Increasing Universal Mass

Jody A. Geiger

Informativity Institute

Chicago, IL USA 60605

jodygeiger@informativity.org

ORCID: 0000-0001-5389-0447

ABSTRACT

We present a Measurement Quantization (MQ) calculation in which the realized total mass of the universe increases at a constant rate of 7.0088794874(27) × 10³⁶ kg s⁻¹. The Internal Frame is the discrete count configuration domain. The System Frame is its non-discrete relational realization through the Frames mapping. Within this framework, fixed dimensionless domain fractions are related to mass allocations that grow with elapsed universe age. Within MQ, the quantum epoch denotes the proposed count regime before a valid System Frame realization. A separate application assigns a mass equivalent to the cosmic microwave background (CMB) using an explicitly normalized quantum-epoch construction and geometric mapping. With the adopted Planck age, the resulting temperature is 2.7246(36) K, compatible within the quoted uncertainties with Fixsen’s 2009 value, 2.72548 ± 0.00057 K [1]. This comparison is a conditional consistency check; it does not independently establish the absolute epoch normalization or the mapping.

Keywords: Universal Mass, Increasing Mass, Mass of the Universe, Observable Mass

1. INTRODUCTION

We begin with the discreteness and countability of measure used in MQ ([2], Appx. I, J). The frame distinction introduced in the abstract allows a count configuration and its continuous relational realization to be described separately ([2], Appx. K, historical notation). The physical-constant relations developed within this framework [3] provide the calibration used for the mass calculation below.

The geometric construction classifies observational referenceability within the specified expanding geometry. The visible domain is presently referenceable; the unobserved domain becomes referenceable later, and together they form the observable domain. The complementary dark domain remains permanently non-referenceable within this geometry ([2], Appx. BB). These descriptions concern MQ referenceability domains; their associated fractions are introduced below.

Let R_U be the realized radial distance of the universe in metres and A_U its age in seconds, with A_U=n_Tut_f, where n_Tu is the realized age count and t_f is the fundamental time in seconds. The dimensionless invariant coefficient is θ_si. Its momentum realization is p_si, in kg m s⁻¹; the adopted International System of Units (SI) realization convention is p_si/( 1 kg m s⁻¹)=θ_si. The fundamental length l_f is in metres and the fundamental mass measure m_f is in kilograms. The age–radius relation is A_U=(R_U)/(θ_sic) ([2], Appx. AZ), where c is the exact speed of light, 299,792,458 m s⁻¹. With (m_f)/(t_f)=(c³)/(G), where G is the upper-count MQ gravitational coupling, evaluated in the large-separation normalization limit, in m³ kg⁻¹ s⁻² ([2], Appx. F), the fundamental-domain mass M_f, in kilograms, is

Equation (1) assigns a fundamental-domain mass to the elapsed universe age. This universe-scale allocation is distinct from the fundamental mass measure introduced above. Its dimensionless fraction Ω_f, the geometric normalization pivot, is fixed by the geometric relation in Eq. (2) ([2], Appx. BB). Thus a constant fraction can accompany a mass that increases with age.

Mass accretion here denotes the increase in realized global mass-equivalent content after System Frame realization. The domain fractions specify relative allocations, while an absolute mass also requires an elapsed age. Combining the geometric fractions with the realized mass and time count relations gives the total mass-accretion rate M_acr, in kg s⁻¹, stated in Eq. (3) and derived in Eqs. (18)–(23).

The expansionary epoch denotes the realized regime after a valid System Frame becomes available. The CMB application in Section 3, subsection 4 uses the mapped expansionary-epoch extent to assign a present-day mass equivalent and obtain the temperature T_CMB=2.7246(36) K. The comparison with observations and its limitations are stated after Eq. (29). We develop the count-based mass relation first, then identify the additional temporal normalization, geometric mapping and adopted-age premises.

2. METHODS

This paper combines classical relations with the MQ premise of discrete, countable reference measures. The speed of light, escape velocity and Heisenberg’s uncertainty principle [4] motivate the construction; the uncertainty principle alone does not establish discrete length or time. Related MQ applications appear in Refs. [5–9]. Here we derive the global mass-accretion rate within those premises and evaluate the conditional CMB calculation.

The discreteness and countability used here are framework premises. Measurement Quantization [10] develops the associated derivations and comparisons with measurement data; those comparisons do not by themselves establish a unique physical interpretation. The published appendices are in Measurement quantization [2]; supporting resources are available through Online Resources.

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

Two spreadsheets are also available. Suppl. 1 contains calculations of the expressions in the introductory paper and its referenced appendices. Suppl. 2 contains calculations for this paper and 49 other papers implementing the MQ approach. The current numerical values reported here are evaluated from the fixed 2022 source inputs rather than imported from historical spreadsheet outputs.

