Light, similar to sound, is closely related to matter – for example, each frequency of sound has its own patterned water surface. In the same way light has properties that give it geometric features and most of them arise from the wave-particle duality, a concept that states that every elementary particle can be described in terms of not only particles, but also waves. And since waves are closely related to frequency (the number of waves in a given time), we can assume that light can generate geometric and patterned shapes, depending on the material or surface it encounters.
Michael Faraday made his first break-through in electromagnetism in 1821. When placing a small magnet around a current-carrying wire, he proved that the force exerted by the current on the magnet was circular. This discovery was a cornerstone for the progress of science, being used today, for example, to generate electricity on a large scale in power stations. James Cleek Maxwell takes the research further and develops the Electromagnetic Theory of Light, proving that light, electricity and magnetism are profoundly connected by forces that he believed to be propagated in the medium called aether. Remarkably, his proposed mechanical model for the aether could account for all known phenomena of electromagnetism.
From electromagnetism to geometry
The forces of electromagnetism and electricity, magnetic attraction and laser light are all hints to a hidden geometric field, the underlay of all other fields, spaces and their behaviors.
The light at atomic level
Take the examples given by the laser experiment, conducted at the University of California San Diego. When projected through a circular cavity, light will rearrange itself into a variety of standing wave patterns. When the wavelength of light is given by an integer number of oscillations, the patterns are more clear and simple.
Reflections of the Sun
When light interacts with ice crystals suspended in the atmosphere, a phenomena similar to the rainbow occurs. The “sundog” is given by the reflection and refraction of light at altitudes higher than 5 km. Ice crystals become a prism from which light bounces when the sun is at 22° above the horizon, giving the circular dispersion. Lower than that, at 20° for example, the optical dispersion is limited to a “pillar” effect, that we usually see in other bright lights, like the moon or street lights.
Singularities of geometry
All field theories suffer from singularities when particles are introduced – a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely, and where the laws of physics as we know them cease to operate. Perhaps at this point, the hidden geometrical structure manifested by all these forces and their respective field-lines, has the potential of eliminating all these singularities.