# Action at a distance (physics)

In physics, action at a distance, or actio in distans, is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often with early theories of gravity and electromagnetism to describe how an object could "know" the mass (in the case of gravity) or charge (in electromagnetism) of another distant object.

## Electricity

Coulomb's law in electrostatics appears to be a theory with action-at-a-distance - Coulomb's law deals with charges which have always been static. Efforts to develop a theory of interaction between moving charges, electrodynamics, led to the necessity to introduce the concept of a field with physical properties. In the theory of electrodynamics as formulated in Maxwell's equations, interactions between moving charges are mediated by propagating deformations of an electromagnetic field. These deformations propagate with the speed of light and therefore do not violate special relativity. The deformations of the field can carry momentum independently, thus facilitating conservation of angular momentum.

## Gravity

Main article: Speed of gravity

### Newton

Newton's theory of gravity offered no prospect of identifying any mediator of gravitational interaction. His theory assumed that gravitation acts instantaneously, regardless of distance. Newton had shown mathematically that if the gravitational interaction is not instantaneous, angular momentum is not conserved, and Kepler'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 geometry.)

A related question, raised by Ernst Mach, was how rotating bodies know how much to bulge at the equator. How do they know their rate of rotation? 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 principle for this question.

### Einstein

According to Albert Einstein's theory of special relativity, 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 suddenly displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the speed of light.

One of the conditions that a relativistic theory of gravitation must meet is to be mediated with a speed that does not exceed lightspeed. 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 relativity 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-Euclidean, resolving the apparent conflict between Newton's proof of the conservation of angular momentum and Einstein's theory of special relativity. 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

Current physical theories incorporate the upper limit on propagation of interaction as one of their basic building blocks, hence ruling out instantaneous action-at-a-distance. While a naïve interpretation of quantum mechanics appears to imply the ability to send signals faster than the speed of light, careful reasoning about these cases shows that no physical signals are actually being sent. Meanwhile the strange but real effect is called Quantum teleportation, see "External links" therein: Einstein coined the term "spooky action at a distance" to describe these situations, which exhibit quantum entanglement. Relativistic quantum field theory requires interactions to propagate at speeds less than or equal to the speed of light, so "quantum entanglement" cannot be used for faster-than-light-speed propagation of matter, energy, or information. However, it must be understood that a change to one entangled particle does indeed affect the other instantaneously, 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. Einstein could not believe this, and therefore he proposed, along with Boris Podolsky and Nathan Rosen, a thought experiment called the EPR paradox. John Bell derived an inequality that showed a testable difference between the predictions of quantum mechanics and local hidden variables theories. Experiments testing Bell-type inequalities in situations analogous to EPR's thought experiments have been consistent with the predictions of quantum mechanics, giving strong evidence for nonlocality.

Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
Interaction 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 percy puddles to a one-way causal effect.
The term SPACE (capitalized) can refer to:
• , a Canadian science-fiction channel
• The Society for Promotion of Alternative Computing and Employment
• DSPACE, a term in computational complexity theory

Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:

The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each

Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. This includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
Flavour in particle physics

Static has several meanings:
• Static electricity, a net charge of an object
• The triboelectric effect, e.g. from shoes rubbing carpet

Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell.
field is an assignment of a physical quantity to every point in space (or, more generally, spacetime). A field is thus viewed as extending throughout a large region of space so that its influence is all-pervading. The strength of a field usually varies over a region.
In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs.
In the context of classical theories of gravitation, the speed of gravity refers to the speed at which a gravitational field propagates. This is the speed at which changes in the distribution of energy and momentum result in noticeable changes in the gravitational field which they
Sir Isaac Newton

Isaac Newton at 46 in
Godfrey Kneller's 1689 portrait
Born 4 January 1643 [OS: 25 December 1642]
Johannes Kepler

A 1610 portrait of Johannes Kepler by an unknown artist
Born November 27 1571
Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements is the earliest known systematic discussion of geometry.
Ernst Mach (pronounced [max], see IPA) (February 18, 1838 – February 19, 1916) was a Bohemian-Austrian physicist and philosopher and is the namesake for the "Mach number" (also known as Mach speed) and the optical illusion known as Mach bands.
Disciplines:
• Physics
Core tenets:
the principle that the inertia of a body arises from its relation to the totality of all other bodies in the universe.
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special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies". Some three centuries earlier, Galileo's principle of relativity had stated that all uniform motion was relative, and that there was no absolute and
speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational
non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines.
special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies". Some three centuries earlier, Galileo's principle of relativity had stated that all uniform motion was relative, and that there was no absolute and
quantum mechanics is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons. Quantum mechanics is a fundamental branch of physics with wide applications in both experimental and theoretical physics.