Causality (physics)

Causality is the relationship between causes and effects. It is considered to be fundamental to all natural science – especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics. From the perspective of physics, causality cannot occur between an effect and an event that is not in the back (past) light cone of said effect. Similarly, a cause cannot have an effect outside its front (future) light cone.'Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system.' Causality is the relationship between causes and effects. It is considered to be fundamental to all natural science – especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics. From the perspective of physics, causality cannot occur between an effect and an event that is not in the back (past) light cone of said effect. Similarly, a cause cannot have an effect outside its front (future) light cone. In classical physics, an effect cannot occur before its cause. In Einstein's theory of special relativity, causality means that an effect can not occur from a cause that is not in the back (past) light cone of that event. Similarly, a cause cannot have an effect outside its front (future) light cone. These restrictions are consistent with the grounded belief (or assumption) that causal influences cannot travel faster than the speed of light and/or backwards in time. In quantum field theory, observables of events with a spacelike relationship, 'elsewhere', have to commute, so the order of observations or measurements of such observables do not impact each other. Causality in this context should not be confused with Newton's second law, which is related to the conservation of momentum, and is a consequence of the spatial homogeneity of physical laws. The word causality in this context means that all effects must have specific causes. As discussed below, this is a principle that is violated in some theories of modern physics. Another requirement, at least valid at the level of human experience, is that cause and effect be mediated across space and time (requirement of contiguity). This requirement has been very influential in the past, in the first place as a result of direct observation of causal processes (like pushing a cart), in the second place as a problematic aspect of Newton's theory of gravitation (attraction of the earth by the sun by means of action at a distance) replacing mechanistic proposals like Descartes' vortex theory; in the third place as an incentive to develop dynamic field theories (e.g., Maxwell's electrodynamics and Einstein's general theory of relativity) restoring contiguity in the transmission of influences in a more successful way than did Descartes' theory. The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) lends heavy influence against the idea of the importance of causality. Causality has accordingly sometimes been downplayed (e.g., Newton's 'Hypotheses non fingo'). According to Ernst Mach the notion of force in Newton's second law was pleonastic, tautological and superfluous. Indeed, it is possible to consider the Newtonian equations of motion of the gravitational interaction of two bodies, as two coupled equations describing the positions r 1 ( t ) {displaystyle scriptstyle {mathbf {r} }_{1}(t)} and r 2 ( t ) {displaystyle scriptstyle {mathbf {r} }_{2}(t)} 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.