Physically Significant Approach to Describing Broken Symmetry

Jody A. Geiger

Informativity Institute

Chicago, IL USA 60605

jodygeiger@informativity.org

ORCID: 0000-0001-5389-0447

ABSTRACT

We examine quantization ratios, which compare a dimensionless coefficient-count product with its nearest-whole-unit resolution, and their relation to realized quantities in Measurement Quantization (MQ). The Internal Frame is the discrete configuration domain. The System Frame is its continuous relational encoding through the Frames mapping, in which physical observables are defined. We use repeating quantization ratios to describe finite count patterns and work through a charge calculation. The configuration relations are dimensionless; the Planck form and laboratory (classical) form have distinct realization roles. Using inputs from the 2022 adjustment of the Committee on Data of the International Science Council (CODATA), the explicit one-count-offset calculation gives a laboratory-form charge that differs from the defined value in the International System of Units (SI) by 3.74025(11) parts per million. A gamma calculation is considered separately with its shared inputs identified. These calculations illustrate the proposed mapping without establishing a unique electromagnetic demarcation (the electromagnetic interaction count scale) or independent experimental agreement. The finite ratio patterns establish an arithmetic result; a physical mechanism for symmetry breaking remains to be demonstrated.

Keywords: Symmetry, Measure, Broken Symmetry, Discrete Phenomena

1. INTRODUCTION

The physical significance of symmetry in nature has long been a subject of debate. Of equal interest is why some patterns terminate or break. MQ writes physical descriptions using dimensionless counts n_L, n_M and n_T of fundamental length l_f, mass m_f and time t_f, whose realized units are m, kg and s. Here n_L denotes radial separation in units of fundamental length. These quantities allow us to distinguish count relations in the configuration domain from their realized physical descriptions.

The countability arguments and proposed physical support are presented in Measurement Quantization ([1], Appx. K, I, J). In the terminology defined in the abstract, discrete configurations belong to the Internal Frame and observables to the System Frame. The quantization ratio introduced in the abstract is evaluated through the continuous numerical realization and its integer resolution. MQ uses such mappings in calculations of physical constants [2]. This paper examines their finite repetition and the consequences for a charge calculation; the mapping assumptions remain distinct from the evidence for a physical realization.

To demonstrate the mathematical procedure, we compare a continuous numerical realization with its integer resolution ([1], Appx. AC). The invariant dimensionless coefficient is θ_si, and n_θ is its dimensionless count. Their quantization ratio is r_q. In Eq. (1), mixed left-floor/right-ceiling brackets mean rounding a dimensionless argument to the nearest whole unit. They denote the MQ nearest-whole-unit convention, rather than either standard floor or ceiling alone.

Equation (1) organizes the numerical count relation used in the following examples. Through the Frames mapping, count relations are associated with realized quantities in the System Frame. Their relations to the fine structure constant ([1], Appx. AA) and the Bohr-radius length scale used in the ground-state orbital relation ([1], Appx. BL) motivate the patterns examined below. A repeated numerical ratio is a configuration property; interpreting it as a physical relation requires the relevant realization.

For the current calibration, θ_si=3.26239030504(25). The count series 11, 22, 33 and 44 has the same quantization ratio and stops repeating at the next multiple. Likewise, 15, 30, 45, 60, 75, 90 and 105 is a seven-instance series. The series beginning with 42 contains 24 matching instances. These termination counts remain unchanged when the propagated coefficient uncertainty is varied by six standard uncertainties. We use the 42 series in the charge example and investigate what its finite repetition establishes.

2. METHODS

This paper applies the MQ count representation to classical expressions used in discussions of gravitational curvature, the speed of light, escape velocity and Heisenberg’s uncertainty principle [1]. The publications [1–7] develop applications of this approach. We use those works as sources for the proposed framework, rather than treating their publication or numerical correspondence as independent validation of the present charge realization.

The discreteness and countability arguments in Measurement Quantization [1] supply the theoretical background for this presentation. That paper proposes physical interpretations and comparisons with measurement data. The present calculation adopts its count and realization assumptions; it does not independently establish physical discreteness or measure a minimum length. The cited appendices and definitions are included in [1], and a preprint is listed in Online Resources.

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

The Online Resources listing describes two spreadsheets. Supplement 1 collects calculations for the introductory paper and its appendices. Supplement 2 collects calculations for this paper and other MQ applications. These resources facilitate numerical evaluation; their availability is not empirical evidence for the realization assumptions. The calculations reported here are specified by the stated equations, 2022 inputs and propagation conditions.

