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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 ...
, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous "
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- ...
". Locality evolved out of the field theories of classical physics. The concept is that for an action at one point to have an influence at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence. The special theory of relativity limits the speed at which all such influences can travel to 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 ...
, c. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. An event at point A cannot cause a result at point B in a time less than T=D/c, where D is the distance between the points and c is the speed of light in a vacuum. Experimental tests show that
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 chemistr ...
seems to violate Bell's inequalities, implying that quantum effects might be non-local, according to some
interpretations 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 ...
.


Pre-quantum mechanics

During the 17th century Newton's principle of
universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the dist ...
was formulated in terms of "action at a distance", thereby violating the principle of locality.
Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
of electric forces was initially also formulated as instantaneous action at a distance, but was later superseded by
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
of electromagnetism, which obey locality. In 1905
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's special theory of relativity postulated that no material or energy can travel faster than the speed of light, and Einstein thereby sought to reformulate physics in a way that obeyed the principle of locality. He later succeeded in producing an alternative theory of gravitation,
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 ...
, which obeys the principle of locality. However, a different challenge to the principle of locality developed subsequently from the theory of
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 chemistr ...
, which Einstein himself had helped to create.


Quantum mechanics


Local realism

In 1935,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
,
Boris Podolsky Boris Yakovlevich Podolsky (russian: link=no, Бори́с Я́ковлевич Подо́льский; June 29, 1896 – November 28, 1966) was a Russian-American physicist of Jewish descent, noted for his work with Albert Einstein and Nathan ...
and Nathan Rosen in their EPR paradox theorised that
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 chemistr ...
might not be a local theory, because a measurement made on one of a pair of separated but '' entangled'' particles causes a ''simultaneous'' effect, the collapse of the
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
, in the remote particle (i.e., an effect exceeding the speed of light). But because of the probabilistic nature of wave function collapse, this violation of locality cannot be used to transmit
information Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
faster than light. In 1964
John Stewart Bell John Stewart Bell FRS (28 July 1928 – 1 October 1990) was a physicist from Northern Ireland and the originator of Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022, the Nobel Prize in Phy ...
formulated the " Bell inequality", which, if violated in actual experiments, implies that quantum mechanics violates either locality or realism, another principle, which relates to the value of unmeasured quantities (
counterfactual definiteness In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume the existence of objects, and properties of ...
). The two principles are commonly referred to as a single principle, local realism. Experimental tests of the Bell inequality, beginning with
John Clauser John Francis Clauser (; born December 1, 1942) is an American theoretical and experimental physicist known for contributions to the foundations of quantum mechanics, in particular the Clauser–Horne–Shimony–Holt inequality. Clauser was a ...
and
Alain Aspect Alain Aspect (; born 15 June 1947) is a French physicist noted for his experimental work on quantum entanglement. Aspect was awarded the 2022 Nobel Prize in Physics, jointly with John Clauser and Anton Zeilinger, "for experiments with entangl ...
's 1980s experiments, show that quantum mechanics seems to violate the inequality, so it must violate either locality or realism. However, critics have noted these experiments included " loopholes", which prevented a definitive answer to this question. This problem is considered to have been resolved during 2015 when three "loophole-free" experiments were carried out In 2015 by independent groups in
Delft University of Technology Delft University of Technology ( nl, Technische Universiteit Delft), also known as TU Delft, is the oldest and largest Dutch public technical university, located in Delft, Netherlands. As of 2022 it is ranked by QS World University Rankings among ...
,
University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich hist ...
and
National Institute of Standards and Technology The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...
(NIST), addressing multiple loopholes at the same time. However, some loopholes might persist, like superdeterminism, with the result that the question may be fundamentally untestable.


Relativistic quantum mechanics

Locality is one of the
axioms An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...
of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if there are two
observable In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum phy ...
s, each localized within two distinct spacetime regions which happen to be at 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 ...
separation from each other, the observables must commute. Alternatively, a solution to the field equations is local if the underlying equations are either
Lorentz invariant In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
or, more generally,
generally covariant In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the ''form'' of physical laws under arbitrary differentiable coordinate transformations. The essential idea is ...
or locally Lorentz invariant.


See also

*
Einstein's thought experiments A hallmark of Albert Einstein's career was his use of visualized thought experiments (german: Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments too ...
* Local hidden-variable theory * Non-locality (disambiguation) *
Quantum nonlocality In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not admit an interpretation in terms of a local realistic theory. Quantum nonlocality has been experime ...
* Cluster decomposition


References


External links

{{wikiquote
Quantum nonlocality vs. Einstein locality
by H. Dieter Zeh Quantum measurement