simultaneity

Simultaneity is the relation of two or more events occurring at the same time. In everyday language and classical physics, time is treated as absolute and simultaneous events are shared by all observers. In the framework of special relativity, simultaneity becomes relative: whether two spatially separated events are simultaneous depends on the observer’s state of motion.

In Newtonian physics, a universal time coordinate allows a single notion of simultaneity across space. Special relativity replaces this with time coordinates that mix with spatial coordinates under changes of reference frame, via the Lorentz transformation. Consequently, events that are simultaneous in one inertial frame may not be simultaneous in another moving frame.

A practical way to define simultaneity in relativity is clock synchronization. The Einstein synchronization convention uses light signals: a clock at A sends a signal to B, which immediately reflects it back; if the clock at B shows a time exactly halfway between the sending and receiving times at A, then A and B are synchronized under the assumption that light travels at the same speed in both directions. The conventionality of simultaneity recognizes that different synchronization conventions (epsilon parameter) can be adopted, yielding slightly different notions of simultaneity.

The concept is illustrated by the train and platform thought experiment: events that are simultaneous on a moving train are not simultaneous for observers on the platform, and vice versa. This does not violate causality, since only events connected by lightlike or timelike separations have a definite causal order.

In general relativity, simultaneity becomes even more frame-dependent due to spacetime curvature, and global simultaneity is not uniquely defined. Practical systems, such as GPS, incorporate relativistic corrections to coordinate time to maintain synchronized timing across large distances.