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{(x2+y2)^(1/2)-R}^2+z2=r2
R=the 'poloidal radius'
r=the 'toroidal radius'
when R=0, we have:
x2+y2+z2=r2
which is the equation of a sphere. So a torus of R=0 is a sphere.
The idea that not everywhere in the universe is same but the universe differs remarkably from region to region is gaining momentum amongst cosmologists. We say that the universe is anisotropic. This is to say that there are regions up there unlike anything we have seen in our world. It is just like what Urantia is saying. This idea is neaded to make sense of our highly fine tuned laws of physics. It is termed 'eternal inflation'.
maybe it's what the Urantia book describes as the Eternal Ilse Of Paradise-the seat of the Unknown Creator where the Sons of God exist none of whom know who or what the Creator is-the outer sphere covering the eternal Isle of Paradise and the inner planets is a substance unlike anything in the formative creation and cannot be penetrated except by a select few who have earned access- few meaning hundreds of billions of souls-within the sphere there are 1 billion planets surrounding the Isle
For some strange reasons, when quantizing a classic field, we begine by considering space as though to be latice made like by stacking many cubes together. So the space in quantum mechanics looks more or less like a huge crystal! To define the surface of the cube, we must ensure that all waves at that region must be of zero amplitude. This is called a BOUNDERY CONDITION. Boundery conditions are absolutely necesary in solving differential equations such as those of quantum mechanics.
Then standing waves, like those on the string of a guitar must exist inside any such cubes. A group of such cubes will form an even bigger cube. So to explain why such cubes have the sizes they have, we can consider a huge cube, the size of the observable universe. Then there exist infinite number of smaller cubes as long as the tinier cubes will exactly fit the bigger cube. This forms wavelengths of harmonic, standing waves.
The shape of the universe is a Torus; since the universe is fractal, then it would be made up of gazillions of smaller torus.... the boundaries are electro-magnetic and many tori can exist in the same place.....I think there is a black hole at the center of each torus....but I can´t know for sure...not this morning anyhow...
Its good you understand it cause the idea of a 'natural' Dyson Sphere is in accordance with the patterns of nature. We see soppy water form perfect spheres. Infact, as a matter of fact, the valen belt surrounding the earth is one such a sphere. However, the more compelling one is the sun's heliosphere. Please find such a pic. Heliosphere is a form of dyson sphere but which filters electrons. So the fermionic, natural dyson spheres exists as a matter of fact. So it only makes sense to wonder of bosonic heliospheres. Such an 'heliosphere' will be the exact Dyson Sphere I am riferring to.
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...heliosphere is the egg-shaped "bubble"(light blue) around our solar system(blue sphere)
that protects us from interstellar emissions. The edge of the heliosphere is called the
heliopause and is where the Sun's emissions stop. The Sun's motion through space
flattens the heliosphere and causes the bright fiery light(bow shock) which is
the friction of the heliopause against interstellar space.
Interesting idea you have there. Makes sense that the universe might have a system that works like this...after all, the universe is totally intelligent and it sends us all the interesting ideas. I was just reading about this the other day...
http://earthsky.org/space/what-is-a-dyson-sphere
on the other hand, I´m thinking that the universe needs the light from the stars for many reasons...so the dyson spheres need to be transparent or in pieces to not totally close this off. I wonder if we can program the ether to work like this...lots to ponder..
So the universe does not extend the way it is indefinitely, with a neverending, even distribution of stars, galaxies and supergalaxies. No no no no! It reaches a point beyond with there is no more stars and matter the way it appear. What marks that sudden end is a huge sphere beyond which light cannot escape. It is akin to our cosmic event horizon. Neither can light from outside that boundery cross it. This neatly explains the Olber's paradox without resorting to big bang.