论文标题
Weyl协方差，第二个时钟效应和对称触发性重力理论的适当时间
Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity
论文作者
论文摘要
在Weyl的论文（Weyl的引力和埃莱克特里齐特（Weyl insitzungsber。preuss。preuss。Akad。），柏林，1918年）之后，爱因斯坦（Einstein）声称，以非现象性为非现象的时空几何形状写的重力模型，即所谓的第二个时钟效应。我们给出了矢量切线到曲线的平行运输的新处方，该曲线在局部通用坐标和Weyl变换下都是不变的，以消除该效果。因此，由于在没有数值的空间中，切线矢量的长度在沿封闭曲线的平行传输过程中不会变化，因此不仅出现第二个时钟效应，而不仅仅是可集成的Weyl时空。从对称远程（或Minkowski-weyl）几何形状的角度来看，我们特别激发了问题。我们还得出结论，如果自然尊重Lorentz的对称和Weyl对称性，那么最简单的几何形状可以始终如一地发展替代性重力模型。 $ q_ {μν} \ neq 0，\; t^μ= 0，\; r^μ_ν= 0 $。因此，我们讨论了适当的时间，无旋转测试体的轨道方程和对称远程引力的拉格朗日。
Just after Weyl's paper (Weyl in Gravitation und Elektrizität, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called second clock effect. We give a new prescription of parallel transport of a vector tangent to a curve which is invariant under both of local general coordinate and Weyl transformations in order to remove that effect. Thus since the length of tangent vector does not change during parallel transport along a closed curve in spacetimes with non-metricity, a second clock effect does not appear in general, not only for the integrable Weyl spacetime. We have specially motivated the problem from the point of view of symmetric teleparallel (or Minkowski-Weyl) geometry. We also conclude that if nature respects Lorentz symmetry and Weyl symmetry, then the simplest geometry in which one can develop consistently alternative gravity models is the symmetric teleparallel geometry; $Q_{μν}\neq 0, \; T^μ=0, \; R^μ_ν=0$. Accordingly we discuss the proper time, the orbit equation of a spinless test body and the Lagrangian for symmetric teleparallel gravity.
