In Einstein's "Relativity," this equation appears in Appendix I (Lorentz Transformations):(adsbygoogle = window.adsbygoogle || []).push({});

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 thattisnota parameter but merely a coordinate, just asx,yandzare.

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 thetcan map to severalx,yandz'sz once a value for it is assigned.

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

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# Minkowski 4-space? Yes or No.

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