sol2
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sol2 said:LQG is discrete and Strings are continuos.
There is no tearing in Strings.
How would you descrbe each particle if it has a energy value?
No Tearing, how is this possible?
Topology is more general than geometry, being simply the study of CONNECTIONS (while geometry is the study of CONNECTED systems with specific SHAPE and SIZE). More specifically, TOPOLOGY STUDIES CLASSES OF SHAPES SUCH THAT ANY SHAPE IN A CLASS CAN BE TRANSFORMED INTO ANY OTHER SHAPE OF THAT CLASS WITHOUT TEARING OR RIPPING. (Thus, a circle can be topologically transformed into a square; a sphere into a pyramid; etc.)
http://ccins.camosun.bc.ca/~jbritton/totopology3.htm
http://ccins.camosun.bc.ca/~jbritton/animcup.gif
http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/donut-coffeecup.gif
http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/wormhole.jpg
Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated.
So now that we understand this effect of no tearing in brane theory how the heck are we ever suppose to understand the dynamics on the brane? What do fermions represent and what do bosons represent? What is held to the brane and what is allowed to roam?
If we had considered fermions held to the brane what effect would em consideration have in the world of gausssian curvatures, yet not remove it from its source? What does red or blue shifting tell us from the source and is held to the brane?
If we had understood the road develped from GR to gravitational wave production what is this wave when quantized, but to have revealled, that such graviton was a evolution that geometrically had to remain consistant through a whole host of geometrical considerations. This statement might seem contradictory inthe recognition of a variance in this evolution.
They each have to be connected. Klein's ordering of geometries is one way, but there is more to it. This I will have to find and place here for considerations. Texture(?), smooth or rough, on that supersymmetrical brane?
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