficit is Q_L² by (13).

Here h is the exact SI Planck constant, 6.62607015 × 10⁻³⁴ J s [6], and π is the dimensionless circle constant. At the electromagnetic demarcation, the finite-count relation (4) reproduces the conventional input ℏ_SI=h/(2π) defined before (21). The upright upper-count MQ relation gives ħ=1.0545349844417293(56) × 10⁻³⁴ J s. Equality at the demarcation follows from the shared input construction.

m_e is the mass of an electron.

a₀ is the conventional Bohr radius, a characteristic atomic length [6], Table XXXIII. It is used here as a representative distance, rather than as a universal ground-state orbital radius.

α_f is the dimensionless fundamental fine-structure factor. Its inverse α_f^-1=42θ_si is defined with respect to the Internal Frame. The previously defined α_p and α_c retain their System Frame meanings. The conventional form differs from the Planck-like form through the Informativity differential. The conventional 2022 inverse is α_c^-1=137.035999177(21), and the current MQ Planck-like result is α_p^-1=137.040785623(21) [6].

The local solar comparison uses γ and Δγ as defined before (26). These quantities are distinct from the historical MQ electromagnetic transformation parameter and from the standard PPN γ; their meanings must not be transferred between those contexts.

Fig. 3. Count of distance measures along AC. Reprinted from [13], Fig. K.1.

The three geometric roles are (Fig. 3):

Reference role—The segment AB supplies the unit-length reference for the local count geometry. Its count is one. This is a geometric reference role within the construction, not an additional physical frame.

Internal role—The segment BC represents a known integer count of the reference unit. This role illustrates the discrete count structure of the Internal Frame.

System role—The segment AC represents the continuously realized separation associated with those counts. This role illustrates the non-discrete relational description in the System Frame.

Appendix C restates the momentum reduction using the current p_si realization defined before (4). The distinction from an angular realization and the limits of the cited photon evidence are stated in Appendix A. Substitution of r=n_Ll_f in the MQ gravitational relation ([13], Appx. C) gives (30); the explicit upper-count limit in (31)–(32) then recovers (33).

Then,

This upper-count identity is consistent with the minimum-count solution ([13], Appx. I) using n_M=1/2 and n_L=n_T=1. The consistency is algebraic within the adopted model; it is not an independent experimental confirmation.

The author has no relevant financial or non-financial interests to disclose.

The author has no competing interests to declare that are relevant to the content of this article.

The published sources cited in this manuscript provide the external numerical inputs. The accompanying calculation and revision records document the derived values, their dependencies, and uncertainty assumptions. No new observational dataset is reported.

[1] A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys. 49 (fourth series; 354 in continuous numbering), 769–822 (1916), doi:10.1002/andp.19163540702, Sec. 22.

[2] M. Planck, Über irreversible Strahlungsvorgänge, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu, Berlin, 5, p. 480 (1899).

[3] P. Mohr, B. Taylor, and D. Newell, CODATA Recommended Values of the Fundamental Physical Constants: 2010, p. 73 (2012), arXiv:1203.5425v1, doi:10.48550/arXiv.1203.5425.

[4] P. J. Mohr, D. B. Newell, and B. N. Taylor, CODATA Recommended Values of the Fundamental Physical Constants: 2014, arXiv:1507.07956v1 (2015), p. 3, doi:10.48550/arXiv.1507.07956.

[5] NIST, CODATA Recommended Values of the Fundamental Physical Constants: 2018, NIST SP 961 (May 2019), https://physics.nist.gov/cuu/pdf/wall_2018.pdf.

[6] P. J. Mohr, D. B. Newell, B. N. Taylor, and E. Tiesinga, CODATA recommended values of the fundamental physical constants: 2022, Rev. Mod. Phys. 97, 025002 (2025), doi:10.1103/RevModPhys.97.025002. Fixed calculation-input edition: arXiv:2409.03787v1 (2024).

