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• n_px, n_sx and n_ix are the pump, signal and idler vector magnitudes n (a function of the pump frequency or the phase matching properties of a nonlinear optical crystal) respectively identified with the subscripts p, s and i followed by an x or y representing the coordinate axis.

• 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.
• 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 the position of an observable with respect to the frame of a center of mass.
• 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.
• G is the gravitational constant, 6.6740779428(56) 10^-11m³kg^-1s^-2 such that its value considers the effects of length contraction associated with discrete measure at the upper count limit. Italicized G identifies a measure not at the limit (e.g., G=6.6738448362(53) 10^-11m³kg^-1s^-2 at the blackbody demarcation).
• r is the distance between an observer and a target.

[10] S. Shwartz and S. E. Harris, Polarization Entangled Photons at X-Ray Energies, Phys. Rev. Lett. 106, 080501 (2011), arXiv: 1012.3499, http://dx.doi.org/10.1103/PhysRevLett.106.080501.

[13] S. Shwartz, R. N. Coffee, J. M. Feldkamp, et. al., X-ray Parametric Down-Conversion in the Langevin Regime, Physical Review Letters, 109, 013602 (July 6, 2012), http://dx.doi.org/10.1103/PhysRevLett.109.013602.

[14] T. E. Glover et al., X-ray and optical wave mixing, Nature, 488, 7413, 603–608 (2012), http://dx.doi.org/10.1038/nature11340.

[15] NIST: CODATA Recommended Values of the Fundamental Physical Constants: 2018, (May 2019), https://physics.nist.gov/cuu/pdf/wall_2018.pdf, http://dx.doi.org/10.1103/RevModPhys.93.025010.

The fundamental constant θ_si is new to modern physics, a measure that when considered with respect to the fundamental expression l_fm_f=2θ_sit_f can be used to resolve expressions and values for the physical constants. Importantly, all phenomena can be described using counts of the fundamental measures, θ_si and/or some combination of the fundamental measures: l_f for length, m_f for mass and t_f for time.

While θ_si can be understood as half of the Planck momentum, we call to the reader's attention that θ_si is also equal in magnitude to the angle of polarization associated with the signal and idler of polarization entangled photons at the degenerate frequency. As resolved by Shwartz and Harris, θ_si can be measured as the angle of polarization for X-rays in a given Bell state at their degenerate frequency, specifically the maximum angle of that measure. Modeled values matching measurement are presented in their 2011 paper, Polarization Entangled Photons at X-ray Energies.

Examples of expressions written using only the fundamental measures include Einstein’s expression for energy, E=2θ_sic; Hubble’s constant when defined with respect to the radius of the universe, H_U=2θ_si; Newton’s constant of gravitation G=c³l_f/2θ_si and the reduced Planck constant ħ=2θ_sil_f.

Lastly, we bring to the reader's attention that the fundamental constant is applicable and fixed for all frames of reference. But, its units are a function of the frame and approach to its measure. This is in part because the fundamental constant θ_si is a composite of the fundamental measures. Depending on the frame of reference, θ_si can have units of momentum, angular measure or no units at all. That is, θ_si's dimensional qualities are a function of the frame of reference.

The most common units for θ_si are that of momentum; its definition a function of the Internal Frame of the universe. If the frame of reference is the System Frame, θ_si will carry no units. This follows in that the universe has no external reference. And in specific situations when describing quantum phenomena, θ_si can be used to describe an angle. This we describe above with respect to experiments carried out by Shwartz, et. al.