The Connection Between Inertia, Spatial Curvature, and System Kinetic Energy
We see that as a thin, 2-fluid boundary expands outward radially in an unstable way, it buckles into sine waves. The first troughs are remarkably stable/steady, meaning they don’t move much farther radially from their source (in space/time). At high flow rates and high viscosity ratios (for example: air into oil), earlier troughs have higher curvature (accretion disk analog: large planets form closer to the sun).
In a straight, linear flow outward (conductive components in The General Energy Equation) the motivating flow field separates (just as water flows around curved rocks in a stream) when it hits the concave-upward troughs. This is a good way to think of the reason for inertia (the difficulty moving objects because of their mass). The motivating outward flow is unable to push the local boundary outward as much as it can the boundary crest of lesser curvature (the inner fluid, instead of pushing the trough outward, takes the path of least resistance around it). The tighter the mass curves space the more massive the object and the harder it is to move.
Why do I refer to the Energy Equation and its analogs? The terms of the General Energy Equation give us insight into the ways physical reality can work. So, to understand the possibilities (besides running analogous experiments), we can understand the behavior of, and interaction of, all energy fields using the pointed language of this equation.
As a spaceship gives off gaseous matter through its jets, we say that for every action there is an equal and opposite reaction. When part of the distributed matter of the ship is used to move matter behind or in opposite direction of velocity of system, then system inertia is reduced, curvature is reduced, so the ship expands more with the boundary (farther from the ship’s gravity well/cg (center of gravity)). (The same thing happens when we walk on a raft.)
In response to the action/reaction forced by a jet, the change in mass distribution, how does space change in curvature? As material of a system (for example: a ship) diffuses/redistributes, the less dense its region, the more space created. The system will then move farther from the center of gravity of a planet (for example) or the gravity well of any larger gravity well.
What can general and special relativity tell us about this density/mass/spatial curvature/ expansion? The relativities represent proven nonlinear behaviors in curvature. Because viscous/linear fluid analogs of The General Energy Equation across the expanding boundary has not yet predicted the onset of instability of very high viscosity contrasts in our linear, conductive 2-fluid problem, this suggests something else is happening close to the singularity source (perhaps some close-in relativistic behavior).
Chandrasekhar, honored recently by the Google browser, has solved the inverse math problem where surface tension interaction (as well as density interaction) results are inversely related to our viscosity contrast flows. Note: Interfacial tension Force Equation for the linear problem is almost identical to Newton’s Gravitational Force Equation for the linear problem (without relativity):
The “m” stands for masses m1 and m2 (the force of gravitational attraction between the two).
The “s” stands for surface tensions in each fluid: s1 and s2.
(Perhaps the gravitational force between masses is similar, in some way, as a tensile force).
The rotational components were found to reduce the linear time of instability of a two-fluid system (perhaps pointing to end conditions to linearity for both equations: both close-in (General Relativity) and far from a massive gravity well (Special Relativity)).
The faster a rocket travels, the less dense the system, the more space the system occupies in a given time.
We believe that outer space is nothing, but perhaps, not nothing, but zero curvature. At zero curvature, that is where statistical error arises. Would this be the same as zero point energy (from which new singularities fueling new universes might arise)?
Is the existence of zero point energy the same as statistical error, or is that error tied to something else? In the 2-fluid boundary or a gravitational boundary, the trough arises and a gravity well may nucleate at a center of gravity (cg). Given time, more time to initiation, curvature of the trough increases due to a change in the fluid regime from linear flow to higher-energy nonlinear flow. (It is the higher-energy nonlinear flow that allows the highest curvature troughs/masses of linear flow to move to orbit one another.)
(In the 2-fluid/2-D unstable boundary, for low viscosity contrast, “cell-division” case, one high curvature trough burrows into the droplet as it expands, cleaving it in half, creating negative curvature close to where the trough meets the outer low-curvature, expanding boundary. In a the high-contrast, high-flow case, “finger” tips on the expanding boundary go into negative curvature (concave downward, against the direction of velocity vectors) along with rotational flow/movement.)
General relativity is suggested by the reduction in time to instability initiation for interfacial tension/viscosity contrast. Special relativity may have an effect on the orbital velocity of outer galaxy star-arms. They tend to rotate faster than linear gravitational theory predicts (as explained in the link below).
Potential and kinetic energy as it relates to a gravity well:
If a gravity well contains a ground state at its cg, then as we pump energy into a system, we accelerate it to higher and higher velocities and equipotential paths/orbits. Within this global energy field there is a delta tension between the system and the gravity well’s cg (that is predicted for nonrelativistic motion by Newton’s Gravitational Equation).
Big questions relate to the above (low flow “cell division” case and the high-flow steady “fingers” at the expanding boundary). How do different regions of curvature on our expanding universal boundary relate to dark energy? Will our projectiles behave differently once they sample regions close to and far from gravity wells?