The conjecture that gravity may be described as the sum of lost fractional counts of fundamental units of length with respect to a more precise calculation using the Pythagorean Theorem appeared to be a strong candidate when one side of the triangle was recognized with the reference value of 1.  Further investigation revealed that the expression differed from Newton's expression by a constant equal to the fixed angular measure, S, specific to quantum entanglement for a given Bell state.

The fundamental constant is a new constant to modern physics, but it also is a component of all other constants.  That is, all constants in modern theory can be expressed as a composite of the fundamental measures and/or the fundamental constant.  It is also one of the few constants that may be directly measured, a specific angle of the polarization of X-rays necessary for quantum entanglement at a maximum Bell state.

With a model of fundamental units of measure, it was now possible to solve for the gravitational constant G entirely as a function of macroscopic measures.  Knowing the value for fundamental length (b=lf), we may now solve for G.

Planck’s expressions for the fundamental measures—length , mass and time—consist entirely of the constants c, G and ħ.  Planck was able to constrain the measures where a certain arrangement could be shown to equal one.  But he was not able to demonstrate their physical significance or explain why the correlation was a required outcome.  With Informativity, the fundamental measures could be resolved with only macroscopic measures.  Combined with the discovery of their physical significance as demonstrated using Heisenberg’s uncertainty principle, a framework for measurement quantization was now possible.

Special relativity first introduced the idea that geometric differences between an observer and a target must be accounted for in order to properly understand the measure of length, mass and time … and that each of the three fundamental measures were not absolute.  With Informativity, a new effect is described that distorts measure.  This effect is quantum in nature and arises from bounds to measurement, a physically significant limit to how small a measure of length or time may exist.  The effect when compared with respect to the deflection of light passing the sun is six orders of magnitude smaller than that of general relativity.

Using upper bounds with respect to measure, an expression for maximum mass density may be resolved placing a limit on baryonic matter density within a black hole.  The bound does not apply to all forms of mass/energy, but does advance our understanding of what the internal structure of black holes is most likely like.  Further expressions compare this bound to the known diameter of measured black holes and finds support for their makeup as being ordinary baryonic matter having a density consistent with this expression.

The following expressions are an outcome of applying measurement quantized terms to our existing understanding of contraction and dilation.  These expressions are specific to measure with respect to a gravitational body and are typically described using General Relativity.  Measurement quantization achieves a quantum understanding of contraction and dilation and is applicable across the entire measurement domain.

The fundamental expression is an outcome of the fundamental measures combined and reduced to their most simple form.  The expression cannot be reduced further.  Note that this form of the expression does not incorporate the Informativity differential.

This expression which describes the relation between the age and diameter of the universe is a reflection of the understanding that the expansion of the universe is a function of the passage of time where multiplied by the rate of expansion.  The expression can take several forms including one that provides an alternate definition for fundamental mass.  It should be noted that fundamental mass is not necessarily the smallest measurable mass in nature.

These expressions are applications of measurement quantization to existing energy expressions first resolved by Einstein and Planck.  The expressions are written in quantum form so as to account for the informativity differential in its greatest detail.

The Informativity differential has a quantum relativistic effect that is not accounted for in modern calculations.  The effect, if it were measured, is small, and affects both Newton’s constant G and Planck’s constant ħ.  The effect is an apparent variation with respect to a center of gravitation. 

With existing quantized energy expressions for both mass and light, further investigation revealed that Planck’s recognition of the quantized nature of blackbody radiation n was precisely a count equal to the inverse of 2π.  This introduces a significant new element to understanding mass and light where their energy is separated in value by a radian measure equal to one complete circle.

Further investigation into the nature of light revealed that angular measure and momentum were one and the same.  Planck’s term for the Planck constant is a product of angular measure with respect to the angular constant necessary for quantum entanglement θsi.

