论文标题

五维一般相对论中的远程标量力

Long-range scalar forces in five-dimensional general relativity

论文作者

Williams, L. L.

论文摘要

Kaluza首先观察到,当5D指标相对于第5个坐标的衍生物设置为零时,以5个维度(5D)编写的真空爱因斯坦方程将精确地重现4D一般相对论和经典电动力学。 5D度量的第15个组件是一个4D长量标量场,而4D限制随着标量场进入一个限制而出现。在这里,我们报告了远程Kaluza标量场的新分析,结果和力效应。这些考虑因素揭示了强烈的电晶状体浮力,这是由于人体的电荷与行星围绕标量场之间的重力耦合而产生的。确定了一个新的,第三个特征的长度,用于质量$ m $和电荷$ q $的电晶状体田地,$μ_0q^2/m $,与Reissner-Nordstrom Lengthsses,$ gm/c^2 $和$ q \ q \ sqrt {gμ_0/c^2} $一起进行。在原子尺度上,源术语的5D协方差要求电,标量和重力都与电荷成正比。我们讨论了这些结果与迪克(Dicke)在远距离标量相互作用和Brans-Dicke标量探测理论方面的基础工作,包括与标量的相互作用意味着可变的静息质量以及关节标量 - 重点相互作用的能量学。我们讨论了唯一可用的自由参数(来源的不变的5D长度元素)中和标量的问题的问题,以中和标量力并避免原本大的标量力预测。我们得出的结论是,大型古典力是对足以伪造5D假设的5D一般相对性的可检验预测。然而,新的物理相互作用长度的出现暗示了远程标量场的进一步未开发的物理。

Kaluza first observed that the vacuum Einstein equations written in 5 dimensions (5D) reproduce exactly 4D general relativity and classical electrodynamics, when derivatives of the 5D metric with respect to the 5th coordinate are set to zero. The 15th component of the 5D metric is a 4D long-range scalar field, and the 4D limit emerges as the scalar field goes to one. Here we report new analysis, results, and force effects from the long-range Kaluza scalar field. These considerations reveal a strong electro-gravitic buoyancy force arising from a gravitational coupling between the electric charge of a body and the scalar field around a planet. A new, third characteristic lengthscale for the electro-gravitic fields of a body of mass $M$ and charge $Q$ is identified, $μ_0 Q^2/M$, to go along with the Reissner-Nordstrom lengthscales, $GM/c^2$ and $Q\sqrt{Gμ_0 /c^2}$. At atomic scales, 5D covariance of the source terms requires that the electric, scalar, and gravitational forces all become proportional to electric charge. We discuss these results relative to foundational work by Dicke on long range scalar interactions and the Brans-Dicke scalar-tensor theory, including how interaction with the scalar implies a variable rest mass, and the energetics of the joint scalar-gravitational interaction. We discuss the problems of tuning the only available free parameter, the invariant 5D length element of the sources, to neutralize the scalar force and avoid the otherwise-large scalar force predictions. We conclude that large classical forces are a testable prediction of 5D general relativity sufficient to falsify the 5D hypothesis. Yet the emergence of a new physical interaction lengthscale is suggestive of further unexplored physics of the long range scalar field.

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