A Simple Explanation of Mirror Symmetry, the SYZ Conjecture, and Gravity

 An article in Quantum Magazine describes the problem with general relativity’s description of gravity:

General relativity yields the predictions of black holes and the Big Bang at the origin of our universe. Yet the “singularities” in these places, mysterious points where the curvature of space-time seems to become infinite, act as flags that signal the breakdown of general relativity. As one approaches the singularity at the center of a black hole, or the Big Bang singularity, the predictions inferred from general relativity stop providing the correct answers. A more fundamental, underlying description of space and time ought to take over. If we uncover this new layer of physics, we may be able to achieve a new understanding of space and time themselves.

I would like to offer a solution. According to the Simple Explanation cosmology, our universe is not shaped like a shuttlecock, as current theories propose, but rather like a donut—a torus. In this case, the  Big Bang occurred at the zero point singularity at the center of the cosmic torus and spread outward not as a sphere or a shuttlecock, but as an ever-expanding torus. Matter, as it emerges from the universal torus, forms itself into a steady stream of multi-dimensional toruses pushing out into the interior of the expanding 3-D donut, never reaching the edge which continues to grow beyond the reach of matter.

A newly emerging mathematical field called “mirror symmetry” demonstrates that there are an infinite number of toruses associated with every apparent object, looping themselves out of our ordinary 3-D space into six neighboring dimensions. An article printed in Quantum Magazine describes the “SYZ conjecture” this way:

 In the same way that we can now explain similarities between very different organisms through elements of a shared genetic code, mathematicians attempted to explain mirror symmetry by breaking down symplectic and complex manifolds into a shared set of basic elements called “torus fibers.”

A torus is a shape with a hole in the middle. An ordinary circle is a one-dimensional torus, and the surface of a donut is a two-dimensional torus. A torus can be of any number of dimensions. Glue lots of lower dimensional tori together in just the right way, and you can build a higher dimensional shape out of them.

To take a simple example, picture the surface of the earth. It is a two-dimensional sphere. You could also think of it as being made from many one-dimensional circles (like many lines of latitude) glued together. All these circles stuck together are a “torus fibration” of the sphere — the individual fibers woven together into a greater whole.

Here is the illustration of the concept provided by Quantum Magazine:

The Simple Explanation has always suggested that gravity is the force felt on the outside of ordinary objects due to presence of unseen toruses associated with ordinary matter. What the illustration refers to as “Point Problems” is actually the emergence of gravity. It seems to me that this symplectic geometry supplies a proof of this concept and, at the same time, resolves physic’s ongoing conundrum regarding the quantum level activity of black holes and the originating Bang.

We can imagine a very simple particle of matter as both that particle that we can see and measure and, at the same time, as a series of torus fibrations.  The fibrations at the poles with their infinite singularities originate the gravitational force, most of which occurs in alternate dimensions, but some of which “leaks” into our 3-D space. In the case of a small particle, the gravitational leakage is correspondingly small. But, when you aggregate particles into massive structures, the gravitational leakage becomes large and noticeable, as if the neighboring dimensions were trying to suck our space time into their dimensions.

The gravitational field around an object increases in proportion to the number of symplectic torus fibrations associated with the object’s ordinary matter. The reason gravity does not travel far from its originating object is because it is physically attached to the structure of the object—more precisely, to the toruses looping into neighboring dimensions. The more infinitely large singularities there are on the other side of the object’s multidimensional formula, the stronger the gravity of the object. The more aggregated ordinary matter, the more looping toruses.

In other words, gravity does not lead to black holes. Rather, massive objects produce so many toroidal fibrations of infinite singularities that the singularities themselves intrude into our 3-D space, revealing themselves and the toruses associated with them. When these singularities intrude into ordinary space, we see them in their normal symmetrical geometrical form as a single torus shape of infinite density and weight—a black hole.

Another conundrum standard physics is wrestling with has to do with “degrees of freedom.” Why, they wonder, do black holes have fewer degrees of freedom than ordinary objects? Meaning, why is their gravity only associated with the 2-dimensional outside surface of the black hole torus?

Since 2011, the Simple Explanation has suggested that gravity emanates from the exterior shell of the invisible torus wrapping around the exterior of ordinary matter.  In the case of a black hole, ordinary matter disappears into the center singularity, leaving only the shell of the symplectic torus to pull at space with its infinite gravitational shell, which is why the black hole’s gravity appears to be constrained  to the surface.

Top view of torus, with yellow arrows representing gravitational force

Side  view of torus, showing gravitational pull as well as material forces pushing out and wrapping around (white arrows)  From “Is Gravity a Toroidal Force?” 5-27-2011 Simple Explanation blog

I am grateful to Quantum Magazine for running these two recent articles on “Why Gravity Is Not Like the Other Forces” and “Mathematicians Explore Mirror Link Between Two Geometric Worlds.”  I believe “mirror symmetry” and the “SZY conjecture” provide the math behind the Simple Explanation’s theory of gravity. In symmetrical fashion, I hope my Simple Explanation will be discovered and considered by mathematicians and physicists struggling with these issues.