Skip to main content

Mathematics for Physics

163 Events

A physical occurrence at a definite place and time that is used to label points of spacetime by four coordinates.

The coordinate representation of an event. An event is a pointlike happening labeled by four coordinates \((x, y, z, t)\). A coordinate is a numerical label along a spacetime axis. This principle is used to locate a happening in a chosen reference frame.

The spacetime coordinates of an event are

\[ (x, y, z, t) \]

where

  • \((x, y, z)\) are the spatial coordinates of the event.
  • \(t\) is the time of the event.

Frame-independent existence. The happening itself does not depend on which inertial observer assigns the coordinates. Spacetime is the four-dimensional set whose elements are events. This principle is used to guarantee that every inertial observer records the same occurrences.

Causal classification by the interval. The relation between two events is fixed by the invariant interval between their coordinates. An invariant spacetime interval is the observer-independent four-dimensional squared separation of two events. This principle is used to decide whether one event can influence another by a signal no faster than light.

Relativity of simultaneity. Two events that share one time \(t\) in one frame need not share one time \(t'\) in a frame in relative motion. Simultaneity is the condition that two events have the same time coordinate in a given frame. This principle is used to show that there is no absolute common now for spatially separated events.

Note: Also called a spacetime event. Also called a spacetime point.

163.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — event as activity at a definite point and instant; spacetime coordinates \((x,y,z,t)\); relativity of simultaneity.
  2. Shankar, R. Fundamentals of Physics I. Yale University Press, 2019. — event as something at a certain place and time; causal classification.
  3. Carroll, S. M. Spacetime and Geometry. Cambridge University Press. — event as an individual point in spacetime; interval between events.
  4. Emam, M. H. Covariant Physics. Oxford University Press, 2021. — occurrence independent of the coordinate labels.