3. RESULTS

The dimensionless coefficient introduced above is calibrated from the inverse fine-structure input 137.035999177(21) in the 2022 recommended values of the Committee on Data for Science and Technology (CODATA) [11]. Inverting the MQ calibration gives 3.26239030504(25); its adopted momentum realization is 3.26239030504(25) kg m s⁻¹ ([2], Appx. AD). These are MQ calculations conditional on the stated relations and SI realization convention. Parenthetical digits give one standard uncertainty in the final displayed digits and include propagated source uncertainty; model uncertainty is unquantified. Shared calibration dependencies are retained. Other representations are discussed in [2], Appx. A, C, P, Q, AZ. Chen et al. [12] discuss mass and angular momentum at null infinity in general relativity; that work does not supply the MQ calibration or an angle-to-momentum conversion.

The MQ notation uses the dimensionless counts n_L, n_M, and n_T for length, mass, and time configurations relative to the fundamental measures already introduced ([2], Sec. 3 and Appx. W). These generic counts are distinguished from the realized universe-age and total-mass counts used below.

The count relations and their System Frame realizations must be used consistently through the Frames mapping ([2], Appx. K, historical notation). In particular, equality of numerical coefficients does not make their physical units interchangeable. This distinction is retained when the physical-constant relations [3] are used in the mass and expansion formulas.

We now develop the mass relation within the stated geometric construction, beginning with the MQ classification of observation.

1. Observational Domains

We begin with the count-scaled fundamental relation linking the fundamental length, mass and time measures through the momentum realization ([2], Appx. V). Its SI form uses the momentum realization, while its geometric coefficient remains dimensionless. Planck’s natural-unit construction [13] supplies historical context, not a direct measurement of the MQ momentum or a reason to omit its units.

Equation (4) requires the count constraint n_Ln_M=n_T; its three counts cannot vary independently. This local identity does not replace the global diameter and total-mass count relations. The diameter D_U, in metres, follows Eq. (5) ([2], Appx. AZ). The dimensionless observable and visible fractions Ω_obs and Ω_vis satisfy Eq. (6) ([2], Appx. BB).

The remaining dimensionless fractions are the unobserved fraction Ω_uobs and the dark fraction Ω_dk. The visible and unobserved portions together form the observable domain, while the dark domain is its complement. Equations (7)–(10) express these geometric fractions in terms of the same calibrated coefficient.

For comparison, the cosmological-constant and cold-dark-matter (ΛCDM) model describes energy components through dimensionless density parameters [14]. The MQ referenceability fractions describe a different geometric classification. The visible and unobserved entries partition the observable domain, the observable and dark entries are complementary, and the fundamental fraction is a separate normalization pivot. The five MQ entries therefore must not be summed as independent components or identified one-to-one with the ΛCDM components. The related MQ account of early-universe history [9] and the inflationary account [15] provide context; numerical proximity of the fractions alone does not establish equivalence between those accounts.

2. Definitions

The dimensionless total domain fraction Ω_tot is normalized to unity. Equations (11)–(13) state the complementary dark–observable partition and the subdivision of the observable domain. Equation (13) repeats Eq. (10) to make this normalization explicit.

Substituting the previously defined age count into Eq. (1) gives the equivalent form in Eq. (14). Its fraction Ω_f is the ratio of the fundamental-domain allocation M_f to the total mass, not an additional disjoint component ([2], Appx. BB and BE).

Table 1 places the MQ fractions beside historical comparison entries reproduced in Measurement quantization [2], Table BB.1 and Table BO.1. Those entries are retained as quotations, not newly derived Planck component constraints. The MQ mass column additionally uses the adopted age and the rate in Eq. (3); it is not determined by the fractions alone. The comparison does not fit independent MQ mass measurements or establish physical identity between the two classifications.

Table 1. Historical comparison entries, MQ domain fractions and age-conditioned mass allocations.

^a Comparison percentages and quoted limits are historical entries in Ref. [2], attributed there to Planck TT,TE,EE+lowE. TT and EE are the temperature and E-mode polarization auto-spectra, TE is their cross-spectrum, and lowE denotes the low-multipole E-mode polarization likelihood [14]. The cold-dark-matter and baryonic component limits have not been independently reproduced from the Planck posterior; no agreement statistic is inferred from them. MQ masses adopt A_U=13.800(24) Gyr from Planck [14] and the rate in Eq. (3). Gyr denotes a billion Julian years. Its symmetric 68% age interval is treated as a standard-uncertainty approximation. Each mass is its domain fraction multiplied by rate and age. Parentheses denote one standard uncertainty in the last digits. Shared dependencies are retained; bounding unknown cross-source covariance leaves the displayed uncertainty digits unchanged. These are conditional MQ allocations.

