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Causality is the relationship between causes and effects. [1] [2] 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 reducible to fundamental interactions. Similarly, a cause cannot have an effect outside its future light cone.
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. [3] [4]
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 relationship, "elsewhere", have to 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) replacing mechanistic proposals like Descartes' vortex theory; in the third place as an incentive to develop dynamic field theories (e.g., Maxwell's electrodynamics and Einstein's general theory of relativity) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.
In modern physics, the notion of causality had to be clarified. The word simultaneous is observer-dependent in special relativity. [5] 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 paradoxes 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.
The word causality in this context means that all effects must have specific physical causes due to fundamental interactions. [6] Causality in this context is not associated with definitional principles such as 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 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 [7] the notion of force in Newton's second law was 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,
as two coupled equations describing the positions and 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-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 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 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 variables, or simply redefining determinism as meaning that probabilities rather than specific effects are determined).
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 ] 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 a more general use of causality as represented by 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 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 ] 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 ]
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.
A force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. The concept of force makes the everyday notion of pushing or pulling mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented by the symbol F.
Faster-than-light travel and communication are the conjectural propagation of matter or information faster than the speed of light. The special theory of relativity implies that only particles with zero rest mass may travel at the speed of light, and that nothing may travel faster.
In classical physics and special relativity, an inertial frame of reference is a stationary or uniformly moving frame of reference. In this viewpoint, objects remain at rest until acted upon by external forces, and the laws of nature can be observed without the need for acceleration correction.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein's 1905 treatment, the theory is presented as being based on just two postulates:
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.
A tachyon or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists believe that faster-than-light particles cannot exist because they are inconsistent with the known laws of physics. If such particles did exist they could be used to send signals faster than light. According to the theory of relativity this would violate causality, leading to logical paradoxes such as the grandfather paradox. Tachyons would exhibit the unusual property of increasing in speed as their energy decreases, and would require infinite energy to slow to the speed of light. No verifiable experimental evidence for the existence of such particles has been found.
Time travel is the hypothetical activity of traveling into the past or future. Time travel is a widely recognized concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a hypothetical device known as a time machine. The idea of a time machine was popularized by H. G. Wells's 1895 novel The Time Machine.
Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and considerations. Like eternalism, determinism focuses on particular events rather than the future as a concept. The opposite of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to chance. Determinism is often contrasted with free will, although some philosophers claim that the two are compatible.
The world line of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics.
In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Stockum in 1937 and later confirmed by Kurt Gödel in 1949, who discovered a solution to the equations of general relativity (GR) allowing CTCs known as the Gödel metric; and since then other GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes. If CTCs exist, their existence would seem to imply at least the theoretical possibility of time travel backwards in time, raising the spectre of the grandfather paradox, although the Novikov self-consistency principle seems to show that such paradoxes could be avoided. Some physicists speculate that the CTCs which appear in certain GR solutions might be ruled out by a future theory of quantum gravity which would replace GR, an idea which Stephen Hawking labeled the chronology protection conjecture. Others note that if every closed timelike curve in a given spacetime passes through an event horizon, a property which can be called chronological censorship, then that spacetime with event horizons excised would still be causally well behaved and an observer might not be able to detect the causal violation.
Indeterminism is the idea that events are not caused, or are not caused deterministically.
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the field theories of classical physics. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.
The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales—even when the latter theory states that it should be possible. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.
A classical field theory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature.
The deductive-nomological model of scientific explanation, also known as Hempel's model, the Hempel–Oppenheim model, the Popper–Hempel model, or the covering law model, is a formal view of scientifically answering questions asking, "Why...?". The DN model poses scientific explanation as a deductive structure, one where truth of its premises entails truth of its conclusion, hinged on accurate prediction or postdiction of the phenomenon to be explained.
The Wheeler–Feynman absorber theory, named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is a theory of electrodynamics based on a relativistic correct extension of action at a distance electron particles. The theory postulates no independent electromagnetic field. Rather, the whole theory is encapsulated by the Lorentz-invariant action of particle trajectories defined as
In mathematical physics, global hyperbolicity is a certain condition on the causal structure of a spacetime manifold. It is called hyperbolic in analogy with the linear theory of wave propagation, where the future state of a system is specified by initial conditions. This is relevant to Albert Einstein's theory of general relativity, and potentially to other metric gravitational theories.
The causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events.
In classical theories of gravitation, the changes in a gravitational field propagate. A change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a gravitational wave, which, as predicted by general relativity and confirmed by observation of the GW170817 neutron star merger, is equal to the speed of light (c).
In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. A weather map, with the surface temperature described by assigning a number to each point on the map, is an example of a scalar field. A surface wind map, assigning an arrow to each point on a map that describes the wind speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field.
