What is the Physical Difference Between Baryonic and Electromagnetic Phenomena?

Jody A. Geiger

Informativity Institute

Chicago, IL USA 60605

jodygeiger@informativity.org

ORCID: 0000-0001-5389-0447

ABSTRACT

Using Measurement Quantization, we compare the energy assigned to one fundamental mass with the photon energy at the reciprocal fundamental time. Under the specified upper-count action normalization, the photon energy is larger by the dimensionless factor 2π. This is a comparison at a defined mass and frequency, rather than a universal ratio for arbitrary baryons and photons. We distinguish the dimensionless MQ coefficient from its momentum and angular realizations and retain the dimensional conversion between them. This distinction allows action expressions to be related to a geometric arc length without identifying action with length. A historical gamma route is retained as a conditional numerical comparison with gravitational and electromagnetic constants. Its normalization and source variants remain unresolved. Cancellation of a common nonzero gamma factor recovers the energy comparison but does not validate the historical coupling formula. The energy ratio follows independently from the selected mass, frequency and action normalization.

Keywords: Photons, Particles, Waves, Planck, Baryonic, Electromagnetic

1. INTRODUCTION

Within Measurement Quantization (MQ), we use the discrete count domain of the Internal Frame and the continuous relational observables of the System Frame, connected by the Frames mapping. We examine the factor 2π in Planck’s constant h [1, 2] and the reduced Planck constant ℏ, both with action units J s. The latter also has angular-momentum dimensions; neither quantity is an arc length or a frequency. The fundamental measures l_f, m_f and t_f have units m, kg and s. Their length-to-time ratio gives c, the speed of light. We denote the energy of one fundamental mass by E_m and the energy of a single photon at frequency ν, in s⁻¹, by E_L; both energies have units J. Equation (1) compares these quantities at the specific frequency reciprocal to fundamental time and with the upper-count action normalization. It does not assign this ratio to arbitrary baryons and photons. Planck’s earlier radiation work [3] provides historical context.

\frac{E_{m}}{E_{L}} = \frac{1}{2 π}

(1)

We also examine the historical comparison of these normalized energies with G, gravitational coupling in m³ kg⁻¹ s⁻², and ε₀, vacuum permittivity in F m⁻¹ ([4], Appx. AT). The conventional transformation parameter γ has a unit-bearing electromagnetic realization in m⁶ C⁻² s⁻⁴. For the historical comparison in Eqs. (2) and (19)–(23), the coupling symbols denote their numerical coefficients in these fixed SI units, and gamma denotes the numerical coefficient of that realization. This explicit numerical convention permits comparison with the dimensionless expression in Eq. (19); it does not equate the physical dimensions of the constants or an energy ratio.

\frac{E_{L}}{E_{m}} γ = \frac{G}{ε_{0}}

(2)

Equation (2) is retained as a relation asserted within the historical numerical model. Its role here is to display a common transformation factor. The specified unit convention permits a numerical comparison but does not establish the physical coupling identity or select among competing historical gamma expressions. The normalized energy result is derived separately from the specified mass, photon frequency and action normalization.

2. METHODS

The count-resolved relations are examined within the proposed MQ framework, using classical expressions for gravitational coupling, the speed of light, escape velocity and Heisenberg’s uncertainty principle. The cited MQ applications [4–10] provide internal theoretical source context; citing them does not independently validate the present normalized energy comparison.

The count assumptions, their derivations and proposed physical support are presented in Measurement Quantization [4]. That work contains the referenced appendices and a fuller set of historical source term and keyword definitions. A preprint is also available in Online Resources.

https://www.researchgate.net/publication/361148724_OnlineResources

Two supplementary spreadsheets are identified in the Online Resources. Suppl. 1 concerns calculations for the introductory paper and its referenced appendices; Suppl. 2 concerns this paper and other MQ applications. The present argument is traced through its stated equations and inputs. Availability of those resources does not by itself establish reproducibility of a measurement comparison.

3. RESULTS

We introduce the count notation and realization distinctions needed to interpret the equations in their order of appearance.

3.1. Nomenclature

The fundamental measures introduced in Sec. 1 supply the units for dimensionless counts n_L, n_M and n_T of length, mass and time, respectively; the separations and periods used here have positive counts ([4], Appx. I, J, W). In the radial expressions, n_L specifies the separation count. The count domain is the Internal Frame; observable separations are realized in the System Frame through the Frames mapping. The conventional Planck units provide a comparison, while the MQ fundamental measures retain their stated count normalization.

