**Oleg Dmitrovich Jefimenko** (October 14, 1922, Kharkiv, Ukrainian SSR – May 14, 2009, Morgantown, West Virginia, United States) was a physicist and Professor Emeritus at West Virginia University.

Jefimenko received his B.A. degree at Lewis and Clark College in 1952 and his M. A. degree at the University of Oregon in 1954. He received his Ph.D. degree at the University of Oregon in 1956. Jefimenko worked for the development of the theory of electromagnetic retardation and relativity. In 1956, he was awarded the Sigma Xi Prize. In 1971 and 1973, he won awards in the AAPT Apparatus Competition. Jefimenko constructed and operated electrostatic generators run by atmospheric electricity.

Jefimenko worked on the generalization of Newton's gravitational theory to time-dependent systems. In his opinion, there is no objective reason for abandoning Newton's force-field gravitational theory (in favor of a metric gravitational theory). He was trying to develop and expand Newton's theory, making it compatible with the principle of causality and making it applicable to time-dependent gravitational interactions.

Jefimenko's expansion, or generalization, is based on the existence of the second gravitational force field, the "cogravitational, or Heaviside's field".^{ [1] } This might also be called a gravimagnetic field. It represents a physical approach profoundly different from the time-space geometry approach of the Einstein general theory of relativity. Oliver Heaviside first predicted this field in the article *A Gravitational and Electromagnetic Analogy* (1893).

Jefimenko suggests that electromagnetic equations can be converted to their gravitational-cogravitational equivalent by replacing electromagnetic symbols and constants with their corresponding gravitational-cogravitational symbols and constants,^{ [2] } given in the table below.

This section may be too technical for most readers to understand.(November 2020) |

Jefimenko posits the following generalized theory of gravitation.^{ [3] }

- Jefimenko, Oleg (2006a),
*Gravitation and Cogravitation: Developing Newton's Theory of Gravitation to its Physical and Mathematical Conclusion*, Star City: Electret Scientific Company, ISBN 0-917406-15-X *Electromagnetic Retardation and Theory of Relativity: New Chapters in the Classical Theory of Fields*, 2nd ed., Electret Scientific, Star City, 2004.*Causality, Electromagnetic Induction, and Gravitation: A Different Approach to the Theory of Electromagnetic and Gravitational Fields*, 2nd ed., Electret Scientific, Star City, 2000.*Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields*, 2nd ed., Electret Scientific, Star City, 1989.*Scientific Graphics with Lotus 1-2-3: Curve Plotting, 3D Graphics, and Pictorial Compositions*. Electret Scientific, Star City, 1987.*30 Music Programs for Timex Sinclair 2068*. Electret Scientific, Star City, 1985.*Electrostatic motors; their history, types, and principles of operation*. Star City [W. Va.], Electret Scientific Co. [1973]. LCCN 73180890*Electrostatic motors; their history, types, and principles of operation; NEW REVISED EDITION, edited by Thomas Valone*. Integrity Research Institute, Beltsville, MD [2011].

In physics the **Lorentz force** is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity **v** in an electric field **E** and a magnetic field **B** experiences a force of

**Maxwell's equations** are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. They describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon. The modern form of the equations in their most common formulation is credited to Oliver Heaviside.

An **electric field** is the physical field that surrounds electrically-charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges, or from time-varying magnetic fields. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

**Poisson's equation** is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate electrostatic or gravitational (force) field. It is a generalization of Laplace's equation, which is also frequently seen in physics. The equation is named after French mathematician and physicist Siméon Denis Poisson.

In physics, chemistry and biology, a **potential gradient** is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.

In classical mechanics, the **gravitational potential** at a location is equal to the work per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.

An **electromagnetic four-potential** is a relativistic vector function from which the electromagnetic field can be derived. It combines both an electric scalar potential and a magnetic vector potential into a single four-vector.

