ZM theory III: Classical oscillators and semi-classical Bohr-Sommerfeld quantization
| dc.creator | Bar-Yam, Yaneer | |
| dc.date | 2006-04-30 | |
| dc.date.accessioned | 2026-07-07T07:09:40Z | |
| dc.date.available | 2026-07-07T07:09:40Z | |
| dc.description | We consider the description of classical oscillatory motion in ZM theory, and explore the relationship of ZM theory to semi-classical Bohr-Sommerfeld quantization. The treatment illustrates some features of ZM theory, especially the inadequacies of classical and semi-classical treatments due to non-analyticity of the mapping of classical trajectories onto the ZM clock field. While the more complete ZM formalism is not developed here, the non-analyticities in the classical treatment resemble issues in the comparison of classical and quantum formalisms. We also show that semi-classical quantization is valid for a periodic manifold in ZM theory, though the quantum number $n=0$ is allowed, as it would be in quantum mechanics for a periodic manifold. Still, this suggests a connection to the first-order success of Bohr theory in describing the phenomenology of atomic quantum states. The approximate nature of the semi-classical treatment of three dimensional atomic orbits is, however, also apparent in relation to ZM theory. These observations are preliminary to a discussion of ZM theory in relation to quantum mechanics and quantum field theory in subsequent papers. | |
| dc.description | 16 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0605005 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0605005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111158 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | ZM theory III: Classical oscillators and semi-classical Bohr-Sommerfeld quantization | |
| dc.type | text |