When you draw a space-time diagram and the associated world line for an object moving through space-time, the diagram will be dependent upon the reference frame you are observing from, right? Like for instance the world line for a moving object when taking a reference frame riding along with that object will always be straight up since there does not appear to be any relative motion.
If this the case, then how is it possible to compare two space-time diagrams — wouldn't the fact that they are from different reference frames discredit the validity of making comparisons between them?
Second, when you observe a moving object from your inertial reference frame, that moving object will have a slanted path through space-time, with the planes of simultaneity also tilted but still orthogonal to the worldline of the object, right? Why must these planes be tilted?
Finally, why are the worldlines for light drawn at a 45º angle? Doesn't this imply that the light travels a same distance in space as it does in time? Shouldn't the line be close to 0 slope since it travels a very great distance in a short amount of time?
Finally, since 45º is the line for light, does this mean that you can not have any object with a world line of lower angle, since this would imply that its speed is faster than that of light?