The discussion revolves around the physical meaning of spacelike geodesics in the context of general relativity and spacetime geometry. Participants explore the distinction between geometric and physical interpretations, the implications of spacelike geodesics, and the conditions under which they may hold physical significance.
Participants express a range of views on the physical meaning of spacelike geodesics, with no consensus reached. Some believe they hold physical significance, while others argue they do not, highlighting the ambiguity in the term "physical meaning." The discussion remains unresolved regarding the implications of spacelike geodesics.
Participants note that the interpretation of spacelike geodesics may depend on specific conventions, such as foliation choices, and that without these, intrinsic physical meaning may be difficult to establish. The discussion also touches on the complexity of defining physical meaning in the context of geometry and spacetime.
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.