Ok so I begin by entertaining the following hypothesis: Suppose a number of points are selected in spacetime, and then all relationships between these points that are invariant under Lorentz transformations are recorded. Given only these relationships, one should be able to reproduce the original set of points. (or a translated/lorenz transformed/reflected version of the original set of points). Now, suppose that we choose three distinct points on one o' them there worldlines of a photon. If we were to specify the Lorentz interval between each pair of points, we would get 0, 0, and 0. This would not tell you which point is in the middle. I'm pretty sure that, even though you can move these points all over the place with Lorentz transformations, it is not actually possible to change which one is in the middle. So my question is, which of the following is true: A) My original hypothesis is wrong. B) There is an invariant that will tell you which point is in the middle (if this is the case, please describe said invariant) C) My assumption about changing the middle point through Lorentz transformations is wrong. Thank you very much for your thoughts.