Causality (physics)
Encyclopedia
Causality is the relationship between causes and effect
s. It is considered to be fundamental to all natural science
, especially physics
. Causality
is also a topic studied from the perspectives of philosophy
and statistics
.
s have a practical interest in their surroundings, and tend to be resistant to the idea that things "just happen." If one or more sheep die, humans will attempt to discover why. Learning what has killed the sheep is an important step in protecting the flock. The question can be phrased as, "What caused the sheep to die?" The answer may be "The wolves broke their necks," or "Eating too much clover
caused them to bloat." These explanations assume the presence of an agent of some kind. In cases where an obvious cause is not discovered, humans may attribute the events to miracle
s or to evil supernatural
agencies, or create an ungrounded theory to present something as a causitive agent. There is a learned preference for some alternative to saying that something occurred without there being a reason
for it. Any event that stands as 'uncaused' may motivate us to understand the salient events in the environment of that event.
When trying to answer questions such as, "Why is the water boiling
?" it is tempting to search for a single responsible figure: "Mother lit the gas burner under the tea kettle." However, closer examination shows that the lighting of a flame is not the only feature that must be accounted for. Closer study shows that the ambient air pressure is a controlling factor, the Earth's gravity holding the water in the pot is a controlling factor, the temperature to which the water has been heated is a controlling factor, etc.
Given a situation in which water is already sitting in a tea kettle on top of a gas burner, then someone lighting the gas under the kettle may be perceived as the "cause" of the water's boiling. But in the same situation the water would also boil if the air pressure were sufficiently reduced. In more complicated situations, more factors that influence outcomes may be involved. Underlying the expectations that most people hold in regard to the interactions of these several factors are everyday experiences in which someone succeeds in producing a desired result. "If I turn this key, the motor will start." This may be a true statement, but underlying it is a very complicated set of conditions that must all be in place. So the idea of "cause" tends to focus on foreground events and leave out necessary factors that reside in the background.
Real world factors can intervene to challenge simplistic ideas of causation. Water in a pressure cooker will not boil at 100 degrees Celsius. The key is turned but the car motor will not start. So at this level of sophistication, it is not difficult to gain acceptance of a more refined idea of causation. And, in practice, few individuals expect to get a desired outcome without having fulfilled the conditions necessary to earn it. People may wish for a million dollars, but they do not wish for hot toast to emerge from a cold and empty toaster.
The most abstract form of the argument from experience is: (1) Do something and get a certain result. (2) Do not do it and do not get the result. Hence, a cause is both sufficient (1) and necessary (2) in order that the event happen.
Another lesson consistent with everyday experience is that these sequences do not work in reverse. For instance, if a cup of boiling water is allowed to sit at room temperature then it will cool to room temperature, but if a cup of room temperature water is allowed to sit at room temperature it will not warm to the point that it boils. So there is a 'sequentiality' in events familiar to humans from their everyday experience. Whenever this 'sequentiality' is detected or believed to be present, the temporally prior change is said to be a cause, and the temporally posterior change is said to be an effect.
One crack in this belief system has been produced by radioactivity. An atom of some radioactive substance such as radium will eventually decay, and in the process it will emit energy. But there is no known triggering event that could serve as the cause of this decay event. In a large collection of radium atoms the rate of decay can be accurately predicted, but the identity of the decayed atoms cannot be determined beforehand. Their decay is random and was considered to be uncaused in an older framework of quantum theory. Under the new formulation, spontaneous emission
for example, is initiated by vacuum fluctuations.
Another crack in this belief system has been produced by quantum mechanical
events such that the same sequence of causal events (or causal factors) regularly produces different effects (i.e. results), but the results may repeat themselves in some random (unknowable) sequence. Furthermore, the percentages of results of each kind can be calculated and they are highly predictable.
