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

There are no specific inputs in the analysis of a 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 relative to the Internal Frame of the universe. We call this effect the Informativity differential. The effect increases with decreasing distance, calculated using the Pythagorean theorem as the remainder of a whole unit count along the hypotenuse AC of a right-angle triangle.

This effect is measurable when considering expressions that include both G and ħ, such as Planck's unit expressions. The reason for this is a function of the relative distance associated with measure. Take for instance a measure of G. One may measure this using a time-of-swing approach, this being a macroscopic approach with no physically significant length contraction. Conversely, G can be measured using an electromagnetic field (i.e., and oil-drop experiment) and such a measure would correspond to the electromagnetic demarcation, a distance significantly affected by length contraction associated with the discrete internal frame. The same concerns apply to ħ or any measurement, although ħ is always measured electromagnetically.

We can resolve the use of physical constants measured with respect to different frames by considering the value of G and ħ (at the upper count limit), and G and ħ (at the blackbody demarcation). Note, we do not italicize terms when measured at the upper count limit. Thus, 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 three 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 Internal Frame of the universe, 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 Internal Frame from the non-discrete features of the System 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 measure is a self-referencing system. 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.

Finally, argument can be made that a reduction of the Heisenberg Uncertainty Principle where v is set to c (the bound) does not establish that measure must be a discrete count of the resultant minimum measures. There is some argument here, but when considering the MQ definition for the inverse fine structure constant (among other constants), we find strong physical support for discreteness. Specifically, the product 42θ_si minus the discrete (i.e., rounded) value of this product RND(42θ_si) give us the fundamental form of the expression. Applying the frame transform and accounting for the Informativity differential resolve the proper value digit-for-digit.

Moreover, the Informativity differential would not exist if the Internal Frame were not discrete. Yet, if we don't account for this length contraction effect, then we are left with a calculation equal to that which is resolved with Planck's expression. Only by accounting for this effect are we afforded the final result, which corresponds with that calculated using the electromagnetic expression, (i.e., the expression can be found in any CODATA publication). Additionally, this difference does not affect just Planck's equation for the fine structure constant, but affects all Planck expressions. It is for these reasons, that the MQ interpretation of a discrete Internal Frame is physically supported.