QR3.2.2 We are Flatlanders

Does light oscillate in a physical direction? To a physical realist, the answer seems obvious as how else could it do so? Physical realism explains sound because it is a longitudinal wave that vibrates air molecules in its travel direction. Hence there is no sound in the vacuum of empty space because there are no air molecules there.

In contrast, light is a transverse wave that vibrates at right angles to its line of travel and it travels in the vacuum of space or we couldn’t see the stars at night. This transverse vibration can’t be in a physical direction because space is isotropic, i.e. “up” from one view is “down” from another. Simply put, physical space has no “free” directions for the positive-negative charges of electromagnetism to vibrate into. Physical realism has no explanation at all for the vibration of light.

Edwin Abbot’s Flatland

Space as a surface however makes it possible for light to move on space as waves move on a lake, but in three dimensions not two. So light, as a transverse quantum wave, vibrates into a plane beyond our space just as complex number theory describes. But while physical realism calls the complex plane unreal, quantum realism calls it real, which makes us 3D “Flatlanders”.

In Abbot’s story Flatland was the home to beings who lived their lives on a flat surface (Abbott, 1884). Everything they did happened in two dimensions not three, so they could see a circle say but could only imagine a sphere as expanding and contracting circles passing through their reality.

Figure 3.8. A transverse circle moving on space is a sine wave

Now imagine a point moving on their flat land that sets values in a transverse circle at right angles to their space (Figure 3.8a). Flatlanders could only conceive of these values existing in a complex plane that didn’t exist for them, as we do for light. As the point moves the complex plane defines a polarization plane in their space (Figure 3.8b), again as we have for light. The result is an “unreal” sine wave amplitude (Figure 3.8c) just as we describe electromagnetism.

Since light appears to us as a transverse rotation outside our space, quantum realism concludes that complex number theory explains electromagnetism because light really is a rotation outside our space:

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

Figure 3.9. Complex rotations

Complex numbers describe a rotation into a dimension outside our space (Figure 3.9). We call the complex plane imaginary because it doesn’t exist in our space, just as Flatlanders would call a plane that doesn’t exist in their space imaginary. Quantum realism needs an extra dimension for light to vibrate on space, so the complex plane really exists. The ability to accept a photon that vibrates into at right angles to its polarization plane outside space will shortly be called a node channel. That we can’t enter this plane doesn’t mean it doesn’t exist, it just means that we are three dimensional Flatlanders.

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PS. 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 degree rotation into an “imaginary” plane, so times 2i is a 180 degree rotation that turns a number into its negative, e.g. 5 x 2i = -5. Times 4i is a 360 degree rotation that has no effect, so 5 x 4i = 5.