—————————— read pre-print on research gate (new window) ——————————

• 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.
• 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).

• 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.

Expressions that include values quantum in measure (i.e., made electromagnetically) are accurate only when all the terms in an expression are resolved with respect to phenomena also quantum in measure. Mixing quantum measurements with macroscopic measurements (i.e. time-of-swing measures of the gravitational constant, G) will lead to a physically significant discrepancy because of the length contraction effect described by the Informativity differential.

The effect is unrelated to Einstein's relativity. As described with a reduction of Heisenberg's uncertainty principle. Specifically, the Internal Frame of the universe carries an emergent property, physically significant fundamental (indivisible) reference measures, for each of the three dimensions. Distance less than a reference is physically insignificant, not because of a technological limitation, but because physical significance in the universe is a function of references. Not only is the notion of references a core principle of relativity, but numerous experimental results that test Heisenberg's uncertainty principle demonstrate the significance of the Planck scale bound. Moreover, any argument for a measure smaller than an established reference would imply physical paradoxes, such as a count of fundamental length measures per increment of time greater than the speed of light.

Calculation of the blackbody demarcation can be resolved with the usual electromagnetic expression defining Planck's constant, as noted in any publication of the CODATA. To resolve the associated demarcation, we begin with the Pythagorean theorem organized such that side a describes the reference n _Lr=1, side b describes the discrete Internal Frame count n_Lr of l_f and side c describes the non-discrete System Frame count, (n_Lr + Q_L). The expression is then reduced to resolve the System Frame distance (84.6005496647(07) l_f) thus providing us the distance that corresponds to the measure of ħ with respect to blackbody radiation. We call this the blackbody demarcation.

Notably, with respect to an MQ nomenclature, values resolved with respect to the upper count bound are not italicized. Any other measure is italicized. This is relevant with respect to measures such as G, which can be resolved macroscopically or electromagnetically, and ħ which is always resolved electromagnetically.

Notably, with increasing distance, the length contraction effects described by the Informativity differential quickly diminish. At 2,247 l_f the effect on distance is already less than the sixth digit. As such, the Informativity differential can often be rounded to one half (Q_Ln_Lr=1/2) for any greater distance.