Causality is one of the most fundamental principles of philosophy, physics, and other sciences. It is essentially the attempt to make sense of observations by linking events (effects) to other events (causes) and explaining the mechanisms behind these relations. A fundamental requirement is that a caused effect can not occur before the cause. Within Einstein's theory of relativity, causality even requires a more stringent restriction: the time between cause and event must be at least the time which light propagating in vacuum needs to get from the location of the cause to the location of the event. In short, no signal can propagate faster than light does in vacuum. The technical details are complicated; the description of space and time in the theory of relativity is sophisticated and not in tune with our natural intuition.
In optics, causality implies that light can never be used for transmitting a signal with a higher velocity than c, the vacuum velocity of light. There are certain situations, where this restriction appears to be violated, because light can propagate with a phase velocity or group velocity greater than c. At a first glance, this may suggest the possibility of superluminal transmission of information. However, Maxwell's theory of electromagnetism and the theory of quantum electrodynamics have been proven to be strictly causal, and there is so far no reason to believe that these theories have to be replaced with non-causal ones. Any description of apparently non-causal effects in light propagation on the basis of Maxwell's equations must logically be flawed at some point, which, however, is not always easy to identify.
In optics, causality has important consequences, e.g. in the form of the Kramers–Kronig relations, relating the frequency-dependent refractive index of a medium to its frequency-dependent absorption properties.
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See also: superluminal transmission, Kramers–Kronig relations
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