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

数学科学：统计力学的精确结果和量子力学的基础

• 批准号: 9504556
• 负责人: Sheldon Goldstein
• 金额: $ 5.1万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504556&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Exact; Results; Statistical; Mathematical; Sciences; Exact; Results; Statistical

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.

DMS-9504556戈德斯坦研究人员打算继续对Bohmian力学的分析，该机械定义了确定性的动力学系统，涉及具有显着特性的普通和部分微分方程的新型组合。拟议的研究涉及（1）分析Bohmian力学相对论扩展的可能性，（2）Bohmian力学与Quantum理论的主要竞争性替代表述的比较，以及（3）从Bohmian的角度来分析统计力学基础的分析。 拟议的研究的重要性在于以下观察结果：1）量子理论的基础是所有物理理论中最基本的基础，在其成立后约六十五年中继续陷入混乱和不一致。 2）博学的力学是施罗辛格方程的自然嵌入，这是量子理论几乎所有解释的数学核心，成为一种清晰，精确的物理理论。如果有人坚持认为该方程与粒子的运动直接相关，就会出现。换句话说，当我们（也许是天真的）我们坚持使用最简单的本体论 - 通过其位置所描述的最简单的本体论，并寻求本体论的自然运动定律时，Bohmian力学是由Schroedinger的方程式出现的。 3）量子理论的所有奥秘都在波哈米亚力学中找到了令人信服的解释 - 实际上，明显的本体论以明显的方式演变出来！ 4）当人们试图在新方向上应用量子理论时，对波哈米亚力学的欣赏可能是巨大的灵活性和清晰度的来源 - 例如，以了解宏观干扰效应的含义 - 以及对新领域（例如量子宇宙学）的含义。 5）Bohmian力学价值背后的基本原则是，它确实有助于以足够的清晰度来表达物理理论，以至于可以真正理解它们。