All Physics Faculty Publications

Title

Quantum Theory as a Biconformal Measurement Theory

Document Type

Article

Journal/Book Title/Conference

International Journal of Geometric Methods in Modern Physics

Volume

3

Issue

2

Publication Date

2006

First Page

315

Last Page

340

DOI

10.1142/S0219887806001168

Arxiv Identifier

arXiv:hep-th/0406159v2

Abstract

Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schrödinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.

Comments

Publisher post-print deposited in arXiv.org.

http://arxiv.org/abs/hep-th/0406159v2