dorsal/arxiv
View SchemaHarmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
| Authors | Y. S. Kim, Marilyn E. Noz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411017 |
| URL | https://arxiv.org/abs/quant-ph/0411017 |
Abstract
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore play the role of combining quantum mechanics with special relativity. Both Paul A. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while they used different approaches to physical problems. Both were also keenly interested in making quantum mechanics compatible with special relativity. It is shown that the coupled harmonic oscillators can bridge these two different approaches to physics.
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"abstract": "Other than scattering problems where perturbation theory is applicable, there\nare basically two ways to solve problems in physics. One is to reduce the\nproblem to harmonic oscillators, and the other is to formulate the problem in\nterms of two-by-two matrices. If two oscillators are coupled, the problem\ncombines both two-by-two matrices and harmonic oscillators. This method then\nbecomes a powerful research tool to cover many different branches of physics.\nIndeed, the concept and methodology in one branch of physics can be translated\ninto another through the common mathematical formalism. Coupled oscillators\nprovide clear illustrative examples for some of the current issues in physics,\nincluding entanglement, decoherence, and Feynman\u0027s rest of the universe. In\naddition, it is noted that the present form of quantum mechanics is largely a\nphysics of harmonic oscillators. Special relativity is the physics of the\nLorentz group which can be represented by the group of by two-by-two matrices\ncommonly called $SL(2,c)$. Thus the coupled harmonic oscillators can therefore\nplay the role of combining quantum mechanics with special relativity. Both Paul\nA. M. Dirac and Richard P. Feynman were fond of harmonic oscillators, while\nthey used different approaches to physical problems. Both were also keenly\ninterested in making quantum mechanics compatible with special relativity. It\nis shown that the coupled harmonic oscillators can bridge these two different\napproaches to physics.",
"arxiv_id": "quant-ph/0411017",
"authors": [
"Y. S. Kim",
"Marilyn E. Noz"
],
"categories": [
"quant-ph",
"hep-ph",
"hep-th"
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"title": "Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman",
"url": "https://arxiv.org/abs/quant-ph/0411017"
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