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## Main Question or Discussion Point

In Einstein's "Relativity," this equation appears in Appendix I (Lorentz Transformations):

x

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, x

I assume that

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

Do we jump off here to "world lines?" or is this completely different?

x

_{1}'^{2}+ y_{1}'^{2}+ z_{1}'^{2}- c^{2}t_{1}'^{2}= x_{1}^{2}+ y_{1}^{2}+ z_{1}^{2}- c^{2}t^{2}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, x

_{1}^{2}+ y_{1}^{2}+ z_{1}^{2}- c^{2}t^{2}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's*z once a value for it is assigned.Do we jump off here to "world lines?" or is this completely different?