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 of the event and ultimately
reducible to
fundamental interactions. 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 descri ...
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
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 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
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) 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.
[ 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 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 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. 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 extrao ...
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.
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. 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 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
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, 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
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'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
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, or if its collapse is due to
hidden variables, or simply redefining determinism as meaning that probabilities rather than specific effects are determined).
Distributed causality
Theories in
physics 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 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, 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,
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, 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. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the
spacetime 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, 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 effect. In other words, the timelines of all joined edges of simplices must agree.
Thus, maybe, causality lies in the foundation of the
spacetime 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. 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.
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