## The Imaginary Norm

**Authors:** Jan Makopa

It is known that the direction of rotation of a position vector in Polar Coordinates is not continuous for angles ʘ = π(a + 1/2). The fallacy has algebraic origins and as a increases, the direction of the position vector at ʘ is oscillating between two opposite discontinuous points we shall call Norms . The pertinent Literature can be argued, as has been done by others in the past that – the direction of a position vector at ʘ cannot be real thence must carry an imaginary component also to justify the occurrence of discontinuities along the Polar plane. To understand how Norms oscillate, we propose the “Norm Wave Function” whose exposition we give herein is based on the geometric expansion of Norms. The once speculative Mohammed Abubakr- proposition on Calpanic Numbers, can now find full justification as a fully-fledged proposition. At the end of it all our contribution in the present work – if any; is that we demonstrate that the hypothetical Norm proposed herein, is imaginary and Norms carry unique properties that may have the potential for strong application in Quantum Theory of the Spinning Photon. This current text is part one of two. This text is a proposition of a Norm Wave Function and it discusses the philosophy behind the discontinuities of rotations while part two will apply the formulation in Quantum Mechanics of Spinning Photons.

**Comments:** 6 Pages.

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### Submission history

[v1] 2018-10-29 02:08:45

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