Theron Duma
Research Mentor: Gabriele Carcassi
Mentor Department: Physics, LSA
Author(s): Not Available
Session: Session 2 (10:00 AM – 10:50 AM)
Presentation Type: Poster 46
Abstract
What is the role of mathematics in the field of physics? Is it merely a tool for calculation, or does it have more profound implications? In this research project, Physical Mathematics for the program Assumptions of Physics, we argue that the mathematics we use is more than just a tool, but rather a language that represents the physical systems we study, and that we ought to be careful about what we choose to use. In this project, we seek to derive mathematical axioms and structures from physical requirements. We start with the notion of verifiable statements to construct a set of experimental domains which can be used for not just experimentation in physics, but for science as a whole. Through the notion of experimental domains, we can construct a natural topological space and begin to define the notion of ensemble spaces in physics. Currently, through the work we have produced, we now seek to unify the notion of what a “state†is in physics. In classical mechanics, we say a state is given by a particle’s position and momentum.In quantum mechanics, because of Heissenburg’s uncertainty principle, our definition of state changes, now being defined as an element in an abstract Hilbert Space. We must have a common notion for what a state is and thus we seek to derive one through ensemble spaces and entropy.
