In Einstein's "Relativity," this equation appears in Appendix I (Lorentz Transformations): x1'2 + y1'2 + z1'2 - c2t1'2 = x12 + y12 + z12 - c2t2 This essentially says that for a given event at a given point and time in space, looking at this event from any frame of reference will give results that satisfy this equation for that event. In other words, x12 + y12 + z12 - c2t2 is a constant. I assume that t is not a parameter but merely a coordinate, just as x, y and z are. I am used to, from analytic geometery and linear algebra, that in the case of a parameter, once a value is assigned, will map to, simutaneously, all the coordinates and, since there is only one value in each coordinate that a given parametric value can map to, then we are essentially describing a line (straight or curvilinear) in space. The above equation, to my thinking, does not represent a parametric equation as the t can map to several x, y and z'sz once a value for it is assigned. Do we jump off here to "world lines?" or is this completely different?