[Motivation for this thought experiment: I really want to see if space travel is possible. If the relationship boundary of our universe between us and the nearest star is expanding between masses, how massive does one have to be to use space to get to the next solar system without it expanding away from us?]
In my last post of April (about ∏) I had question marks after the two types of relativities Einstein suggested. Though I have yet to see if it is possible to derive the light constant, or the Lorentz Transformation from The General Energy Equation, I do know something about the changing power of random perturbations to influence or cross relationship boundaries depending on their curvature and tension.
For our experiment, we used two viscous fluids, the inner with less viscosity than the outer. That gave a relationship between the two (the Atwood ratio). The inverse of that relationship for the first normal mode of the equation gave the time to instability of the offset mode and the successive times to each wave perturbation (for highly viscous fluids: only time-dependent fluid conduction).
The slower the frequency of wave infringement on the relationship boundary between the two fluids, the more time for the rotational components to take effect. (Rotational components in The General Energy Equation would be like rotational vs straight-line flow is analogous to torsion vs tensile-or-stress-flow, or magnetic vs electrical-conduction.)
If we accept that the change in waves and their corresponding crests of their relationship boundaries are far more energetic than the high viscosity deformations we observed (for example in more-unruly, higher-energy flows, like the air into water radial instability flows (See THE EXPERIMENT), then we see that in our universe, both curvature and gravitational tension would vary depending on location.
I came across a speculation that in the expansion of the universe that the curvature could be superimposed on any boundary without affecting the behavior there:
As Gauss discovered at the beginning of the 19th century, properties of space such as curvature can be described in terms of intrinsic quantities that can be measured without needing to think about what it is curving in.
I think what Gauss was saying is that since mathematics gives us a way to talk about virtual curvature, there need not be any real space involved in modeling curvature of an expanding universe. (Gauss found a way to speak about experimentally observed data in experimental space (virtual space) in a statistical manner).
This observation was made during speculation about the expanded universe being like an blown-up balloon (albeit stable expansion: meaning no growing incident waves: troughs or crests). The universe modeled here is just in the thin rubber of the balloon. However when we look with our telescopes along the “rubber” of the universe, we now see that the light from galaxies far away takes a spiral route. Meaning we see into a past expansion of the rubber which is radially light years closer to the pre-expanded universe.
The thought I’m trying to express here is that though in our experiment of low energy and high viscosities can give us insight into universal expansion and what might be happening on the relationship boundaries in our universe.
[Note: low Atwood ratios produce slower times for wave initiation. The highest Atwood ratio gives one second to mode-one instability. But further research into Atwood ratios of nearly one, showed initiations that different from one second. I believe that interfacial tension changes at those high ratios and flow rates, just as gravitational tension and curvature do for General Relativity near large masses in our universe.]
Let’s imagine that just like interfacial tension times curvature tells us something about the ability of information and energy to cross a relationship boundary between two fluids, that gravitational tension times curvature tells us something about information and energy crossing a relationship boundary in our universe.
To get a better idea of what we might find in expansion (how much or which part of the relationship boundary expands) lets look at the regions illustrated by the cell:
Close to the source, but offset from it, the first trough (mode one) forms. We see that there is a narrow region of the trough tunneling through the cell and “lips” where it emerges into normal spacetime. We have suggested elsewhere that the “lips” are of convex curvature (in the opposite direction to the troughs) and most probably the reason for the relatively constant orbital speed of stars at the limbs of galaxies. This feature should play into where, and the rate at which, the space between galaxies (the relationship boundaries) expand.
Up until this point, all I knew was the suggestion that the spaces between masses expanded but the space close to masses didn’t. Since there are gravitational relationships between stars and galaxies, the tension between these celestial objects may not be the smallest there is. As long as there is a nonzero gravitational tension, there may be a relationship boundary.
Hawking talks about our universe ending in massive black holes giving off Hawking radiation. What if part of the areas of smallest gravitational tension also give off this radiation and what if something like this radiation is like a diffusive boundary (the kind we see in miscible fluids/fluids that mix/where atoms in the fluid are released from their bonds)?
Notice that in the cell illustration, the tightly curved bottom of the trough has great inertia (the relationship boundary of the fluid is expanded by the fluid flowing outward and rotationally around its perimeter). That means, first of all, that the highly curved trough does not move easily, and, also, that information cannot cross it as well.
Because the rest of the trough are like parallel radial lines to the surface, they are in great gravitational tension (the crest “lips” pulling outward). Complex systems can only form on the crest if, as it expands, the curvature goes to near zero (and therefore it cannot resist information (or energy) flow).
So what do we know about space travel outside massive gravity wells, or between them?
We know that Proxima Centauri is about four light years away from us. We know that the stars in the Big Dipper Constellation are much farther away, and the farther way a celestial object is, the faster it will move away from us in space. Stars in The Dipper won’t necessarily move radially but we can see them move.
The above gif shows us how stars move and the universe expands in time. If these estimates of movement are correct then 5 light years will not put much of a dent in distance expanded between us and our nearest neighbor solar systems. The movement of stars in these models over time, would allow the radial length (14 light years) to predict the hemispheric length of our universe (42 light years) with a slow expansion.
If a single crest is our universe, and we are part of that destabilized crest, then the expansion between and back to massive objects is not a simple stretching like a stable of a rubber balloon, but much more complex (since it involves the shape of complexity, for example, of the undulating tissue of the human brain.