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Relative Merits of the Two Famous Formulations of Bohmian Mechanics

Atiq, Mahdi | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39774 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Golshani, Mehdi
  7. Abstract:
  8. The goal of this thesis is to evaluate the strengths and weaknesses of the two existing formulations of Bohmian mechanics. The first one was proposed by Bohm, and emphasizes on the dynamics being second-order, and in which, the key tool for explaining the quantum phenomena is a non-classical potential, called "the quantum potential". In this approach, the postulates of de Broglie's "pilot-wave" theory, which now is known as Bohmian mechanics, are non-fundamental and are special to the atomic level. The possibility is proposed that these postulates become subjected to some modifications at the nuclear or lower levels, but no particular way for performing such modifications is suggested. The second approach is the "minimal" approach or the DGZ approach. In this approach, by assuming the dynamics to be of the first-order, it is emphasized that the Schrödinger and guidance equations are sufficient for Bohmian mechanics, and there is no need for the additional concepts like the quantum potential, and that all quantum phenomena are described in the causal interpretation framework, without the help of quantum potential. We have compared these two approaches and found that the best way to judge between formulations is to emphasis on their points of difference, rather than their common points. In fact, while we have not reduced the entirely general Bohmian framework, by the postulates of pilot-wave theory, to a special form, the two approaches have very common points, and the choice between them reduces ultimately to the personal theoretical interests of physicists. Consequently, by emphasizing on the main differences between the two approaches, which consist of the quantum potential and the possibility of modification of the theory at the nuclear level, we tried to find an acceptable criterion for the judgment between the two approaches. The resulting conclusion seems to be significant. We could obtain the form of quantum potential without appealing to the Schrödinger equation, and then we found a particular way for the modification of the theory, so that it is applicable at the nuclear level as well. Our way consists of using "non-Bohmian quantum potentials" which are negligible at the atomic level and are important at the nuclear level. Finally, we found that the quantum potential is not a superfluous concept, but is one of the most powerful tools for the extension of quantum theory to 'the nuclear level'. Furthermore, contrary to predictions of Bohm, neither the guiding equation nor the Born's rule, are violated at the nuclear level and the only changed element is the Schrödinger equation
  9. Keywords:
  10. Quantum Potential ; Guiding Equation ; Non-Bohmian Quantum Potential ; Durr-Goldestein-Zanghi (DGZ)Method

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