Fundamental Relation & Boundary Expressions

A central query in the study of relations and boundary expressions^{2(Sec. 3.9)} surrounds a single question; why can all expressions be reduced to either the fundamental expression^{1(Eq. 47)} or a measurement bound?^{1(Eqs. 27-29)} Notably, there appear to be no expressions that cannot be reduced to either l_fm_f=2θ_sit_f^{1 (Sec. 3.16)} or a bound such as l_f/t_f or m_f/t_f. And to some extent, this is not surprising for a self-referencing system of measures such as our universe.^{2 (Sec. 3.7)} In any endeavor to reduce the laws of nature to a single nomenclature, this is a behavior that follows automatically. More specifically, when the least common denominator to the three measures is found,^{1(Sec. 3.2)} it is natural that a nomenclature of all expressions would easily be reduced as such. And as such, it becomes one goal of the CQP Group to continue mapping all physical expressions in terms of the fundamental measures.^{1(Sec. 3.2)}

Within the physical realm we find the mathematics of measure also central to developing a deeper understanding of MQ. By example, where one fundamental unit of time defines a unit of measure,^{1(Eq. 21)} the inverse of that numerical value in seconds defines an upper count bound,^{1(Eq. 29)} that is a maximum frequency of time events. The upper count bound applies to all three measures^{1(Eqs. 27-29)} and where examples of phenomena (i.e. dark matter)^{3(Sec. 3.4)} exceed a bound (i.e. the Newtonian Crossover),^{3(Fig. 4)} we observe exceptions to the laws of nature that are measured locally. MQ opens the door to understanding the behavior of matter at the extreames, whether that is cosmological^{3(Fig. 5)} in scale or localized, such as the equivalence principle, an innate and immutable property of all quantized measurement systems.^{2(Eq. 59)}

Self-referencing boundary expressions also invite for the first time discrete definitions for concepts that have up to this point remained difficult to approach. For instance, what is length, time and mass?^{2(Sec. 3.7)} What defines the bounds of a universe?^{1(Sec. 3.1)} What exists beyond a bound or better yet, what is the best way to describe the enviornment external to a bounded system? If length, mass and time are entirely properties of the universe,^{2(Sec. 3.7)} then what property exists external to the universe that gives rise to the universe? These are all new fields of inquiry that MQ may now approach, some of which have been resolved and published.³

Finally, if not for consistency of the standard model, we may ask the simple question; how many spatial dimensions are permitted within a universe?^{2(Sec. 3.7)} MQ offers a new approach to this question with new possibilities. For instance, are the observed spatial dimensions simply a result where numerology requires a count of three to produce the concept of spatiality? Can it be shown that a four dimensional space has measurable physical properties distinct from a 3D space? What are those properties?

Notably, there are several approaches that favor a mathematics with greater spatial dimensions, but if not one physical property differentiates between the possible constructs, then we must fall back on our understanding of information theory. The behavior of a system can be only a property of what is known to the observer at the time considered.^{1(Eqs. 27-29)}

Objectives

• Continued investigation into the classification of expressions as extrapolations of the fundamental expression^{1(Eq. 47)} or as boundary relations^{1(Eqs. 27-29)} between the fundamental measures.^{1(Sec. 3.2)}
• Further experimental testing of the fundamental expression^{1(Eq. 47)} to confirm that this is the most fundamental relation in the universe.
• Investigation of upper bound relations^{1(Eqs. 27-29)} such as the mass frequency bound denoted by the Newtonian Crossover^{3(Fig. 4)} in a description of galactic star motion.

Inquiry

• Can we discern additional properies from the MQ definitions for length, mass and time?^{1(Sec. 3.2)}
• What is a bound and with that can we infer the existence of properties beyond the universe?
• Can geometry tell us more about dimensionality - why there are three dimensions and perhaps why there may not be any physically significant spatial dimensions in excess of three?^{2(Sec. 3.7)}

Supporting Research

• Fundamental Expression
• Bounds to Measurement Frequency
• Dimensionality
• Fundamental Measures
• Crossover from Newtonian Behavior