The existence of the so-called ‘dark’ issues of mechanics implies that our present accounting for mass and energy is incorrect in terms of applicability on a cosmological scale, and the question arises as to where the difficulty might lie. The phenomenon of quantum entanglement indicates that systems of particles exist that individually display certain characteristics, while collectively the same characteristic is absent simply because it has cancelled out between individual particles. It may therefore be necessary to develop theoretical frameworks in which long-held conservation beliefs do not necessarily always apply. The present paper summarises the formulation described in earlier papers (Hill, JM. On the formal origin of dark energy. Z Angew Math Phys 2018; 69:133-145; Hill, JM. Some further comments on special relativity and dark energy. Z Angew Math Phys 2019; 70: 5–14; Hill, JM. Special relativity, de Broglie waves, dark energy and quantum mechanics. Z Angew Math Phys 2019; 70: 131–153.), which provides a framework that allows exceptions to the law that matter cannot be created or destroyed. In these papers, it is proposed that dark energy arises from conventional mechanical theory, neglecting the work done in the direction of time and consequently neglecting the de Broglie wave energy E . These papers develop expressions for the de Broglie wave energy E by making a distinction between particle energy e = m c 2 and the total work done by the particle W = e + E , that which accumulates from both a spatial physical force f and a force g in the direction of time. In any experiment, either particles or de Broglie waves are reported, so that only one of e or E is physically measured, and particles appear for e < E and de Broglie waves occur for E < e , but in either event both a measurable and an immeasurable energy exists. Conventional quantum mechanics operates under circumstances such that f vanishes and g becomes purely imaginary. If both f and g are generated as the gradient of a potential, the total particle energy is necessarily conserved in the conventional manner.

中文翻译：

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德布罗意粒子波力学系统综述

所谓的力学“黑暗”问题的存在意味着我们目前对质量和能量的解释在宇宙学尺度上的适用性方面是不正确的，问题在于困难可能在哪里。量子纠缠现象表明粒子系统存在，它们单独显示出某些特征，而整体上不存在相同的特征，因为它在单个粒子之间相互抵消。因此，可能有必要发展长期持有的保护信念不一定总是适用的理论框架。本论文总结了早期论文 (Hill, JM. On the form origin of dark energy. Z Angew Math Phys 2018; 69:133-145; Hill, JM. 对狭义相对论和暗能量的一些进一步评论。Z Angew 数学物理 2019；70：5-14；希尔，JM。狭义相对论、德布罗意波、暗能量和量子力学。Z Angew 数学物理 2019；70: 131–153.)，它提供了一个框架，允许对物质不能被创造或破坏的法律例外。在这些论文中，提出暗能量来自常规力学理论，忽略了在时间方向上所做的功，从而忽略了德布罗意波能 E 。这些论文通过区分粒子能量 e = mc 2 和粒子所做的总功 W = e + E ，即由空间物理力 f 和力 g 累积的总功，开发了德布罗意波能 E 的表达式顺着时间的方向。在任何实验中，要么报告粒子要么报告德布罗意波，因此仅物理测量 e 或 E 之一，粒子出现时 e < E 和德布罗意波出现时 E < e ，但在任何一种情况下，都存在可测量和不可测量的能量。传统的量子力学在 f 消失而 g 变成纯虚数的情况下运行。如果 f 和 g 都是作为势梯度产生的，则总粒子能量必须以常规方式守恒。