广义相对论课堂7不变性原理、相对论电磁学、Einstein等效.ppt

NATURE PHYSICS?|?LETTERQuantum non-locality based on finite-speed causal influences leads to superluminal signalling J-D. Bancal, S. Pironio, A. Acín, Y-C. Liang, V. Scarani ?N. Gisin We derive our results assuming that the speed of causal influences?v?is defined with respect to a privileged reference frame (or a particular foliation of spacetime into space-like hyperplanes). It should be stressed that although the assumption of a privileged frame is not in line with the spirit of relativity, there is also no empirical evidence implying its absence. In fact, even in a perfectly Lorentz-invariant theory, there can be natural preferred frames owing to the non-Lorentz-invariant distribution of matter—a well-known example of this is the reference frame in which the cosmic microwave background radiation seems to be isotropic (see, for example, ref.?17). Moreover, note that there do exist physical theories that assume a privileged reference frame and are compatible with all observed data, such as Bohmian mechanics18,?19, the collapse theory of Ghirardi, Rimini and Weber20?and its relativistic generalization21. Although both of these theories reproduce all tested (non-relativistic) quantum predictions, they violate the principle of continuity mentioned above (otherwise they would not be compatible with no-signalling as our result implies). 不变性原理 以广义坐标变换为例 Kretchmann 1917 方程协变covariant 形式不变covariance （Galileo、Lorentz、广义） 协变性原理 无约束 物理上实验结果 动力学量=几何体 方程不变invariance不但形式而且内容 绝对体～常数 纯粹数学常数、物理学常数 函数（坐标变换函数、Jacobian） 分量（闵氏度规） 动力学体——物理变量——依赖物质状态（条件）：粒子位置、动量、场强、能量密度...... 例 牛一律：V=常数？a=0 进化到狭义相对论第一定律 诘问Rosser第434页——定律和具体运动方程 Rahilly 三维空间中光线球面——椭球面 例Galilei 径向自由下落vs抛物 维基百科 The relationship between general covariance and general relativity may be summarized by quoting a standard textbook:[2] Mathematics was not sufficiently refined in 1917 to cleave apart the demands for no prior geometry and for a geometric, coordinate-independent formulation of physics.?Ein