Originally Posted by **aaaa202** Spacetime is described geometrically by the metric:
ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
From where does it follow that space is still to be treated as euclidean? |

That expression you wrote is called the "metric" the magnitude of ds is called the "interval". This is what makes spacetime non-euclidean. The expression ds^2 = dx^2 + dy^2 + dz^2 makes the space euclidean.