3. RESULTS

Here “broken symmetry” denotes termination of an equal-ratio count pattern under nearest-whole-unit resolution. No symmetry transformation of a physical action, physical state or dynamical transition is established by this arithmetic example. Its proposed physical significance depends on a further realization argument. Quantization ratios describe the discrete–continuous mismatch between the Internal Frame count configuration and its System Frame encoding ([1], Appx. AC). The metric differential names this representation-level mismatch, rather than a physical deformation ([1], Appx. T). In MQ, the Informativity differential denotes non-Lorentz length contraction associated with normalization of conserved count under the Frames mapping, and is distinct from curvature ([1], Appx. D).

The coefficient has distinct angular and momentum realizations ([1], Appx. A, Q, S). We denote the momentum realization by p_si in kg m s⁻¹ and the angular realization by Θ_si in rad. Their numerical coefficients are inherited through their respective realization operators; their dimensions remain different. Equations (1)–(2) use the dimensionless coefficient. Equation (3) uses its momentum realization.

We use “fundamental,” “Planck form” and “classical form” to distinguish stages of the calculation ([1], Appx. AM). A dimensionless configuration expression first supplies a numerical relation. The specified realization assigns the Planck form its physical units. The Informativity differential then maps that form to the laboratory form. This sequence does not identify a dimensionless configuration expression itself with a measured physical quantity.

Quantization ratios enter the charge construction ([1], Appx. AM). For the repetition examples, use n_θ=42 and apply Eq. (2) to successive counts 42, 84, 126 and so on. The first 24 instances give the same ratio; the next instance does not. Equality of these ratios is tested through equality of their integer denominators under scaling. It is not established by a tolerance chosen to conceal small differences.

The 42 series also defines the fundamental inverse fine structure quantity α_f^-1=42θ_si ([1], Appx. AA). Its Planck and classical forms are α_p^-1 and α_c^-1, respectively. The last is the 2022 CODATA inverse fine structure input [8], used in the coefficient calibration. Their distinct numerical values must not be conflated. The relation motivates the calculation that follows, rather than proving that every physical phenomenon belongs to this series.

1. Calculations

We begin with count relations associated with a measured phenomenon and specify the realization used to compare their numerical values. With the metric differential introduced above, the calculation keeps the dimensionless coefficient separate from the momentum realization and the reduced Planck quantities that carry units. The mapping mismatch itself supplies neither a unit conversion nor an additional physical deformation.

We retain three demarcation constructions. Equation (3) is the blackbody construction ([1], Appx. AB), with finite-count ℏ in J s. For comparison, upright ħ denotes the upper-count quantity. The speed of light is c=299792458 m s^-1, an exact input [8]. The fundamental measures and coefficient are calculated from the 2022 fine structure input using the MQ orbital and count relations ([1], Appx. AA, BL). Parenthetical uncertainties in Eqs. (4)–(14) are input-propagated standard uncertainties in the last reported digits. This calibration yields coincident numerical counts for the three constructions; it does not demonstrate that their physical demarcations must be identical. We use the precise configuration condition in Eq. (7) for the subsequent calculation. The residual Q_L is dimensionless, with the product in Eq. (6) derived from Eq. (24); the normalization factor used here for the Informativity differential is 2Q_Ln_L ([1], Appx. D).

The second construction uses charge coupling and the dimensionless fine structure relation. Equation (7) imposes the configuration condition that the product of the radial count and coefficient is 276. Table 1 shows the nearby integer products and corresponding coefficient-count ratios. The table compares candidate count configurations; it does not establish a uniqueness theorem for physical demarcations.

Table 1. Quantization ratios for nearby configuration products. Recalculated from the relations in [1] using 2022 inputs.

For the calculation developed here, we select the product 276 as the configuration condition in Eq. (7). Equation (8) resolves its radial count; Eqs. (9)–(10) give the corresponding length and residual-count product. The neighboring table entries are retained to show how integer resolution changes the quantization ratio.

The third construction in Eq. (11) uses elementary charge ([1], Eq. AN.7). Here e is the exact SI input charge, 1.602176634 × 10⁻¹⁹ C [8]. We reserve e_c for the calculated laboratory-form approximation introduced before Eq. (25). The SI gamma relation is γ=2k_eG, where k_e is the Coulomb constant in N m² C⁻² and upright G is the upper-count gravitational coupling in m³ kg⁻¹ s⁻². Gamma has units m⁶ s⁻⁴ C⁻² in this realization. Gamma and the fundamental measures use the same 2022 calibration with shared dependencies retained. Reusing the exact charge input prevents its closure from serving as an independent charge prediction. Equations (12)–(14) report this construction separately from the first two.

