Old Mechanics, Gravity, Electromagnetics and Relativity in One Theory: Part I

This paper research is the first part of the scientific theory that seeks to unify the sciences of physics with the minimal number of mathematical formulas as possible. We will prove that all equations of forces in nature can be concised in two mathematical formulas, no difference between gravitational or electrical forces or any other type of Types of conventional forces, and through the equivalence of the concepts of matrix and vector, in this theory we will be linking the four-dimensional forces equations with the classical physics as an introduction to connect the rest of the physical sciences.


Introduction
Numerous of recent books in physics discourse the summarizing of Maxwell's four equations into two equations, without addressing the possibility to generalize this concept to the rest of the forces, and work to link them with classical physics, which is the goal of publishing this research.
Whereas we cannot link all the physical sciences in one theory, unless the base upon which this theory was built represents a good and common ground for all of these sciences, So at the beginning will get to know some mathematical concepts (for example the relationship between the matrix and the vector) in a new and concise manner, with the remarks that we will deliberately ignore some proofs and details of those concepts to shorten the pages of this research that will exceed tens of pages.
In this part of the theory we will prove that all equations of force in nature How to cite this paper: Abou Layla, A.K. (2018) Old Mechanics, Gravity, Electromagnetics and Relativity in One Theory: c F ⋅  , including Lagrange equation, which will we address in the coming research, and the results obtained in this research will be applied only to the electrical and magnetic forces, with no other ones, since these forces are the most prominent in the books of physics.
In the next parts we will explore the possibility of combining the theories of General Relativity and Quantum Mechanics with this theory in the minimal mathematical relationships as possible.
However, the purpose of publishing this paper can be summarized as follows 1) Introducing new mathematical ideas and concepts which will help to unify physics; 2) Unification of the physical sciences with as few equations as possible (in this part, most of the forces known as only two forms); 3) Linking modern physical science with ancient physics without resorting to any hypotheses (such as the stability of the speed of light in the theory of relativity).

A.E Filed
In this paper, the space

The Main Determinant
The main determinant of (m + 1) × (n) matrix has been defined. Denote by where m: the number of the vectors in the group; 1 2 , , m i i i  -the numbers of columns which has been chosen.
The magnitude or length of the vector

Is Defined by Setting
On the other hand, we have from vector relations the equation

V V A B A V B B V A 
Here the last vector equals the Equation (1) From (3.2), we therefore get

V C A B 
Here the new vector appearing on the right-hand side equals the Equation (II).

The Force Equations on A.E Filed
On A.E filed, there are only two types of forces namely cross and dot forces

Calculate the Cross Force Fcross
According to the three-orthogonal vectors e 1 , e 2 , e 3 we can rewrite the field

Calculate the Dot Force Fdot
Let dot F be 4-Force in the form

Calculate the Conventional Ordinary Force
The 4-momentum P of a particle of mass m 0 at position can be written as The 3-velocity v of the particle is defined by where ω is called an angular velocity vector of the rotating system, թ is the 4-momentum of the coordinate system itself, թ = (թ 0 , թ )