In physics, the **electric displacement field** or **electric induction** is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "**D**" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding of Gauss's law. In the International System of Units (SI), it is expressed in units of coulomb per meter square (C⋅m^{−2}).

A **classical field theory** is a physical theory that predicts how one or more physical fields interact with matter through **field equations**, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically meant to describe electromagnetism and gravitation, two of the fundamental forces of nature.

In special and general relativity, the **four-current** is the four-dimensional analogue of the electric current density. Also known as **vector current**, it is used in the geometric context of *four-dimensional spacetime*, rather than three-dimensional space and time separately. Mathematically it is a four-vector, and is Lorentz covariant.

In physics, precisely in the study of the theory of general relativity and many alternatives to it, the **post-Newtonian formalism** is a calculational tool that expresses Einstein's (nonlinear) equations of gravity in terms of the lowest-order deviations from Newton's law of universal gravitation. This allows approximations to Einstein's equations to be made in the case of weak fields. Higher-order terms can be added to increase accuracy, but for strong fields, it may be preferable to solve the complete equations numerically. Some of these post-Newtonian approximations are expansions in a small parameter, which is the ratio of the velocity of the matter forming the gravitational field to the speed of light, which in this case is better called the speed of gravity. In the limit, when the fundamental speed of gravity becomes infinite, the post-Newtonian expansion reduces to Newton's law of gravity.

In electromagnetism, **Jefimenko's equations** give the electric field and magnetic field due to a distribution of electric charges and electric current in space, that takes into account the propagation delay of the fields due to the finite speed of light and relativistic effects. Therefore they can be used for *moving* charges and currents. They are the particular solutions to Maxwell's equations for any arbitrary distribution of charges and currents.

**Lorentz–Heaviside units** constitute a system of units within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant *ε*_{0} and magnetic constant *µ*_{0} do not appear, having been incorporated implicitly into the electromagnetic quantities by the way they are defined. Heaviside-Lorentz units may be regarded as normalizing *ε*_{0} = 1 and *µ*_{0} = 1, while at the same time revising Maxwell's equations to use the speed of light *c* instead.

In electromagnetism and applications, an **inhomogeneous electromagnetic wave equation**, or **nonhomogeneous electromagnetic wave equation**, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and currents. The source terms in the wave equations make the partial differential equations *inhomogeneous*, if the source terms are zero the equations reduce to the homogeneous electromagnetic wave equations. The equations follow from Maxwell's equations.

There are various **mathematical descriptions of the electromagnetic field** that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this article, several approaches are discussed, although the equations are in terms of electric and magnetic fields, potentials, and charges with currents, generally speaking.

In electrodynamics, the **retarded potentials** are the electromagnetic potentials for the electromagnetic field generated by time-varying electric current or charge distributions in the past. The fields propagate at the speed of light *c*, so the delay of the fields connecting cause and effect at earlier and later times is an important factor: the signal takes a finite time to propagate from a point in the charge or current distribution to another point in space, see figure below.

In physics, **Gauss's law for gravity**, also known as **Gauss's flux theorem for gravity**, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. Gauss's law for gravity is often more convenient to work from than is Newton's law.

The theory of special relativity plays an important role in the modern theory of classical electromagnetism. It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another. It sheds light on the relationship between electricity and magnetism, showing that frame of reference determines if an observation follows electrostatic or magnetic laws. It motivates a compact and convenient notation for the laws of electromagnetism, namely the "manifestly covariant" tensor form.

**Gravitoelectromagnetism**, abbreviated **GEM**, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. **Gravitomagnetism** is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.

**Lagrangian field theory** is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom.

- ↑ de Climont, Jean (2018).
*The Worldwide List of Alternative Theories and Critics*. p. 1047. ISBN 9782902425174. - ↑ Jefimenko (2006a), pp. 129.
- ↑ Jefimenko (2006), pp. 13.

- Oleg D. Jefimenko. Dept of physics.

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