If space is relative rather than absolute, how can the integral of velocity give you a position? Doesn't an independent position assume absolute space?
For background, review Equations of Motion, Barycenters, Relativity, and Branes
A note on terminology
This construct assumes that the quanta of energy is space in n dimensions with a volume of the (geodesic) Planck unit to the nth power. Thus a fourbrane becomes equivalent to a unit of fourspace. I will use both terms for ease of communication. When we move up to 5 dimensions, spacetime will technically be nonequivalent to fourspace as the term fourspace may be excluding one of the dimensions of spacetime. Since Einstein equated mass and energy I will be describing them as the same substance, independent of reference frame (being more objective than invariant mass), with the term MassEnergy. As we decreasingly describe MassEnergy relative to other dimensions by integration, we increasingly are reducing relative motion into absolute position. If there existed only five dimensions, every unit of MassEnergy would have a discrete position in an absolute fivespace. This model also assumes that photons have a vanishingly small inertial mass due to their cumulative accelerating effect on solar sails. This mass in threespace must then be correspondingly accelerated, which may equivalently be seen as a fourspace mass having a constant velocity, or a fivespace mass existing at a discrete position!
Relativity proposes that gravity is described as a curvature of spacetime, and this is commonly demonstrated on a relativistic 2brane in 3space by using a latex sheet and spheres of varying weights. This holds the third spatial dimension as proportional to the MassEnergy density relative to Earth's barycenter. An accurate extending of the analogy into fourspace would use a threespace model (assuming an absolute fourspace) with a regular grid overlaid in the threespace that experiences density wells in the vicinity of bodies of mass. We shall see how this model can further be extended into fivespace (assuming exactly five dimensions) and the model's implications.
The barycentric (and therefore polar) integral of MassEnergy in fourspace with respect to a fifth dimension is proportional to its (geodesic) volume. Thus fourspace is more volumetrically condensed (with regards to a fifth dimension) as you approach a center of mass. This accounts for how photons appear to decelerate as refracted and then accelerate again as they exit. Here, mass is described as a threebrane with relation to the remaining two dimensions accounting for the squared change of position (d^3x/dt^2). This employs fractional calculus for non-integer derivatives.
Threespace (common) magnets are accelerating MassEnergy (and therefore space) through their barycenters parallel to one of the three dimensions directly perceivable to humans. Gravity then is accelerating MassEnergy in a direction perpendicular to all three of the spatial dimensions, accounting for the accelerated space's apparent disappearance at the barycenter.
As mass is converted to energy and travels away from the center of mass, as in a star, the density of its fourspace decreases as it moves outward. This accounts for stable elliptical orbits: while space is increasingly dense closer to the barycenter causing a satellite to accelerate inward, the emitted energy carries with it the corresponding spatial quanta. An analogy of this is a ball rolling down an inclined conveyer belt. The stable conveyor belt (of created space) will hold in equilibrium any downward accelerating ball (satellite) of discrete mass at an explicit distance from the base (barycenter).
This model also rejects Bohr's quantum probability model. Consider standing atop a ladder in your garage, then dropping a dime from a height of 12 feet with your eyes closed. Despite understanding physics at the macroscopic level it would be very difficult to predict the resting position of the dime. This is due primarily to the chaotic hydrodynamic atmospheric effect of resistance on its orientation, as well as the non-Cartesian variability in the garage floor surface. This analogous quantum foam is merely the unseen fine detail when viewed via a relativistic course focusing.
Why should 5 dimensions be proposed at all? Even if this turns out to be a relatively more useful model, how may we be sure it legitimately corresponds to reality? I propose an experiment that would be able to invalidate this model. The double-slit experiment effectively accelerates MassEnergy (with respect to two other dimensions) which passes through the slits and interferes with its own pattern of propagation. I posit that this interference is due to the superposition of the MassEnergy diffusing through neighboring spatial quanta surrounding the double-slit apparatus. This accounts for single photons supposedly interfering with themselves. For this 5space model to hold true the MassEnergy would need to dissipate through three dimensions with respect to two others (d^3x/dt^2). This seems intuitively obvious since in the referenc frame independent MassEnergy of the photon would need to constantly accelerate, and may travel through any of the three spatial dimensions. For this hypothesis to not be falsified the double-slit experiment would be repeated with a new mask of three holes. Photons passing through this trinary optics array would be expected to superpose a three-tiered interference pattern even when sent through one-by-one due to accelerated diffusion or time variance depending on your frame of reference.
Alternatively in 4+1 dimensions, the strength of the gravitational attraction between two bodies separated by a distance of r would be inversely proportional to r^3.
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