structure of spacetime

[AntonioLao]

The mathematical theory of differential geometry, in particular the theory of surfaces was founded by Leonhard Euler (1707-83). His idea of developable surfaces (surfaces which can be flattened out on a plane without distortion) was independently extended by Gaspard Monge (1746-181 into a theory of double curvature. In 1827, Carl Friedrich Gauss (1777-1855) wrote one definitive paper: General Investigations of Curved Surfaces. He promoted the idea that a surface is a space in itself (later modernized into a manifold by Georg Friedrich Bernhard Riemann (1826-66) who generalized it for the study of non-Euclidean geometry). It is this theory of manifolds that made possible the discovery of Calabi-Yau manifolds hoping for the unification of string theory and Einstein’s general theory of relativity for quantizing the structure of spacetime.


One of the important ideas of all these centuries’ discoveries was the idea of double curvature and how these can be developable into the two dimensionality of Hadamard matrix. Double curvature also implies two distinct Möbius topologies: the H-plus and the H-minus. Each is its own design of double curvature forming a Hopf link. Two Hopf links can be distinguished not by their individual metric but by attaching a direction. For a closed curvature this is a tangential direction of angular motion. In physics, this double curvature becomes a principle of double least action described by the square of the local infinitesimal Lagrangian. This is really equivalent to the square of the zero-point energy at the same spacetime location. Hypothetically, if there are the same number of H-pluses and H-minuses in the neighborhood of this spacetime location and they are evenly or uniformly distributed then the double integral of the square of the Lagrangian over two spatio-temporal directions is identically zero. The stabilized spacetime structures at relative minimum energy are all approximated by cubic lattices. At absolute minimum of energy the structures of spacetime are perfect cubic lattices as composite for a light quantum of the photon. A photon is composed of 4 H-pluses and 4 H-minuses evenly or uniformly distributed within its infinitesimal spacetime neighborhood at the 8 vertices of a cube.

[mkirkpatrick]

It is as well to know ones way around the structure of spacetime so as not to get lost in the maze of energies that interact with one another.


regards michael.

[AntonioLao]

If you have a choice, would you choose a spherical spacetime or a Mobius spacetime?

[mkirkpatrick]

If you have a choice, would you choose a spherical spacetime or a Mobius spacetime?

I would go for Mobius spacetime,I trust it more to deliver.


regards michael.

[AntonioLao]

What I like about Mobius topology is that it allows the transmigration of the soul and the elimination of the independent time dimension.

[mkirkpatrick]

What I like about Mobius topology is that it allows the transmigration of the soul and the elimination of the independent time dimension.

Mobius topology has some wonderful and unique qualities.

regards michael

[AntonioLao]

Mobius topology is one-sided, single edge, and nonorientable pattern of physical reality.

[mkirkpatrick]

Mobius topology is one-sided, single edge, and nonorientable pattern of physical reality.

And we are all aboard on its journey through experience.


regards michael.

[AntonioLao]

It's a journey of no return. In classical physics, it is called the increase of entropy as the arrow of time.

[mkirkpatrick]

It's a journey of no return. In classical physics, it is called the increase of entropy as the arrow of time.

Who wants to return anyway? Forever onward.


regards michael.