Causality is the relationship between causes and effects. While causality is also a topic studied from the perspectives of philosophy and physics, it is
operationalized
In research design, especially in psychology, social sciences, life sciences and physics, operationalization or operationalisation is a process of defining the measurement of a phenomenon which is not directly measurable, though its existence is in ...
so that causes of an event must be in the past
light cone
In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take thro ...
of the event and ultimately
reducible to
fundamental interaction
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electrom ...
s. Similarly, a cause cannot have an effect outside its future light cone.
As a physical concept
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
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations, these descr ...
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
In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take thro ...
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
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
and
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
that act as causal influences cannot travel faster than the speed of light and/or backwards in time. In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
, observables of events with a
spacelike
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
relationship, "elsewhere", have to
commute
Commute, commutation or commutative may refer to:
* Commuting, the process of travelling between a place of residence and a place of work
Mathematics
* Commutative property, a property of a mathematical operation whose result is insensitive to th ...
, 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
In physics, action at a distance is the concept that an object can be affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space.
Non-c ...
) replacing mechanistic proposals like
Descartes' vortex theory
Mechanical explanations of gravitation (or kinetic theories of gravitation) are attempts to explain the action of gravity by aid of basic mechanical processes, such as pressure forces caused by pushes, without the use of any action at a distance. ...
; in the third place as an incentive to develop dynamic
field theories (e.g.,
Maxwell's electrodynamics and
Einstein's general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...
) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.
In
modern physics
Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity and general ...
, the notion of causality had to be clarified. The word ''simultaneous'' is observer-dependent in
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
.
[ A. Einstein, "Zur Elektrodynamik bewegter Koerper", ''Annalen der Physik'' 17, 891–921 (1905).] The principle is
relativity of simultaneity
In physics, the relativity of simultaneity is the concept that ''distant simultaneity'' – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. This possi ...
. Consequently, the relativistic principle of causality says that the cause must precede its effect ''according to all
inertial
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration ...
observers''. This is equivalent to the statement that the cause and its effect are separated by a
timelike
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
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
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
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
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
.
In the theory of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and 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
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
is curved. New subtleties must be taken into account when we investigate causality in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
and relativistic
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
in particular. In those two theories, causality is closely related to the
principle of locality
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 ins ...
. However, the principle of locality is disputed: whether it strictly holds depends on the
interpretation of quantum mechanics
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraord ...
chosen, especially for experiments involving
quantum entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...
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 paradox
Time travel is a common theme in fiction, mainly since the late 19th century, and has been depicted in a variety of media, such as literature, television, film, and advertisements.
The concept of time travel by mechanical means was popularized ...
es such as the
grandfather paradox
A temporal paradox, time paradox, or time travel paradox is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time and time travel. The notion of time travel to the future complies with current understanding ...
, 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 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 ...
.
Determinism (or, what causality is ''not'')
The word ''causality'' in this context means that all effects must have specific physical causes due to fundamental interactions.
["Causality." Cambridge English Dictionary. Accessed November 18, 2018. https://dictionary.cambridge.org/us/dictionary/english/causality] Causality in this context is not associated with definitional principles such as
Newton's second law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
. 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
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
, which itself is a
consequence 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
''Hypotheses non fingo'' (Latin for "I frame no hypotheses", or "I contrive no hypotheses") is a phrase used by Isaac Newton in an essay, "General Scholium", which was appended to the second (1713) edition of the '' Principia''.
Original remark
A ...
"). According to
Ernst Mach
Ernst Waldfried Josef Wenzel Mach ( , ; 18 February 1838 – 19 February 1916) was a Moravian-born Austrian physicist and philosopher, who contributed to the physics of shock waves. The ratio of one's speed to that of sound is named the Mach ...
[Ernst Mach, ''Die Mechanik in ihrer Entwicklung, Historisch-kritisch dargestellt'', Akademie-Verlag, Berlin, 1988, section 2.7.] the notion of force in Newton's second law was
pleonastic
Pleonasm (; , ) is Redundancy (linguistics), redundancy in linguistic expression, such as "black darkness" or "burning fire". It is a manifestation of Tautology (language), tautology by traditional rhetorical criteria and might be considered a fa ...
