Causality in physics Causality (physics)

1 causality in physics

1.1 distributed causality
1.2 causal dynamical triangulation
1.3 causal sets

causality in physics

in classical physics, effect can t occur before cause. in theory of relativity, causality means effect can not occur cause not in (past) light cone of event. similarly, cause can not have effect outside front (future) light cone. these restrictions consistent grounded belief (or assumption) causal influences cannot travel faster speed of light and/or backwards in time. in quantum field theory, observables of events spacelike relationship, elsewhere , have commute, order of observations or measurements of such observables not impact each other.

causality should not confused newton s second law, related conservation of momentum, , consequence of spatial homogeneity of physical laws. name causality suggests effects must have specific causes, concept unrelated common use of causality in physics, , violated in mainstream interpretations of quantum mechanics.

another requirement, @ least valid @ level of human experience, cause , effect mediated across space , time (requirement of contiguity). requirement has been influential in past, in first place result of direct observation of causal processes (like pushing cart), in second place problematic aspect of newton s theory of gravitation (attraction of earth sun means of action @ distance) replacing mechanistic proposals descartes vortex theory; in third place incentive develop dynamic field theories (e.g., maxwell s electrodynamics , einstein s general theory of relativity) restoring contiguity in transmission of influences in more successful way did descartes theory.

the empiricists aversion metaphysical explanations (like descartes vortex theory) lends heavy influence against idea of importance of causality. causality has accordingly been downplayed (e.g., newton s hypotheses non fingo ). according ernst mach notion of force in newton s second law pleonastic, tautological , superfluous. indeed, possible consider newtonian equations of motion of gravitational interaction of 2 bodies,

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{\displaystyle 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 2 coupled equations describing positions







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of 2 bodies, without interpreting right hand sides of these equations forces; equations describe process of interaction, without necessity interpret 1 body cause of motion of other, , allow 1 predict states of system @ later (as earlier) times.

the ordinary situations in humans singled out factors in physical interaction being prior , therefore supplying because of interaction ones in humans decided bring state of affairs , directed energies producing state of affairs—a process took time establish , left new state of affairs persisted beyond time of activity of actor. difficult , pointless, however, explain motions of binary stars respect each other in way.

the possibility of such time-independent view @ basis of deductive-nomological (d-n) view of scientific explanation, considering event explained if can subsumed under scientific law. in d-n view, physical state considered explained if, applying (deterministic) law, can derived given initial conditions. (such initial conditions include momenta , distance each other of binary stars @ given moment.) such explanation determinism referred causal determinism. disadvantage of d-n view causality , determinism more or less identified. thus, in classical physics, assumed events caused earlier ones according known laws of nature, culminating in pierre-simon laplace s claim if current state of world known precision, computed time in future or past (see laplace s demon). however, referred laplace determinism (rather `laplace causality ) because hinges on determinism in mathematical models dealt in mathematical cauchy problem. confusion of causality , determinism particularly acute in quantum mechanics, theory being acausal in sense unable in many cases identify causes of observed effects or predict effects of identical causes, arguably deterministic in interpretations (e.g. if wave function presumed not collapse in many-worlds interpretation, or if collapse due hidden variables, or redefining determinism meaning probabilities rather specific effects determined).

in modern physics, notion of causality had clarified. insights of theory of special relativity confirmed assumption of causality, made meaning of word simultaneous observer-dependent. consequently, relativistic principle of causality says cause must precede effect according inertial observers. equivalent statement cause , effect separated timelike interval, , effect belongs future of cause. if timelike interval separates 2 events, means signal sent between them @ less speed of light. on other hand, if signals move faster speed of light, violate causality because allow signal sent across spacelike intervals, means @ least inertial observers signal travel backward in time. reason, special relativity not allow communication faster speed of light.

in theory of general relativity, concept of causality generalized in straightforward way: effect must belong future light cone of cause, if spacetime curved. new subtleties must taken account when investigate causality in quantum mechanics , relativistic quantum field theory in particular. in quantum field theory, causality closely related principle of locality. however, principle of locality disputed: whether strictly holds depends on interpretation of quantum mechanics chosen, experiments involving quantum entanglement satisfy bell s theorem.

despite these subtleties, causality remains important , valid concept in physical theories. example, notion events can ordered causes , effects necessary prevent (or @ least outline) causality paradoxes such grandfather paradox, asks happens if time-traveler kills own grandfather before ever meets time-traveler s grandmother. see chronology protection conjecture.

distributed causality

theories in physics butterfly effect chaos theory open possibility of type of distributed parameter systems in causality. butterfly effect theory proposes:

small variations of initial condition of nonlinear dynamical system may produce large variations in long term behavior of system.

this opens opportunity understand distributed causality.

a related way interpret butterfly effect see highlighting difference between application of notion of causality in physics , more general use of causality represented mackie s inus conditions. in classical (newtonian) physics, in general, conditions (explicitly) taken account, both necessary , sufficient. instance, when massive sphere caused roll down slope starting point of unstable equilibrium, velocity assumed caused force of gravity accelerating it; small push needed set motion not explicitly dealt cause. in order physical cause there must proportionality ensuing effect. distinction drawn between triggering , causation of ball s motion. same token butterfly can seen triggering tornado, cause being assumed seated in atmospherical energies present beforehand, rather in movements of butterfly.

causal dynamical triangulation

causal dynamical triangulation (abbreviated cdt ) invented renate loll, jan ambjørn , jerzy jurkiewicz, , popularized fotini markopoulou , lee smolin, approach quantum gravity loop quantum gravity background independent. means not assume pre-existing arena (dimensional space), rather attempts show how spacetime fabric evolves. loops 05 conference, hosted many loop quantum gravity theorists, included several presentations discussed cdt in great depth, , revealed pivotal insight theorists. has sparked considerable interest appears have semi-classical description. @ large scales, re-creates familiar 4-dimensional spacetime, shows spacetime 2-d near planck scale, , reveals fractal structure on slices of constant time. using structure called simplex, divides spacetime tiny triangular sections. simplex generalized form of triangle, in various dimensions. 3-simplex called tetrahedron, , 4-simplex, basic building block in theory, known pentatope, or pentachoron. each simplex geometrically flat, simplices can glued in variety of ways create curved spacetimes. previous attempts @ triangulation of quantum spaces have produced jumbled universes far many dimensions, or minimal universes few, cdt avoids problem allowing configurations cause precedes effect. in other words, timelines of joined edges of simplices must agree.

thus, maybe, causality lies in foundation of spacetime geometry.

causal sets

in causal set theory causality takes more prominent place. basis approach quantum gravity in theorem david malament. theorem states causal structure of spacetime suffices reconstruct conformal class. knowing conformal factor , causal structure enough know spacetime. based on rafael sorkin proposed idea of causal set theory.

causal set theory fundamentally discrete approach quantum gravity. causal structure of spacetime represented poset, while conformal factor can reconstructed identifying each poset element unit volume.