Within MQ, the Informativity differential describes the proposed count-dependent, non-Lorentz contraction of realized spatial separations associated with normalization of conserved count under the Frames mapping ([4], Appx. D). It is distinct from the metric differential, which characterizes the discrete–continuous representation mismatch and is not itself a physical deformation. These terms describe different aspects of the realization construction. Their definitions do not independently establish a physical contraction effect. The count dependence permits finite-separation expressions to be distinguished from their upper-count limits [10].

We use Q_L for the dimensionless fractional length-count residual in the radial construction, with n_L positive. Equation (30) gives its relation to the separation count. The product Q_Ln_L retains finite-count dependence and tends to one half only in the upper-count limit.

The typography of G distinguishes a finite-count evaluation from the upright upper-count-limit quantity G. The upper-count reduced Planck constant is likewise upright. Equation (3) evaluates gravitational coupling at the electromagnetic demarcation, the fixed interaction count distance used for electromagnetic realization in MQ. Its count is fixed by the dimensionless coefficient introduced below; Eq. (4) takes the upper-count limit ([4], Appx. AB, AE, AN). A fixed-count evaluation and a limit are different mathematical operations.

3.2. Terminology

MQ denotes its dimensionless invariant coefficient by θ_si. Its angular realization Θ_si carries rad, while its momentum realization p_si carries kg m s⁻¹. The realizations inherit the numerical coefficient through their respective realization maps while retaining distinct physical dimensions. This notation distinguishes the physical contexts combined in the historical account [4].

The dimensional factor C_pθ converts the angular realization to the momentum realization and has units kg m s⁻¹ rad⁻¹. It is defined as momentum realization divided by angular realization and is used explicitly in Eqs. (13) and (18). Shwartz and Harris [11] provide the X-ray phase-matching comparison; [12, 13] provide separate Bell-state and Bell-theorem background. These sources do not independently determine the MQ conversion factor.

The coefficient can be calculated through the MQ fine-structure relations ([4], Appx. AD). The historical input used here is 3.26239030392. Shwartz and Harris [11], Table I, calculate signal and idler angles of 3.26239 rad for a 25 keV pump in diamond, using the (111) lattice vector at frequency degeneracy. Their result is a phase-matching calculation. The additional digits in the MQ input are not precision established by that external table.

3.3. Finite-Count Relations in the MQ Internal Frame

Within the finite-count MQ construction, the Informativity differential must be retained when comparing coupling and action expressions ([4], Appx. D). This model-defined effect is distinct from Lorentz contraction. Mixing an upper-count value with a finite-demarcation value without the associated realization relation changes the normalization of the comparison.

Equation (3) evaluates G at the electromagnetic demarcation specified by n_L=276/θ_si. Equation (4) uses Q_Ln_L tending to one half and therefore gives G in terms of the fundamental mass and time. The two expressions distinguish a finite interaction scale from a limiting regime ([4], Appx. AB, AE, AN, M).

G = {2 Q_{L} n_{L} c^{3} \frac{t_{f}}{m_{f}} |}_{n_{L} = 276 / θ_{si}}

(3)

G = \lim_{n_{L} \to \infty} 2 Q_{L} n_{L} c^{3} \frac{t_{f}}{m_{f}} = c^{3} \frac{t_{f}}{m_{f}}

(4)

The historical comparison in [4], Table 2, uses the CODATA 2010 and 2014 adjustments [14, 15] as observational benchmarks. These dated comparison sets are retained for their source context. The 2022 CODATA adjustment [2] is the reference edition for a new quantitative comparison. Equations (3) and (4) specify MQ evaluations and do not themselves establish experimental agreement or identify an apparatus with a frame realization. Such a test requires measurement conditions, correlations and propagated uncertainties. In the redefined SI, Planck’s constant has a fixed exact value [1, 2]. An MQ action realization must be related explicitly to that SI quantity before numerical agreement is asserted. The illustrative angular calculations in Tables 1 and 2 retain their stated historical input and are not presented as new CODATA-based determinations.

We next use the fundamental-measure normalization to compare a mass energy with a photon energy, then examine how the action expressions relate to the angular and momentum realizations.

3.4. Comparing Baryons to Photons

Equation (5) applies the rest-energy relation to a mass count n_M [1], with historical context in [16]. Its second form substitutes the momentum realization through the fundamental relation linking the fundamental length, mass and time measures to the momentum realization ([4], Appx. V). For the comparison that follows, we set n_M=1, so Eq. (6) refers to the energy assigned to one fundamental mass. This comparison does not assert that every baryon has the reference mass.

