You can never escape your light cone.
Light Spheres
Lets envision the light from a candle. The light is a sphere around it that propagates in all directions.
Because the speed of light is the maximum speed that anything can travel, any object inside this sphere will now be inside of it forever. You can never catch up to the expanding sphere.
Everything not within this light sphere is forever outside of your influence.
Light Cones
Instead of showing multiple spheres to represent time, lets make time it’s own dimension to show the expansion of the light sphere.
We can now visualize these expanding spheres as sections of a cone.
This “Light Cone” represents the boundary of Causality.
Everything in the universe has an independent light cone at every moment in time.
Not only do you have a future light cone, but you also have a past light cone.
This represents all possible events that could influence the present moment.
The convergence, known as the apex, can represent any event where we want to know the boundaries of its causal relationships.
The path taken through the light cone is called the worldline.
Light always moves along the surface of the cone, as the surface represents the speed of light through space.
Side Note
This made me wonder about the temporal to spacial velocity trade off discussed in You Are Moving at the Speed of Light and how it relates to light cones. If you remember this diagram:
It appears that this circle and the light cones encapsulate the same space, the causality boundary.
The upper semi-circle is the future light cone, the x-axis is the cones surface, and the bottom semi-circle is the past light cone.
The angle in the circle from -180° to 180° is the relative angle from the center of the cone to it’s surface.
In this equivalence diagram, I’ve marked the relevant lines on each model. And while the bottom semi-circle represents moving backwards in time, it is still technically correct as this would be bounded by the past light cone.