I'm trying to make sense of the following statement on Wikipedia:
>Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from four-dimensional Euclidean space.
which I came across while reading about... you know, Minkowski spaces. I've seen Minkowski space being defined as follows:
>Minkowski spacetime is a 4-dimensional real vector space M on which is defined a nondegenerate, symmetric, bilinear form g of index 1.
and it makes sense. However, this does not exclude the possibility of g taking on a negative value, like it could for the Minkowski metric, and therefore (M, g) is not a metric space in the sense that is familiar from analysis. I found that g is a pseudo-Riemannian metric instead, and therefore it shouldn't be possible to simply compare (M, g) to the known Euclidian 4-space.
But then what would be the canonical choice of a metric or topology on M? I've found the path topology is a candidate, is Wikipedia's statement based on this choice of topology?
>Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from four-dimensional Euclidean space.
which I came across while reading about... you know, Minkowski spaces. I've seen Minkowski space being defined as follows:
>Minkowski spacetime is a 4-dimensional real vector space M on which is defined a nondegenerate, symmetric, bilinear form g of index 1.
and it makes sense. However, this does not exclude the possibility of g taking on a negative value, like it could for the Minkowski metric, and therefore (M, g) is not a metric space in the sense that is familiar from analysis. I found that g is a pseudo-Riemannian metric instead, and therefore it shouldn't be possible to simply compare (M, g) to the known Euclidian 4-space.
But then what would be the canonical choice of a metric or topology on M? I've found the path topology is a candidate, is Wikipedia's statement based on this choice of topology?
