In a more general expression of t', with t allowed to vary,
t'= SQRT(t2-(vt)2)
t'= tSQRT(1-v2)
(which identifies the geometric source and significance of the Lorentz term 1-v2).
Now allowing m0 to vary, and substituting tr ("relative time") for t',
p = m0vt/tr
thus obtaining a more revealing expression than that with the standard use of the Lorentz term, profiling the dynamic role of time. We can thereby recognize momentum as a function of the relative motion of time in space. In other words, momentum is not just the product of the motion of a mass in time and space, it is directly related to the motion in time by one body in the spatial aspect of the coordinate system of another.
Two more corollaries of the principle of the continuum, the covariance of space and time, follow:
4. Motion in time is dynamic, and possessing of kinetic energy and momentum. Furthermore, it may be inferred that the motion of mass in time is absolute as-such (i.e., motion in time is incessant), and as motion across space, it is the actual basis of kinetic energy.
5. Uniform motion is both relative and absolute. A body that moves in time moves in space, and absolutely; it can only be considered "at rest" as a matter of convenience. Uniform motion in spacetime is, however, relative between bodies, varying in their spatial and temporal components.
Time and Gravitation
Perhaps the most significant benefit of this conception of time is that it can finally account for the energy associated with gravitation in General Relativity. To think of gravitation as a deformation of the geometry of spacetime in the presence of mass has always entailed the problematic of resolving the essentially static principle of geometry with the force-like interactions and sustained pressures between the surfaces of gravitating bodies. But if time is dynamic, and time is relentless, then the evident force between bodies interacting gravitationally can be attributed to the "force" of motion in time: If two bodies are moving freely, divergent in time due to their relative motion, and at least one of them is massive enough to produce a significant curvature of spacetime in its vicinity, the other will veer toward it, and if direct contact is made, there will be a continuous pressure as each continues to seek a vector in time perpendicular to its own orientation in space. This is a precise description of what we observe and experience, it supplies the explanation for the energy that cannot be attributed by the general-relativistic geometric description of gravitation, and it renders the search for a quantum theory of gravity unnecessary and inappropriate.
I've written elsewhere: "The source of the energy usually identified as gravitational can" be attributed to an intrinsic and ceaseless dynamic of mass-energy moving in time, independent of gravitation, and obscured by the conflation of gravitation and inertial acceleration in circumstances when they happen to coincide (as at a gravitational surface) but revealed by a recognition of their fundamental distinction." (Arnold, 2013)
6. "Gravitational energy" is temporal energy. If gravitation is the geometric warping of spacetime in the presence of mass, as geometry it bears no similarity to force, and cannot account for the persistence of weight. The kinetic energy of motion in time across space is entirely adequate to account for motion that is warped by gravitation, and for the continuous pressure (weight) induced at a gravitational surface.
Conclusion
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