E_{m} = n_{M} m_{f} c^{2} = n_{M} (\frac{2 p_{si} t_{f}}{l_{f}}) c^{2}

(5)

E_{m} = 2 p_{si} c

(6)

In Eq. (7), n is the dimensionless number of photons at the same frequency. We use one photon, n=1, and set ν=1/t_f. The action normalization is h=4πp_sil_f, obtained from the upper-count reduced Planck identity ([4], Appx. L). Here this is the specified MQ action realization; the standard photon energy law is supported by [1]. Substituting the fundamental length-to-time ratio gives Eq. (8).

E_{L} = n h ν = n (\frac{4 π p_{si} l_{f}}{t_{f}})

(7)

E_{L} = 4 π p_{si} c

(8)

Equations (9) and (10) compare the two energies under the single-photon and single-fundamental-mass assumptions stated above. The momentum realization and speed cancel, leaving the dimensionless factor 2π. The result follows from the selected frequency and upper-count action normalization. It does not imply that the photon number and mass count represent the same physical quantity, or that the ratio is independent of those choices.

\frac{E_{m}}{E_{L}} = \frac{2 p_{si} c}{4 π p_{si} c} = \frac{1}{2 π}

(9)

E_{L} = 2 π E_{m}

(10)

Equation (11) uses the lower-case label E_l for the same fixed-frequency photon energy in Eq. (10). We retain this photon-energy label when its frequency varies in Sec. 3.7. Equation (11) rewrites the comparison using photon frequency and Planck’s constant. The factor 2π is dimensionless. It does not itself have frequency, angle or arc-length units, and the equation does not associate this factor with elapsed time independently of the selected frequency.

E_{m} = \frac{E_{l}}{2 π} = \frac{h v}{2 π} = (\frac{1}{2 π}) h v

(11)

The reduced Planck constant carries action dimensions, which can be expressed as momentum times length. A geometric arc length instead requires a radius and an angular realization. We connect these descriptions through the explicitly defined conversion factor, preserving the distinction between action and geometric length. The following equations test consistency of that conversion within the chosen MQ normalization.

Arc length at fundamental radius and angular realization, with dimensionless, momentum and action comparisons — Fig. 1. Arc length at radius l_f and angular realization Θ_si, in rad. Adapted from [5], Fig. 2.

3.5. Correlating Angular Measure and Momentum

Figure 1 depicts the geometric arc length L_si, in m, at radius l_f and angular realization Θ_si. Equation (12) defines this arc-length realization; Eq. (13) obtains the angle from momentum using the conversion factor introduced in Sec. 3.2. The normalized numerical comparison shown in the figure does not equate the dimensions of arc length and action.

L_{si} = l_{f} Θ_{si}

(12)

Θ_{si} = \frac{p_{si}}{C_{p θ}}

(13)

For the radial reference leg of the count geometry, we write r for the realized radial separation, in m, equal to n_Ll_f. This reference length is distinct from the hypotenuse represented by the separation count plus its residual. Equation (14) uses the momentum realization in the finite-count gravitational coupling relation ([4], Appx. C). Equation (15) instead uses the upper-count coupling and takes the limit explicitly before replacing Q_Ln_L by one half. The two expressions must be interpreted with their stated coupling realization.

\frac{Q_{L} c^{3}}{r p_{si}} = \frac{G}{r^{2}}

(14)

p_{si} = \lim_{n_{L} \to \infty} \frac{Q_{L} n_{L} l_{f} c^{3}}{G} = \frac{l_{f} c^{3}}{2 G}

(15)

Equation (16) substitutes the upper-count coupling from Eq. (4). Equation (17) then relates the momentum realization to the fundamental mass and time and to the upper-count reduced Planck constant ([4], Appx. F, S, V). Every term in these momentum identities has units kg m s⁻¹.

p_{si} = \frac{l_{f}}{2} (\frac{c^{3}}{G}) = \frac{l_{f} m_{f}}{2 t_{f}}

(16)

p_{si} = \frac{l_{f} m_{f}}{2 t_{f}} = \frac{ħ}{2 l_{f}}

(17)

Equation (18) uses the conversion factor defined in Sec. 3.2. It preserves the angle and momentum units but is not an independent prediction of the factor.

