Consistent Quantification as a Unifying Principle in Physics and the Sciences

Science relies on numeric quantification, which can be traced back to Euclid, Galileo, and Newton. While  many now take this success for granted, some scientists have pondered the “unreasonable effectiveness  of mathematics”, questioned its necessity, while others continue to strive to understand the foundations  of the quantum mechanical formalism. These are deep questions. This project is focused on studying the ways in which physical phenomena are quantified with numbers. Symmetries strongly constrain the ways  in which one can consistently assign numbers to phenomena for quantification. As a result, symmetries  determine the form of the mathematical formalism that can be used to describe a phenomenon. For  example, we have demonstrated that the mathematics of quantum mechanics and the mathematics of three–dimensional spacetime can be derived together from the same symmetries. This leads to a very different perspective of physical laws as mathematical descriptions of phenomena. Specifically, I will study the emergence of the mathematical laws describing space and time, and forces, as well as more  advanced quantum mechanics. The mathematical techniques of consistent quantification are applicable to quantification in the other sciences as well, such as the quantification of different aspects of complexity.