Effects of Quantization on Classical Space-time Systems

There is a debate in physics as to the underlying structure that we attempt to measure. That debate may be summarized as two questions. Is mathematics coincidental to the physical relations we observe in nature? Or, are the physical relations in part or in whole an outcome of mathematical relations.

At the extreame, we may imagine a virtual world of artificial life within a computer generated world. The inhabitants and their environment would, as such, demonstrate an environment that was in whole an outcome of mathematical relations. At a minimum, we might also imagine a physical world with some geometric relations and the remaining physical in origin, each property collectively contributing to the observed behavior of matter.

Let us now consider a specific case of the latter, part geometric and part physical. For instance, we might propose a world consisting of two objects each moving relative to the other, each following one of two parallel lines. The two objects never meet. Provided each object has a constant and identical velocity, several invariant laws of nature would be observed relatively. For instance, the force of gravity between the two objects would never change. The inhabitants of this two object world might even call this behavior a universal law of conservation, the 'conservation of gravitation'.

We may then ask, is 'conservation of gravitation' a law of nature or a product of the system geometry? Naturally, while some details could certainly be debated, the spirit of this example is that the inhabitants have mistakenly identified a system geometry for a property of nature. The inhabitants would in all liklihood have some suite of laws and constants that are entirely geometric in origin. Once the geometry is understood, the invariant values are then realized to be a function of the geometry and not some fundamental value of nature.

We may then step back from our omnipresent view of this world and ask important questions with respect to our own world. Notably, is math a coincidental tool to the expression of the laws of nature? While we may certainly hold steadfast to the idea that there exists some physical basis for that which we measure, what happens to this view as more and more of the constants and relations of nature are identified as geometric in origin, one-by-one moving from the coincidental class of physical description to the less favored class of geometric?

This is an important question in MQ for obvious reasons. The MQ approach uses Heisenberg's uncertainty principle^{3(Eqs. 19-23)} to demonstrate the physical significance of discrete fundamental units of measure.^{1(Sec. 3.2)} But, there is no quality associated with discreteness that is physical and when applied to measure assigning such a property becomes ever more difficult. Moreover, all three measures are found to be discrete, each with a very specific magnitude, and having an upper and lower count bound with respect to the remaining measures. Again, each of the identified properties of the fundamental measures^{1(Sec. 3.2)} are mathematical leaving no other property prerequisite to a description of nature.

The value of MQ is not to debate the nature of reality. And as such, the presentation is somewhat a distraction from the utility of applying the concepts of measurement quantization to the description of phenomena. But, said principles are instramental in preparing the reader for a deeper understanding of MQ as an approach.

For now, we do not debate if the universe is a construct of geometric relations or if geometric relations are all that are needed to describe the universe. We only consider that both approaches have to this point proven successful across the board, almost without exception (i.e. singularities being one such fault in mathematical endeavor). Thus, taking a mathematical approach to an extream (i.e. the proposal that no relation in nature may exceed some

• upper count bound of fundamental length l_f per count of fundamental time t_f ... that being light c=l_f/t_f)

is just as physically significant as entertaining an

• upper count bound of fundamental mass m_f per count of fundamental time t_f or an
• upper count bound of fundamental mass m_f per count of fundamental length l_f.^{3,1(Eqs. 27-29)}

Each of the proposals are arguably significant and indistinguishable from the physical reality we endeavor to describe.

The goals of this group are to describe all the constants and laws of nature using only the fundamental measures^{1(Sec. 3.2)} and the fundamental constant θ_si.^{1(Sec. 3.1)} Much of this work has already been accomplished by Planck and continued by others. MQ is a new tool and enables new approaches to this field resolving in even greater detail the fundamental measures to six significant digits^{1(Sec. 3.2)} several physical descrepancies such as the gravitational constant,^{1(Eq. 9)} Planck's reduced constant,^{1(Sec. 3.4)} the Fine Structure Constant, the expansion of the universe^{1(Sec. 3.11)} and other physically significant measures.

A secondary goal of this group is to then determine what are the properties of the universe, how many phenomena are entirely a by-product of the geometry of the universe, what are the differences between phenomena that are a product of the self-referencing^{1(Sec. 3.8)} geometry of the universe and which phenomena are a product of the geometry of the universe itself (self-defining).^{1(Sec. 3.8)} To some extent, the goals of this area of study fall along the same lines as existing Information Theory, but come with a new approach, MQ. And with that and the initial discussions at the outset, there is a considerable landscape with which to devise new experiments in our quest to understand reality.

Objectives

• Experiments are needed to refine our understanding of existing quantum mechanics in terms of MQ. Can the language of quantum mechanics be written anew entirely in terms of MQ?^{3(Sec. 2.3)} This is perhaps one of the greatest and more challenging endeavors of this group.

• As noted, another significant challenge is the straight-forward reduction of all existing constants and laws of nature into expressions consisting only of the fundamental measures^{1(Sec. 3.2)} and/or the fundamental constant.^{1(Sec. 3.1)}

• Further experiments are needed to better understand if there are physical differences between phenomena that are geometric in nature and those that are physical in origin. If we are to maintain that the universe is fundamentally physical, there needs to be some physically significant property distinct from mathematical relation or geometry that can be used to clearly identify physically significant properties of nature.

• A more detailed investigation should be conducted to determine which phenomena are properties of the universe and which are local properties having no or little relation with respect to the system as a whole. These two groupings are distinguished in MQ as either self-referencing or self-defining phenomena,^{1(Sec. 3.8)} dark energy^{1(Sec. 3.11)} being an example of the latter.

Inquiry

• On a more wholistic view and in light of several new approaches afforded by MQ, we should return to our existing understanding of information theory and ask, even in a universe entirely a product of logic, is there still not some physically invariant quality against which the mathematical relations are defined? What is this quality? In short, to understand the universe and its external environment we need to understand what new or existing properties characterize that external environment (for lack of a better term we will call the multiverse). We now have a tool with which to ask this question. We know that the multiverse has the property of count (i.e. one universe), has the property of binary (i.e. logical opposition) and has a quality of three (i.e. the three measures, the three spactial dimensions). Can we identify other qualities? Can we begin to construct a multiverse with these properties alone?

Supporting Research

• Gravitational Curvature
• Gravitational Contraction and Dilation
• Informativity differential
• Equivalence between Motion and Gravity
• Bounds to Measurement Frequency