**Authors:** Rodney Bartlett

The General Theory of Relativity (1) will be useful in this article dealing with an aspect of the quantum world. Specifically – the analogy of the theory’s curvature of space-time to a rubber sheet. A small body like the Earth is said to warp space-time only a little and create a dimple in the sheet. A larger body such as the Sun curves space-time much more and forms a deep valley in the rubber. And a black hole is often pictured as warping space-time so much that it tears a hole through the rubber fabric. Transferring the analogy to the quantum realm – the motion of electrons can be visualized as their gliding across hills and valleys of pure energy (gravitational energy). This is because Relativity says gravity is caused by the curvature of space-time. Therefore, gravity … gravitational energy … IS space-time. Materials that don’t conduct electricity (insulators) have deep valleys which electrons struggle to escape from. In 2004, U.S.A. physicist Charles Kane noticed something strange in his computer simulations of electrons flowing through different materials: an insulator whose quantum state had the equivalent of a hole. Kane had not found the first quantum black hole but had discovered the first topological insulator – a then theoretical material that could conduct electricity on its surface but not within its interior. (In 2007, American physicist M. Zahid Hasan led the team that made the first 3D topological insulator.) About 90 years ago, while experimenting with the equations of quantum physics, German physicist Hermann Weyl showed that a massless and charged particle (now called the Weyl fermion) could theoretically exist. (2) In topological insulators, the hole in its quantum state causes electrons to come together and behave like a single particle called a Weyl fermion. The Weyl fermion can be related to Topological Insulators (TI), the Majorana fermion^ can be related to future quantum computers’ Topological Superconductors (TS), while topological insulators and topological superconductors may be regarded as the inverse of each other. This state of topological materials and “unnatural” fermions can be expressed by another phenomenon which I call vector-tensor-scalar geometry. ^ The Majorana fermion was predicted in 1937 by Italian physicist Ettore Majorana playing with the same quantum math that had intrigued Weyl. Like a Weyl fermion, a Majorana fermion has no mass. It also has no charge, despite being made of a bunch of negatively charged electrons. (3)

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