Editing Causality (physics)

{{Short description|Physics of the cause–effect relation}}
{{About|the physical definition of "causality"|causality in general|Causality}}
{{other uses of|Causation}}
{{Refimprove|date=July 2008}}
'''Causality''' is the relationship between causes and effects.<ref>Green, Celia (2003). ''The Lost Cause: Causation and the Mind–Body Problem''. Oxford: Oxford Forum. {{ISBN|0-9536772-1-4}}. Includes three chapters on causality at the microlevel in physics.</ref><ref>Bunge, Mario (1959). ''Causality: the place of the causal principle in modern science''. Cambridge: Harvard University Press.</ref> While causality is also a topic studied from the perspectives of philosophy and physics, it is [[operationalized]] so that causes of an event must be in the past [[light cone]] of the event and ultimately [[Reductionism|reducible]] to [[fundamental interaction]]s. Similarly, a cause cannot have an effect outside its future light cone.

== Macroscopic vs microscopic causality ==
Causality can be defined macroscopically, at the level of human observers, or microscopically, for fundamental events at the atomic level. 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. Physical models can obey the weak principle without obeying the strong version.<ref>{{Cite journal |last=Cramer |first=John G. |date=1980-07-15 |title=Generalized absorber theory and the Einstein-Podolsky-Rosen paradox |url=https://link.aps.org/doi/10.1103/PhysRevD.22.362 |journal=Physical Review D |language=en |volume=22 |issue=2 |pages=362–376 |doi=10.1103/PhysRevD.22.362 |bibcode=1980PhRvD..22..362C |issn=0556-2821|url-access=subscription }}</ref><ref>{{Cite book |last=Price |first=Huw |title=Time's arrow & Archimedes' point: new directions for the physics of time |date=1997 |publisher=Oxford University Press |isbn=978-0-19-511798-1 |edition=1. issued as an Oxford Univ. Press paperback |series=Oxford paperbacks |location=New York}}</ref>

== Macroscopic causality ==
In classical physics, an effect cannot occur ''before'' its cause which is why solutions such as the advanced time solutions of the [[Liénard–Wiechert potential]] are discarded as physically meaningless. 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. Similarly, a cause cannot have an effect outside its front (future) light cone. 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. In [[quantum field theory]], observables of events with a [[Spacelike curve|spacelike]] relationship, "elsewhere", have to [[Commutative property|commute]], so the order of observations or measurements of such observables do not impact each other.

Another requirement of causality 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 (physics)|action at a distance]]) replacing mechanistic proposals like [[Mechanical explanations of gravitation#Vortex Theory|Descartes' vortex theory]]; in the third place as an incentive to develop dynamic [[Classical field theory|field theories]] (e.g., [[Electromagnetism#Classical electrodynamics|Maxwell's electrodynamics]] and [[Einstein field equations|Einstein's general theory of relativity]]) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.<ref>{{Cite journal |last=Chandler |first=Colston |last2=Stapp |first2=Henry P. |date=1969-05-01 |title=Macroscopic Causality Conditions and Properties of Scattering Amplitudes |url=https://pubs.aip.org/aip/jmp/article-abstract/10/5/826/222875/Macroscopic-Causality-Conditions-and-Properties-of?redirectedFrom=fulltext |journal=Journal of Mathematical Physics |volume=10 |issue=5 |pages=826–859 |doi=10.1063/1.1664913 |issn=0022-2488}}</ref>

== Simultaneity ==
In [[modern physics]], the notion of causality had to be clarified. The word ''simultaneous'' is observer-dependent in [[special relativity]].<ref>[[Albert Einstein|A. Einstein]], "Zur Elektrodynamik bewegter Koerper", ''Annalen der Physik'' '''17''', 891–921 (1905).</ref> The principle is [[relativity of simultaneity]]. Consequently, the relativistic principle of causality says that the cause must precede its effect ''according to all [[inertial]] observers''. This is equivalent to the statement that the cause and its effect are separated by a [[timelike]] interval, and the effect belongs to the future of its cause. If a timelike interval separates the two events, this means that a signal could be sent between them at less than the speed of light. On the other hand, if signals could move faster than the speed of light, this would violate causality because it would allow a signal to be sent across [[spacelike]] intervals, which means that at least to some inertial observers the signal would travel ''backward in time''. For this reason, special relativity does not allow communication faster than the [[speed of light]].

In the theory of [[general relativity]], the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the [[spacetime]] is curved. New subtleties must be taken into account when we investigate causality in [[quantum mechanics]] and relativistic [[quantum field theory]] in particular. In those two theories, causality is closely related to the [[principle of locality]]. 
[[Bell's Theorem]] shows that conditions of "local causality" in experiments involving [[quantum entanglement]] result in non-classical correlations predicted by quantum mechanics.

Despite these subtleties, causality remains an important and valid concept in physical theories. For example, the notion that events can be ordered into causes and effects is necessary to prevent (or at least outline) [[causality paradox]]es such as the [[grandfather paradox]], which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. See also [[Chronology protection conjecture]].

== Determinism (or, what causality is ''not'') ==
The word ''causality'' in this context means that all effects must have specific physical causes due to fundamental interactions.<ref name=":0">"Causality." Cambridge English Dictionary. Accessed November 18, 2018. https://dictionary.cambridge.org/us/dictionary/english/causality</ref> Causality in this context is not associated with definitional principles such as [[Second law of motion|Newton's second law]]. As such, in the context of ''causality,'' a force does not ''cause'' a mass to accelerate nor vice versa. Rather, Newton's second law can be derived from the [[conservation of momentum]], which itself is a [[Noether's theorem|consequence of the spatial homogeneity of physical laws]].