Let M_tot be the total realized mass and M_obs its observable-domain mass, both in kilograms. The geometric fractions acquire their dimensional mass interpretation through (M_f)/(M_tot)=Ω_f, (M_obs)/(M_tot)=Ω_obs. Multiplying all associated masses by the same elapsed-age factor preserves their fractions. Converting the fundamental-domain allocation to total mass then gives Eq. (15).

The bracket in Eq. (15) contains a dimensionless fraction. Combining Eqs. (2) and (8) gives the first dark-fraction expression in Eq. (16), while complementarity in Eq. (12) gives Eq. (17). These are two expressions for the same normalized quantity.

Equating the two dark-fraction expressions eliminates the dark fraction and leads to the total-mass reduction below. The complementary-domain relation is also developed in [2], Appx. BC.

3. Calculations

Equation (18) equates the two dimensionless expressions for the dark fraction. Equation (19) repeats the normalized conversion in Eq. (15). Substituting the age-count form M_f=n_Tum_fθ_si and the geometric fraction Ω_f=(2)/(θ_si²) reduces the total mass to Eq. (20) ([2], Appx. BE).

The dimensionless realized total mass count is n_Mu, with M_tot=n_Mum_f. Equation (21) follows from the final expression in Eq. (20). Dividing its mass by the associated elapsed age gives Eq. (22). The count ratio is dimensionless; multiplication by the fundamental mass-to-time ratio supplies the rate units.

Using the momentum realization defined before Eq. (1) converts the count-derived rate to the explicitly dimensional SI form in Eq. (23). This recovers the rate stated in Eq. (3).

For a fixed calibration, the rate in Eq. (23) is constant. Equation (5) makes the radius proportional to age, so the spherical volume grows with the cube of age. The rate per unit volume consequently decreases with the cube of age, whereas total accumulated mass divided by volume decreases with the square of age. This global MQ mass accounting is distinct from later gravitational redistribution into local structures.

4. CMB Consistency Calculation

The separate CMB application uses the same fine-structure calibration and momentum realization ([2], Appx. AD). It assigns a present-day mass equivalent through the proposed quantum-epoch construction, distributes the assigned energy over the present-day volume, and converts that density to a temperature. This identification is an additional physical premise. The calculation requires the normalization, mapping and adopted-age premises below; it does not derive the radiation’s thermal or redshift history or its spectrum.

The quantum epoch is associated with a radius smaller than √3 times the fundamental length ([2], Appx. BF). This construction lacks the external discrete length reference used for realized expansion. Let A_qe denote its assigned SI-equivalent temporal extent and A_ee the mapped expansionary-epoch extent, both in seconds ([2], Appx. BG and BH). Equation (24) adopts a one-second normalization for this System Frame encoding through the Frames mapping. Its base e is Euler’s dimensionless exponential constant. This convention does not assign elapsed time within the quantum epoch or establish an independently derived absolute duration. Its propagated source uncertainty is conditional on the normalization. Years in Eq. (25) are Julian years of 31,557,600 seconds.

At the proposed transition to the expansionary epoch ([2], Appx. BH), Eq. (25) supplies the mapped extent used in Eq. (26) to assign M_CMB, in kilograms, as the present-day CMB mass equivalent in this volume model. The cube-root factor expresses the MQ geometric Frames mapping; it is not established here as a Lorentz transformation between measured inertial clocks. Equation (26) multiplies the rate by that mapped extent, whereas Table 1 uses the present universe age. Both factors depend on the same inverse fine-structure input, so their covariance is retained. The result inherits the normalization and mapping premises. It is not a demonstration that radiation energy remains unchanged during cosmic expansion.

With the present-day volume V_U, in m³, Eq. (27) gives the volume-averaged CMB energy density ρ in J m⁻³. Its denominator is the spherical volume obtained from the radius obtained from the diameter–age relation in Eq. (5), using the age adopted in Table 1. The symbol π is the dimensionless circle constant. Equation (28) supplies the radiation constant a in J m⁻³ K⁻⁴. Here σ is the Stefan–Boltzmann constant in W m⁻² K⁻⁴, k the Boltzmann constant in J K⁻¹ and h the SI Planck constant in J s; their exact SI definitions determine the radiation constant without an additional measured input [11]. The distinct MQ upper-count action is not substituted for SI h. The positive fourth root in Eq. (29) then gives the temperature T_CMB in kelvin. Shared calibration dependencies are retained; bounding the unknown cross-source covariance does not change the reported uncertainty digits.

The result in Eq. (29) is compatible within the quoted uncertainties with Fixsen’s literature-based determination, 2.72548 ± 0.00057 K [1]. Its interpretation remains conditional on the epoch normalization, geometric mapping, assigned present-day mass equivalent and Planck age [14]. That age is inferred using CMB information, and the Planck analysis fixes the monopole temperature. This comparison therefore checks consistency of the stated construction; it does not independently determine the absolute epoch scale or verify the mapping.