The three constructions have the same numerical result under the stated calibration. This conditional equality supplies no evidence that all electromagnetic demarcations are uniquely one physical value. For the remaining example, we adopt the precise configuration relation in Eq. (7). Equation (15) resolves the corresponding nearest-whole-unit coefficient count. Its recalculated argument remains well within the rounding interval for 42.

For this count, the fundamental inverse fine structure quantity is α_f^-1=42θ_si ([1], Appx. AA). It is distinct from the calibrated classical inverse fine structure input. The relation supplies the count used in the one-count-offset example below.

We now work through the charge construction ([1], Appx. AM). In Eqs. (16)–(22), all quantities denote dimensionless configuration-domain representatives, including those whose symbols also identify realized measures elsewhere. The variables b and d describe the two configuration quantities, with nonzero d. Equation (16) is an imposed relationship, not an identity for arbitrary values. This dimensionless role permits the difference and ratio to be compared. Physical charge units are assigned at the Planck-form realization in Eq. (23).

At the stated configuration bound ([1], Appx. S), e_f denotes the dimensionless fundamental charge representative and f(m_f) the configuration function of the mass representative. The latter is m_f² in the charge construction ([1], Eq. AM.2). The upper-count action representative has half-value θ_sil_f ([1], Appx. S). The X-ray papers [9–11] motivate comparisons in the original source, but supply no measured charge normalization for this calculation. Equation (17) uses the first power of the coefficient in its denominator.

Take d=θ_si and b=e_fm_f²/l_f in the dimensionless relation (16). Substitution gives Eq. (18). Multiplication by θ_sil_f gives Eq. (19), and solving for the fundamental representative gives Eq. (20). Using the configuration fundamental-measure relations reduces it to Eq. (21). These are algebraic configuration relations, rather than a dimensional derivation of charge units.

Next, Eq. (22) evaluates the explicit one-count offset from 42 to 41. Its dimensionless ratio is r_q41. Equation (23) gives e_p, the Planck form in C, obtained by the specified realization of the configured numerical result and its ratio. The physical unit assignment at this stage is part of the realization prescription; it does not follow by attaching SI dimensions to the configuration-domain subtraction in Eq. (18). The refined-offset alternative is excluded; this manuscript retains only the explicit 42-to-41 approximation.

Finally, Eq. (24) evaluates the residual-count product at the selected Eq. (7) demarcation. In Eqs. (25)–(28), e_p is the Planck-form charge in C, e_c is the calculated laboratory-form approximation in C, and Δ_(P-C) is their difference in C. The exact SI comparison input remains e. Equation (26) subtracts the difference, Eq. (27) gives the equivalent multiplicative form, and Eq. (28) reports the approximation.

Table 2 evaluates the SI gamma charge expression through vacuum permittivity ɛ₀ in F m⁻¹, vacuum permeability μ₀ in N A⁻², and the Coulomb constant k_e in N m² C⁻². The conventional Greek μ₀ is the magnetic constant denoted by u₀ in the MQ knowledge base (MQKB) registry; it is the same quantity. These algebraically related routes use the same exact input e in their 2022 source relations [8]. Reference [12] is retained as a historical resource. The table records the charge returned by each route, not the permittivity or permeability value. The explicit offset approximation is evaluated separately in Eq. (28).

Table 2. Charge closure through the three SI gamma routes under the common 2022 calibration. Charge entries are in units of 10⁻¹⁹ C.^a

^a The exact SI charge e is an input to this inversion [8]. All charge entries reproduce that input under the common calibration; their repetition does not represent independent measurements or zero model uncertainty.

The direct offset calculation in Eq. (28) gives 1.60217064146(18) × 10⁻¹⁹ C, a relative difference of −3.74025(11) parts per million from the defined SI charge. The uncertainty propagates the 2022 calibration input through the stated approximation; it excludes model discrepancy and uncertainty in the unit-realization prescription. The result does not support the earlier ten-digit agreement claim. An independent test would require a specified observable and comparison data not reused in its calibration.

We return to finite repetition of quantization ratios. Table 3 extends the search over initial coefficient counts and records the last matching multiple. The initial count labels a configuration series. The series beginning at 42 is the one selected in this paper; its association with realized quantities uses the specified MQ relations rather than identifying every table row with an independently established universe.

Table 3. Finite repetition of quantization ratios for coefficient counts. Recalculated using the 2022 coefficient.

Each row, for example 31, 62 and 93, describes a finite series with a different initial coefficient count. The ground-state orbital relation supplies the proposed atomic context ([1], Appx. BL). Table 3 provides no stability analysis of these alternatives and no observational evidence for a multiverse.

