Action at a distance
In physics, action at a distance is the concept that an object's motion can be affected by another object without being in physical contact with it (see mechanical contact); that is, the non-local interaction of objects that are separated in space. Coulomb's law and Newton's law of universal gravitation are based on action at a distance.
Historically, action at a distance was the earliest scientific model for gravity and electricity 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 of electrons and of special relativity led to new action at a distance models providing alternative to field theories. Under our modern understanding, the four fundamental interactions (gravity, electromagnetism, the strong interaction and the weak interaction) in all of physics are not described by action at a distance.
Categories of action
In the study of mechanics, action at a distance is one of three fundamental actions on matter that cause motion. The other two are direct impact (elastic or inelastic collisions) and actions in a continuous medium as in fluid mechanics or solid mechanics.<ref name=Hesse1955>Hesse, Mary B. (1955). "Action at a Distance in Classical Physics". Isis. 46 (4): 337–353. doi:10.1086/348429. ISSN 0021-1753. JSTOR 227576. S2CID 121166354.</ref>: 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.<ref name=Hesse2005>Hesse, Mary B. (2005). Forces and fields: the concept of action at a distance in the history of physics (Dover ed.). Mineola, N.Y: Dover Publications. ISBN 978-0-486-44240-2.</ref>: 198 Aether 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".<ref name=Hesse1955/>: 338
Direct impact of macroscopic objects seems visually distinguishable from action at a distance. If however the objects are constructed of atoms, and the volume of those atoms is not defined and atoms interact by electric and magnetic forces, the distinction is less clear.<ref name=Hesse2005/>
Roles
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.<ref name=Hesse1955/> For example, astronomical tables of planetary positions can be compactly summarized using Newton'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 of comets to be predicted as well as predicting the existence of previously unknown planets, like Neptune.<ref>Feather, Norman (1959). An Introduction to the Physics of Mass Length and Time – Hardcover. Edinburgh University Press.</ref>: 210 These triumphs of physics predated the alternative more accurate model for gravity based on general relativity by many decades.
Introductory physics textbooks discuss central forces, like gravity, by models based on action-at-distance without discussing the cause of such forces or issues with it until the topics of relativity and fields are discussed. For example, see The Feynman Lectures on Physics on gravity.<ref>Feynman, Richard P., Robert B. Leighton, and Matthew Sands. The Feynman lectures on physics, Vol. I: The new millennium edition: mainly mechanics, radiation, and heat. Vol. 1. Basic books, 2011.</ref>
History
Early inquiries into motion
Action-at-a-distance as a physical concept requires identifying objects, distances, and their motion. In antiquity, ideas about the natural world were not organized in these terms. Objects in motion were modeled as living beings.<ref name=Hesse1955/> 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's laws of planetary motion summarized Tycho Brahe's astronomical observations.<ref name=Hesse2005/>: 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.
Newtonian gravity
In 1687 Isaac Newton published his Principia which combined his laws of motion with a new mathematical analysis able to reproduce Kepler's empirical results.<ref name=Hesse2005/>: 134 His explanation was in the form of a law 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.<ref name=Whittaker/>: 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.<ref>Ducheyne, S. "Newton on Action at a Distance". Journal of the History of Philosophy vol. 52.4 (2014): 675–702.</ref> Newton, in his words, considered action at a distance to be:
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".<ref name=Hesse1955/>: 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 of Halley's comet<ref>Hughes, D. W. (1987-09-30). "The history of Halley's Comet". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 323 (1572): 349–367. Bibcode:1987RSPTA.323..349H. doi:10.1098/rsta.1987.0091. ISSN 0080-4614. S2CID 123592786.</ref> and aiding the discovery of planet Neptune in 1846.<ref>J J O'Connor; E F Robertson (September 1996). "Mathematical discovery of planets". Retrieved 2009-09-11.</ref> 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.<ref name=Hesse1955/>
Electrical action at a distance
