Topology of the Quantum Dimension – Complex Rotation

A mirror image can be created as follows: each point x in the real world become a point minus x in the mirror world. Bob now sees the camera twice: through the direct optical pathway … and from the mirror world. The light is reflected in the mirror in accordance with the principle “angle of incidence equals angle of reflection”.

We can also think of this mapping from x to minus x as a rotation – in fact, as a rotation through 180°. Thus, the rotation through 180° corresponds to minus one. A further rotation takes us back to the starting point again, for twice 180° makes 360°.

The key to the complex dimension is this: consider a rotation through 90° – so that two such rotations would make 180°, that is, correspond to minus one. That means, however, that the rotation through 90° must correspond to the square root of minus one – in other words, a number that does not exist in real numbers!

The mathematicians have termed this generalisation of the real numbers “imaginary numbers”, or “complex numbers” … In fact, the complex numbers are the key which will open the door to the quantum dimension.