Action at a distance is the concept inphysics that an object'smotion can be affected by another object without the two being inphysical contact; that is, it is the concept of the non-local interaction of objects that are separated in space.Coulomb's law andNewton's law of universal gravitation are based on action at a distance.

Historically, action at a distance was the earliest scientific model forgravity andelectricity and it continues to be useful in many practical cases. In the 19th and 20th centuries, field models arose to explain these phenomena with more precision. The discovery ofelectrons and ofspecial relativity led to new action at a distance models providing alternative to field theories. Under our modern understanding, the fourfundamental interactions (gravity,electromagnetism, thestrong interaction and theweak interaction) in all of physics are not described by action at a distance.

In the study ofmechanics, action at a distance is one of three fundamental actions on matter that cause motion. The other two are direct impact (elastic orinelastic collisions) and actions in acontinuous medium as influid mechanics orsolid mechanics.^[1]: 338 Historically, physical explanations for particular phenomena have moved between these three categories over time as new models were developed.

Action-at-a-distance and actions in a continuous medium may be easily distinguished when the medium dynamics are visible, like waves in water or in an elastic solid. In the case of electricity or gravity, no medium is required. In the nineteenth century, criteria like the effect of actions on intervening matter, the observation of a time delay, the apparent storage of energy, or even the possibility of a plausible mechanical model for action transmission were all accepted as evidence against action at a distance.^[2]: 198Aether theories were alternative proposals to replace apparent action-at-a-distance in gravity and electromagnetism, in terms of continuous action inside an (invisible) medium called "aether".^[1]: 338

Direct impact of macroscopic objects seems visually distinguishable from action at a distance. If however the objects are constructed ofatoms, and the volume of those atoms is not defined and atoms interact by electric and magnetic forces, the distinction is less clear.^[2]

The concept of action at a distance acts in multiple roles in physics and it can co-exist with other models according to the needs of each physical problem.

One role is as a summary of physical phenomena, independent of any understanding of the cause of such an action.^[1] For example, astronomical tables of planetary positions can be compactly summarized usingNewton's law of universal gravitation, which assumes the planets interact without contact or an intervening medium. As a summary of data, the concept does not need to be evaluated as a plausible physical model.

Action at a distance also acts as a model explaining physical phenomena even in the presence of other models. Again in the case of gravity, hypothesizing an instantaneous force between masses allows the return time ofcomets to be predicted as well as predicting the existence of previously unknown planets, likeNeptune.^[3]: 210 These triumphs of physics predated the alternative more accurate model for gravity based on general relativity by many decades.

Introductory physics textbooks discusscentral forces, like gravity, by models based on action-at-distance without discussing the cause of such forces or issues with it until the topics ofrelativity andfields are discussed. For example, seeThe Feynman Lectures on Physics on gravity.^[4]

Action-at-a-distance as a physical concept requires identifying objects, distances, and their motion. Inantiquity, ideas about the natural world were not organized in these terms. Objects in motion were modeled as living beings.^[1] Around 1600, the scientific method began to take root.René Descartes held a more fundamental view, developing ideas of matter and action independent of theology.Galileo Galilei wrote about experimental measurements of falling and rolling objects.Johannes Kepler'slaws of planetary motion summarizedTycho Brahe's astronomical observations.^[2]: 132 Many experiments with electrical and magnetic materials led to new ideas about forces. These efforts set the stage for Newton's work on forces and gravity.

In 1687Isaac Newton published hisPrincipia which combined hislaws of motion with a new mathematical analysis able to reproduce Kepler's empirical results.^[2]: 134 His explanation was in the form of alaw of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to the square of the distance between them.^[5]: 28 Thus the motions of planets were predicted by assuming forces working over great distances.

This mathematical expression of the force did not imply a cause. Newton considered action-at-a-distance to be an inadequate model for gravity.^[6] Newton, in his words, considered action at a distance to be:

so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.^[7]

— Isaac Newton, Letters to Bentley, 1692/3

Metaphysical scientists of the early 1700s strongly objected to the unexplained action-at-a-distance in Newton's theory.Gottfried Wilhelm Leibniz complained that the mechanism of gravity was "invisible, intangible, and not mechanical".^[1]: 339 Moreover, initial comparisons with astronomical data were not favorable. As mathematical techniques improved throughout the 1700s, the theory showed increasing success, predicting the date of the return ofHalley's comet^[8] and aiding the discovery of planetNeptune in 1846.^[9] These successes and the increasingly empirical focus of science towards the 19th century led to acceptance of Newton's theory of gravity despite distaste for action-at-a-distance.^[1]

