causality

causality, in philosophy, the relationship between cause and effect. A distinction is often made between a cause that produces something new (e.g., a moth from a caterpillar) and one that produces a change in an existing substance (e.g., a statue from a piece of marble). Aristotle distinguished four causes—efficient, final, material, and formal—that may be illustrated by the following example: a statue is created by a sculptor (the efficient) who makes changes in marble (the material) in order to have a beautiful object (the final) with the characteristics of a statue (the formal). Later philosophers developed other classifications of causes, often duplicatory. The scientific conception that given circumstances under controlled conditions must inevitably produce standard results is generally accepted by philosophers. Systems vary, however, in the degree of emphasis that they place on the role of chance in changing a situation. David Hume argued that, in seeking to explain any object or event, we have evidence but no proof that its putative cause produced an effect on it. Immanuel Kant thought the idea of cause is a fundamental category of understanding and a necessary condition for experience; others argue a strictly mechanical theory of causality. The introduction of the uncertainty principle into modern physics has necessitated a modification of traditional concepts.

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causality [kȯ′zal·əd·ē]

(mechanics)

In classical mechanics, the principle that the specification of the dynamical variables of a system at a given time, and of the external forces acting on the system, completely determines the values of dynamical variables at later times. Also known as determinism.

(physics)

The principle that an event cannot precede its cause; in a relativistic theory, an event cannot have an effect outside its future light cone.

In relativistic quantum field theory, the principle that the field operators at different space-time points commute (for boson fields; anticommute in the case of fermion fields) if the separation of the points is spacelike.

(quantum mechanics)

The principle that the specification of the dynamical state of a system at a given time, and of the interaction of the system with its environment, determines the dynamical state of the system at later times, from which a probability distribution for the observation of any dynamical variable may be determined. Also known as determinism.

(science and technology)

The existence of regularities which control natural phenomena.

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Causality

In physics, the requirement that interactions in any space-time region can influence the evolution of the system only at subsequent times; that is, past events are causes of future events, and future events can never be the causes of events in the past. Causality thus depends on time orientability, the possibility of distinguishing past from future. Not all spacetimes are orientable.

The laws of a deterministic theory (for example, classical mechanics) are such that the state of a closed system (for example, the positions and momenta of particles in the system) at one instant determines the state of that system at any future time. Deterministic causality does not necessarily imply practical predictability. It was long implicitly assumed that slight differences in initial conditions would not lead to rapid divergence of later behavior, so that predictability was a consequence of determinism. Behavior in which two particles starting at slightly different positions and velocities diverge rapidly is called chaotic. Such behavior is ubiquitous in nature, and can lead to the practical impossibility of prediction of future states despite the deterministic character of the physical laws. See Chaos

Quantum mechanics is deterministic in the sense that, given the state of a system at one instant, it is possible to calculate later states. However, the situation differs from that in classical mechanics in two fundamental respects. First, conjugate variables, for example, position x and momentum p, cannot be simultaneously determined with complete precision. Second, the state variable &psgr; gives only probabilities that a given eigenstate will be found after the performance of a measurement, and such probabilities are also all that is calculable about a later state &psgr;^′ by the deterministic prediction. Despite its probabilistic character, the quantum state still evolves deterministically. However, which eigenvalue (say, of position) will actually be found in a measurement is unpredictable. See Determinism, Eigenvalue (quantum mechanics), Quantum mechanics, Quantum theory of measurement, Uncertainty principle

Nonrelativistic mechanics assumes that causal action can be propagated instantaneously, and thus that an absolute simultaneity is definable. This is not true in special relativity. While the state of a system can still be understood in terms of the positions and momenta of its particles, time order, as well as temporal and spatial length, becomes relative to the observer's frame, and there is no possible choice of simultaneous events in the universe that is the same in all reference frames. Only space-time intervals in a fused “spacetime” are invariant with respect to choice of reference frame. The theory of special relativity thus rejects the possibility of instantaneous causal action. Instead, the existence of a maximum velocity of signal transmission determines which events can causally influence others and which cannot. The investigation of a spacetime with regard to which events can causally influence (signal) other regions and which cannot is known as the study of the causal structure of the spacetime. See Space-time