Testing a Planck scale mechanism by applying to matter a law for light: A new gravity theory that closely mimics standard theory

Abstract

The Planck scale is thought to be where space, time and matter as we know them begin, and seems to be vital to physics. Our ideas about that scale are unclear. String theory is dependent on supersymmetry, which unexpectedly has not been found—this leaves no reliable picture. In some views the world is chaotic there, making it hard to explain the order at larger scales. Direct experiment cannot reach that scale, but indirect experiment and mathematics can. It would be wrong to assume, because of string theory, that only complex mathematics is relevant. This paper is the second of three from a conceptual basis with a small group of simple but lateral assumptions about the structure of space, and the nature of light and matter. It leads to interpretations, in some areas to rederivations, in others to new mathematics that closely mimics existing physics. Two spinoffs from the main theory are dimensional quantum mechanics [J. M. Kerr, Phys. Essays 33, 1 2019)], and here Planck scale gravity (PSG), in which a gravity mechanism reproduces Newtonian theory and parts of general relativity (GR). In a simple approach, the result is essentially to test the idea that matter at a small scale is similar to light, as both are waves in the fabric of the dimensions, traveling in different directions through the structure of space, which takes the form of parallel cylinders. If one assumes matter travels at c around the circumference of the cylinders, making loops at the Planck scale not unlike the closed string, one can apply to matter a law normally applied to light. What comes out is the mathematics of gravity, with what might be seen as “smoking gun evidence” (p. 11), showing that every point on any trajectory through a gravitational field is connected to every other point on it. PSG is mathematically different from GR, but it mimics it across a range of physics, in most cases to eight decimal places. It is conceptually equivalent to GR in many areas including gravitational waves, and diverges in a few places, leading to testable predictions.