- #1
ConradDJ
Gold Member
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I recently Googled "spacetime topology" and found that the topology of Minkowski spacetime is generally described as that of an R4 manifold.
This is not my field, but I'm surprised. Perhaps mathematically the (---+) "Lorentz signature" can be taken as a secondary characteristic of the manifold... but physically, it seems very basic to the topology of spacetime that any two points on a "light-like interval" are directly connected.
I understand that they are not the same point in spacetime, and I understand that there is a time-direction in the connection between them. That is, when I look at a star, there is a "null" spacetime distance between the place and time the photon was emitted and the place and time where it reaches my eye -- but this is a one-way "causal" connection from the star to my eye.
Does anyone know of a treatment of spacetime topology that discusses this kind of directed connection across a "null interval"?
This is not my field, but I'm surprised. Perhaps mathematically the (---+) "Lorentz signature" can be taken as a secondary characteristic of the manifold... but physically, it seems very basic to the topology of spacetime that any two points on a "light-like interval" are directly connected.
I understand that they are not the same point in spacetime, and I understand that there is a time-direction in the connection between them. That is, when I look at a star, there is a "null" spacetime distance between the place and time the photon was emitted and the place and time where it reaches my eye -- but this is a one-way "causal" connection from the star to my eye.
Does anyone know of a treatment of spacetime topology that discusses this kind of directed connection across a "null interval"?