- #1

- 696

- 3

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?