Results of this kind are seen in the macro world of human beings only in the case of crooked roulette wheels or other such crooked gambling devices since legitimate roulette wheels should have an equal probability of stopping at each position.
a cause may be represented by a force
acting on a body, and an effect by the acceleration which follows as quantitatively explained by Newton's second law. For different physical theories the notions of cause and effect may be different. For instance, in Aristotelian physics
the effect is not said to be acceleration but to be velocity (one must push a cart twice as hard in order to have its velocity doubled). In the general theory of relativity, too, acceleration is not an effect (since it is not a generally relativistic vector
); the general relativistic effects comparable to those of Newtonian mechanics are the deviations from geodesic motion
in curved spacetime
. Also, the meaning of "uncaused motion" is dependent on the theory being employed: for Aristotle it is (absolute) rest, for Newton it is inertial motion (constant velocity with respect to an inertial frame of reference
), in the general theory of relativity it is geodesic motion (to be compared with frictionless motion on the surface of a sphere at constant tangential velocity along a great circle
). So what constitutes a "cause" and what constitutes an "effect" depends on the total system of explanation in which the putative causal sequence is embedded.
A formulation of physical laws in terms of cause and effect is useful for the purposes of explanation
and prediction
. For instance, in Newtonian mechanics an observed acceleration can be explained by reference to an applied force. So Newton's second law can be used to predict the force necessary to realize a desired acceleration.
In classical physics a cause should always precede its effect. In relativity theory this requirement is strengthened so as to limit causes to the back (past) light cone
of the event to be explained (the "effect"); nor can an event be a cause of any event outside the former event's front (future) light cone. These restrictions are consistent with the grounded belief (or assumption) that causal influences cannot travel faster than the speed of light and/or backwards in time.
Another requirement, at least valid at the level of human experience, 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 did Descartes' theory.
The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) lends heavy influence against the idea of the importance of causality. Causality has accordingly sometimes been downplayed (e.g. Newton's "Hypotheses non fingo
"). According to Ernst Mach
the notion of force in Newton's second law was pleonastic
, tautological and superfluous. Indeed it is possible to consider the Newtonian equations of motion of the gravitational interaction between the sun (s) and a planet (p),
as two coupled equations describing the positions
and 
of planet and sun, without interpreting the right hand sides of these equations as forces; the equations just describe a process of interaction, without any necessity to interpret the sun as the cause of the motion of the planet (or vice versa), and allow one to predict the states of the system s+p 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.
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 of causality and determinism is particularly acute in quantum mechanics
, this theory being acausal (in consequence of its inability to provide descriptions of the causes of all actually observed effects) but deterministic in the mathematical sense.
In modern physics
, the notion of causality had to be clarified. The insights of the theory of special relativity
confirmed the assumption of causality, but they made the meaning of the word "simultaneous" observer-dependent. 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 quantum field theory, causality is closely related to the principle of locality
. However, the principle of locality is disputed: whether it strictly holds depends on the interpretation of quantum mechanics
chosen, especially for experiments involving quantum entanglement
that satisfy Bell's Theorem
.
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
.
like the Butterfly effect
from chaos theory
open up the possibility of a type of distributed parameter systems
in causality. The butterfly effect theory proposes:
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 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. 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.
, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin
, is an approach to quantum gravity
that like loop quantum gravity
is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime
fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in great depth, and revealed it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale
, and reveals a fractal
structure on slices of constant time. Using a structure called a simplex
, it divides spacetime into tiny triangular sections. A simplex is the generalized form of a triangle
, in various dimensions. A 3-simplex is usually called a tetrahedron
, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron
. Each simplex is geometrically flat, but simplices can be "glued" together in a variety of ways to create curved spacetimes. Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few, CDT avoids this problem by allowing only those configurations where cause precedes any event. In other words, the timelines of all joined edges of simplices must agree.
Thus, maybe, causality lies in the foundation of the spacetime
geometry.
Effect
Effect may refer to:* A result or change of something** List of effects** Cause and effect, an idiom describing causalityIn pharmacy and pharmacology:* Drug effect, a change resulting from the administration of a drug...
s. It is considered to be fundamental to all natural science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, especially physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
. Causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
is also a topic studied from the perspectives of philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
.