While the expressions for quantum uncertainty had been resolved for several months prior, not until now was it realized that with a reduction the expression provided evidence for the physical significance of the fundamental measures.  This is one of several significant discoveries as it unites measure with this theoretical model.  Notably, this expression also sets the foundation for understanding quantum mechanics.  In this example measurement uncertainty is reduced to a count of the fundamental measures, once again pointing the finger at the geometric relations so important to measure, that which not only defines what we observe, but the physical relations that govern matter.

Here a formal recognition of measurement counts having a fixed upper bound is expressed.  Each measure is bound to an upper frequency of 1.85492 1043 units per second.  While measures can be any value equal or less than this frequency, measurement counts cannot exceed this frequency.

Many of the fundamental constants had to this point been reduced and shown to consist of only the fundamental measures.  With the number of quantized expressions growing, a simple and elegant solution also appeared for the gravitational constant G.  The discovery was natural and inspiring as it is precisely as one would expect, the upper bound of mass frequency with respect to the upper bound in length frequency for each of the three dimensions.

In April of 2017 the first calculation of Hubble’s constant was made with respect to the expansion of the universe, universal expansion.  An important distinction was made to discern the calculation from the expansion of galaxies moving away from one another within the universe, stellar expansion.  Within the months that followed the Hubble frequency and new equivalent expressions for Hubble’s constant were resolved.  Notably, when defined with respect to the universe as a system, it was shown that Hubble’s constant was just 2θsi, yet another physical constant shown to be a product of the fundamental expression.

As Einstein established in the early 1900's, the perspective of an observer is vital in defining the physical characteristics of observed phenomena.  This is no less true when we describe cosmological phenomena.  There are phenomena that may be measured with respect to the universe as a system and at the same time measured relative to an inertial frame from within the universe.  Each frame of reference requires a distinct approach to properly resolve measure.  This in turn contributes to what we see as observers.

Investigation of the expansion of the universe and the relationship that exist between self-referencing and self-defining expressions may be used to resolve mass distribution, specifically distribution values for dark matter, dark energy, visible matter and observable matter.  The resulting geometric expression reveals that dark matter and dark energy are each mass distributions as understood from different points of view.  With this an understanding as to what drives the expansion and the underlying mechanics can be realized.

Mass accretion was the first prediction of Informativity not anticipated in modern theory.  The result required exceptional proof and began a period of research for physical evidence that would support the prediction.  That research led to a model of inflation and calculations of the age, quantity, density and temperature of the cosmic microwave background.  All calculations matched our best measurement data to four significant digits.

Following six weeks of research, a complete story that allowed precise calculations of the age, energy, density and temperature of the cosmic microwave background (CMB) was resolved.  Not only did the calculations match our best measurement data to four significant digits, but the calculations validated that there was no faster-than-light inflationary period.  The inflationary period or epoch was characterized by a rate of expansion quantum in nature.  The rate of expansion was calculated and supported by the physical record along with an explanation as to why expansion occurred, the process a by-product of the tenants of Informativity.

Shortly following calculations of inflation and the cosmic microwave background, some time was taken to express contraction and dilation expressions with respect to motion thus completing a description of relative measure within and outside of the effects of gravitation.

While the Pythagorean expression for the contraction and dilation of measure in a gravitational field had been resolved several months prior, it was not until now that I noted the absence of measure within the expression.  The modern description of space-time being curved could now be refined as this expression contained no measure terms.  Rather, the expression consisted entirely of counts of the fundamental measures.  The apparent curvature of space-time as described in modern theory is attributable to count differentials.  And specifically, where the measure of space is uniform, those count differentials are a by-product of measurement quantization, that portion of space which is less than the fundamental measure and specifically described by the Informativity differential.  It is this count differential that presents expressions suggesting curvature and gives rise to the effects of gravitation.

It is with the one-to-one correspondence between nLl and QLf that we may correlation length contraction directly with gravitation.  Specifically, we equate the phenomenon of gravity as expressed by QLf to the phenomenon of length contraction as expressed with the count differential nLl.

Both QLf and nLl are counts of a fundamental unit of length, thus providing a new approach to their relation.  We emphasize that this is a numerical equality and when presented as such we side-step the traditional approach of arguing physical equivalence.