Electrical and magnetic phenomena also began to be explored systematically in the early 1600s. InWilliam Gilbert's early theory of "electric effluvia," a kind of electric atmosphere, he rules out action-at-a-distance on the grounds that "no action can be performed by matter save by contact".^[11] However subsequent experiments, especially those byStephen Gray showed electrical effects over distance. Gray developed an experiment call the "electric boy" demonstrating electric transfer without direct contact.^[10]Franz Aepinus was the first to show, in 1759, that a theory of action at a distance for electricity provides a simpler replacement for the electric effluvia theory.^[5]: 42 Despite this success, Aepinus himself considered the nature of the forces to be unexplained: he did "not approve of the doctrine which assumes the possibility of action at a distance", setting the stage for a shift to theories based on aether.^[11]: 549

By 1785Charles-Augustin de Coulomb showed that two electric charges at rest experience a force inversely proportional to the square of the distance between them, a result now calledCoulomb's law. The striking similarity to gravity strengthened the case for action at a distance, at least as a mathematical model.^[12]

As mathematical methods improved, especially through the work ofPierre-Simon Laplace,Joseph-Louis Lagrange, andSiméon Denis Poisson, more sophisticated mathematical methods began to influence the thinking of scientists. The concept ofpotential energy applied to smalltest particles led to the concept of ascalar field, a mathematical model representing the forces throughout space. While this mathematical model is not a mechanical medium, the mental picture of such a field resembles a medium.^[2]: 197

Michael Faraday was the first who suggested that action at a distance was inadequate as an account of electric and magnetic forces, even in the form of a (mathematical) potential field.^[1]: 341 Faraday, an empirical experimentalist, cited three reasons in support of some medium transmitting electrical force: 1)electrostatic induction across an insulator depends on the nature of the insulator, 2) cutting a charged insulator causes opposite charges to appear on each half, and 3) electric discharge sparks are curved at an insulator. From these reasons he concluded that the particles of an insulator must bepolarized, with each particle contributing to continuous action. He also experimented with magnets, demonstrating lines of force made visible by iron filings. However, in both cases his field-like model depends on particles that interact through an action-at-a-distance: his mechanical field-like model has no more fundamental physical cause than the long-range central field model.^[1]: 348

Faraday's observations, as well as others, ledJames Clerk Maxwell to a breakthrough formulation in 1865, a set ofequations that combined electricity and magnetism, both static and dynamic, and which included electromagnetic radiation – light.^[5]: 253 Maxwell started with elaborate mechanical models but ultimately produced a purely mathematical treatment using dynamicalvector fields. The sense that these fields must be set to vibrate to propagate light set off a search of a medium of propagation; the medium was called theluminiferous aether or theaether.^[5]: 279

In 1873 Maxwell addressed action at a distance explicitly.^[13] He reviews Faraday's lines of force, carefully pointing out that Faraday himself did not provide a mechanical model of these lines in terms of a medium. Nevertheless the many properties of these lines of force imply these "lines must not be regarded as mere mathematical abstractions". Faraday himself viewed these lines of force as a model, a "valuable aid" to the experimentalist, a means to suggest further experiments.

In distinguishing between different kinds of action Faraday suggested three criteria: 1) do additional material objects alter the action?, 2) does the action take time, and 3) does it depend upon the receiving end? For electricity, Faraday knew that all three criteria were met for electric action, but gravity was thought to only meet the third one. After Maxwell's time a fourth criteria, the transmission of energy, was added, thought to also apply to electricity but not gravity. With the advent of new theories of gravity, the modern account would give gravity all of the criteria except dependence on additional objects.

The success of Maxwell's field equations led to numerous efforts in the later decades of the 19th century to represent electrical, magnetic, and gravitational fields, primarily with mechanical models.^[5]: 279 No model emerged that explained the existing phenomena. In particular no good model forstellar aberration, the shift in the position of stars with the Earth's relative velocity. The best models required the ether to be stationary while the Earth moved, butexperimental efforts to measure the effect of Earth's motion through the aether found no effect.

