Do World Lines Exist?

The world line of the Earth is helical in spacetime (a curve in a four-dimensional space) and does not return to the same point. A curve M in [spacetime] is called a worldline of a particle if its tangent is future timelike at each point. ... A world line traces out the path of a single point in spacetime.

What is a point in spacetime?

Mathematical events have zero duration and represent a single point in spacetime. The path of a particle through spacetime can be considered to be a succession of events. The series of events can be linked together to form a line which represents a particle's progress through spacetime.

What must be true about the slope of the worldline of a light pulse?

At any point, the slope of the worldline is d(ct)/dx = (c dt)/(v dt) = c/v. Thus a light pulse with v = ±c has a slope of ±1 on a spacetime diagram, giving angles of 45° with the ±x-axes. Since material particles have speeds less than c, all worldlines for material particles are steeper than those 45° angles.