With age comes wisdom, so let's be wise?

When learning and describing concepts in relativity, one may use something called a wordline. The worldline shows somethings path through both space and time. This is different from trajectory or whatever, which just shows path through space. 

Here you can see particles moving through space and time. There is a line going straight upwards (red one), this would be a particle that is staying completely still. There is also a line going 45-ish degrees (yellow), and that is a photon. A photon will always have the same path in this kind of diagram, because the speed of light is constant relative to the observer. The orange one is another particle moving with a non-zero velocity relative to the red particle.

If we were to change our frame of reference so that we are moving along with one of the moving particles (so that it effectively stands still), the diagram would look more like this

You may notice that the orange line now stands up straight. That is because this particle is the reference point and therefore doesn't move. Of course, the red one now moves the opposite way from the orange one as expected. As I said earlier, the yellow line is the same in this diagram, because the speed of light is constant relative to the observer.

Worldlines are fairly useful tools when studying relativity. There is just one more thing I want to mention; The principle of maximal aging! Because spacetime is a bit different from normal space, in how it is defined, it acts a bit different too (wow, what a logical leap!) Where a distance in normal space can be measured as \(\Delta S_{normal space}^2 = \Delta x^2 + \Delta y^2\), while a distance in timespace is measured as \(\Delta S_{timespace}^2 = \Delta t^2 - \Delta x^2\). The minus sign makes a surprisingly huge difference when you start working with it. For example, the shortest line between two points in spacetime isn't a straight line, rather the longest line is a straight line between the points.

[I would put in a diagram here showing how that worked out, but unfortunately that diagram would have to be made in real space, so that is a no-can-do]

This is the principle of maximal aging; A particle not affected by any forces (special note here: Gravity is, in fact, not an actual force, but rather an effect of the curvature of spacetime that makes particles that move through it move differently) will follow the longest path through spacetime, which is a straight line. Relativity is fucking weird.