The Maths of General Relativity (1/8) - Spacetime and Worldlines

Einstein and general relativists view spacetime not as separate space and time but as a unified four-dimensional structure underlying physical reality.

Every object—an apple, planet, photon, or person—traces its own unique worldline through spacetime’s four-dimensional structure.

Any observer analyzing an object’s trajectory must graduate the worldline to transform a static geometric curve into a description of dynamic motion.

Every object experiences its own proper time (τ, tau), which governs its internal evolution regardless of external coordinate systems or observers.

Physicists and mathematicians impose coordinate systems on spacetime to translate geometric relationships into numerical equations, enabling calculations and predictions.

Observers must carefully distinguish between coordinate time (t), which depends on their chosen reference frame, and proper time (τ), which belongs intrinsically to the object being observed.

Every object in the universe, from stationary apples resting on Earth to photons racing through space, constantly moves through spacetime without exception.

All objects possess total spacetime velocity (four-velocity) that redistributes between spatial and temporal components depending on their motion through space.