The strong causality principle forbids information transfer faster than the speed of light; the weak causality principle operates at the microscopic level and need not lead to information transfer.
In both Einstein's theory of special and general relativity, causality means that an effect cannot occur from a cause that is not in the back (past) light cone of that event.
These restrictions are consistent with the constraint that mass and energy that act as causal influences cannot travel faster than the speed of light and/or backwards in time.
Consequently, the relativistic principle of causality says that the cause must precede its effect according to all inertial observers.
The word causality in this context means that all effects must have specific physical causes due to fundamental interactions.
The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) meant that scholastic arguments about what caused phenomena were either rejected for being untestable or were just ignored.
The complaint that physics does not explain the cause of phenomena has accordingly been dismissed as a problem that is philosophical or metaphysical rather than empirical (e.g., Newton's "Hypotheses non fingo").
According to Ernst Mach[7] the notion of force in Newton's second law was pleonastic, tautological and superfluous and, as indicated above, is not considered a consequence of any principle of causality.
of the two bodies, without interpreting the right hand sides of these equations as forces; the equations just describe a process of interaction, without any necessity to interpret one body as the cause of the motion of the other, and allow one to predict the states of the system at later (as well as earlier) times.
In the D-N view, a physical state is considered to be explained if, applying the (deterministic) law, it can be derived from given initial conditions.
Thus, in classical physics, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace's claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past (see Laplace's demon).
Confusion between causality and determinism is particularly acute in quantum mechanics, this theory being acausal in the sense that it is unable in many cases to identify the causes of actually observed effects or to predict the effects of identical causes, but arguably deterministic in some interpretations (e.g. if the wave function is presumed not to actually collapse as in the many-worlds interpretation, or if its collapse is due to hidden variables, or simply redefining determinism as meaning that probabilities rather than specific effects are determined).
[citation needed] The butterfly effect theory proposes: "Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system."
Based on this, Rafael Sorkin proposed the idea of Causal Set Theory, which is a fundamentally discrete approach to quantum gravity.