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

There are no specific inputs in the analysis and reduction of Heisenberg's Uncertainty Principle.

• l_p, m_p and t_p are Planck’s Units for length, mass and time.
• n_L, n_M and n_T are physically significant discrete counts of l_f, m_f and t_f respectively.
• 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.
• 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).

Physical support for the fundamental references of length, mass, and time is resolved as a function of the length contraction associated with discrete measure. We call this effect the Informativity differential. Notably, it is a feature of the self-referencing discrete measurement framework of the observer. The effect increases with decreasing distance, calculated using the Pythagorean theorem as the remainder of a whole unit count along the hypotenuse AC.

This effect is particularly noticable when considering expressions that include both G and ħ, such as Planck's unit expressions. This is to say, such expressions present measures - the Planck units - relative to different frames of reference, G respective of a macroscopic measure, ħ typically respective of blackbody radiation, a quantum phenomenon.

We can resolve the issue by considering the value of G and ħ (at the upper count limit), and G and ħ (at the blackbody demarcation). While not specific to the experiments that the CODATA collaboration used to resolve a published value for each of these constants, this approach is sufficient to demonstrate digit-for-digit correspondence with all values published in the most recent publications noted in the table below. Correspondence between measure and calculation is identified in columns using solid and dashed lines. Bolded values are resolved separately in the linked pre-print.

With respect to the fundamental expression l_fm_f=2θ_sit_f, a description of measure is constrained to a function of other measures. And while we can use phenomena such as gravitation, light and the uncertainty principle to demonstrate that measure is discrete and countable, those descriptions are in themselves a function of the self-referencing frame of the observer; by example Planck's unit expressions for length, mass and time. In short, using existing expressions of classical theory implement a self-referencing framework of terms which are defined with respect to one another.

This reference conundrum is resolved with MQ where we distinguish the discrete features of the Measurement Frame from the non-discrete features of the Target Frame of the universe (which has no external reference). With this approach we consider the difference between these frames to then resolve each of the physical constants and the laws of nature.

Notably, we take this moment to recognize that measure is not fundamental to nature, in light of the associated count structure. That is, those principles which define the physical constants exist because of the count relations between the fundamental references for length, mass, and time. A nomenclature consisting entirely of the notions of measure is an unfortunate self-referencing system of description. Only from a system as a system approach and its relation to the internal frame can we resolve a complete understanding of the physical constants.