Tolman亮度距离、Poincare光距离和Cayley-Klein双曲距离
Tolman's Luminosity-Distance, Poincare's Light-Distance and Cayley-Klein's Hyperbolic Distance
摘要：
从庞加莱的光距定义出发，利用洛伦兹变换（LT）推导出了宇宙学中的托尔曼光距公式，在闵可夫斯基度规中，如果距离是真时（如人们常争论的那样），那么光距也一定是最短的距离，就像真时长一样（不像爱因斯坦在静止系中的最长长度）。通过在爱因斯坦基本同步中引入庞加莱固有光距，导出了观察者与退镜之间的扩张距离（含相对论多普勒因子）。这样的距离对应的不是欧几里得距离（爱因斯坦的刚性杆），而是具有洛巴切夫斯基视界的双曲距离（凯莱-克莱因）。从一个基本的距离-速度比例双曲线出发，推导出哈勃定律。通过遵循Penrose的Lobatchevskian表示，我们将狭义相对论（SR）转化为双曲宇宙相对论（HCR）。在双曲旋转运动（基本主动LT或爱因斯坦助推）中，哈勃常数（双曲角速度）与最小Milgrom基本固有加速度（双曲离心加速度）耦合。
英文摘要：
We deduce Tolman's formula of luminosity-distance in Cosmology from Poincare's definition of light-distance with Lorentz Transformation (LT).In Minkowskian metric, if distance is proper time (as it is often argued) then light-distance must be also the shortest distance, like proper duration (unlike Einstein's longest length within rest system). By introducing Poincare's proper light-distance in Einstein's basic synchronization we deduce a dilated distance between observer and receding mirror (with relativistic Doppler factor). Such a distance corresponds not to an Euclidean distance (Einstein's rigid rod) but to an Hyperbolic distance (Cayley-Klein) with a Lobatchevskian Horizon. From a basic proportionality hyperbolic distance-velocity, we deduce the law of Hubble. By following Penrose's Lobatchevskian representation of LT, we transform Special Relativity (SR) into an Hyperbolic Cosmological Relativity (HCR). by using only the LT but the whole LT. In Hyperbolic Rotation motion (basic active LT or Einstein's boost), Hubble constant (hyperbolic angular velocity) is coupled with a minimal Milgrom's basic proper acceleration (hyperbolic centrifugal acceleration).
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。
