Abstract: This proposal updates the wave/particle theory of light to say that light is a regular solid, and conforms to a modified version of Euler's rule. Named the Trion-Re’, this shape creates a critical self-organizing matrix with three curved and equal faces. To account for the curvature of space, this modification shifts the rules for a platonic solid making the Trion-Re’ the sixth such regular solid and a unique structure of space/time. Traditionally, there are five Platonic Solids with congruent angles and equal, flat faces. However, since the accelerating expansion of the universe suggests that all of space is curved; we must modify the rule and include curved surfaces, in which case a new solid emerges more rudimentary than the tetrahedron. The Trion-Re’, described as follows: 2-vertices, 3-flexible edges, 3-equal faces, an inside and an outside and has spinability. The Trion-Re’ can be used to generate new versions of the other five Platonic Solids.
Michael Robert Evans
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Evans, Michael, R.
Introduction: In this formal proposal the Platonic Solids are categorically being extended from five to six in number, yielding possibly the most basic structure of space/time, a dynamic three sided object that is totally closed and considered characteristically unique. The 5-regular polyhedra are composed of equal line segments and have all equal faces and angles. Of these regular polyhedra composed of identical line segments the Trion-Re’ is the sixth, with the 3-d line segment composing the other polyhedra. However, since the accelerating expansion of the universe suggests that all of space is curved, we must modify Euler's rule and include curved surfaces, in which case a new solid emerges more rudimentary than the tetrahedron.
There are two points; one for the beginning and one for the end of each event which light and time undergo. Thus the Trion-Re’ can be taken advantage of as a representation of “all that is created by light.” Gravity is explained as the force which causes the curvature of space/time in Relativity, but in this case it is quantified, not just with magnitude but also with a specifically defined geometric structure and volume. This object in turn can be used to create the rest of the Platonic Solids and all the other geometric structures which go into creating the universe and the elements of matter and chemistry. The Trion-Re’ represents the element light. It is perceived as spinning, having flexibility, and occupying a certain amount of space. Its spin-rate may be determined by its frequency. Its flexibility gives it the ability to be bent and reflected, and the space it occupies quantifies a certain volume of space time. The volume of the Trion-Re’ at one planck length has been determined experimentally to be 8.889386 x 10-36 meters cubed. The ratio of it’s length to it’s volume is 0.1818 ∞. This paper introduces a new theory, light as a solid object. It points out that the curvature of space time means that in a higher dimensional sense there is no first or second dimension, everything has volume. The ratio of the volume of the Trion-Re’ to it's length is given as eleven halves in units squared. When this ratio is multiplied by plancks length it gives the minimum volume. When this volume is multiplied by the energy density of pure space it gives the minimum energy. This minimum energy should correlate to
the fundamental charge of the electron by another coefficient which correlates energy with charge.
In order to explain the nature of light, this proposal expands the current notion, of the wave/particle duality of light, and introduces a third criteria: light is a solid, occupying space. This solid can form all other structures by “connecting the dots” from one point to the next, and as such, a simple archetypal form. With regards to time, time is both curved and "quantized." Curved, because all of space is expanding and being bent by gravity, which is time. Quantized because the Planck second is considered the smallest unit of sensical time. The Trion-Re’ represents both of these aspects and shows how the wave/particle duality is really represented by a single thing - a solid.
The paper points out that the only a 3-d space connects the two furthest distances in space, also representing the two furthest distances in time. So the curvature of the Trion-Re’ represents the curvature, not just of space, but of time; how gravity bends space; and how motion and the expansion of the universe bends time. It also points out that as the planck distance is the smallest sensical distance. It means that everything can be reduced to a single object with three sides and a minimal volume, the Trion Re’. There is no first and second dimension only a 3-d object which connects the two closest distances in space, the Planck length, which is the smallest you can imagine a photon to be. So the minimum volume of the Trion-Re’ represents the quantization of space and the deduction of the structure of the universe to a simplest form.
Conclusion: In closing, modifying the rules for the Platonic Solids to account for the curvature of time introduces a new solid with only three faces, more rudimentary than the tetrahedron. This solid can then be used to construct the remaining five solids. By analogy, it is hypothesized that this shape is the structure of the most basic element of the universe, light itself. By taking the volume of the Trion Re’ at one Planck length, it is predicted applications may be found to determine the basis of certain physical constants
and update the concepts of 0-dimension strings. We highly encourage more parties to
study the possibilities of this new geometric proposal for an overarching theory of the structure of the universe based on a characteristic solid. We would like to impress the point that three is the minimum number of sides required to create a solid, therefore, the Trion-Re’ would be the most basic indivisible regular geometric solid.
KEY WORDS: Euler's rule; matrix; planck length; platonic solids; space/time; string theory; Trion-Re’; wave/particle theory of light;