If our space is a three-dimensional surface, light waves can travel on it as water waves travel on a pool surface, given that a four-dimensional quantum space contains our space.
One might expect that adding a dimension to a three-dimensional space adds one new direction but according to mathematics it adds three, all at right angles to each other. The quantum space around a point of our space thus provides three new quantum directions, each at right angles to the three perpendicular planes that cut that point (Figure 3.18) (Note 1). This allows a quantum entity that exists at point in our space, like an electron, to vibrate independently in three orthogonal directions.
Light as a moving transverse wave however can only vibrate two orthogonal ways because its movement direction uses up one dimension. For a transverse wave, the plane at right angles to its vibration amplitude is its polarization plane, which can’t be at right angles to its movement direction. For a photon, current physics calls this direction imaginary but if quantum directions exist, it actually does vibrate at right angles to its polarization plane.
This model then explains why light moving in a given direction can polarize in two ways, vertical and horizontal, based on the two quantum directions available to its axis of movement. These polarizations are also at right angles to each other, so a filter blocking vertical polarized light doesn’t block horizontal polarized light, and vice-versa, as observed, but what happens if the filter turns on an angle?
Note 1: If physical space has dimensions (X, Y, Z), let quantum space have dimensions (X, Y, Z, Q), where Q is a fourth quantum dimension. A point in physical space with three orthogonal planes XY, XZ and YZ through it then has three orthogonal quantum directions outside our space. A photon with any polarization plane can vibrate into a quantum direction at right angles to it.