Basic concepts of cause and effect
HumanHuman
Humans are the only living species in the Homo genus...
s have a practical interest in their surroundings, and tend to be resistant to the idea that things "just happen." If one or more sheep die, humans will attempt to discover why. Learning what has killed the sheep is an important step in protecting the flock. The question can be phrased as, "What caused the sheep to die?" The answer may be "The wolves broke their necks," or "Eating too much clover
Clover
Clover , or trefoil, is a genus of about 300 species of plants in the leguminous pea family Fabaceae. The genus has a cosmopolitan distribution; the highest diversity is found in the temperate Northern Hemisphere, but many species also occur in South America and Africa, including at high altitudes...
caused them to bloat." These explanations assume the presence of an agent of some kind. In cases where an obvious cause is not discovered, humans may attribute the events to miracle
Miracle
A miracle often denotes an event attributed to divine intervention. Alternatively, it may be an event attributed to a miracle worker, saint, or religious leader. A miracle is sometimes thought of as a perceptible interruption of the laws of nature. Others suggest that a god may work with the laws...
s or to evil supernatural
Supernatural
The supernatural or is that which is not subject to the laws of nature, or more figuratively, that which is said to exist above and beyond nature...
agencies, or create an ungrounded theory to present something as a causitive agent. There is a learned preference for some alternative to saying that something occurred without there being a reason
Reason
Reason is a term that refers to the capacity human beings have to make sense of things, to establish and verify facts, and to change or justify practices, institutions, and beliefs. It is closely associated with such characteristically human activities as philosophy, science, language, ...
for it. Any event that stands as 'uncaused' may motivate us to understand the salient events in the environment of that event.
When trying to answer questions such as, "Why is the water boiling
Boiling
Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapor pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding environmental pressure. While below the boiling point a liquid...
?" it is tempting to search for a single responsible figure: "Mother lit the gas burner under the tea kettle." However, closer examination shows that the lighting of a flame is not the only feature that must be accounted for. Closer study shows that the ambient air pressure is a controlling factor, the Earth's gravity holding the water in the pot is a controlling factor, the temperature to which the water has been heated is a controlling factor, etc.
Given a situation in which water is already sitting in a tea kettle on top of a gas burner, then someone lighting the gas under the kettle may be perceived as the "cause" of the water's boiling. But in the same situation the water would also boil if the air pressure were sufficiently reduced. In more complicated situations, more factors that influence outcomes may be involved. Underlying the expectations that most people hold in regard to the interactions of these several factors are everyday experiences in which someone succeeds in producing a desired result. "If I turn this key, the motor will start." This may be a true statement, but underlying it is a very complicated set of conditions that must all be in place. So the idea of "cause" tends to focus on foreground events and leave out necessary factors that reside in the background.
Real world factors can intervene to challenge simplistic ideas of causation. Water in a pressure cooker will not boil at 100 degrees Celsius. The key is turned but the car motor will not start. So at this level of sophistication, it is not difficult to gain acceptance of a more refined idea of causation. And, in practice, few individuals expect to get a desired outcome without having fulfilled the conditions necessary to earn it. People may wish for a million dollars, but they do not wish for hot toast to emerge from a cold and empty toaster.
The most abstract form of the argument from experience is: (1) Do something and get a certain result. (2) Do not do it and do not get the result. Hence, a cause is both sufficient (1) and necessary (2) in order that the event happen.
Another lesson consistent with everyday experience is that these sequences do not work in reverse. For instance, if a cup of boiling water is allowed to sit at room temperature then it will cool to room temperature, but if a cup of room temperature water is allowed to sit at room temperature it will not warm to the point that it boils. So there is a 'sequentiality' in events familiar to humans from their everyday experience. Whenever this 'sequentiality' is detected or believed to be present, the temporally prior change is said to be a cause, and the temporally posterior change is said to be an effect.
One crack in this belief system has been produced by radioactivity. An atom of some radioactive substance such as radium will eventually decay, and in the process it will emit energy. But there is no known triggering event that could serve as the cause of this decay event. In a large collection of radium atoms the rate of decay can be accurately predicted, but the identity of the decayed atoms cannot be determined beforehand. Their decay is random and was considered to be uncaused in an older framework of quantum theory. Under the new formulation, spontaneous emission
Spontaneous emission
Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...
for example, is initiated by vacuum fluctuations.
Another crack in this belief system has been produced by quantum mechanical
Introduction to quantum mechanics
Quantum mechanics is the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles....
events such that the same sequence of causal events (or causal factors) regularly produces different effects (i.e. results), but the results may repeat themselves in some random (unknowable) sequence. Furthermore, the percentages of results of each kind can be calculated and they are highly predictable.