The development of Informativity has been met with many new challenges, one being why the observable universe was not one and the same with the fundamental mass.  The fundamental mass specifically limits observable mass by definition, that mass frequency equivalent to the upper bound in mass events that may be discerned at any point in space-time.  Why then, was the observable mass greater? 

Because of the contraction and dilation effects of measure caused by the expansion of the universe.

Work surrounding the contraction and dilation of measure also brought resolution to a significant puzzle regarding calculations of the age of the cosmic microwave background.  Where the age of the CMB could be resolved as 363,309 years, the events that triggered the end of inflation occurred at 678,889 years in the local frame.  It then became apparent that the difference was due to time dilation between with respect to the local frame of reference.

The Unity Expression arose out of work on the contraction and dilation of measure with respect to the universe.  After some manipulation this expression was resolved uniquely defining and constraining measure.  Up to this point, the best that could be known about measure was provided by the fundamental expression.  With the Unity Expression we could now resolve the fundamental measures as a consequence of the numerical count ratios that define our universe.

With a quantum model of gravity written in terms of motion, it was now possible to describe the gravitational field entirely as a change in position between two points.  In other words, it was possible to describe the gravitational field using the same terms used to describe motion in the absence of gravitation.

The first derivation is a quantum description of motion.  The second derivation is the same description with respect to a gravitational field.  Each are resolved to a common set of terms and finally set equal to one another.

The descriptions demonstrate that the two phenomena are equivalent.  Most importantly, equivalence is no longer an observed correspondence, but a physical equivalence and an outcome of the model.

A final proof to an upper limit in physical dimensions is still under development, but the laws that describe nature regularly remind us that mathematical extrapolations beyond the three visible dimensions are not supported.  This is most evident in the unity expression that describes the expansion of the universe.  Specifically, where we see the expansion parameter, we must take the cube root, each root representing one of the three dimensions.  While mathematics does offer us the ability to describe nature with a greater number of dimensions, such interpretations bare no physical significance beyond the base on which they are predicated.

What is presently referred to as the dark matter phenomenon combines two unexplained observations.  One, the velocity of stars orbiting a galaxy is approximately nine times faster than what we would expect the observable mass to hold.  In other words, given the mass we can see, we would expect the stars to fly outward.  Secondly, as we consider stars further from the galactic core (or a center of mass) we would expect their respective velocity to decrease.  This is not observed.  Rather, their velocity remains the same.  The solution combines two elements, the expansion of space and an upper bound to the observation of mass.  The expansion of space (i.e. dark energy) distorts our view in a way that causes the radius of the universe look larger than gravitationally appropriate.  And secondly, an upper bound to mass events constrains gravitational pull.  The net effect is an invariant rotational velocity with respect to an increasing orbital radius.  The solution is entirely classical and involves no fitting or modification of the known laws of physics. 

While the mystery surrounding the dark matter phenomenon has certainly been difficult, perhaps as puzzling is why galactic rotational is largely consistent with classical mechanics near the core of a galaxy while inconsistent for distances further out.  With Informativity the answer is quite clear and well defined.  In the case of the Milky Way, the crossover is at 9.32848 10³ light-years.  This is the point at which the effective mass exceeds the mass frequency bound.  That is, the number of mass events reaching a point in space exceeds the upper bound to mass frequency.  When this happens, additional mass events are indistinguishable.  The effect sets an upper bound to gravitational pull and it is this in combination with the expansion of space (i.e. dark energy) that causes stars to orbit at an invariant velocity regardless of distance about a galactic core.

There are likely many solutions that resolve an understanding of kinetic energy, but what is unique here is the connection between the invariant rotational velocity of a star about a galactic core (exclusive of the effects of universal expansion) and energy, all written entirely in terms of the fundamental units of measure.  In short, the expression for kinetic energy can be shown to be a boundary expression, entirely an outcome of constants (line 2).  Only when we generalize the terms (line 3) do we resolve the well-known expression for kinetic energy.  The correlation brings together under one approach the logical bounds of the physically significant units of measure with the generalized measure counts of any system.