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]]<ref name=":1">Ernst Mach, ''Die Mechanik in ihrer Entwicklung, Historisch-kritisch dargestellt'', Akademie-Verlag, Berlin, 1988, section 2.7.</ref> the notion of force in Newton's second law was [[Pleonasm|pleonastic]], tautological and superfluous and, as indicated above, is not considered a consequence of any principle of causality. Indeed, it is possible to consider the Newtonian equations of motion of the gravitational interaction of two bodies,

:<math> m_1 \frac{d^2 {\mathbf r}_1 }{ dt^2} = -\frac{m_1 m_2 G ({\mathbf r}_1 - {\mathbf r}_2)}{ |{\mathbf r}_1 - {\mathbf r}_2|^3};\; m_2 \frac{d^2 {\mathbf r}_2 }{dt^2} = -\frac{m_1 m_2 G ({\mathbf r}_2 - {\mathbf r}_1) }{ |{\mathbf r}_2 - {\mathbf r}_1|^3}, </math>

as two coupled equations describing the positions <math> \scriptstyle {\mathbf r}_1(t) </math> and <math> \scriptstyle {\mathbf r}_2(t) </math> 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.

The ordinary situations in which humans singled out some factors in a physical interaction as being prior and therefore supplying the "because" of the interaction were often ones in which humans decided to bring about some state of affairs and directed their energies to producing that state of affairs—a process that took time to establish and left a new state of affairs that persisted beyond the time of activity of the actor. It would be difficult and pointless, however, to explain the motions of binary stars with respect to each other in that way which, indeed, are [[Time reversibility|time-reversible]] and agnostic to the [[arrow of time]], but with such a direction of time established, the entire evolution system could then be completely determined.

The possibility of such a time-independent view is at the basis of the [[deductive-nomological]] (D-N) view of scientific explanation, considering an event to be explained if it can be subsumed under a [[scientific law]]. 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. (Such initial conditions could include the momenta and distance from each other of binary stars at any given moment.) Such 'explanation by determinism' is sometimes referred to as [[Determinism#Varieties|causal determinism]]. A disadvantage of the D-N view is that causality and determinism are more or less identified. 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]]). However, this is usually referred to as Laplace ''determinism'' (rather than 'Laplace causality') because it hinges on [[Determinism#In mathematical models|determinism in mathematical models]] as dealt with in the mathematical [[Cauchy problem]].

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 variable theory|hidden variables]], or simply redefining determinism as meaning that probabilities rather than specific effects are determined).

==Distributed causality==
Theories in [[physics]] like the [[butterfly effect]] from [[chaos theory]] open up the possibility of a type of [[distributed parameter systems]] in causality. {{Citation needed|date=March 2016}} The butterfly effect theory proposes:
<blockquote>"Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system."</blockquote> This opens up the opportunity to understand a distributed causality.

A related way to interpret the butterfly effect is to see it as highlighting the difference between the application of the notion of causality in physics and a [[Causality|more general use of causality]] as represented by [[INUS|Mackie's INUS conditions]]. In classical (Newtonian) physics, in general, only those conditions are (explicitly) taken into account, that are both necessary and sufficient. For instance, when a massive sphere is caused to roll down a slope starting from a point of [[Mechanical equilibrium|unstable equilibrium]], then its velocity is assumed to be caused by the force of gravity accelerating it; the small push that was needed to set it into motion is not explicitly dealt with as a cause. In order to be a physical cause there must be a certain proportionality with the ensuing effect. A distinction is drawn between triggering and causation of the ball's motion.{{Citation needed|date=July 2020}} By the same token the butterfly can be seen as triggering a tornado, its cause being assumed to be seated in the atmospherical energies already present beforehand, rather than in the movements of a butterfly.{{Citation needed|date=July 2020}}

==Causal sets==
{{main|Causal sets}}
In causal set theory, causality takes an even more prominent place. The basis for this approach to [[quantum gravity]] is in a theorem by [[David Malament]]. This theorem states that the [[causal structure]] of a spacetime suffices to reconstruct its [[conformal class]], so knowing the conformal factor and the causal structure is enough to know the spacetime. Based on this, [[Rafael Sorkin]] proposed the idea of Causal Set Theory, which is a fundamentally discrete approach to quantum gravity. The causal structure of the spacetime is represented as a [[poset]], while the conformal factor can be reconstructed by identifying each poset element with a unit volume.

==See also==
{{cols}}
* {{annotated link|Causality}} (general)
* {{annotated link|Causal contact}}
* {{annotated link|Causal system}}
* {{annotated link|Particle horizon}}
* {{annotated link|Philosophy of physics}}
* {{annotated link|Retrocausality}}
* {{annotated link|Synchronicity}}
* {{annotated link|Wheeler–Feynman absorber theory|Wheeler–Feynman time-symmetric theory for electrodynamics}}
{{colend}}

==References==
{{reflist}}

==Further reading==
*Bohm, David. (2005). ''Causality and Chance in Modern Physics''. London: Taylor and Francis.
*Espinoza, Miguel (2006). ''Théorie du déterminisme causal''. Paris: L'Harmattan. {{ISBN|2-296-01198-5}}.

==External links==
* [http://plato.stanford.edu/entries/causation-process/ Causal Processes, Stanford Encyclopedia of Philosophy]
* [https://web.archive.org/web/20061002122145/http://www.black-holes.org/relativity3.html Caltech Tutorial on Relativity] — A nice discussion of how observers moving relatively to each other see different slices of time.
* [https://arxiv.org/abs/gr-qc/0107091 Faster-than-c signals, special relativity, and causality]. This article explains that faster than light signals do not necessarily lead to a violation of causality.

[[Category:Causality]]
[[Category:Concepts in physics]]
[[Category:Time]]
[[Category:Philosophy of physics]]
[[Category:Time travel]]

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