Relativity of simultaneity

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.

According to the special theory of relativity, it is impossible to say in an absolute sense that two distinct events occur at the same time if those events are separated in space. For example, a car crash in London and another in New York, which appear to happen at the same time to an observer on the earth, will appear to have occurred at slightly different times to an observer on an airplane flying between London and New York. The question of whether the events are simultaneous is relative: in the stationary earth reference frame the two accidents may happen at the same time but in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events could be causally connected (i.e. the time between event A and event B is greater than the distance between them divided by the speed of light), the order is preserved (i.e., "event A precedes event B") in all frames of reference.

If we imagine one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events. This is illustrated in the ladder paradox, a thought experiment which uses the example of a ladder moving at high speed through a garage.

A mathematical form of the relativity of simultaneity ("local time") was introduced by Hendrik Lorentz in 1892, and physically interpreted (to first order in v/c) as the result of a synchronization using light signals by Henri Poincaré in 1900. However, both Lorentz and Poincaré based their conceptions on the aether as a preferred but undetectable frame of reference, and continued to distinguish between "true time" (in the aether) and "apparent" times for moving observers. It was Albert Einstein in 1905 who abandoned the (classical) aether and emphasized the significance of relativity of simultaneity to our understanding of space and time. He deduced the failure of absolute simultaneity from two stated assumptions:

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