Editing Causality (physics) (section)

== Simultaneity ==
In [[modern physics]], the notion of causality had to be clarified. The word ''simultaneous'' is observer-dependent in [[special relativity]].<ref>[[Albert Einstein|A. Einstein]], "Zur Elektrodynamik bewegter Koerper", ''Annalen der Physik'' '''17''', 891–921 (1905).</ref> The principle is [[relativity of simultaneity]]. Consequently, the relativistic principle of causality says that the cause must precede its effect ''according to all [[inertial]] observers''. This is equivalent to the statement that the cause and its effect are separated by a [[timelike]] interval, and the effect belongs to the future of its cause. If a timelike interval separates the two events, this means that a signal could be sent between them at less than the speed of light. On the other hand, if signals could move faster than the speed of light, this would violate causality because it would allow a signal to be sent across [[spacelike]] intervals, which means that at least to some inertial observers the signal would travel ''backward in time''. For this reason, special relativity does not allow communication faster than the [[speed of light]].

In the theory of [[general relativity]], the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the [[spacetime]] is curved. New subtleties must be taken into account when we investigate causality in [[quantum mechanics]] and relativistic [[quantum field theory]] in particular. In those two theories, causality is closely related to the [[principle of locality]]. 
[[Bell's Theorem]] shows that conditions of "local causality" in experiments involving [[quantum entanglement]] result in non-classical correlations predicted by quantum mechanics.

Despite these subtleties, causality remains an important and valid concept in physical theories. For example, the notion that events can be ordered into causes and effects is necessary to prevent (or at least outline) [[causality paradox]]es such as the [[grandfather paradox]], which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. See also [[Chronology protection conjecture]].