In 1892Hendrik Lorentz proposed a modified aether based on the emerging microscopic molecular model rather than the strictly macroscopic continuous theory of Maxwell.^[14]: 326 Lorentz investigated the mutual interaction of a moving solitary electrons within a stationary aether.^[5]: 393 He rederived Maxwell's equations in this way but, critically, in the process he changed them to represent the wave in the coordinates moving electrons. He showed that the wave equations had the same form if they were transformed using a particular scalingfactor,$${\displaystyle \gamma =\frac{1}{\sqrt{1-(u^2/c^2)}}.}$$ where${\displaystyle u}$ is the velocity of the moving electrons and${\displaystyle c}$ is the speed of light. Lorentz noted that if this factor were applied as alength contraction to moving matter in a stationary ether, it would eliminate any effect of motion through the ether, in agreement with experiment.

In 1899,Henri Poincaré questioned the existence of an aether, showing that theprinciple of relativity prohibits the absolute motion assumed by proponents of the aether model. He named the transformation used by Lorentz theLorentz transformation but interpreted it as a transformation between two inertial frames with relative velocity${\displaystyle u}$. This transformation makes the electromagnetic equations look the same in every uniformly moving inertial frame. Then, in 1905,Albert Einstein demonstrated that the principle of relativity, applied to the simultaneity of time and the constantspeed of light, precisely predicts the Lorentz transformation. This theory ofspecial relativity quickly became the modern concept ofspacetime.

Thus the aether model, initially so very different from action at a distance, slowly changed to resemble simple empty space.^[5]: 393

In 1905, Poincaré proposedgravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations^[15] and suggested that, in analogy to an acceleratingelectrical charge producingelectromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves.^[16] However, until 1915 gravity stood apart as a force still described by action-at-a-distance. In that year, Einstein showed that a field theory of spacetime,general relativity, consistent with relativity can explain gravity. New effects resulting from this theory were dramatic forcosmology but minor for planetary motion and physics on Earth.Einstein himself noted Newton's "enormous practical success".^[17]

In the early decades of the 20th century,Karl Schwarzschild,^[18]Hugo Tetrode,^[19] andAdriaan Fokker^[20] independently developed non-instantaneous models for action at a distance consistent with special relativity. In 1949John Archibald Wheeler andRichard Feynman built on these models to develop a new field-free theory of electromagnetism.While Maxwell's field equations are generally successful, the Lorentz model of a moving electron interacting with the field encounters mathematical difficulties: the self-energy of the moving point charge within the field is infinite.^[21]: 187 TheWheeler–Feynman absorber theory of electromagnetism avoids the self-energy issue.^[21]: 213 They interpretAbraham–Lorentz force, the apparent force resisting electron acceleration, as a real force returning from all the other existing charges in the universe.

The Wheeler–Feynman theory has inspired new thinking about thearrow of time and about the nature ofquantum non-locality.^[22] The theory has implications for cosmology; it has been extended toquantum mechanics.^[23] A similar approach has been applied to develop an alternative theory of gravity consistent with general relativity.^[24]John G. Cramer has extended the Wheeler–Feynman ideas to create thetransactional interpretation of quantum mechanics.

Albert Einstein wrote toMax Born about issues in quantum mechanics in 1947 and used a phrase translated as "spooky action at a distance", and in 1964,John Stewart Bell proved that quantum mechanics predicted stronger statistical correlations in the outcomes of certain far-apart measurements than anylocal theory possibly could.^[25] The phrase has been picked up and used as a description for the cause of small non-classical correlations between physically separated measurement ofentangled quantum states. The correlations are predicted by quantum mechanics (theBell theorem) and verified by experiments (theBell test). Rather than a postulate like Newton's gravitational force, this use of "action-at-a-distance" concerns observed correlations which cannot be explained with localized particle-based models.^[26][27] Describing these correlations as "action-at-a-distance" requires assuming that particles became entangled and then traveled to distant locations, an assumption that is not required by quantum mechanics.^[28]

Quantum field theory does not need action at a distance. At the most fundamental level, only four forces are needed. Each force is described as resulting from the exchange of specificbosons. Two are short range: thestrong interaction mediated bymesons and theweak interaction mediated by theweak boson; two are long range:electromagnetism mediated by thephoton andgravity hypothesized to be mediated by thegraviton.^[29]: 132 However, the entire concept of force is of secondary concern in advanced modern particle physics. Energy forms the basis of physical models and the wordaction has shifted away from implying a force to a specific technical meaning, an integral over the difference betweenpotential energy andkinetic energy.^[29]: 173

• Central force – Mechanical force towards or away from a point
• Principle of locality – Physical principle that only immediate surroundings can influence an object
• Quantum nonlocality – Deviations from local realism

•  This article incorporates text from afree content work. Licensed under CC-BY-SA. Text taken fromNewton’s action at a distance – Different views​, Nicolae Sfetcu.

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• Concepts in physics

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