Causality (physics)

This article is about the physical definition of "causality". For causality in general, seeCausality.

For other uses of "Causation", seeCausation (disambiguation).

Physicalcausalityis a physical relationship betweencausesand effects.It is considered to be fundamental to allnatural sciencesandbehavioural sciences,especiallyphysics.Causalityis also a topic studied from the perspectives ofphilosophy,statisticsandlogic.Causality means that an effect can not occur from a cause that is not in the back (past)light coneof that event. Similarly, a cause can not have an effect outside its front (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. Thestrong causality principleforbids information transfer faster than thespeed of light;theweak causality principleoperates at the microscopic level and need not lead to information transfer. Physical models can obey the weak principle without obeying the strong version.

Macroscopic causality

In classical physics, an effect cannot occurbeforeits cause which is why solutions such as the advanced time solutions of theLiénard–Wiechert potentialare 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 coneof that event. Similarly, a cause cannot have an effect outside its front (future) light cone. These restrictions are consistent with the constraint thatmassandenergythat act as causal influences cannot travel faster than the speed of light and/or backwards in time. Inquantum field theory,observables of events with aspacelikerelationship, "elsewhere", have tocommute,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 ofcontiguity). 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 ofaction at a distance) replacing mechanistic proposals likeDescartes' vortex theory;in the third place as an incentive to develop dynamicfield theories(e.g.,Maxwell's electrodynamicsandEinstein's general theory of relativity) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.

Simultaneity

Inmodern physics,the notion of causality had to be clarified. The wordsimultaneousis observer-dependent inspecial relativity.The principle isrelativity of simultaneity.Consequently, the relativistic principle of causality says that the cause must precede its effectaccording to allinertialobservers.This is equivalent to the statement that the cause and its effect are separated by atimelikeinterval, 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 acrossspacelikeintervals, which means that at least to some inertial observers the signal would travelbackward in time.For this reason, special relativity does not allow communication faster than thespeed of light.

In the theory ofgeneral 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 thespacetimeis curved. New subtleties must be taken into account when we investigate causality inquantum mechanicsand relativisticquantum field theoryin particular. In those two theories, causality is closely related to theprinciple of locality. Bell's Theoremshows that conditions of "local causality" in experiments involvingquantum entanglementresult 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 paradoxessuch as thegrandfather paradox,which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. See alsoChronology protection conjecture.

Determinism (or, what causality isnot)

The wordcausalityin this context means that all effects must have specific physical causes due to fundamental interactions.Causality in this context is not associated with definitional principles such asNewton's second law.As such, in the context ofcausality,a force does notcausea mass to accelerate nor vice versa. Rather, Newton's Second Law can be derived from theconservation of momentum,which itself is aconsequence 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 thecauseof phenomena has accordingly been dismissed as a problem that is philosophical or metaphysical rather than empirical (e.g., Newton's "Hypotheses non fingo"). According toErnst Machthe notion of force in Newton's second law waspleonastic,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,

$m_{1}{\frac {d^{2}{\mathbf {r} }_{1}}{dt^{2}}}=-{\frac {m_{1}m_{2}G({\mathbf {r} }_{1}-{\mathbf {r} }_{2})}{|{\mathbf {r} }_{1}-{\mathbf {r} }_{2}|^{3}}};\;m_{2}{\frac {d^{2}{\mathbf {r} }_{2}}{dt^{2}}}=-{\frac {m_{1}m_{2}G({\mathbf {r} }_{2}-{\mathbf {r} }_{1})}{|{\mathbf {r} }_{2}-{\mathbf {r} }_{1}|^{3}}},$

as two coupled equations describing the positions$\scriptstyle {\mathbf {r} }_{1}(t)$and$\scriptstyle {\mathbf {r} }_{2}(t)$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.

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, aretime-reversibleand agnostic to thearrow 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 thedeductive-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 ascausal determinism.A disadvantage of the D-N view is that causality and determinism are more or less identified. Thus, inclassical physics,it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating inPierre-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 (seeLaplace's demon). However, this is usually referred to as Laplacedeterminism(rather than 'Laplace causality') because it hinges ondeterminism in mathematical modelsas dealt with in the mathematicalCauchy problem.

Confusion between causality and determinism is particularly acute inquantum 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 themany-worlds interpretation,or if its collapse is due tohidden variables,or simply redefining determinism as meaning that probabilities rather than specific effects are determined).

Distributed causality

Theories inphysicslike thebutterfly effectfromchaos theoryopen up the possibility of a type ofdistributed parameter systemsin causality.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."

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 amore general use of causalityas represented byMackie'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 ofunstable 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.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.

Causal sets

Main article: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 byDavid Malament.This theorem states that thecausal structureof a spacetime suffices to reconstruct itsconformal class,so knowing the conformal factor and the causal structure is enough to know the spacetime. Based on this,Rafael Sorkinproposed the idea of Causal Set Theory, which is a fundamentally discrete approach to quantum gravity. The causal structure of the spacetime is represented as aposet,while the conformal factor can be reconstructed by identifying each poset element with a unit volume.

Interaction, force and the conservation of momentum

By physical causation is meant an effect that was caused by physical interference propagated by force from object A to object B. Momentum is propagated by force according to theNoether's theoremapplied totranslational invarianceinLagrangian field theory,which is used to describe the fundamental forces of nature when applied to thestandard model.

See also

• Causality– How one process influences another (general)
• Causal contact– Sharing an event that affects entities in a causal way
• Causal system– System where the output depends only on past and current inputs
• Particle horizon– Distance measurement used in cosmology
• Philosophy of physics– Truths and principles of the study of matter, space, time and energy
• Retrocausality– Concept in which the future affects the past
• Synchronicity– Jungian concept of the meaningfulness of acausal coincidences
• Wheeler–Feynman time-symmetric theory for electrodynamics– Interpretation of electrodynamics

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.ISBN2-296-01198-5.

External links

• Causal Processes, Stanford Encyclopedia of Philosophy
• Caltech Tutorial on Relativity— A nice discussion of how observers moving relatively to each other see different slices of time.
• 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.