We consider an spacelike infinitesimal separation [tex]{ds}^{2}[/tex]<0

ds=+ or -ib [an imaginary quantity]

Now I integrate ds along some path from A to B. What happens if the imaginary parts cancel out on integration[if we can manage to cancel them out]?I mean, is it physically significant in any way?

We may have a slight variation of the problem:

Three spacetime points,A B and C lying at the corners of an infinitesimally small triangle are chosen[Of course this triangle does not lie on a flat surface]

ds from A to B=ib

ds from B to C =-ib

ds from A to C via B=0

Now is it possible to locate a direct path from A to C[which is not through C] which gives a null separation?

Is it quite possible that ds may simultaneously correspond to the two types of separation along different paths.

[The paths connecting the points are not straight lines[in general] but are infinitesimally small in length]

ds=+ or -ib [an imaginary quantity]

Now I integrate ds along some path from A to B. What happens if the imaginary parts cancel out on integration[if we can manage to cancel them out]?I mean, is it physically significant in any way?

We may have a slight variation of the problem:

Three spacetime points,A B and C lying at the corners of an infinitesimally small triangle are chosen[Of course this triangle does not lie on a flat surface]

ds from A to B=ib

ds from B to C =-ib

ds from A to C via B=0

Now is it possible to locate a direct path from A to C[which is not through C] which gives a null separation?

Is it quite possible that ds may simultaneously correspond to the two types of separation along different paths.

[The paths connecting the points are not straight lines[in general] but are infinitesimally small in length]

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