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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.
• Q_Ln_Lr, also known as the Informativity differential describes the length contraction associated with discrete measure.
• n_Lr describes the count of l_f representative of the position of an observable with respect to the frame of a center of mass.
• n_L, n_M and n_T are physically significant discrete counts of l_f, m_f and t_f respectively.
• α_P^-1 is the inverse Planck form of the fine structure constant.
• e_c is elementary charge when measured relative to electromagnetic phenomena
• m_e is the mass of an electron
• a₀ describes the ground state orbital of an atom

Applying the MQ nomenclature to classical expressions describing elementary charge as well as Planck’s description of the ground state orbital of the atom offer opportunity to better understand how discrete properties of measure constrain descriptions in our effort to resolve properties of particles. In specific, we find that charge cannot be a fraction of Planck's quantum of electromagnetic action and be physically significant. Therein, if quarks do carry charges that are fractional, then charge has no physical significance outside of what exists as a composite of two or more quarks.

We begin by presenting an MQ description of charge. Prerequisite to this derivation we must first discuss frames of reference. Modern theory acknowledges two frames - both what MQ would identifies as either the frame of the observer or the frame of the observed phenomenon. We call these the Reference Frames and they identify the notions of fundamental length, mass and time. To this MQ expands on the existing nomenclature such that descriptions of phenomena are broken down by dimension, each to include some count n_L, n_M, and/or n_T of a fundamental reference l_f, m_f, and/or t_f.

To this, MQ adds two more frames, the Internal and System Frames of the universe. Using the lower bound case of Heisenberg's uncertainty principle along witht he expressions for the speed of light and escape velocity, we can show that measure within the Internal Frame is discrete and countable, these properties and emergent property of the frame. With this geometric instantiation and a physical measure of the radial rate of expansion the fundamental measures can be resolved. Therein, the fundamental measures are resolved as properties of the Internal Frame, serving as countable references for all measure. Such that the universe has no external reference, the System Frame is non-discrete.

Therein, we can break down the classical expression for charge into its MQ components. We provide as example an MQ description of the fine structure constant. This measure is physically correlated to the charge coupling demarcation. In that demarcations are calculated as a function of the measure of a phenomenon, we can avoid circular reasoning by using a similar electromagnetic phenomenon, in this case the blackbody demarcation. Knowning the frame difference is half, this gives us a count of 42θ_si relative to the Internal Frame count of 84.6 l_f, what we call the inverse fundamental form of the fine structure constant. We then account for the length contraction associated with discrete measure - what we call the Informativity differential at the demarcation - and how that effect accounts for the difference between the Planck and electromagnetic expressions of a₀. We continue this process for each term, the details which can be found on the page describing elementary charge.

We recognize that e is composed entirely of mathematical and physical constants. The expression describes charge as a phenomenon that does not change. If the radial expansion of the universe were changing over time, the fundamental measures would change and this would effect the speed of light. It would also affect the ground state orbital of an atom and where spectral lines appear, for instance, with respect to hydrogen. Looking at the light of stars from the early universe, we find no evidence of change. And as such, we find no physical support for the idea that physical constants have changed. It follows that charge has not changed since the earliest observable point during the expansionary epoch and must exhibit a behavior consistent with a whole unit count.

Turning our attention to Planck’s expression for the ground state orbital of an atom, we investigate this relation more closely. Such that m_e=n_Mm_f, then

Thus, the ground state orbital of an atom is also a function of the fundamental measures. The first set of terms, in parenthesis, describes the metric differential as a difference. In this case, the metric differential is the inverse fine structure constant inclusive of the frame transform and the Informativity differential. The latter terms l_f/n_m describe fundamental length per count of fundamental mass. a₀ is then a consequence of the measure of fundamental length relative to the Internal Frame of the universe per count of n_M adjusted for the difference between the System and Internal Frames (i.e., the metric differential). Its value does not vary.