In

physicsPhysics 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...

,

**action at a distance** is the

interactionInteraction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way causal effect...

of two objects which are separated in

spaceSpace is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

with no known mediator of the interaction. This term was used most often in the context of early theories of gravity and

electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

to describe how an object responds to the influence of distant massive or charged bodies. More generally "Action at a distance" describes the break between human intuition, where objects have to touch to interact, and physical theory. The exploration and resolution of this problematic phenomenon lead to significant developments in physics, from the concept of a field, to descriptions of quantum entanglement and the mediator particles of the standard model.

## Electricity

Efforts to account for action at a distance in the theory of electromagnetism led to the development of the concept of a

fieldIn physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...

which mediated interactions between currents and charges across empty space. According to field theory we account for the

Coulomb (electrostatic) interaction between charged particles through the fact that charges produce around themselves an electric field, which can be felt by other charges as a force. The concept of the field was elevated to fundamental importance in

Maxwell's equationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

, which used the field to elegantly account for all electromagnetic interactions, as well as light (which, until then, had been a completely unrelated phenomenon). In Maxwell's theory, the field is its own physical entity, carrying momenta and energy across space, and action at a distance is only the apparent effect of local interactions of charges with their surrounding field.

Electrodynamics can be described without fields (in

MinkowskiMinkowski is a surname, and may refer to:* Eugène Minkowski , French psychiatrist* Hermann Minkowski Russian-born German mathematician and physicist, known for:** Minkowski addition** Minkowski–Bouligand dimension...

flat space) as the direct interaction of particles with light-like separation vectors. This results in the Fokker-Tetrode-Schwartzchild action integral. This kind of electrodynamic theory is often called "direct interaction" to distinguish it from field theories where action at a distance is mediated by a localized field (localized in the sense that its dynamics are determined by the nearby field parameters). This description of electrodynamics, in contrast with Maxwell's theory, explains apparent action at a distance not by postulating a mediating entity (the field) but by appealing to the natural geometry of special relativity in which two events in spacetime can be physically distinct and still have "zero"

separationIn 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...

. Perceived action at a distance is a result of human bias for spatial separation, charged particles can be separated in space, and yet geometrically connected.

Various proofs, beginning with that of

DiracPaul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

have shown that direct interaction theories (under reasonable assumptions) do not admit

LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

or

HamiltonianHamiltonian may refer toIn mathematics :* Hamiltonian system* Hamiltonian path, in graph theory** Hamiltonian cycle, a special case of a Hamiltonian path* Hamiltonian group, in group theory* Hamiltonian...

formulations (these are the so-called No Interaction Theorems). Consequently, the Fokker-Tetrode action is mostly a historic novelty. Still, attempts to recapture action at a distance without a field, which is often difficult to quantize, lead directly to the development of the quantum electrodynamics of

FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

and

SchwingerJulian Seymour Schwinger was an American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.Schwinger is recognized as one of the...

.

### Newton

NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's theory of gravity offered no prospect of identifying any mediator of gravitational interaction. His theory assumed that gravitation acts instantaneously, regardless of distance.

KeplerJohannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

's observations gave strong evidence that in planetary motion angular momentum is conserved. (The mathematical proof is only valid in the case of a

Euclidean geometryEuclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

.) Gravity is also known as a force of attraction between two objects because of their mass.

A related question, raised by

Ernst MachErnst Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as the Mach number and the study of shock waves...

, was how rotating bodies know how much to bulge at the equator. This, it seems, requires an action-at-a-distance from distant matter, informing the rotating object about the state of the universe. Einstein coined the term

Mach's principleIn theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach....

for this question.

### Einstein

According to

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's theory of

special relativitySpecial 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...

, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of information. If one of the interacting objects were to suddenly be displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the

speed of lightThe 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...

.

One of the conditions that a relativistic theory of gravitation must meet is to be mediated with a speed that does not exceed c, the speed of light in a vacuum. It could be seen from the previous success of electrodynamics that the relativistic theory of gravitation would have to use the concept of a field or something similar.

This problem has been resolved by Einstein's theory of

general relativityGeneral 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...

in which gravitational interaction is mediated by deformation of space-time geometry. Matter warps the geometry of space-time and these effects are, as with electric and magnetic fields, propagated at the speed of light. Thus, in the presence of matter, space-time becomes

non-EuclideanNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...

, resolving the apparent conflict between Newton's proof of the conservation of angular momentum and Einstein's theory of

special relativitySpecial 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...

