Action at a distance

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 physically contact (as in mechanical contact) by the other object. That is, it 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 lead to new action at a distance models providing alternative to field theories.
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.
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, there is no medium 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. 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".
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 understand of the cause of such action. 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 need not 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 predicting the existence of a previously unknown planets, like Neptune. 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, se The Feynman Lectures on Physics on gravity.
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 by living being. Around 1600, the scientific method began to take root. René Descartes started over with 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 Many experiments with electrical and magnetic materials lead 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 new mathematical analysis to explain Kepler's empirical results. 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 their separation squared. Thus the motions of planets was predicted by assuming distant forces working over great distance.
This mathematical expression of the force did not imply a cause. Newton considered action at a distance to be an inadequate model for gravity. Newton, in his words considered action at a distance to be
Metaphysical scientists of the early 1700's 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". Moreover, initial comparisons with astronomical data were not favorable. As mathematical techniques improved throughout the 1700's, the theory showed more and more success, predicting the date of the return of Halley's comet and aiding the the discovery of planet Neptune in 1846. These successes and the increasingly empirical focus of science towards the 19th century lead to acceptance of Newton's theory of gravity despite distaste for action at a distance.
Electrical action at a distance
Electrical and magnetic phenomena also began to be explored systematically in the early 1600's. 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".
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.
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. 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.
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 mathematical model.
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 particle lead 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.
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. 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 in 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.
Faraday's observations, as well as others, lead 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. Maxwell started with elaborate mechanical models but ultimately produced 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 luminiferous aether or the aether.
In 1873 Maxwell addressed action at a distance explicitly. 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 lead to numerous efforts in the later decades of the 19th century to represent electrical, magnetic, and gravitational fields, primarily with mechanical models. 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 gave 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. Lorentz investigated the mutual interaction of a moving solitary electrons within a stationary aether. 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,
where is the velocity of the moving electrons and 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 existent of aether, showing that the principle of relativity prohibits the absolute motion assumed by proponents of the aether model. He name the transformation used by Lorentz the Lorentz transformation but interpreted it as a transformation between two inertia frames with relative velocity . 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 simulenatity of time and the constant speed of light predicts precisely 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
resembled simple empty space.
In 1905, Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations 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. 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".
Modern action at a distance
In the early decades of the 20th century Karl Schwarzschild, Hugo Tetrode, and Adriaan Fokker. 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. The Wheeler-Feynman absorber theory of electromagnetism that avoids the self energy issue. 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. The theory has implications for cosmology; it has been extended to quantum mechanics. A similar approach has been applied to develop an alternative theory of gravity consistent with general relativity. 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
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.
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. 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.
See also
References
External links
Action at a distance
Concepts in physics