Show that the expressions (ds)2 (c dt)2- (dx)2 - (dy) - (dz)2 is invariant (i. e, a scalar quantity) under lorentz transformations. this is the "four-dimensional distance" between events and is also known as the metric. show that if (ds)2 < 0 the two events cannot be causally connected, i. e., there cannot not be any information transmitted from one to the other even at light speed