worldline
A worldline is the complete path an object traces through spacetime — not just where it goes, but where it is at every moment of its existence. On a spacetime diagram it is a continuous curve from the object's beginning to its end, threading through every event the object passes through. Even something sitting perfectly still has a worldline: it stays in place but still moves steadily upward through time.
Because nothing can outrun light, every massive object's worldline must stay tilted more steeply than 45° — closer to vertical than a light ray. A straight worldline means steady, force-free motion; a curved or bent one means the object is accelerating, pushed by some force. Reading the slope at any point tells you how fast the object is moving there.
The deepest feature of a worldline is its 'length' as measured by the spacetime metric, which is not the length your ruler would read but the time the object's own clock records along the way — its proper time. Two travellers who part and later reunite generally have worldlines of different lengths, and so have aged by different amounts. This is the geometric heart of the twin paradox: the one who took the longer-looking path on paper actually experiences the shorter proper time.
The proper time τ is the spacetime 'length' of the worldline — the time the object's own clock records.
Counterintuitively, in spacetime the straight worldline between two events is the LONGEST in proper time, not the shortest — the opposite of straight lines in ordinary space. Acceleration (a bent worldline) always costs you elapsed time.