- #1
Gerenuk
- 1,034
- 5
How do you prove that for a set of coordinates you are supposed to take
[tex]\mathrm{d}s^2=\mathrm{d}x_i\mathrm{d}x^i[/tex]
for the distance? I mean in a very abstract fashion. All I know is that there is some coordinate mesh. Why don't I take other powers for the distance for example?
Or if that bilinear equation is only a special case, then why is our space obeying it?
[tex]\mathrm{d}s^2=\mathrm{d}x_i\mathrm{d}x^i[/tex]
for the distance? I mean in a very abstract fashion. All I know is that there is some coordinate mesh. Why don't I take other powers for the distance for example?
Or if that bilinear equation is only a special case, then why is our space obeying it?