Entangled photons – The Omega-donut in the quantum dimension

Just as with the linear polarised photon from Station U1-08, we substitute the probability ½ in every angle by rotating wheels having the radius √(1/2), which oscillate on a circular axis between +√(1/2) and -√(1/2). This oscillating 3D circle delineates the form of a symmetrical baked donut.

If a right-hand circular polarised photon is in superimposition with a left-hand circular polarised photon, the rotations are equalised. That means that superposition state must be rotationally invariant. Thus, Omega is then simply described by an oscillating circle. All amplitudes have the same length √(1/2).

As a next step, we will break down the Omega Donut in such a way that we can introduce the “horizontal” and “vertical” measuring axes as a coordinate system. Thus, we will perform a basis transformation from the basis R, L to the basis H, V. In a simplified notation, we are showing here the direction of the antinode.

As Omega is rotationally symmetrical, the V/H coordinate system can be rotated at will. The double arrow axes indicate the directions of the antinode. This, again, is a basis transformation. The direction of the antinode is then marked as “V hat” and as “H hat”.