Classical Physics

This section will explore classical physics using the algebra of the split-octonions. In essence, the goal of this chapter is to show that split-octonions are a replacement for tensor arithmetic, consistent with standard mathematics.

The split-octonion representation has four distinct types of objects.

Scalars: Real valued entities, that should have units associated with them. These are represented by lowercase letters.

Positions: Locations in space-time. These are expresses as split-octonions with the polar and pseudo-scalar identically 0. Usually this is given in distance, with time in the real coordinate and scaled by c. These are represented by uppercase letters.

Vectors: These are expressed like positions. Together with positions these form an affine space. These are represented by uppercase letters with an arrow over them.

Geometric objects: All other objects are described using split-octonions. These are written in bold, and are understood to be a function of the coordinate frame.

The goal is to write the equations of physics in terms of frame invariant objects represented using the split-octonions.

Section 1: Transformations between coordinates
Section 2: Position, velocity and acceleration
Section 3: Newton’s Laws

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