Electrical and magnetic phenomena also began to be explored systematically in the early 1600s. In William 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".<ref name=Sanford>Sanford, Fernando (1921). "Some Early Theories Regarding Electrical Forces—The Electric Emanation Theory". The Scientific Monthly. 12 (6): 544–550. Bibcode:1921SciMo..12..544S. ISSN 0096-3771.</ref> However subsequent experiments, especially those by Stephen Gray showed electrical effects over distance. Gray developed an impressive experiment call the "electric boy" demonstrating electric transfer without direct contact.<ref name=Park1898/> 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.<ref name="Whittaker">Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 1: The classical theories (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3.</ref>: 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.<ref name=Sanford/>: 549
By 1785 Charles-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 called Coulomb's law. The striking similarity to gravity strengthened the case for action at a distance, at least as a mathematical model.<ref>Woodruff, A. E. “Action at a Distance in Nineteenth Century Electrodynamics.” Isis, vol. 53, no. 4, 1962, pp. 439–59. JSTOR, http://www.jstor.org/stable/227719. Accessed 24 Oct. 2023.</ref>
As mathematical methods improved, especially through the work of Pierre-Simon Laplace, Joseph-Louis Lagrange, and Siméon Denis Poisson, more sophisticated mathematical methods began to influence the thinking of scientists. The concept of potential energy applied to small test particles led to the concept of a scalar 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.<ref name=Hesse2005/>: 197
Fields as an alternative
It was Michael Faraday who first suggested that action at a distance, even in the form of a (mathematical) potential field, was inadequate as an account of electric and magnetic forces.<ref name=Hesse1955/>: 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 be polarized, 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.<ref name=Hesse1955/>: 348
Faraday's observations, as well as others, led James Clerk Maxwell to a breakthrough formulation in 1865, a set of equations that combined electricity and magnetism, both static and dynamic, and which included electromagnetic radiation – light.<ref name=Whittaker/>: 253 Maxwell started with elaborate mechanical models but ultimately produced a purely mathematical treatment using dynamical vector 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 the luminiferous aether or the aether.<ref name=Whittaker/>: 279
In 1873 Maxwell addressed action at a distance explicitly.<ref>Maxwell, J. C., On action at a distance, Proceedings of the Royal Institution of Great Britain, VII, 48–49, 1873–1875. Reproduced in Kuehn, K. (2016). Action-at-a-Distance. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-21816-8_30</ref> 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 suggests 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.
Fields fade into spacetime
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.<ref name=Whittaker/>: 279 No model emerged that explained the existing phenomena. In particular no good model for stellar 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, but experimental efforts to measure the effect of Earth's motion through the aether found no effect.
In 1892 Hendrik Lorentz proposed a modified aether based on the emerging microscopic molecular model rather than the strictly macroscopic continuous theory of Maxwell.<ref name=Darrigol >Darrigol, Olivier (2005). Electrodynamics from Ampère to Einstein (Reprinted ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-850593-8.</ref>: 326 Lorentz investigated the mutual interaction of a moving solitary electrons within a stationary aether.<ref name=Whittaker/>: 393 He rederived Maxwell's equations in this way but, critically, in the process he changed 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 scaling factor, <math display=block>\gamma = \frac{1}{\sqrt{1-(u^2/c^2)}}.</math> where <math>u</math> is the velocity of the moving electrons and <math>c</math> is the speed of light. Lorentz noted that if this factor were applied as a length 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 the principle of relativity prohibits the absolute motion assumed by proponents of the aether model. He named the transformation used by Lorentz the Lorentz transformation but interpreted it as a transformation between two inertial frames with relative velocity <math>u</math>. 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 constant speed of light, precisely predicts the Lorentz transformation. This theory of special relativity quickly became the modern concept of spacetime.
