metric tensor or trivector

[AntonioLao]

Tensors are mathematical generalization of scalars, vectors, matrices, and multi-dimensional mathematical spaces. As a branch of advanced mathematics, it is usually introduced at the graduate level. Tensor analysis has its root in vector analysis whose main purpose is to study systems of forces acting simultaneously in time but not necessarily at the same point of physical space. The need to describe systems of forces acting simultaneously at the same point in space tantamount to understanding both special and general relativity demanded the creation of a new branch of higher mathematics called the absolute differential calculus of tensors. A book of the same name was published by the Italian mathematician Tullio Levi-Civita whose English translation first appeared in 1926. Both vectors and tensors are all invariance physical quantities and as such are all independent of any coordinate system. Although tensors can be extended to higher physical dimensions greater than four, its empirical success was limited only to both special and general relativity as applied to Riemannian differential non-Euclidean geometry.

However, if the topology of the spacetime continuum corresponds more closely to a Möbius structure, its 1D correspondence is a Cantor set, its 2D correspondence is a Sierpinski carpet, and its 3D correspondence is a Menger sponge then the use of trivectors to describe actions on the one-sided surface is made independent of a theory of parallel displacements. What is needed is simply a new physical principle of directional invariance. There are eight irreducible properties and each can be represented by a unique trivector. A three dimensional object can only exist if and only if it has all eight properties. On the other hand, if an object has multiple copies of these properties then the object can be said to start the physical process of gaining mass.

[Lloyd Gillespie]

One problem Antonio__Math does not determine physical space...

Physical space determines math...

Civita was an excellent mathematician__grounded...

[AntonioLao]

Trivectors are physical quantities like mass and energy and they help describe the quantization of squares of energies. These will eventually be agreeable to many research people once cold fusion is realized. Tullio Levi-Civita was a mathematician not a physicist. Einstein was a physicist not a mathematician. They might have misunderstood each other.