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• 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.
• 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.
• E_l is the energy of one quantum of electromagnetic radiation.
• E_m is the energy of half a fundamental unit of mass *m_m.
• n_L, n_M and n_T are physically significant discrete counts of l_f, m_f and t_f respectively.
• Q_L is the fractional portion of a count of l_f when engaging in a more precise calculation.
• 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.
• v is velocity measured between an observer and a target.
• m is the mass of the target phenomenon.
• h is Planck’s constant.
• 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).

We can use Measurement Quantization (MQ) to break down existing classical descriptions for a fundamental unit of energy with respect to baryonic and electromagnetic phenomena.

MQ is a nomenclature physically assessed using a new discrete approach to describing gravitational curvature. The MQ approach replaces classical terms with fundamental measures and counts of those measures. For instance, velocity v would be written as n_Ll_f/n_Tt_f. When writing Heisenberg's uncertainty principle to describe the Planck scale bound we discover that all the measure terms (l_f, m_f, t_f) cancel out leaving only the count terms. This allows us to resolve a physically significant, discrete and countable approach to classical expression.

It is notable that a consideration of the uncertainty principle at the Planck scale bound does not necessarily imply that all measure with respect to the Internal Frame of the universe is discrete. This is established separately, by taking the difference between the discrete and non-discrete System Frame to resolve expressions and values for the physical constants without reference to any of the existing physical constants. Importantly, the resultant values match our best measurements digit-for-digit to the same precision.

These example expressions focus our attention on the whole-unit count n of a quantized unit of electromagnetic radiation where described by Planck's expression E=nhv. In MQ form, we find that the difference between a fundamental unit of mass m_f and a quanta of electromagnetic radiation is a single rotation of radian measure.

What was previously two physically distinct phenomena is now understood as a difference in terms of geometry. Traditionally, this property is coupled with the momentum of the phenomenon and recognized as angular momentum. We call into question this interpretation. For one, why should baryonic and electromagnetic phenomena have an energy difference equal to a full circle? We suggest this is telling us something about the underlying significance of these phenomena and that significance is geometric.

We present the relation between each phenomenon.

Written in Planck form, such that E=nhv, we find that n must be 1/2π.

To gain more depth of understanding, consider now other examples where π arises between phenomena different in construct. For instance, consider the relation between gravitation and the electric constant.

Once again, the two phenomena are separated in value by 2π. Gamma γ represents a consolidation of terms incorporating four additional geometries that describe the relation between the discrete Internal and System Frames of the universe. Gamma represents a frame transform, not directly associated with n.

Consider now the CMB power spectrum, such that the x-axis coordinate of the peak of each curve is distinguished as a function of π to some power.

And then there is a relativistic offset with which we must adjust each x-value (π/θ_si)^2/3 thus accounting for the skewing effects of measure between the quantum and expansionary epochs, two time periods with differing rates of expansion.

Consider also the energy of a fundamental unit of mass, E=2θ_sic. Such that 2θ_si is the rate of expansion of the universe H_U, and c is the velocity of a point on its leading edge relative to that edge, we find that the energy of m_f is the expansion parameter times the perimeter velocity. The correlation calls into question if we fully understand what difference exists between a universe and a fundamental unit of mass.

We bring together a suite of phenomena each which differ by some scalar of π and we correlate them, thus demonstrating that it is π which stands between them. Yet, we know quite firmly that π describes a geometry. Are baryonic and electromagnetic phenomena distinguished by a spatial geometry?