4. DISCUSSION

Equations (20)–(23) express increasing total mass as a consequence of the MQ count construction and its fixed calibration. The critical-density interpretation discussed in [2], Sec. 3, p. 18 additionally requires a consistent gravitational coupling and expansion relation. Neither the constant rate alone nor the numerical proximity of the Table 1 fractions establishes that interpretation independently. The question is therefore whether the complete set of realized relations admits independent observational tests.

An empirical test must specify a change in the realized length, mass or time relations and derive its observable consequence. Light-speed comparisons and the atomic ground-state construction in [2], Appx. BL are possible contexts for such tests. The coefficient–momentum distinction and shared calibration dependencies must be retained, and the tested observable must provide information beyond the inputs used to fix the relation.

Equation (5) specifies a constant radial expansion speed within this construction. Connecting that radial relation to a local observational expansion history requires the specified mapping; the coefficient alone does not establish a local acceleration history.

The derived result is a constant global mass-accretion rate within the stated MQ realization, with fixed geometric fractions as the associated masses grow. The present CMB temperature supplies a conditional consistency check. A complete physical cosmology would also need a specified evolution consistent with local energy–momentum accounting, radiation redshift and thermalization. High-redshift molecular-excitation observations constrain the CMB temperature at earlier epochs [16]; Eqs. (24)–(29) do not predict those observations. The present comparison alone does not distinguish competing cosmological histories.

5. APPENDICES

APPENDIX A: TERMS

Extended terms and historical notation are given in Measurement Quantization [10]. The definitions used in this paper retain the frame, unit and realization distinctions stated above.

The coefficient and momentum realization are specified before Eq. (1) and calibrated in Section 3. The angular interpretation in [2], Appx. A is a separate MQ representation. Ref. [17] develops a theory of polarization-entangled X-ray generation; Refs. [18] and [19] concern X-ray down-conversion and X-ray/optical wave mixing. These works do not independently establish the MQ angle-to-momentum identification or the epoch mapping. Their optical angles must retain their experimental meanings.

The speed of light is defined before Eq. (1); its exact SI value is retained in the 2022 adjustment [20,11].

At the upper count limit, the MQ gravitational coupling G calculated from the same calibration is 6.6740779383(10) × 10⁻¹¹ m³ kg⁻¹ s⁻². Its finite electromagnetic-demarcation realization G is 6.6738448317(10) × 10⁻¹¹ m³ kg⁻¹ s⁻². The electromagnetic demarcation is the fixed electromagnetic interaction-count separation. These are distinct MQ realizations and are not the conventional CODATA gravitational recommendation.

The fundamental measures are introduced before Eq. (1); they differ from the conventional Planck units by the specified MQ realization.

l_p, m_p and t_p denote conventional Planck length in metres, mass in kilograms and time in seconds.

The generic count notation is introduced in Section 3; realized universe-age and mass counts are specified separately.

The canonical length-count notation n_L is used for local length configurations; realized global diameter counts belong to their specified mapping.

For a separation referenced to a center of mass, the same canonical length-count notation is used with the local reference stated explicitly.

The dimensionless count n_Lc identifies a change in the realized position of light where that distinction is required.

The metric differential is the representation-level mismatch when discrete count structure is encoded continuously through the Frames mapping; it is not itself a physical deformation. The dimensionless System Frame count n_θ follows the specified metric differential and nearest-whole-unit convention. The calibrated length count is 84.6005456716(65). The mixed brackets denote rounding the dimensionless argument to the nearest whole unit; applying them to half that count gives, for example, ⌊(84.6005456716)/(2)⌉=42.

The argument x in ⌊x⌉ is real and dimensionless.

The dimensionless residual Q_L is the fractional length-count contribution in the specified discrete construction.

In MQ, the Informativity differential describes the non-Lorentz length contraction associated with realizing discrete count structure through the Frames mapping. The product Q_Ln_L enters the Informativity differential in this length-count context.

The SI reduced Planck constant ℏ is 1.054571817646156… × 10⁻³⁴ J s; the distinct upright upper-count MQ action ħ is 1.0545349844417293(56) × 10⁻³⁴ J s. Equation (28) uses the SI Planck constant h rather than the upper-count MQ action.

m_e is the electron mass in kilograms.

a₀ is the Bohr radius in metres, used in the orbital relations supporting the calibration.

The fundamental inverse fine-structure form belongs to the discrete count construction; the Planck-like form is the intermediate continuous representation before finite-count normalization, and the classical form is the finite-count realization comparable with a laboratory determination ([2], Appx. AD). They must not be interchanged solely by changing a frame label.

The historical dimensionless electromagnetic transformation parameter γ is distinct from the geometric epoch mapping in Eq. (25). It is not an additional independent input to the calibration used here.

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 has data included as electronic supplementary material.

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