Barrett, The Honors College Thesis/Creative Project Collection
Barrett, The Honors College at Arizona State University proudly showcases the work of undergraduate honors students by sharing this collection exclusively with the ASU community.
Barrett accepts high performing, academically engaged undergraduate students and works with them in collaboration with all of the other academic units at Arizona State University. All Barrett students complete a thesis or creative project which is an opportunity to explore an intellectual interest and produce an original piece of scholarly research. The thesis or creative project is supervised and defended in front of a faculty committee. Students are able to engage with professors who are nationally recognized in their fields and committed to working with honors students. Completing a Barrett thesis or creative project is an opportunity for undergraduate honors students to contribute to the ASU academic community in a meaningful way.
Filtering by
- All Subjects: quantum
- All Subjects: Canonical Commutation Relations
- Creators: Department of Physics
This research endeavor explores the 1964 reasoning of Irish physicist John Bell and how it pertains to the provoking Einstein-Podolsky-Rosen Paradox. It is necessary to establish the machinations of formalisms ranging from conservation laws to quantum mechanical principles. The notion that locality is unable to be reconciled with the quantum paradigm is upheld through analysis and the subsequent Aspect experiments in the years 1980-1982. No matter the complexity, any local hidden variable theory is incompatible with the formulation of standard quantum mechanics. A number of strikingly ambiguous and abstract concepts are addressed in this pursuit to deduce quantum's validity, including separability and reality. `Elements of reality' characteristic of unique spaces are defined using basis terminology and logic from EPR. The discussion draws directly from Bell's succinct 1964 Physics 1 paper as well as numerous other useful sources. The fundamental principle and insight gleaned is that quantum physics is indeed nonlocal; the door into its metaphysical and philosophical implications has long since been opened. Yet the nexus of information pertaining to Bell's inequality and EPR logic does nothing but assert the impeccable success of quantum physics' ability to describe nature.
In thesis we will build up our operator theory for finite and infinite dimensional systems. We then prove that Heisenberg and Schrodinger representations are equivalent for systems with finite degrees of freedom. We will then make a case to switch to a C*-algebra formulation of quantum mechanics as we will prove that the Schrodinger and Heisenberg pictures become inadequate to full describe systems with infinitely many degrees of freedom because of inequivalent representations. This becomes important as we shift from single particle systems to quantum field theory, statistical mechanics, and many other areas of study. The goal of this thesis is to introduce these mathematical topics rigorously and prove that they are necessary for further study in particle physics.