[7] J.A. Geiger, Measurement Quantization Unites Classical and Quantum Physics, J. High Energy Phys. Gravit. Cosmol. , CC BY 4.0, Vol. 4, No. 2, 262–311 (Apr 2018). https://doi.org/10.4236/jhepgc.2018.42019.

[8] J.A. Geiger, Quantum Model of Gravity Unifies Relativistic Effects, Describes Inflation/Expansion Transition, Matches CMB Data, J. High Energy Phys. Gravit. Cosmol., Vol. 4, No. 4 (Oct 2018). https://doi.org/10.4236/jhepgc.2018.44038.

[9] J.A. Geiger, Measurement Quantization Describes Galactic Rotational Velocities, Obviates Dark Matter Conjecture, J. High Energy Phys. Gravit. Cosmol., Vol. 5, No. 2 (Apr 2019). https://doi.org/10.4236/jhepgc.2019.52028.

[10] J.A. Geiger, Physical Significance of Measure, J. High Energy Phys. Gravit. Cosmol., Vol. 6, No. 1 (Jan 2020). https://doi.org/10.4236/jhepgc.2020.61008.

[11] J.A. Geiger, Measurement Quantization Describes History of Universe – Quantum Inflation, Transition to Expansion, CMB Power Spectrum, J. High Energy Phys. Gravit. Cosmol., Vol. 6, No. 2 (Apr 2020). https://doi.org/10.4236/jhepgc.2020.62015.

[12] J. A. Geiger, Measurement Quantization Describes the Physical Constants, Int. J. Theor. Math. Phys. 11(1), 29–59 (2021).

[13] J. A. Geiger, Measurement Quantization, Int. J. Geom. Methods Mod. Phys. 20(04), 2350069 (Jan. 2023), CC BY 4.0, doi:10.1142/S021988782350069X.

[14] Heisenberg, W., Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik, 43 (3–4): 172–198 (1927), Bibcode:1927ZPhy.43.172H, doi:10.1007/BF01397280, S2CID 122763326.

[15] A. Prša and P. Harmanec, Towards an increased accuracy of fundamental properties of stars: Proposing a set of nominal astrophysical parameters and constants, Proc. IAU 7, S282, 339–340 (2012), doi:10.1017/S1743921311027803, Table 1.

[16] M. Haberreiter, W. Schmutz, and A. G. Kosovichev, Solving the discrepancy between the seismic and photospheric solar radius, Astrophys. J. 675, L53–L56 (2008), doi:10.1086/529492, Table 3.

[17] A. Prša et al., Nominal values for selected solar and planetary quantities: IAU 2015 Resolution B3, Astron. J. 152, 41 (2016), doi:10.3847/0004-6256/152/2/41.

[18] B. Bertotti, L. Iess, and P. Tortora, A test of general relativity using radio links with the Cassini spacecraft, Nature 425, 374–376 (2003), doi:10.1038/nature01997.

[19] S. Shwartz and S. E. Harris, Polarization Entangled Photons at X-Ray Energies, Phys. Rev. Lett. 106, 080501 (2011), arXiv: 1012.3499, doi:10.1103/PhysRevLett.106.080501.

[20] S. Shwartz, R. N. Coffee, J. M. Feldkamp, et. al., X-ray Parametric Down-Conversion in the Langevin Regime, Physical Review Letters, 109, 013602 (July 6, 2012), doi:10.1103/PhysRevLett.109.013602.

[21] T. E. Glover et al., X-ray and optical wave mixing, Nature, 488, 7413, 603–608 (2012), doi:10.1038/nature11340.

[22] P.-N. Chen, M.-T. Wang, Y.-K. Wang, and S.-T. Yau, Conserved quantities in general relativity—the view from null infinity, in The Physics and Mathematics of Elliott Lieb, Vol. I, 211–224 (EMS Press, 2022), doi:10.4171/90-1/9. Author version: arXiv:2204.04010.