Mathematical Sciences: Exact Results in Statistical Mechanics and the Foundations of Quantum Mechanics

Project Details

Description

DMS-9504556 Goldstein The investigator intends to continue his analysis of Bohmian mechanics, which defines a deterministic dynamical system involving a novel combination of ordinary and partial differential equations having remarkable properties. The proposed research involves (1) an analysis of the possibility of relativistic extensions of Bohmian mechanics, (2) comparisons of Bohmian mechanics with the major competing alternative formulations of quantum theory, and (3) an analysis of the foundations of statistical mechanics from a Bohmian perspective. The importance of the proposed research lies in the following observations: 1) The foundations of quantum theory, the most fundamental of all physical theories, continue to be mired in confusion and incoherence some sixty-five years after its inception. 2) Bohmian mechanics is the natural embedding of Schroedinger's equation, which is the mathematical core of almost all interpretations of quantum theory, into a clear, precise physical theory. It emerges if one merely insists that this equation be directly relevant to the motion of particles. In other words, Bohmian mechanics arises, roughly speaking, from Schroedinger's equation when (perhaps naively) we insist upon the simplest ontology---particles described by their positions---and seek a natural law of motion for this ontology. 3) All the mysteries of quantum theory find a compelling explanation in Bohmian mechanics---in effect, in the obvious ontology evolving in the obvious way! 4) An appreciation of Bohmian mechanics can be the source of enormous flexibility and clarity when one attempts to apply quantum theory in new directions---for example, to understand the implications of macroscopic interference effects---and to new domains, such as quantum cosmology. 5) The underlying principle behind the value of Bohmian mechanics is that it really does help to formulate physical theories with sufficient clarity that they can genuinely be understood.

StatusFinished
Effective start/end date7/1/95 → 6/30/99

Funding

  • National Science Foundation: $51,000.00

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