. Mach's question regarding the bulging of rotating bodies is resolved because local space-time geometry is informing a rotating body about the rest of the universe. In Newton's theory of motion, space acts on objects, but is not acted upon. In Einstein's theory of motion, matter acts upon space-time geometry, deforming it, and space-time geometry acts upon matter.

## Quantum mechanics

Since the early 20th century,

quantum mechanicsQuantum 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...

has posed new challenges for the view that physical processes should obey

localityIn 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...

. The collapse of the wave function of an

electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

being measured, for instance, is presumed to be instantaneous. Whether this counts as action-at-a-distance hinges on the nature of the wave function and its collapse, issues over which there is still considerable debate amongst scientists and philosophers. One important line of debate originated with Einstein, who challenged the idea that the wave function offers a complete description of the physical reality of a particle by showing that such a view leads to a paradox. Einstein, along with

Boris PodolskyBoris Yakovlevich Podolsky , was an American physicist of Russian Jewish descent.-Education:In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in what was then the Russian Empire, and he moved to the United States in 1913...

and

Nathan RosenNathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...

, proposed a

thought experimentA thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

to demonstrate how two physical quantities with non-commuting operators (e.g. position and momentum) can have simultaneous reality. Since the wave function does not ascribe simultaneous reality to both quantities and yet they can be shown to exist simultaneously, Einstein, Podolsky and Rosen (EPR) argued that the quantum mechanical description of reality must not be complete.

This thought experiment, which came to be known as the

EPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...

, hinges on the principle of locality. A common presentation of the paradox is as such: two particles interact briefly and then are sent off in opposite directions. One could imagine an atomic transition that releases two photons A and B (spin-1 particles) with no overall change in momentum. The photons end up so far away from each other that one can no longer influence the other (this is the principle of locality). As long as the photons act only locally, the perfect anticorrelation of their momenta will hold. That is, if photon A has a momentum of 1 (in appropriate units) then by the conservation of momentum photon B must have a momentum of -1. Therefore, EPR's argument goes, we could measure the position of photon A, and also simultaneously know photon A's momentum by measuring photon B (since A's momentum must be the opposite of B's).

Because EPR's proposal involved properties that were not captured in the wave equation and which were local and real, it became known as a local 'hidden variables' theory. After the EPR paper, several scientists such as de Broglie took up interest in local hidden variables theories. In the 1960s

John BellJohn Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

derived an inequality that showed a testable difference between the predictions of quantum mechanics and

localIn 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...

hidden variablesHidden variables may refer to:* Hidden variable theories, in physics a class of theories trying to explain away the statistical nature of quantum mechanics* Latent variables, in statistics, variables that are inferred from other observed variables...

theories.

ExperimentsThe Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

testing Bell-type inequalities in situations analogous to EPR's thought experiments have been consistent with the predictions of quantum mechanics, suggesting that local hidden variables theories can be ruled out. Whether or not this is interpreted as evidence for

nonlocalityQuantum nonlocality is the phenomenon by which measurements made at a microscopic level necessarily refute one or more notions that are regarded as intuitively true in classical mechanics...

depends on one's

interpretation of quantum mechanicsAn 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...

. In the standard interpretation the wave function is still considered a complete description so the nonlocality is generally accepted, but there is still debate over what this means physically.

One important question raised by this ambiguity is whether Einstein's theory of relativity is compatible with the experimental results demonstrating nonlocality. Relativistic

quantum field theoryQuantum 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...

requires interactions to propagate at speeds less than or equal to the speed of light, so "

quantum entanglementQuantum 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...

" cannot be used for faster-than-light-speed propagation of matter, energy, or information. Measurements of one particle will be correlated with measurements on the other particle, but this is only known after the experiment is performed and notes are compared, therefore there is no way to actually send

*information* faster than the speed of light. On the other hand, relativity predicts causal ambiguities will result from the nonlocal interaction. In terms of the EPR experiment, in some reference frames measurement of photon A will cause the wave function to collapse, but in other reference frames the measurement of photon B will cause the collapse.

Non-standard interpretations of quantum mechanics also vary in their response to the EPR-type experiments.

Bohm interpretationThe de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

gives an explanation based on nonlocal hidden variables for the correlations seen in entanglement. Many advocates of the

many-worlds interpretationThe many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...

argue that it can explain these correlations in a way that does not require a violation of locality, by allowing measurements to have non-unique outcomes.

## See also

- Quantum teleportation
Quantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...

- Quantum pseudo-telepathy
Quantum pseudo-telepathy is a phenomenon in quantum game theory resulting in anomalously high success rates in coordination games between separated players. These high success rates would require communication between the players in a purely classical world; however, the game is set up such that...

- Wheeler–Feynman absorber theory