用狭义相对论的推广检验空间的各向异性
Testing for Anisotropy of Space via an Extension of Special Relativity
摘要：
在狭义相对论中，测试空间各向异性通常意味着测试光的各向异性传播。本文探讨了一种不同的可能性，在这种可能性中，光仍然假设在所有的帧中以不变的速度各向同性地传播，而其他物理效应则表现出方向依赖性。如果在坐标变换的推导中没有假设空间各向同性，则所得方程与洛伦兹关系式的差异在于附加因子$(\dfrac{c - v}{c + v})^κ$，其中$κ$是各向异性指数，其取决于选择作为x轴的方向。时间膨胀和长度收缩变得依赖于方向。各向异性指数是与帧无关的，因此如果$κ$是非零的，则不存在优选的各向同性帧。多普勒频移可以用来测量这个指数，并通过实验确定我们宇宙实际拥有的各向异性程度。
英文摘要：
In special relativity, testing for spatial anisotropy usually means testing for anisotropic propagation of light. This paper explores a different possibility, in which light is still assumed to propagate isotropically in all frames with an invariant speed, yet other physical effects exhibit a direction dependence. If spatial isotropy is not assumed in the derivation of the coordinates transformations, the resulting equations differ from the Lorentz relations by an additional factor $(\dfrac{c - v}{c + v})^κ$, where $κ$ is the anisotropy exponent, which depends on the direction chosen as the x-axis. Time dilation and length contractions become direction dependent. The anisotropy exponent is frame-independent, so no preferred isotropic frame exists if $κ$ is non-vanishing. The Doppler shift can be used to measure this exponent and determine experimentally the degree of anisotropy our universe actually possesses.
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