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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.
• 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).
• 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.

• 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.
• 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).

For the past century we have mapped out the nature of quantum behavior and while we can describe this mathematically, the physical underpinnings as to why quantum behavior exists have remained illusive. The Measurement Quantization (MQ) approach to classical description offers a physically correlated explanation as to the logical and physical relations that lead to quantum behavior.

To this, we cite several approaches to physical description, beginning with an MQ description of discrete gravity. With such a description, we use the Pythagorean theorem to correlate the discrete Reference and Measurement Frames, and along the hypotenuse the non-discrete Target Frame of the universe. There is a transform between the Target and Measurement Frames which can be measured. We call this transform, the fundamental constant θ_si. It is measured macroscopically with respect to the angle of polarization of X-Rays necessary to entangle photons in specific Bell states at their degenerate frequency. This experiment was first carried out by Shwartz and Harris and presented in their 2011 paper, Polarization Entangled Photons at X-Ray Energies. Notably, θ_si can also be calculated as a function of the fine structure constant to 13 significant digits.

Using the MQ approach, these angles can physically assessed in classical form as a function of c, G and ħ. While G is measured macroscopically, Planck’s reduced constant resolves the angle for the signal and the idler only where a length contraction effect - the Informativity differential - is taken into consideration. This effect is unique to discrete measure, a new form of length contraction not related to that described by Einstein's relativity.

So, what have we learned with this approach? Notably, we find that the three notions of measure - length, mass, and time - are discrete and countable. This proof was not previously possible, enabled with the new discrete description of gravitational curvature. The approach is physically assessed by measurements confirming the existence of length contraction using measures of G and ħ. This is achieved with existing CODATA and is presented in the paper, Measurement Quantization.

Therein, we find that measure has significance only as a function of physically significant fundamental references, with respect to the Measurement Frame of the observer. Thus, the Target Frame of the universe - having no external reference - must be non-discrete. With respect to gravitational curvature, and such that side a always equals a count of 1 (notice we use counts in MQ, now measures such as meters), such that side b equals some count of the reference observed, it follows that side c would equal side b plus some fractional count Q_L having no physical significance with respect to the Measurement Frame of the observer. This fractional count is lost with each increment in elapsed time, the result describing the phenomenon of gravitational curvature.

We can make several observations. For one, the physical constants and the laws of nature are derived from the difference between the discrete and non-discrete frames as described in the paper entitled, Measurement Quantization Describes the Physical Constants. The length contraction associated with discrete measure applies only to the notion of space, in that time and mass are both linear (i.e., the Pythagorean theorem is not applicable). Phenomena less in length than the fundamental length l_f, are subject to a subset of physical laws. By example, the force of gravity is a consequence of the difference between the discrete and non-discrete frames. Thus, gravity does not exist below the Planck scale. The properties of phenomena below the Planck scale have no physical significance with respect to phenomena and events occurring above Planck scale phenomena. But these phenomena do exist and as such there is information which carries across both above and below the Planck scale. For instance, a count of particles, a predominate motion vector with probability a function of initial direction, etc.

With these principles, we establish a framework with which to then assess and describe quantum behavior. These observations exist as a result of the MQ approach to classical description, afforded by and based on the physical evidence presented in several papers discussed throughout existing publications and pre-prints.