p_{si} = C_{p θ} Θ_{si}

(18)

Tables 1 and 2 express the angular mapping through two forms of the same momentum realization ([4], Appx. P, Q, S, W). The pump, signal and idler labels are θ_p, θ_s and θ_i; θ_Max is the historical row label for the main angular branch, not an independently defined maximum or a new invariant. The pump, signal and idler columns specify the three angles on that branch. The angles are in rad. The selected branches resemble those in the theoretical phase-matching table of [11], under the conditions stated in Sec. 3.2. Shwartz et al. [17] measure X-ray down-conversion coincidence rates; Glover et al. [18] measure X-ray and optical sum-frequency generation. Those experiments provide related nonlinear-optics context, not tests of the MQ conversion factor or these table uncertainties.

Table 1. Angular realizations calculated from the reduced-Planck momentum expression. The conversion factor distinguishes angle from momentum. Updated from [4], Table P.1. a

Angle	θ_p	Pump (radians)	θ_s	Signal (radians)	θ_i	Idler (radians)
Offsets	$\frac{ħ}{2 l_{f} C_{p θ}} - π rad$	0.1207976503	$π rad - \frac{ħ}{2 l_{f} C_{p θ}}$	−0.1207976503	$π rad - \frac{ħ}{2 l_{f} C_{p θ}}$	−0.1207976503
θ_Max	$2 π rad - \frac{ħ}{2 l_{f} C_{p θ}}$	3.0207950033	$\frac{ħ}{2 l_{f} C_{p θ}}$	3.2623903039	$\frac{ħ}{2 l_{f} C_{p θ}}$	3.2623903039

a Illustrative central values use the historical coefficient 3.26239030392 and the displayed angular mapping. Decimal places document that calculation and do not indicate independently measured precision. No propagated uncertainty is assigned. Signed offsets follow the displayed algebra; their magnitudes are equal. See [11, 17, 18] for the distinct theoretical and experimental contexts.

Table 2. Angular realizations calculated from the upper-count gravitational momentum expression and the same conversion factor. Updated from [4], Table Q.1. a

Angle	θ_p	Pump (radians)	θ_s	Signal (radians)	θ_i	Idler (radians)
Offsets	$\frac{l_{f} c^{3}}{2 G C_{p θ}} - π rad$	0.1207976503	$π rad - \frac{l_{f} c^{3}}{2 G C_{p θ}}$	−0.1207976503	$π rad - \frac{l_{f} c^{3}}{2 G C_{p θ}}$	−0.1207976503
θ_Max	$2 π rad - \frac{l_{f} c^{3}}{2 G C_{p θ}}$	3.0207950033	$\frac{l_{f} c^{3}}{2 G C_{p θ}}$	3.2623903039	$\frac{l_{f} c^{3}}{2 G C_{p θ}}$	3.2623903039

a Uses the same historical input and conversion factor as Table 1. Agreement follows algebraically from the two forms of the same momentum realization. The central values have the same illustrative precision limits as Table 1; [11, 17, 18] do not supply their uncertainties.

An empirical test of this mapping requires an independently specified conversion factor and measured angles with stated uncertainties. Defining the factor from the proposed angular realization and then recovering that realization establishes internal consistency. Because Tables 1 and 2 use equivalent forms of the same momentum realization and the same input coefficient, their agreement is not an independent determination of that factor or of the invariant coefficient.

3.6. Correlating Gravitation and Electromagnetism

The historical gamma route compares gravitation and electromagnetism using an earlier elementary-charge demarcation construction ([4], Appx. AM, AP, AS, AT). It uses an auxiliary measured electromagnetic constant and is retained as a conditional historical numerical calculation. Its precision relative to the current elementary-charge construction is not established by the present comparison. The current MQ description uses the fundamental realization factor γ_F, derived from MQ fundamental quantities; that factor is distinct from the conventional gamma retained here. Its count formula is dimensionless, but a dimensional realization linking it to physical coupling constants is not specified in this comparison. Equation (19) retains the historical expression in [4], Eq. (AT.5). In that local equation, r_q41 denotes the historical dimensionless count-41 metric ratio, obtained by dividing 41 times the invariant coefficient by the nearest-whole-unit value of that product. All quantities on its right side are dimensionless, and the left side is the numerical gamma coefficient under the convention established before Eq. (2). The factor formed from θ_si and its nearest-whole-unit value retains the historical approximation. The mixed left-floor/right-ceiling brackets denote nearest-whole-unit rounding. This historical formula is used for the present demonstration without assigning it the precision or input independence of the current derivation.

