Joseph Heerema
Research Mentor: Gabriele Carcassi
Mentor Department: Physics, LSA
Author(s): Gabriele Carcassi, Joseph Heerema
Session: Session 3 (11:00 AM – 11:50 AM)
Presentation Type: Poster 14
Abstract
As modern physics has progressed, there has been a notable push for mathematical formalization. This has resulted in the muddling of basic mathematical assumptions and removed physics itself from consideration when developing new theory. The aim of assumptions of physics as a whole is to establish an axiomatic set of assumptions from which the basic laws of physics can be derived, while still respecting the principles of experimental physics. Utilizing the logic of verifiable statements, we establish a formal definition of experimental verifiability. Additionally, we implement the characterization of experimentally verifiable statements with properties or quantities. From these structures, we derive a general topological space, which represents broadly the experimentally verifiable preparations of a physical system. Imposing a basic set of axioms, we establish a number of useful properties, such as convexity, in order to recover the usual concept of an ensemble space. We additionally extend definitions of properties and quantities into ensemble spaces to recover statistical measurement as expected in physical ensemble spaces. Current research focuses on determining qualities of the embedding of ensemble spaces into topological vector spaces. To this end we are currently working on proving that in the finite dimensional case, as a result of an existing axiom developed within the project, this embedding is continuous. It is believed that this will recover a more useful basis of the topology on the ensemble space. Broadly speaking, this may help us in the larger goal of recovering the notion of deterministic and reversible procedures within these generalized ensemble spaces.
