[volantis]

Originally Posted by AntonioLao

Thanks for your comments. What i'm searching is the ordinality and cardinality of of the real number systems (irrationals, rationals, whole numbers, natural numbers, integers) and their logical connections with the complex numbers and hypercomplex numbers (quaternions, vectors, tensors, spinors, etc.).

The you would really like my book. I show how the ordinal structure of how the Aether interacts with matter to produce things like crystals, flowers, sea shells, and other growth structures of physical matter.

Of course, I also fully quantify the cardinal quantities of quanta. The Gforce, Aether, and matter are all perfectly discrete. As a result, you will understand the origin of the cardinal fine structure constants and subatomic g-factors. You will also see the Pythagorean triangles, the Golden Ratio, and their related equations emerge right at the level where Aether first meets matter.

My main objective is to understand the logical meaning of direction and its relations to the concept of dimension.

I cover this as well. All dimensions have a forward and backward component. We could start with length, which is probably the easiest to understand. Length is a line. From any point on the line one could arbitrarily choose to go in one of two directions. The other direction is 180 degrees out of phase. Length also has a reciprocal manifestation. The reciprocal of length is the wave number. To think of wavenumber, imagine a bicycle wheel riding across the pavement. Each full revolution of the wheel marks a length. We could call the length the obverse form of the dimension and the wavenumber the reciprocal form of the dimension. The obverse form is a cardinal value of length, the reciprocal form is an ordinal value of length.

We normally think of time as a dimension and frequency as its reciprocal. At the quantum level, it is the other way around. Frequency is the normal, or obverse and time is the reciprocal. Frequency has a cardinal value and time has an ordinal value.

Multiplication takes place between cardinal dimensions or it takes place between ordinal dimensions. But cardinal dimensions divide by ordinal dimensions and ordinal dimensions divide by cardinal dimensions.

Mass is an obverse dimension, and there is also a reciprocal of mass. Mass is a cardinal value where its reciprocal is an ordinal value. The Gforce and Aether are made from reciprocal mass and thus are ordinal in nature, as opposed to the mass we are familiar with, which is cardinal in nature.

Charge is a reciprocal dimension in most cases. When it appears as an obverse dimension (as in the unit of current) then charge is a quantity. But in most cases, charge is ordinal. We can thing of cardinal mass and charge as being associated with objective reality. Ordinal mass and charge is associated with the environment of reality. Quite naturally, the environment is non-material, but it is necessary for the environment to exist in order for matter to exist.

Einstein's General Relativity Theory is really a tensor between the environment and matter. I quantify this as well.

I'm working on invariance properties of singular square matrices of zero determinants for quantization of spacetime as the origin of square of energy, quantized space, continuous space, 1st power of energy, inertial mass, gravitational mass, electric charge, weak charge, and color charge.

You can continue to work with the mass-energy paradigm Einstein used. But you will not get any further than Einstein did. The theory has many serious flaws, and really isn't a theory at all. It is an elaborate mistake.

I'm not saying this as an attack on Einstein's work, but merely pointing out a fact that becomes very obvious after studying the Aether Physics Model.

You will find that the primary angular momentum and Aether paradigm is far more meaningful and accurate for physicists than the mass-energy paradigm.