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Illusion of space-time and quantum mechanics

机译：时空与量子力学的错觉

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This article amalgamates some results published previously by the author with theirnatural extension. The discussion is also more detailed than in the preceding papers and themathematical introduction more accessible to a wider readership. The basic idea concerns aconstruction of the classical space-time from a de Sitter linear connection on a five-dimensionalmanifold when the transformations of the reference cross section in its bundle of linear frames arerestricted to the Lorentz subgroup. The restriction is related to the classical space-timemeasurements. When the absence of measurements allows the restriction to be lifted, the dimensionof the constructed space can be reduced to time only. Since the five-dimensional geometry containsa fundamental unit of length, assumed to be the Planck length, a link with quantum theory can beestablished. The nonlocal behavior of particles is thus associated with a radically changed geometrywithin unobserved regions of space-time. The quantum mechanical phase plane has a geometricalmeaning within the five-dimensional geometry. The requirement that the geometry allows thespace-time to be constructed puts conditions on the linear connection of the five-dimensionalmanifold as well as on the resulting geometry of the constructed space-time. The simplest and at thesame time most restrictive way to satisfy the conditions assumes that all connection components inthe direction of /x~5are zero and leads to the equationR_(αβ)=(1/l~2)g _(αβ)on five-dimensionalmanifold and Einstein's vacuum equations on the constructed space-time. When the Lorentzcomponents of the connection A_(5j)~iin the direction of /x~5are not zero, there exists a set ofequations that reduce to the Einstein–Maxwell equations on the space-time with A_(5j)~iplaying the roleof the electromagnetic field tensor.
机译：本文将作者先前发表的某些结果与自然扩展合并在一起。讨论也比之前的论文更加详细，更广泛的读者更容易获得数学介绍。基本思想涉及当参考截面在其线性框架束中的变换仅限于洛伦兹子群时，从五维流形上的de Sitter线性连接构造经典时空。该限制与经典的时空测量有关。当缺少测量值可以解除限制时，可以将构造空间的尺寸减小为仅时间。由于五维几何结构包含一个基本的长度单位（假定为普朗克长度），因此可以建立与量子理论的联系。因此，粒子的非局部行为与在未观察到的时空区域内的急剧变化的几何形状有关。量子力学相平面在五维几何中具有几何意义。几何结构允许时空的构造要求为五维流形的线性连接以及所构造的时空的最终几何结构提供了条件。满足条件的最简单，同时也是最严格的限制条件是，假设/ x〜5方向上的所有连接分量均为零，并在五阶上导致方程R_（αβ）=（1 / l〜2）g _（αβ）-构造时空上的三维流形和爱因斯坦真空方程。当连接A_（5j）〜i在/ x〜5方向上的洛伦兹分量不为零时，存在一组等式，它们在时空上简化为Einstein-Maxwell方程，其中A_（5j）〜i扮演着电磁场张量。

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