Transformative Quantum Geometry and the Concept of Discrete Quantum Spaces of the Universe

Abstract

The conventional geometry calculates the areas and volumes of different geometric figures in the macroscopic domain by considering area as the product of length and breadth, and volume as the product of length, breadth, and height. However, the literature provides no explanation for why area and volume are calculated as products of spatial dimensions. The unit-square concept of area and volume is also biased in this manner. So, this research has been conducted to address these conceptual gaps; to do so, we introduced a new framework, i.e., Transformative Quantum Geometry (TQG). In this research article, the areas and volumes of geometric entities such as squares, circles, cylinders, and spheres are calculated in terms of Planck’s length. Planck’s length is a universally accepted, the smallest possible length of the universe in direct space. A model of transformative quantum geometry is being developed and presented in this article, where the areas and volumes are being considered to be the summation of overlapped distances only from x and y directions for 2D geometric entities like squares and circles, and the summation of distances for the 3D geometric entities from x , y, and z directions. The mathematical formulas for the areas and volumes of squares, circles, cubes, cylinders, spheres, etc., are first developed in the microscopic domain and then extended to the macroscopic domai