angular separation

[AntonioLao]

An angle (not to be confused with a biblical angel) is a physical quantity that by itself is invisible. This is true for both a plane angle and a solid angle. Plane angles are usually measured using the physical units of radians while solid angles are measured using steradians. To make plane angles visible two bounding straight lines as intersection of planes is necessary. To make solid angles visible the bounding lateral surface of a cone is required. Each of these scenarios measures two angles, the lesser and the greater or two equal angles. However, for all practical purposes, measuring the lesser angles is sufficiently applied. On the other hand, if the measured angle covers the entire domain then the lesser and the greater become identical. In other words, they both occupy the same spacetime location. What distinguishes their separate existence is simply the directional property of its orientation whether spatially clockwise or counterclockwise. In a time continuum, it is equivalent to two time directions, into the future or into the past.

This sense of direction is easily visualized for all plane angles but for solid angles any sense of direction is easily lost to a definition of physical dimension. This becomes the compelling reason why the lightcone concept of special relativity is very difficult to understand since the propagation of light from its source covers the entire solid angle domain of a sphere instead that of a cone. Nevertheless, the speed limit of light suggests an inequality of angular separation for all solid angle measurements such that the greater angles always imply superluminal propagations.