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• θ_si can be measured as the polarization angle of quantum entangled X-rays at the degenerate frequency of a maximal Bell state. As an angle θ_si=3.26239 rad ± 2 μrad; as a momentum θ_si=3.26239030392(48) kg m s^-1 and with respect to the Target Frame, θ_si has no units. The relation of angle and mass is mathematically demonstrated, as well, by No-Ping Chen, et. al.
• l_f, m_f and t_f are the fundamental measures, more precise expressions for Planck’s units – length, mass, and time – that consider the effects of length contraction associated with discrete measure.

• c is the speed of light which may also be written as c=n_Ll_f/n_Tt_f=299,792,458 m/s such that n_L=n_T=1 is physically significant.
• Q_L is the fractional portion of a count of l_f when engaging in a more precise calculation.
• n_Lr 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.
• Δ_f is the metric differential between frames.
• Q_Ln_Lr, also known as the Informativity differential describes the length contraction associated with discrete measure.
• ɛ₀ is the electric constant
• μ₀ is the magnetic constant
• e_f is the fundamental form of elementary charge, defined with respect to the Target Frame before adjusting for the metric and Informativity differentials.
• e_p is the Planck form of elementary charge, defined with respect to the Measurement Frame, accounts for the metric differential between frames.
• e_c is the classical form of elementary charge, accounts for the metric and Informativity differential.
• ħ is the reduced Planck constant, 1.054571817 10^-34 m² kg s^-1. When accounting for the Informativity differential at the upper count bound, this term is not italicized (i.e., ħ=1.0545349844(45) ^-34 m² kg s^-1).
• α_f^-1 is the fundamental form of the inverse fine structure constant defined with respect to the Target Frame.
• α_p^-1 is the Planck-like form of the inverse fine structure constant defined with respect to the Measurement Frame.
• α_c^-1 is the classical form of the inverse fine structure constant as adopted by the CODATA collaboration. This term accounts for length contraction associated with discrete measure.
• M_b is the bound mass which represents the upper count bound of m_f that can be measured per t_f in a homogenous mass distribution.
• γ is a collection of terms that describe the geometry between the Target and Measurement Frames.

It is difficult to resolve an expression for elementary charge for several reasons. Notably, with respect to the System Frame there is no known expression for charge consisting of only the fundamental measures. With respect to the Reference and Internal frames, there is also no known correlation of elementary charge to the fundamental measures: length, mass and time. For these reasons, developing a physically significant description of elementary charge in a Measurement Quantization (MQ) nomenclature requires an approximation, while at the same time retaining a physically significant instantiation.

We approach the problem with the equality of two expressions – one defined with respect to the non-discrete System Frame of the universe and the other defined with respect to the discrete Internal Frame – to resolve an expression that allows us to correlate the two frames^{(6,Sec. II.D)}. Specifically,

With this we then integrate elementary charge as a function of the fundamental measures, such that we resolve the fundamental expression for e_f with respect to the non-discrete System Frame as a function of b.

We avoid issues with physical insignificance for two reasons. One, we know the difference value (i.e. 1) associated with the discrete System Frame and we know its corresponding non-discrete value associated with the Internal Frame. We also know the expression for momentum θ_si=(1/2)l_fm_f/t_f, indicating that we should divide by two, hence ħ/2. And, where we have previously resolved the mass frequency bound^{(3,Eqs. 81-83)} as would describe a galaxy, we resolve the upper count bound^{(1,Eqs. 27-29)} of m_f with respect to the count of t_f. This is further described in the third paper ^{(3,Appx. 5.3)}.

Thus, we find that f(m_f)=m_f² with respect to θ_si=l_fm_f/2t_f (i.e., the remaining terms). Mapping both to θ_si, then b=m_f²/(ħ/2). Using ħ=2θ_sil_f we reduce. The approach confirms the identification of θ_si as the divisor/difference d. Thus, we remove θ_si from the base b and account for the squared relation of m_f at the bound. And then we present a fundamental expression for elementary charge e_f with respect to the non-discrete System Frame.

The process to present charge in terms of the local frame follows the same adjustments we implement in a derivation of the fine structure constant^{(6,Eq. 75)} or any physically significant measure. First, we apply the metric differential. This is described as a product of the quantization ratio^{(6,Eq. 140)} between the two frames. The frame difference is equal to one relative to the blackbody demarcation^{(6,Apx. C)}. We describe this as n_θ-1 such that n_θ=42.

The Planck equivalent of elementary charge is then.

Next, we account for the Informativity differential^{(6,Sec. II.G)} relative to the blackbody demarcation^{(6,Apx. C)} 84.6005496647(07)l_f. This will allow us to resolve the difference between the Planck-like e_p and classical forms of the elementary charge e_c;

Subtracting the Informativity differential 2Q_Ln_Lr of e_p from e_p (i.e., 1-2Q_Ln_Lr), then

We compare the result with the 2018 CODATA value.

We have presented an expression describing elementary charge using only the fundamental measures^{(5,Sec. III.B)}. Notably, the result differs by one part in the sixth digit. There are two contributors to this variance. First, we have accounted for the Informativity differential^{(6,Sec. II.G)} at the blackbody demarcation. This will effect precision in the eight digit. Second, we use the metric offset as a frame difference to then resolve the fundamental form of e. This would be correct if we had a Planck-like description of e in terms of the fundamental measures. We do not.

The approach taken does not arise from our classical understanding of charge, but instead resolves as a function of discrete offsets between subtractive and divisor relations at the lower count bound. The approach is physically significant, but not well understood. It is also incomplete.

That said, we find charge to be a function of m kg^-2 accompanied by three geometries. The first is described by the Informativity differential 2Q_Ln_Lr. The second is described by quantization ratios^{(6,Eq. 140)} and allows translation of measures between the discrete and non-discrete frames. The third, describes the metric offset (i.e. 1) between frames. Collectively, the three geometries and the dimensional ratio m kg^-2 describe the phenomenon we recognize as elementary charge.