1. The action then is proportional to the curvature of the world line . 2. All curves through point p have a tangent vector, not only world lines . 3. For world lines of photons passing the origin in different directions and holds. 4. Hundreds of cookbooks from around the world line his office and hallway walls. 5. A world line traces out the path of a single point in spacetime. 6. The red lines represent world lines in newtonian space and time. 7. Geometrically, "'U "'is a normalized vector tangent to the world line of the particle. 8. The idea of world lines originates in physics and was pioneered by Hermann Minkowski. 9. The history of an object traces a curve in spacetime, called its world line . 10. The idea is based on the world lines traced out across spacetime by every electron.