@狐狸先生的回答在实用性的层面上已经足够好了,不过因为我自己很久以前曾经思考过广相里类似的问题所以回答一下,首先引用一段Carroll在Spacetime and Geometry里104页的一段话,这段话其实已经回答了楼主想要问的问题了:………we simply must learn to live with the fact that two vectors can only be compared in a natural way if they are elements of the same tangent space. For example, two particles passing by each other have a well-defined relative velocity, which cannot be greater than the speed of light. But two particles at different points on a curved manifold do not have any well-defined notion of relative velocity -- the concept simply makes no sense……深刻理解这段话的话,楼主的问题就不再是问题,而我接下来要谈的东西基本由此展开首先
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