γ = \frac{2 (θ_{si} - 1)^{2}}{(Q_{L} n_{L})^{4} (84 θ_{si} - ⌊ 42 θ_{si} ⌉) r_{q 41}^{2}}

(19)

Equation (20) records the historical coupling relation in the same fixed-unit numerical convention ([4], Appx. AT, Eq. (AT.7)). Its equal sign refers to the quantities within that retained model, rather than exact agreement with every independently measured constant. Equation (21) repeats the normalized energy relation from Eq. (10). Substitution gives Eq. (22), displaying the common gamma factor.

G = 2 π ε_{0} γ

(20)

E_{L} = 2 π E_{m}

(21)

\frac{E_{L}}{E_{m}} γ = \frac{G}{ε_{0}}

(22)

The historical comparison uses one nonzero gamma coefficient throughout, permitting its formal cancellation. Ratios of numerical coupling coefficients depend on the stated units, so Eqs. (19) and (20) remain confined to the fixed-unit convention of Sec. 1. Cancellation does not resolve the historical formula’s normalization or competing source variants. The dimensionless energy comparison is derived independently from the specified mass, frequency and action normalization in Sec. 3.4.

3.7. Reassessing Baryons and Photons

We now vary the photon frequency while keeping the comparison mass fixed at one fundamental mass. The positive dimensionless time count n_T specifies a period of n_Tt_f, so the frequency is ν=1/(n_Tt_f). The case n_T=1 recovers the earlier fundamental-frequency comparison. For this variable-frequency comparison, E_l retains the photon-energy meaning introduced before Eq. (11), while E_L in Eqs. (21)–(23) retains its fixed-frequency meaning.

\frac{E_{L}}{E_{m}} γ = 2 π γ

(23)

\frac{E_{l}}{E_{m}} = \frac{2 π}{n_{T}}

(24)

For a common nonzero gamma coefficient, cancellation in Eq. (23) recovers the fixed-frequency energy relation. Equation (24) then follows by changing the photon period while keeping one photon and one fundamental mass fixed, as specified above. It can also be derived directly from the single-photon energy and the fixed fundamental-mass energy, without using the historical coupling relation. The unresolved gamma normalization and source variants therefore do not determine this energy ratio, but they remain relevant to any claimed relation between the physical coupling constants. We next return to the upper-count action normalization. Equation (25) equates two expressions for momentum, and Eq. (26) follows by multiplying the reduced-Planck identity by 2π ([4], Appx. L, S, V).

\frac{l_{f} m_{f}}{2 t_{f}} = \frac{ħ}{2 l_{f}}

(25)

h = (\frac{2 π}{t_{f}}) (l_{f}^{2} m_{f})

(26)

Equation (26) contains a factor with reciprocal-time dimensions, while

l_{f}^{2} m_{f}

supplies mass times squared length. Their product has action dimensions. The equivalent form in Eq. (27) expresses action through momentum times length, then uses the conversion factor to relate it to the arc-length realization ([4], Appx. R). The dimensionless factor 2π is distinct from the arc length itself.

h = 4 π l_{f} p_{si} = 4 π C_{p θ} L_{si}

(27)

ħ = 2 C_{p θ} L_{si}

(28)

Equation (28) preserves this conversion for the upper-count reduced Planck constant. At the reference radius l_f, the geometry in Fig. 1 describes an assigned angular realization. It does not determine a photon’s physical size, rest mass or beam momentum. Equation (29) gives another action identity by replacing the length-to-time ratio with the speed of light.

h = 2 π l_{f} m_{f} \frac{l_{f}}{t_{f}} = (2 π l_{f} m_{f}) c

(29)

The result is conditional on the stated MQ count and upper-count action normalization. Its energy ratio varies with the selected photon frequency and comparison mass. The angle, momentum and action relations preserve their dimensional conversions. The metric differential supplies the MQ representation context ([4], Appx. T). The required relation between the MQ action realization and the fixed SI Planck constant remains to be established before these identities can support a quantitative comparison with measured photon energies. These identities alone do not establish an experimentally verified physical distinction between arbitrary baryonic and electromagnetic phenomena.

4. DISCUSSION

In MQ, referenceable measure means relational measure admitted by a consistent Frames mapping. A bound on such measure must be distinguished from the values assigned to different physical quantities. A length not resolved as a fundamental count does not by itself determine the measurability of mass, elapsed time or momentum. Those quantities retain their own units and measurement conditions. The present normalized comparison therefore does not establish a universal particle size or an uncertainty relation from its energy ratio alone.

