- #36
Antonio Lao
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sol2 said:Can you show correspondance of the graviton, as a double torus genus two?
It seems that i can show this only in a one dimensional topological structure of the Hopf ring.
sol2 said:Can you show correspondance of the graviton, as a double torus genus two?
sol2 said:Is there a connection in how we are view the higher aspects of geometry in regard to probabiilty determinations?
Antonio:The unification of U(1), SU(2), SU(3), and gravity maybe beyond the Planck scale seems to indicate to me that the resultant force derived from all fundamental orthogonal forces of nature in a small region of spacetime is tremendous because they are the vector sum of the infinite numbers of spacetime point each is associated with a contant magnitude force but its direction can vary. But to think that there must be a reason why the gravitational force is very weak is because gravity is the difference between two great orthogonal forces that are not equal in their numerical values.
Antonio:From the interactions, they seem to indicate two kinds of mass. represents kinetic mass and represents potential mass which is another name for inertial mass and gravitational mass. Therefore, the graviton is made of exclusively. But can also be derived from the interaction between an and an . In this case, it's a higher excitation state of the graviton. Basically, all fermions are higher excitation states of the fundamental unit graviton . And all bosons are higher excitation states of the fundamental unit . Both H's are the square of energy .
A topological space is described as being simply connected if every loop it contains can be shrunk to a single point; a loop with this property is called contractible. For example, ordinary Euclidean space is simply connected, and so is the surface of a sphere, but the surface of a doughnut isn't. The group of rotations in three dimensions, SO(3), is not simply connected, because the set of rotations around any fixed direction by angles ranging from – to forms a loop that is not contractible. This becomes clear if you picture SO(3) as a solid sphere of radius , with a rotation by the angle around an axis pointing in the direction of a unit vector u being represented by the vector u. Antipodal points on the surface of the sphere correspond to identical rotations, so any continuous path that crosses the surface must re-appear on the opposite side of the sphere. Having formed a loop from any diameter of the sphere, the two endpoints of the diameter will necessarily remain on opposite sides. Gathering up portions of the loop and poking them through the surface won't make the loop contractible, because doing this to any segment that lies between two points on the surface breaks the original segment in three, and only pairs of such segments could be contracted down to points.
http://gregegan.customer.netspace.net.au/APPLETS/21/DiracNotes.html
http://gregegan.customer.netspace.net.au/APPLETS/21/21.html
Certainly the geometry of space-time is dynamic. Each dimension is a force unwrapping the space in a direction perpendicular to all previous.Antonio Lao said:Riemannian geometry is static. But if the geometry is dynamic, i.e. introducing a force into the geometry, then the sphere can never be a closed surface.
Michael F. Dmitriyev said:Therefore the cube in the fourth dimension is transformed to sphere.
Cube and corresponding matrixes it is the STATICS. Rotation of a cube concerning all three coordinates forms a sphere. The fifth and the following dimensions are sphere too because any rotation of sphere gives a sphere in the result.Antonio Lao said:Then in the fifth, the 4-sphere is transformed back to a cube? Could you write down the transform matrix for me?
The sphere is not a simple figure. Its surface does not contain direct lines.sol2 said:If we entertain the sphere these are interesting ideas.
How would they compare to the Klein bottle back to back, or compare to the mobius band?
Michael F. Dmitriyev said:The sphere is not a simple figure. Its surface does not contain direct lines.
The sphere can be received through rotation of a cube only.
It satisfies to the requirement of a principle of perpendicularity to all previous dimensions.
Except of that, we lIve in the dynamic space which was valid named as "SPACETIME".