arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1903.04087quant-ph
收藏

量子力学中的波粒统一

Uniting the wave and the particle in quantum mechanics

Peter Holland

备注：
v3: published version, background material and proofs moved to appendices, results unchanged
发表信息：
Quantum Studies: Mathematics and Foundations, 7(1), 155-178 (2020) [published online 5 October 2019]
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

提出了量子力学中波粒统一的场论。这是因为我们对德布罗意-玻姆（deBB）理论的三个弱点进行了研究：它依赖量子概率公式来证明粒子定律;它对粒子对导波的相互作用的缺乏漠不关心;它缺乏一个统一的模型来表示它不可分割的组成部分。这些问题在一个分析框架内得到解决，要求波粒复合物与量子系统没有可观察到的差异。这个方案是通过呼吁对称性（全球规范和时空平移）和施加相应的守恒诺特密度（物质，动量和能量）与薛定谔对应物的平等来实现的。结合时间反演协方差的条件，这意味着量子势介导波粒相互作用的粒子的deBB定律（我们还展示了时间反演假设如何被统计条件所取代）。该方法阐明了复合材料的质量的性质，以及它的能量动量守恒定律。我们的主要结果是统一的薛定谔方程和deBB法在一个非齐次方程，其解决方案合并的波函数和奇异孤子模型的粒子在一个统一的时空场。波函数不受粒子的反作用，因为它是统一场的均匀部分，粒子对它的源有贡献。这个理论适用于多体系统。我们回顾德布罗意的反对意见的导频波理论，并建议，我们的场论模型提供了一个实现他迄今未完成的双解方案。给出了deBB理论的一组修正假设，其中统一场被作为基本描述元素。

英文摘要：

We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie-Bohm (deBB) theory: its reliance on the quantum probability formula to justify the particle law; its insouciance regarding the absence of reciprocal action of the particle on the guiding wave; and its lack of a unified model to represent its inseparable components. These problems are resolved within an analytical framework by requiring that the wave-particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, momentum and energy) with their Schrodinger counterparts. In conjunction with the condition of time reversal covariance this implies the deBB law for the particle where the quantum potential mediates the wave-particle interaction (we also show how the time reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the mass of the composite, and its energy-momentum conservation laws. Our principal result is the unification of the Schrodinger equation and the deBB law in an inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes. The theory applies to many-body systems. We review the objections of de Broglie to the pilot-wave theory and suggest that our field-theoretic model provides a realization of his hitherto unfulfilled double-solution programme. A revised set of postulates for the deBB theory is given in which the unified field is taken as the basic descriptive element.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