Thus the aether model, initially so very different from action at a distance, slowly changed to resemble simple empty space.<ref name=Whittaker/>: 393
In 1905, Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations<ref>Poincaré, Henri (1905). "Sur la dynamique de l'électron" (PDF). Académie des sciences, Note de H. Poincaré. C.R. T. 140: 1504–1508.</ref> and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves.<ref name="CGShistory"> Cervantes-Cota, J.L.; Galindo-Uribarri, S.; Smoot, G.F. (2016). "A Brief History of Gravitational Waves". Universe. 2 (3): 22. arXiv:1609.09400. Bibcode:2016Univ....2...22C. doi:10.3390/universe2030022. S2CID 2187981.</ref> 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 for cosmology but minor for planetary motion and physics on Earth. Einstein himself noted Newton's "enormous practical success".<ref>Pais, A. (1979-10-01). "Einstein and the quantum theory". Reviews of Modern Physics. 51 (4): 863–914. Bibcode:1979RvMP...51..863P. doi:10.1103/RevModPhys.51.863. ISSN 0034-6861.</ref>
Modern action at a distance
In the early decades of the 20th century Karl Schwarzschild,<ref name= "schwarzschil1903b">K. Schwarzschild, Nachr. ges. Wiss. Gottingen (1903) 128,132</ref> Hugo Tetrode,<ref>H. Tetrode, Zeitschrift für Physik 10:137, 1922</ref> and Adriaan Fokker.<ref>A. D. Fokker, Zeitschrift für Physik 58:386, 1929</ref> independently developed non-instantaneous models for action at a distance consistent with special relativity. In 1949 John Archibald Wheeler and Richard 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.<ref name=Barut>Barut, Asim O. (1980). Electrodynamics and classical theory of fields & particles. Dover books on physics and chemistry (Unabridged and corr. republ. of the ed. New York, Macmillan, 1964 ed.). New York: Dover Publ. ISBN 978-0-486-64038-9.</ref>: 187 The Wheeler-Feynman absorber theory of electromagnetism avoids the self-energy issue.<ref name=Barut/>: 213 They interpret Abraham–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 the arrow of time and about the nature of quantum non-locality.<ref>Price, Huw (1996). Time's arrow and Archimedes' point: new directions for the physics of time. New York Oxford: Oxford university press. ISBN 978-0-19-510095-2.</ref> The theory has implications for cosmology; it has been extended to quantum mechanics.<ref>Hoyle, F.; Narlikar, J. V. (1995-01-01). "Cosmology and action-at-a-distance electrodynamics". Reviews of Modern Physics. 67 (1): 113–155. Bibcode:1995RvMP...67..113H. doi:10.1103/RevModPhys.67.113. ISSN 0034-6861.</ref> A similar approach has been applied to develop an alternative theory of gravity consistent with general relativity.<ref>Narlikar, J.V. (2003). "Action at a Distance and Cosmology: A Historical Perspective". Annual Review of Astronomy and Astrophysics. 41 (1): 169–189. Bibcode:2003ARA&A..41..169N. doi:10.1146/annurev.astro.41.112202.151716. ISSN 0066-4146.</ref> John G. Cramer has extended the Wheeler-Feynman ideas to create the transactional interpretation of quantum mechanics.
"Spooky action at a distance"
Einstein wrote to Max Born about issues in quantum mechanics in 1947 and used a phrase translated as "spooky action at a distance". The phrase has been picked up and used as a description for the cause of small non-classical correlations between physically separated measurement of entangled quantum states. The correlations are predicted by quantum mechanics and verified by experiments. Rather than a postulate like Newton's gravitational force, this use of "action-at-a-distance" concerns observed correlations which are not easy to explain within simple interpretations of quantum mechanics.<ref>"Entanglement is spooky, but not action at a distance". Science News. 2023-10-30.</ref><ref>Boughn, Stephen (2022-04-16). "There Is No Spooky Action at a Distance in Quantum Mechanics". Entropy. 24 (4): 560. Bibcode:2022Entrp..24..560B. doi:10.3390/e24040560. ISSN 1099-4300. PMC 9029371. PMID 35455223.</ref><ref>Berkovitz, Joseph (2008). Zalta, Edward N. (ed.). "Action at a Distance in Quantum Mechanics". Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.</ref>
Force in quantum field theory
Quantum field theory does not need action at a distance. At the most fundamental level only four forces are needed and each are described as resulting from the exchange of specific bosons. Two are short range: the strong interaction mediated by mesons and the weak interaction mediated by the weak boson; two are long range: electromagnetism mediated by the photon and gravity hypothesized to be mediated by the graviton.<ref name=SimplyZee>Zee, Anthony (2023). Quantum field theory, as simply as possible. Princeton Oxford: Princeton University Press. ISBN 978-0-691-17429-7.</ref>: 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 word action has shifted away from implying a force to a specific technical meaning, an integral over the difference between potential energy and kinetic energy.<ref name=SimplyZee/>: 173
See also
- 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
References
External links
This article incorporates text from a free content work. Licensed under CC-BY-SA. Text taken from Newton’s action at a distance – Different views, Nicolae Sfetcu, .
