# I where does the line element of Minkowiski space come from?

1. Jul 26, 2017

### Ahmed Atef

How is it derived?
ds^2 =-cdt^2+dx^2+dy^2+dz^2

2. Jul 26, 2017

### puzzled fish

Had this been ds^2 =+cdt^2+dx^2+dy^2+dz^2 it would've been the Pythagorean Theorem.

3. Jul 26, 2017

### Ahmed Atef

If it was ecludian space

4. Jul 26, 2017

### George Jones

Staff Emeritus
I would say that it is not derived (except maybe as an approximation to more general spacetimes), i.e., it is arrived at by induction, not by deduction.

5. Jul 28, 2017

### PAllen

Well, it can derived depending on what your assumptions are. If you assume the Lorentz transform, then the Minkowski line element follows as the only possible metric that is invariant under Lorentz transforms. Similarly, if you assume the Minkowski metric, you can derive the Lorentz transform.