Relativistic electromagnetism is a physical phenomenon explained in

electromagnetic field An electromagnetic field (also EM field) is a physical field, varying in space and time, that represents the electric and magnetic influences generated by and acting upon electric charges. The field at any point in space and time can be regarde ...

theory due to

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that calculates the amount of force (physics), force between two electric charge, electrically charged particles at rest. This electric for ...

and

Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant vel ...

Electromechanics

After Maxwell proposed the differential equation model of the electromagnetic field in 1873, the mechanism of action of fields came into question, for instance in the Kelvin's master class held at

Johns Hopkins University The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J ...

in 1884 and commemorated a century later. The requirement that the equations remain consistent when viewed from various moving observers led to

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...

, a geometric theory of 4-space where intermediation is by light and radiation. The

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

geometry provided a context for technical description of electric technology, especially generators, motors, and lighting at first. The

Coulomb force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the ''electrostatic ...

was generalized to the

Lorentz force In electromagnetism, the Lorentz force is the force exerted on a charged particle by electric and magnetic fields. It determines how charged particles move in electromagnetic environments and underlies many physical phenomena, from the operation ...

. For example, with this model

transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...

s and

power grid ''Power Grid'' is the English-language version of the second edition of the multiplayer German-style board game ''Funkenschlag'', designed by Friedemann Friese and first released in 2004. ''Power Grid'' was released by Rio Grande Games. I ...

s were developed and

radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the u ...

communication explored. An effort to mount a full-fledged electromechanics on a relativistic basis is seen in the work of Leigh Page, from the project outline in 1912 to his

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...

''Electrodynamics'' (1940) The interplay (according to the differential equations) of electric and magnetic field as viewed over moving observers is examined. What is

charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...

electrostatics Electrostatics is a branch of physics that studies slow-moving or stationary electric charges. Since classical antiquity, classical times, it has been known that some materials, such as amber, attract lightweight particles after triboelectric e ...

becomes ''proper charge density'' and generates a magnetic field for a moving observer. A revival of interest in this method for education and training of electrical and electronics engineers broke out in the 1960s after

Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...

's textbook. Rosser's book ''Classical Electromagnetism via Relativity'' was popular, as was

Anthony French Anthony Philip French (19 November 1920 – 3 February 2017) was a British physicist. At the time of his death he was professor emeritus of physics at the Massachusetts Institute of Technology. Biography French was born on 19 November 192 ...

's treatment in his textbook which illustrated diagrammatically the proper charge density. One author proclaimed, "Maxwell — Out of Newton, Coulomb, and Einstein". The use of retarded potentials to describe electromagnetic fields from source-charges is an expression of relativistic electromagnetism.

Principle

The question of how an electric field in one

inertial frame of reference In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative ...

looks in different reference frames moving with respect to the first is crucial to understanding fields created by moving sources. In the special case, the sources that create the field are at rest with respect to one of the reference frames. Given the

electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

in the frame where the sources are at rest, one can ask: what is the electric field in some other frame? Knowing the electric field at some point (in space and time) in the rest frame of the sources, and knowing the relative

velocity Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...

of the two frames provided all the information needed to calculate the electric field at the same point in the other frame. In other words, the electric field in the other frame does not depend on the particular distribution of the source charges, only on the local value of the electric field in the first frame at that point. Thus, the electric field is a ''complete'' representation of the influence of the far-away charges. Alternatively, introductory treatments of

magnetism Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, ...

introduce the

Biot–Savart law In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the ...

, which describes the magnetic field associated with an

electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

. An observer at rest with respect to a system of static, free charges will see no magnetic field. However, a moving observer looking at the same set of charges does perceive a current, and thus a magnetic field. That is, the magnetic field is simply the electric field, as seen in a moving coordinate system.

Redundancy

The title of this article is redundant since all mathematical theories of electromagnetism are relativistic. Indeed, as Einstein wrote, "The special theory of relativity ... was simply a systematic development of the electrodynamics of Clerk Maxwell and Lorentz". Combination of spatial and temporal variables in Maxwell's theory required admission of a four-manifold. Finite light speed and other constant motion lines were described with

analytic geometry In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and als ...

Orthogonality In mathematics, orthogonality is the generalization of the geometric notion of '' perpendicularity''. Although many authors use the two terms ''perpendicular'' and ''orthogonal'' interchangeably, the term ''perpendicular'' is more specifically ...

of electric and magnetic vector fields in space was extended by

hyperbolic orthogonality In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Two events will be simultaneous when they are on a line hyp ...

for the temporal factor. When

Ludwik Silberstein Ludwik Silberstein (May 17, 1872 – January 17, 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework. His textbook '' The Theory of Relativity'' was published by Macmill ...

published his textbook ''The Theory of Relativity'' (1914) he related the new geometry to electromagnetism. Faraday's law of induction was suggestive to Einstein when he wrote in 1905 about the "reciprocal electrodynamic action of a magnet and a conductor".A. Einstein (1905) s:On the Electrodynamics of Moving Bodies (1920 edition) Nevertheless, the aspiration, reflected in references for this article, is for an analytic geometry of spacetime and charges providing a deductive route to forces and currents in practice. Such a royal route to electromagnetic understanding may be lacking, but a path has been opened with

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

: The tangent space at an event in spacetime is a four-dimensional vector space, operable by linear transformations. Symmetries observed by electricians find expression in

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat ...

and differential geometry. Using

exterior algebra In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector ...

to construct a 2-form ''F'' from electric and magnetic fields, and the implied dual 2-form ★''F'', the equations and (current) express Maxwell's theory with a differential form approach.

Electromechanics

Principle

Redundancy

See also

Notes and references

Further reading