Results of this kind are seen in the macro world of human beings only in the case of crooked roulette wheels or other such crooked gambling devices since legitimate roulette wheels should have an equal probability of stopping at each position.
Various concepts of cause and effect in physics
In physics it is useful to interpret certain terms of a physical theory as causes and other terms as effects. Thus, in classical (Newtonian) mechanicsNewton's laws of motion
Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
a cause may be represented by a force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
acting on a body, and an effect by the acceleration which follows as quantitatively explained by Newton's second law. For different physical theories the notions of cause and effect may be different. For instance, in Aristotelian physics
Physics (Aristotle)
The Physics of Aristotle is one of the foundational books of Western science and philosophy...
the effect is not said to be acceleration but to be velocity (one must push a cart twice as hard in order to have its velocity doubled). In the general theory of relativity, too, acceleration is not an effect (since it is not a generally relativistic vector
Tensor
Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...
); the general relativistic effects comparable to those of Newtonian mechanics are the deviations from geodesic motion
Geodesic (general relativity)
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational, force is a particular type of geodesic...
in curved spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
. Also, the meaning of "uncaused motion" is dependent on the theory being employed: for Aristotle it is (absolute) rest, for Newton it is inertial motion (constant velocity with respect to an inertial frame of reference
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...
), in the general theory of relativity it is geodesic motion (to be compared with frictionless motion on the surface of a sphere at constant tangential velocity along a great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...
). So what constitutes a "cause" and what constitutes an "effect" depends on the total system of explanation in which the putative causal sequence is embedded.
A formulation of physical laws in terms of cause and effect is useful for the purposes of explanation
Explanation
An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....
and prediction
Prediction
A prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...
. For instance, in Newtonian mechanics an observed acceleration can be explained by reference to an applied force. So Newton's second law can be used to predict the force necessary to realize a desired acceleration.
In classical physics a cause should always precede its effect. In relativity theory this requirement is strengthened so as to limit causes to the back (past) light cone
Light cone
A light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime...
of the event to be explained (the "effect"); nor can an event be a cause of any event outside the former event's front (future) light cone. These restrictions are consistent with the grounded belief (or assumption) that causal influences cannot travel faster than the speed of light and/or backwards in time.
Another requirement, at least valid at the level of human experience, 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
Action at a distance (physics)
In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant...
) replacing mechanistic proposals like Descartes' vortex theory; in the third place as an incentive to develop dynamic field theories
Classical field theory
A classical field theory is a physical theory that describes the study of how one or more physical fields interact with matter. The word 'classical' is used in contrast to those field theories that incorporate quantum mechanics ....
(e.g. Maxwell's electrodynamics and Einstein's general theory of relativity
Einstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
) restoring contiguity in the transmission of influences in a more successful way than did Descartes' theory.
The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) lends heavy influence against the idea of the importance of causality. Causality has accordingly sometimes been downplayed (e.g. Newton's "Hypotheses non fingo
Hypotheses non fingo
Hypotheses non fingo is a famous phrase used by Isaac Newton in an essay General Scholium which was appended to the second edition of the Principia....
"). According to Ernst Mach
Ernst Mach
Ernst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...
the notion of force in Newton's second law was pleonastic
Pleonasm
Pleonasm is the use of more words or word-parts than is necessary for clear expression: examples are black darkness, or burning fire...
, tautological and superfluous. Indeed it is possible to consider the Newtonian equations of motion of the gravitational interaction between the sun (s) and a planet (p),
as two coupled equations describing the positions
and of planet and sun, without interpreting the right hand sides of these equations as forces; the equations just describe a process of interaction, without any necessity to interpret the sun as the cause of the motion of the planet (or vice versa), and allow one to predict the states of the system s+p 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.
The possibility of such a time-independent view is at the basis of the deductive-nomological
Deductive-nomological
The deductive-nomological model is a formalized view of scientific explanation in natural language. It characterizes scientific explanations primarily as deductive arguments with at least one natural law statement among its premises...
(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
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace
Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...
'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
Laplace's demon
In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814...
). 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
Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions which are given on a hypersurface in the domain. Cauchy problems are an extension of initial value problems and are to be contrasted with boundary value problems...
