Editing Causality (section)

==== Physics ====
{{Main|Causality (physics)}}

One has to be careful in the use of the word cause in physics. Properly speaking, the hypothesized cause and the hypothesized effect are each temporally transient processes. For example, force is a useful concept for the explanation of acceleration, but force is not by itself a cause. More is needed. For example, a temporally transient process might be characterized by a definite change of force at a definite time. Such a process can be regarded as a cause. Causality is not inherently implied in [[equations of motion]], but postulated as an additional [[constraint (classical mechanics)|constraint]] that needs to be satisfied (i.e. a cause always precedes its effect). This constraint has mathematical implications<ref name=kinsler2011>
{{cite journal
| author=Kinsler, P.
| s2cid=56034806
| year=2011
| title=How to be causal
| journal=Eur. J. Phys.
| volume=32
| issue=6
| pages=1687–1700
| doi=10.1088/0143-0807/32/6/022
| arxiv=1106.1792|bibcode = 2011EJPh...32.1687K }}</ref> such as the [[Kramers-Kronig relations]].

Causality is one of the most fundamental and essential notions of physics.<ref>[[Albert Einstein|Einstein, A.]] (1910/2005). 'On Boltzmann's Principle and some immediate consequences thereof', unpublished manuscript of a 1910 lecture by Einstein, translated by B. Duplantier and E. Parks, reprinted on pp. 183–199 in ''Einstein,1905–2005, Poincaré Seminar 2005'', edited by T. Damour, O. Darrigol, B. Duplantier, V. Rivasseau, Birkhäuser Verlag, Basel, {{ISBN|3-7643-7435-7}}, from ''Einstein, Albert: The Collected Papers of Albert Einstein'', 1987–2005, Hebrew University and Princeton University Press; p. 183: "All natural science is based upon the hypothesis of the complete causal connection of all events."</ref> Causal efficacy cannot 'propagate' faster than light. Otherwise, reference coordinate systems could be constructed (using the [[Lorentz transform]] of [[special relativity]]) in which an observer would see an effect precede its cause (i.e. the postulate of causality would be violated).

Causal notions appear in the context of the flow of mass-energy. Any actual process has causal efficacy that can propagate no faster than light. In contrast, an abstraction has no causal efficacy. Its mathematical expression does not propagate in the ordinary sense of the word, though it may refer to virtual or nominal 'velocities' with magnitudes greater than that of light. For example, wave packets are mathematical objects that have [[group velocity]] and [[phase velocity]]. The energy of a wave packet travels at the group velocity (under normal circumstances); since energy has causal efficacy, the group velocity cannot be faster than the speed of light. The phase of a wave packet travels at the phase velocity; since phase is not causal, the phase velocity of a wave packet can be faster than light.<ref>{{cite book |last1=Griffiths |first1=David |title=Introduction to electrodynamics |date=2017 |publisher=Cambridge University Press |isbn=978-1-108-42041-9 |page=418 |edition=Fourth}}</ref>

Causal notions are important in general relativity to the extent that the existence of an arrow of time demands that the universe's semi-[[Riemannian manifold]] be orientable, so that "future" and "past" are globally definable quantities.