庞加莱椭圆背后的相对论运动学
The relativistic kinematics underlying Poincare's ellipse
摘要：
我们表明，庞加莱的拉长椭圆，立即推导出洛伦兹变换（LT）的运动学基础，是不一样的爱因斯坦的运动学。两个主要的区别是：一方面是洛伦兹收缩与LT的关系，另一方面是多普勒公式与波四矢量的关系。爱因斯坦的波四矢量（光、光子、横规范的量子理论）与庞加莱的波四矢量（光、电磁波、洛伦兹规范的经典理论）不同，因此多普勒公式也不相同。庞加莱的多普勒公式并不独立于时空的度量。我们表明，庞加莱的度量的时空是基于宇宙学定义的距离和预测的空间扩展的远程对象（哈勃），直接与庞加莱的多普勒公式。
英文摘要：
We show that the kinematics underlying Poincare's elongated ellipse, immediately deduced from Lorentz Transformation (LT), is not the same as Einstein's kinematics. The two main differences are : On one hand the relationship of Lorentz contraction with LT, and on the other hand, the relationship of Doppler formula with wave four-vector. Einstein's wave four-vector (quantum theory of light, photon, transverse gauge) is not the same as Poincare's wave four-vector (classical theory of light, electromagnetic wave, Lorenz gauge) and therefore the Doppler formulas are not the same. Poincare's Doppler formula is not independent of the metric of space-time. We show that Poincare's metrics of space-time is based on a cosmological definition of distance and predicts an expansion of space for remote objects (Hubble), directly connected with Poincare's Doppler formula.
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