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The weaker the causality condition on a spacetime, the more unphysical the spacetime is. Spacetimes with closed timelike curves, for example, present severe interpretational difficulties. See the grandfather paradox. It is reasonable to believe that any physical spacetime will satisfy the strongest causality condition: global hyperbolicity.
Although this definition uses the reflexive convention we could have chosen the irreflexive convention in which the order relation is irreflexive and asymmetric. The causal relation of a Lorentzian manifold (without closed causal curves) satisfies the first three conditions. It is the local finiteness condition that introduces spacetime ...
The causality violating set is the set of points through which closed causal curves pass. The boundary of the causality violating set is a Cauchy horizon . If the Cauchy horizon is generated by closed null geodesics, then there's a redshift factor associated with each of them.
Causality is an influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. [1]
The idea that the output of a function at any time depends only on past and present values of input is defined by the property commonly referred to as causality. A system that has some dependence on input values from the future (in addition to possible dependence on past or current input values) is termed a non-causal or acausal system , and a ...
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed.
Judea Pearl defines a causal model as an ordered triple ,, , where U is a set of exogenous variables whose values are determined by factors outside the model; V is a set of endogenous variables whose values are determined by factors within the model; and E is a set of structural equations that express the value of each endogenous variable as a function of the values of the other variables in U ...
Causal reasoning is the process of identifying causality: the relationship between a cause and its effect.The study of causality extends from ancient philosophy to contemporary neuropsychology; assumptions about the nature of causality may be shown to be functions of a previous event preceding a later one.