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arXiv physics/0412068physics.gen-ph
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弯曲时空中的狭义相对论

Special Theory of Relativity in Curved Space Time

Moninder Singh Modgil

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13 pages
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摘要：

时空测量，狭义相对论的实验需要在弯曲的时空中修正。发现在具有度规$g$的时空中，必须用$γ_g=1/\sqrt{g_{μν} V^μV^ν}$代替狭义相对论因子$γ$，其中$V_μ=(1,v,0,0)$是4-速度，$v$是两个标架之间的相对速度。其中的新奇之处是矛盾的快子态，由于时空曲率，当速度小于光速时，$γ_g$变为虚的。相对论质量成为时空曲率的函数，$m=\sqrt{g_{μν}P^μP^ν}$，其中$P_μ=(E,p)$是4-动量，标志着马赫原理的新形式，其中一个整体对象-即度规张量，正在影响内部。

英文摘要：

Space-time measurements, of gedanken experiments of special relativity need modification in curved spaces-times. It is found that in a space-time with metric $g$, the special relativistic factor $γ$, has to be replaced by $γ_g=1/\sqrt{g_{μν} V^μV^ν}$, where $V_μ=(1,v,0,0)$, is the 4-velocity, and $v$ the relative velocity between the two frames Examples are given for Schwarzschild metric, Friedmann-Robertson-Walker metric, and the Gödel metric. Among the novelties are paradoxical tachyonic states, with $γ_g$ becoming imaginary, for velocities less than that of light, due to space-time curvature. Relativistic mass becomes a function of space-time curvature, $m=\sqrt{g_{μν}P^μP^ν}$, where $P_μ=(E,p)$ is the 4-momentum, signaling a new form of Mach's principle, in which a global object - namely the metric tensor, is effecting interia.

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