The radial construction describes a dimensionless fractional length-count residual Q_L. Its relation to the positive separation count is given in Eq. (30). The associated gravitational expression also requires the fundamental measures and the coupling relation; the residual alone is not a force.

Equation (30) rewrites the positive-count radial residual identity ([4], Appx. D, Eq. (D.5)). The related gravitational construction is given in [4], Appx. C. The expression alone does not derive attraction, repulsion or a common law for all four interactions.

\frac{Q_{L}}{n_{L}} = \frac{\sqrt{1 + n_{L}^{2}}}{n_{L}} - 1

(30)

The question of whether two phenomena can occupy the same space is not resolved by the radial residual identity. Addressing it requires additional physical structure beyond the normalized energy and realization relations developed here.

5. TERMS AND SYMBOL DEFINITIONS

Measurement Quantization [4] supplies the historical source terminology for these derivations. This section indexes notation introduced in the main text and retains supplementary source notation without repeating its first-use definitions.

θ_si, Θ_si, p_si and C_pθ are introduced in Sec. 3.2. The historical angular comparison [11, 17, 18] is discussed with Tables 1 and 2. Chen et al. [19], Secs. 4.2–4.3, discuss conserved quantities and supertranslation invariance at null infinity. This is separate relativistic context and supplies no replacement for the dimensional conversion used here.

c is introduced in Sec. 1 as the speed of light. The equal-count case of the fundamental length-to-time relation supplies the normalization used here; its defined SI value is 299,792,458 m s⁻¹ [1].

G and G are introduced in Secs. 1 and 3.1. Equations (3) and (4) distinguish the electromagnetic-demarcation evaluation from the upper-count limit.

l_f, m_f and t_f are introduced in Sec. 1. They supply the units in the count relations, momentum identities and action expressions.

l_p, m_p and t_p denote the conventional Planck units of length, mass and time, in m, kg and s, in the source comparisons.

n_L, n_M and n_T are introduced in Sec. 3.1. The photon number n is introduced before Eq. (7). The period count n_T is used explicitly in Sec. 3.7.

The radial separation count n_L is used in Eqs. (3), (4), (14), (15) and (30).

The center-of-mass reference specifies the local meaning of radial separation; it does not require a second length-count subscript.

n_Lc denotes the dimensionless count of fundamental lengths associated with a change in the position of light relative to the observer in the source nomenclature.

n_θ denotes the dimensionless System Frame count of the invariant coefficient, resolved from the Internal Frame demarcation and adjusted for the metric differential. The historical count example is

⌊ \frac{84.60055}{2} ⌉ = 42

. It uses the nearest-whole-unit mixed bracket convention introduced in Sec. 3.6 and is not a half-unit tie.

Ordinary paired floor brackets denote floor, and ordinary paired ceiling brackets denote ceiling. The mixed left-floor/right-ceiling pair has the declared MQ nearest-whole-unit meaning.

Q_L is introduced in Sec. 3.1, and Eq. (30) supplies its positive-count identity.

The count-dependent normalization associated with the Informativity differential is explained in Sec. 3.1. The upper-count limit is explicit in Eqs. (4) and (15).

h and ℏ are introduced in Sec. 1. Equations (25)–(29) use the upper-count action normalization.

m_e denotes electron mass, in kg, in the source derivations.

a₀ denotes the Bohr radius, in m, in the source derivations.

α_{f}^{- 1}

α_{p}^{- 1}

and

α_{c}^{- 1}

denote the dimensionless fundamental, Planck-like and classical inverse fine-structure forms in the current MQ source nomenclature. The fundamental form is defined in the Internal Frame, and the Planck-like and classical forms in the System Frame. The classical form also accounts for the Informativity differential [4]. These forms are distinct from the momentum realization.

γ and the numerical convention used for its historical coupling comparison are introduced before Eq. (2). Section 3.6 distinguishes that earlier approximation from the current elementary-charge construction and its fundamental factor γ_F. The cancellation and period dependence are explained in Sec. 3.7.

STATEMENTS AND DECLARATIONS

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.

DATA AVAILABILITY

Supplementary calculation resources are identified in Sec. 2 and the Online Resources link. The equation identities and historical central input used for Tables 1 and 2 are specified in this manuscript.

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