On the gravitational nature of time
A novel geometry is presented which yields several observed quantities that are not accounted for by classical relativistic models. Relative motion is reexamined and a numerically equivalent function is applied. This function dictates that velocities should remain equivalent across reference frames, which in turn implies that it is not time alone that dilates, but rather the time elapsed between two arbitrary points in space for a given velocity as those two points are further separated in the reference frame in relative motion.
A peculiar velocity of
This model predicts a mechanism of gravity which can, with further research, offer an explanation for the bullet cluster's varied mass affects, the apparent lack of gravitational aberration, and potentially excess galactic rotation curves without the need for CDM.^{1}
Introduction
Consider an observer at relative rest
Following the premise that if an observer who will remain at relative rest conspires with a second observer that the second observer should travel at precisely velocity
Despite the mathematical convenience of describing many physical processes as a function of time,
Given further that velocity is a vector of a magnitude directly influenced by the observer, and that
Of course the approximation of describing some physical process
Covariance, Contravariance and Shared Coordinate Systems
A critical piece of the model being proposed is the notion that absolute motion is indeed physically consequential. This should not discount the significance of relative motion as defined by SR^{3}, but rather expand upon it to include external, tertiary reference frames.
Consider equation with respect to figure . If observer
While current relativistic models dilate time in accordance with both SR and GR, they in turn must dilate time dependent variables. This breaks the most fundamental symmetries, including those that exist not as a matter of observation and experiment, but of pure definition. Symmetry breaking models are objectively permissible when nature itself appears to break symmetries we've come to take for granted, but breaking identities that flow from pure definition is a clear indicator that the model is based on a misunderstanding of the underlying mechanisms.
Let us further examine the scenario described earlier, in which an observer in relative motion travels at a predetermined velocity. Despite the fact that
This yields a geometric interpretation of time as a density axis, such that
Equation is numerically equivalent, but symbolically inaccurate according to the model being proposed. A modified version that follows the
While contradictory to current relativistic models, this dilation of space is in accordance with the concept of cosmic inflation, and requires fewer modifications to prerelativity theories than SR itself. By providing the ability to define a state of absolute rest and absolute motion this model can provide a significant leap forward in observational astronomy while remedying multiple relativistic paradoxes. As this model of spatial dilation is examined further, a gravitational and inflationary geometry arises that no longer yields singularities or a 'big bang'. This does not discredit the theory that those states at one time existed, but rather calls into question the fundamental nature of chronological ordering on a cosmic scale.
Relativity and Tertiary Reference Frames
Let us consider this proposed dilation of space as it relates to both cosmic inflation and the equivalence principle.^{4} As SR and GR rely heavily on both the equivalence principle and Mach's principle^{5}, we should then examine the inflationary properties of this model necessary to produce local gravitational effects. Recall that:
If we instead inverse this equation so that it is not
Note that this dilation of space towards
Differentiating this with respect to
Applying as a Spatial Dilation Scalar
As
Note that the negative
Let us then factor
While numerically equivalent, this result in the form of
Note that
as a Function of Velocity
Let us reexamine the classical
Rearranging this to find
If we consider equation in the context of equation , we find:
While observational astronomy struggles to accurately quantify our local peculiar velocity on a supergalactic^{8} scale due to inherent hurdles fundamental to the measurement of light traveling through interstellar dust, this value follows closely with several observational studies. The probability distribution plot below was taken from Gordon, Land and Slosar,1 while Jha, Riess and Kirshner2 found a PV^{9} of
Physically Accurate Time Scales
This model of divergent coordinate systems supposes that the fourth coordinate in 4vector equations, commonly attributed to time, is a position along this density axis. Let us further examine how the nature of this density axis differs from our current understanding of time, and describe the physics of a Universe without the need for a time derivative in any classical sense.
Let
Consider figure , in which over the course of the integral
the linear distance according to the observer at relative rest,
Since this model proposes that it is distance rather than time that dilates according to the magnitude of
Let us then consider this rate of change,
Does this spatial dilation scalar somehow imply a resolution to both the fine tuning paradox and the Fermi paradox? While speculative, it could be that life as we know it is best suited to exist at densities and velocities such that the dilation of space as a scalar of the magnitude of motion through space approaches
Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.
Gravitational Acceleration
Let a body of mass
If we then consider this equation in the context of relative spatial dilation, where
As we are only concerned with the positional derivative at
If we consider that time itself is this dilation of space as a function of the magnitude of motion through space, as
then we should scale
We can then define the velocity of a body in free fall for time
By finding the spatial dilation at every point along the radial vector
Conclusion
While Einstein changed our understanding of the Universe on a fundamental level with his revelation regarding time dilation, SR and GR break down under extreme quantities, either very massive or very small, and produce paradoxes at velocities of equal or greater magnitude than
And perhaps most importantly, if
Acknowledgements
To my aunt, Mary Beth for instilling a sense of wonder and curiosity, my grandfather for leading by example, and T, for demonstrating that space and time obey laws far beyond our own understanding; without whom this theory wouldn't exist.
Footnotes

CDM
Cold dark matter â†© 
The word final here is used very loosely. What is meant by "final" is something analogous to a tensor quantity of sorts; a rate of change that remains unchanged between reference frames.
As described elsewhere, the notion that a quantity remains constant in each reference frame does not necessarily require that that same quantity remains constant between reference frames. â†© 
SR
Special Relativity â†© 
Equivalence Principle:
The principle that the acceleration on the surface of a gravitational source is indistinguishable from the force experienced while on an upward accelerating platform of an equal magnitude. â†© 
Mach's Principle:
The somewhat controversial principle that the inertia of a body is a function of the combined gravitation of all other bodies in the Universe. â†© 
In
space. â†© 
Spatial system accounting for the three dimensions of Euclidean space, as well as the nonEuclidean density axis being proposed. â†©

Of a distance scale that extends beyond our own galaxy. â†©

Peculiar Velocity â†©