The discussion centers on the physical meaning of spacelike geodesics in the context of general relativity. Participants clarify that while spacelike geodesics represent the longest path between two events in curved spacetime, their physical interpretation is less straightforward than that of timelike geodesics, which correspond to proper time. The conversation highlights the importance of geometry in physics, arguing that geometric relationships are integral to understanding physical interactions, despite some participants questioning the physical significance of spacelike geodesics without specific conventions.
PREREQUISITESPhysicists, mathematicians, and students of general relativity seeking to deepen their understanding of the interplay between geometry and physical phenomena, particularly in the context of spacelike and timelike geodesics.
As discussed in a recent thread, to endow the underlying set (i.e. the set of spacetime points) of an affine structure the set of tangent spaces at each point must met let me say a 'consistency condition'. Basically vectors belonging to different tangent spaces have to be understood/treated as elements of the same vector space (i.e. the translation vector space) in a such way that axioms of affine space are fullfilled.vanhees71 said:That's also true, if you interpret the tangent space at the point under consideration as an affine point space.