Transverse waves vibrate at right angles to their movement but light moves in every physical way, so it has to vibrate outside space to do that. If light vibrated in a physical direction, it couldn’t move that way, so space wouldn’t be isotropic (the same in every direction). In simple terms, after space gives light three movement dimensions, there are no free directions for a transverse wave to vibrate into, so physical events can’t explain light waves at all.
In contrast, if space is a surface, then light moves on space as waves move on a lake, except in three dimensions not two. Light is then a transverse wave vibrating outside space, just as complex number theory described in the last module, and this makes us 3D “Flatlanders”.
In Abbot’s story, Flatlanders were beings who lived their lives on a flat surface (Abbott, 1884), so they saw only two dimensions not three. For example, they could see a circle, but had to imagine a sphere as a circle rotating into a plane outside their world. Now imagine a point entity moving on their land that sets values in a circle at right angles to their flat space (Figure 3.8a). The Flatlanders would then see it as a sine wave vibrating in a plane that was imaginary for them, just as we see light as vibrating in an imaginary complex plane. As the point moves, it would define a polarization plane in their space (Figure 3.8b), again as we have for light. To explain this, they might postulate a sine wave that is imaginary to them (Figure 3.8c), just as we do for electromagnetism..
This approach suggests that complex numbers explain electromagnetism because light really does vibrate outside space, so:
“In quantum mechanics there really are complex numbers, and the wave function really is a complex-valued function of space-time.” (Lederman & Hill, 2004), p346.
Complex numbers describe light as rotating into a plane outside our space (Note 1), see Figure 3.9. Science calls this rotation imaginary because it doesn’t exist in our space, just as Flatlanders might call a rotation outside their space imaginary. But in their case, there really is a third dimension, so our case could be the same. If our space is a surface within a higher dimensional space, then light can vibrate into another plane as the equations say.
In the quantum model, our space is a surface inside a quantum network that lets light vibrate transversely. Quantum waves like light can’t leave that surface any more than waves on a sea can leave its surface, so if we are the same, we can’t leave our space. We are then three-dimensional Flatlanders. This explains how light vibrates but not what is vibrating, so what is the medium of light?
Note 1. Complex number theory describes a rotation into an imaginary plane. In normal multiplication, multiplying a number by two doubles it, e.g. 5 x 2 = 10. Multiplying by 4 adds it four times, e.g. 5 x 4 = 20. In complex multiplication, i is a 90° rotation into an “imaginary” plane, so times 2i is a 180° rotation that turns a number into its negative, e.g. 5 x 2i = -5. Times 4i is a 360° rotation that has no effect, so 5 x 4i = 5.