. Confusion of causality and determinism is particularly acute in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, this theory being acausal (in consequence of its inability to provide descriptions of the causes of all actually observed effects) but deterministic in the mathematical sense.
In modern physics
Modern physics
The term modern physics refers to the post-Newtonian conception of physics. The term implies that classical descriptions of phenomena are lacking, and that an accurate, "modern", description of reality requires theories to incorporate elements of quantum mechanics or Einsteinian relativity, or both...
, the notion of causality had to be clarified. The insights of the theory of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
confirmed the assumption of causality, but they made the meaning of the word "simultaneous" observer-dependent. 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
.
In the theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, 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
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
is curved. New subtleties must be taken into account when we investigate causality in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
and relativistic quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
in particular. In quantum field theory, causality is closely related to the principle of locality
Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...
. However, the principle of locality is disputed: whether it strictly holds depends on the interpretation of quantum mechanics
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
chosen, especially for experiments involving quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
that satisfy Bell's Theorem
Bell's theorem
In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...
.
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
Grandfather paradox
The grandfather paradox is a proposed paradox of time travel first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent . The paradox is this: suppose a man traveled back in time and killed his biological grandfather before the latter met the traveler's...
, 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
Chronology protection conjecture
The chronology protection conjecture is a conjecture by the physicist Professor Stephen Hawking that the laws of physics are such as to prevent time travel on all but sub-microscopic scales. Mathematically, the permissibility of time travel is represented by the existence of closed timelike curves...
.
Distributed causality
Theories in physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
like the Butterfly effect
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...
from chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
open up the possibility of a type of distributed parameter systems
Distributed parameter systems
A distributed parameter system is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems...
in 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
Butterfly effect
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions; where a small change at one place in a nonlinear system can result in large differences to a later state...
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
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
as represented by Mackie's INUS conditions. In 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
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....
, 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 dynamical triangulation
Causal dynamical triangulation (abbreviated as "CDT") invented by Renate LollRenate Loll
Renate Loll is a physicist who works at the , The Netherlands. She received her Ph.D. from , London, in 1989. In 2001 she joined the permanent staff of the ITP, after spending several years at the Max Planck Institute for Gravitational Physics in Golm, Germany...
, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...
, is an approach to quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
that like loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in great depth, and revealed it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale
Planck scale
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
, and reveals a fractal
Fractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...
structure on slices of constant time. Using a structure called a simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
, it divides spacetime into tiny triangular sections. A simplex is the generalized form of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
, in various dimensions. A 3-simplex is usually called a tetrahedron
Tetrahedron
In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron
Pentachoron
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the pentachoron, pentatope, or hyperpyramid...
. Each simplex is geometrically flat, but simplices can be "glued" together in a variety of ways to create curved spacetimes. Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few, CDT avoids this problem by allowing only those configurations where cause precedes any event. In other words, the timelines of all joined edges of simplices must agree.
Thus, maybe, causality lies in the foundation of the spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
geometry.
See also
- RetrocausalityRetrocausalityRetrocausality is any of several hypothetical phenomena or processes that reverse causality, allowing an effect to occur before its cause....
- Causal StructureCausal structureIn mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.- Introduction :In modern physics spacetime is represented by a Lorentzian manifold...
- Causal SetsCausal setsThe causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order...
- Particle horizon
- Philosophy of physicsPhilosophy of physicsIn philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
- Causal contactCausal contactTwo entities are in causal contact if there may be an event that has affected both in a causal way. Every object of mass in space, for instance, exerts a field force on all other objects of mass, according to Newton's law of universal gravitation...
- Wheeler–Feynman time-symmetric theory for electrodynamics
Further reading
- Bohm, David. (2005). Causality and Chance in Modern Physics. London: Taylor and Francis.
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.
- by John G. Cramer:
- EPR Communication: Signals from the Future? "In this column I want to tell you about this causality-violating communications scheme and its possible consequences." **The Transactional Interpretation of Quantum Mechanics "3.10 The Arrow of Time in the Transactional Interpretation – The formalism of quantum mechanics, at least in its relativistically invariant formulation, is completely even handed in dealing with the "arrow" of time, the distinction between future and past time directions."