The 42 series terminates at 1008, its 24th instance. At the next multiple, 1050, the nearest-whole-unit denominator no longer scales by the same integer factor, and the quantization ratio changes. The termination follows from the rounding cells of the recalculated coefficient. Different initial counts have different repeat counts in Table 3. The verified result is finite repetition under the stated coefficient and nearest-whole-unit rule.

4. DISCUSSION

Quantization ratios provide a way to compare continuous numerical realizations with their integer resolutions. The 42 series used in this calculation contains 24 matching instances. Its fundamental inverse fine structure relation motivates the selected configuration condition and charge example, but does not demonstrate that all known phenomena must belong to the series. Other rows offer alternative count configurations. Their interpretation as stable physical realizations remains a separate question requiring further investigation.

The established result is finite repetition of the numerical ratios under the specified coefficient and rounding rule. Connecting that termination to physical symmetry breaking requires a defined physical symmetry, a realization of the relevant states and a test of the predicted change. The present charge example supplies configuration algebra followed by a prescribed unit realization and the Informativity differential. Its 2022 recalculation leaves a quantified charge discrepancy; the SI gamma closure provides an internal check. Neither result independently validates a physical symmetry-breaking mechanism.

5. APPENDICES

APPENDIX A: TERMS

The definitions below refer to first-use explanations in the text and supply the remaining notation needed for the original source context. The fuller MQ term and keyword definitions are given in Measurement Quantization [1]. Configuration representatives in Eqs. (16)–(22) are dimensionless; the corresponding physical units apply only in the stated realizations.

The coefficient and its momentum and angular realizations are distinguished in Sec. 3. The calibrated coefficient is θ_si=3.26239030504(25). Reference [9], Table I, lists 3.26239 rad among calculated signal and idler angles for maximally entangled states at the degenerate frequency, within its diamond phase-matching model. It is not a precision measurement of this coefficient or of its momentum realization. Reference [10] tests X-ray down-conversion coincidence rates with a loss-inclusive Langevin description; [11] observes X-ray and optical sum-frequency generation in diamond. These results do not determine the unit assignment in Eq. (23). Reference [13], Secs. 4.3–4.4, concerns angular momentum and conserved quantities at null infinity in general relativity, a separate physical setting.

The speed of light and its exact source value are introduced before Eq. (3). The fundamental-measure relation used here is c=l_f/t_f. The dimensionless representatives of these quantities used in Eqs. (17)–(21) have the separate configuration role stated there.

The standard Planck units l_p, m_p and t_p denote Planck length, mass and time, respectively. They are distinct from the fundamental measures used in this calculation.

The count symbols introduced in Sec. 1 retain their meanings. The radial count used in the reviewed equations is n_L; the obsolete radial subscript is not a separate quantity.

The radial count in this manuscript denotes separation from the stated reference configuration. A motion count and a radial count require distinct interpretation and should not be identified solely because both count fundamental lengths.

Equations (7)–(10) specify the selected radial count through the configuration product 276. Its first-use definition is retained in Sec. 1.

The additional symbol n_Lc denotes a dimensionless count of fundamental length associated with a light-travel interval in the original source context.

The coefficient count and its nearest-whole-unit resolution are introduced before Eq. (1) and evaluated in Eq. (15). Equation (22) applies the stated one-count offset locally.

The mixed brackets used throughout this manuscript have the nearest-whole-unit meaning introduced before Eq. (1). No standard floor-only operation is intended.

The residual is introduced before Eq. (6) and its exact positive-count expression is given in Eq. (24). Its product with the radial count lies below one half at positive finite count.

The Informativity differential supplies the normalization used in Eqs. (25)–(27). Equation (25) expresses the departure from unity, while Eq. (27) applies the normalization factor to the Planck-form charge.

The symbol m_e denotes electron mass in the orbital calibration relation ([1], Appx. BL). Its product with the Bohr radius is eliminated through the CODATA orbital identity before uncertainty propagation.

The symbol a₀ denotes the Bohr-radius scale used in that orbital relation ([1], Appx. BL). It is not independently combined with a correlated electron-mass input in this calculation.

The three inverse fine structure forms introduced in Sec. 3 retain their fundamental, Planck and classical roles. Their numerical calibration uses the 2022 classical input and its uncertainty, not three independent determinations.

Gamma and its dimensions for the SI charge construction are introduced before Eq. (11). Table 2 uses three correlated source representations of that same relation. It does not introduce three independent gamma measurements.

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

The manuscript identifies electronic supplementary material in the Online Resources listing. Those supplements and the International Bureau of Weights and Measures (BIPM) statement [12] are retained as historical resources. All calculations reported here use the verified 2022 CODATA publication [8] and the stated MQ relations. The historical spreadsheets are not an independent experimental dataset.

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