, 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
The arrow of time, also called time's arrow, is the concept positing the "one-way direction" or " asymmetry" of time. It was developed in 1927 by the British astrophysicist Arthur Eddington, and is an unsolved general physics question. This ...
, 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
The deductive-nomological model (DN 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, ...
(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
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...
. A disadvantage of the D-N view is that causality and determinism are more or less identified. Thus, in
classical physics
Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
, 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, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
'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
In the history of science, Laplace's demon was a notable published articulation of causal determinism on a scientific basis by Pierre-Simon Laplace in 1814. According to determinism, if someone (the demon) knows the precise location and momentu ...
). 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
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value proble ...
.
Confusion between causality and determinism is particularly acute in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, 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
Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...
in some interpretations (e.g. if the wave function is presumed not to actually collapse as in the
many-worlds interpretation
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum me ...
, or if its collapse is due to
hidden variables
Hidden variables may refer to:
* Confounding, in statistics, an extraneous variable in a statistical model that correlates (directly or inversely) with both the dependent variable and the independent variable
* Hidden transformation, in computer ...
, or simply redefining determinism as meaning that probabilities rather than specific effects are determined).
Distributed causality
Theories in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
like the
butterfly effect from
chaos theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...
open up the possibility of a type of
distributed parameter systems
In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are system ...
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 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 In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form ...
, 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 Loll
Renate Loll (born 19 June 1962, Aachen) is a Professor in Theoretical Physics at the Institute for Mathematics, Astrophysics and Particle Physics of the Radboud University in Nijmegen, Netherlands. She previously worked at the Institute for Th ...
,
Jan Ambjørn and Jerzy Jurkiewicz, and popularized by
Fotini Markopoulou
Fotini G. Markopoulou-Kalamara ( el, Φωτεινή Μαρκοπούλου-Καλαμαρά; born April 3, 1971) is a Greek theoretical physicist interested in quantum gravity, foundational mathematics, quantum mechanics and a design engineer wo ...
and
Lee Smolin
Lee Smolin (; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo and a member of the graduate faculty of the ...
, is an approach to
quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
that like
loop quantum gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
is
background independent Background independence is a condition in theoretical physics that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various field (physics), fields within the spacetime. In particula ...
. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
fabric itself evolves. Th
Loops '05conference, 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-dimensional near the
Planck scale, and reveals a
fractal
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
structure on slices of constant time. Using a structure called a
simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. ...
, it divides spacetime into tiny triangular sections. A simplex is the generalized form of a
triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
, in various dimensions. A 3-simplex is usually called a
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or
pentachoron
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is ...
. 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 effect. In other words, the timelines of all joined edges of simplices must agree.
Thus, maybe, causality lies in the foundation of the
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
geometry.
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 by
David Malament
David B. Malament (born 21 December 1947) is an American philosopher of science, specializing in the philosophy of physics.
Biography
Malament attended Stuyvesant High School and received a B.A. in mathematics 1968 at Columbia College, Columbia ...
. This theorem states that the
causal structure
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
Introduction
In modern physics (especially general relativity) spacetime is represented by a Lorentzian ma ...
of a spacetime suffices to reconstruct its
conformal class
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal map, conformal) transformations on a space.
In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space high ...
, so knowing the conformal factor and the causal structure is enough to know the spacetime. Based on this,
Rafael Sorkin Rafael Dolnick Sorkin (born c. 1945) is an American physicist. He is professor emeritus of physics at Syracuse University and the Perimeter Institute for Theoretical Physics, and a Fellow of the American Physical Society. He is best known as initi ...
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
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a Set (mathematics), set. A poset consists of a set toget ...
, while the conformal factor can be reconstructed by identifying each poset element with a unit volume.
See also
* (general)
*
*
*
*
*
*
*
References
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. {{ISBN, 2-296-01198-5.
External links
Causal Processes, Stanford Encyclopedia of Philosophy— 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.
Causality
Concepts in physics
Philosophy of physics
Time travel
ko:인과율
it:Sistema causale
ja:因果律