Maxwell equations

The centimetre-gram-second system (CGS) is a system of physical units. It is always the same for mechanical units, but there are several variants of electric additions. The system goes back to a proposal made in 1832 by the German mathematician Carl Friedrich Gauss and was in 1874 extended by the British physicists James Clerk Maxwell and William Thomson with a set of electromagnetic units. The sizes (order of magnitude) of many CGS units turned out to be inconvenient for practical purposes, therefore the CGS system neve ...

Including:

• Centimetre gram second system of units - Electromagnetic units

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In physics, wave-particle duality holds that light and matter can exhibit properties of both waves and of particles. It is a central concept of quantum mechanics. The idea is rooted in a debate over the nature of light and matter dating back to the 1600s, when competing theories of light were proposed by Christiaan Huygens and Isaac Newton. Through the work of Albert Einstein, Louis de Broglie and many others, it is now established that small objects, such as atoms, have both wave and particle nature, and that quantum mechanics provi ...

Including:

• Wave-particle duality - History
• Wave-particle duality - Huygens and Newton; Earliest theories of light
• Wave-particle duality - Fresnel Maxwell and Young
• Wave-particle duality - Einstein and photons
• Wave-particle duality - De Broglie
• Wave-particle duality - Wave nature of large objects
• Wave-particle duality - Theoretical review
• Wave-particle duality - Applications

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In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. It is of central importance to the theory of quantum mechanics, playing a role analogous to Newton's second law in classical mechanics. In the mathematical formulation of quantum mechanics, each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space. This state vector encodes the p ...

Including:

• Schrödinger equation - Time-independent Schrödinger equation
• Schrödinger equation - Schrödinger wave equation
• Schrödinger equation - The wavefunction
• Schrödinger equation - Operators in the position basis
• Schrödinger equation - Non-relativistic Schrödinger wave equation
• Schrödinger equation - Probability currents
• Schrödinger equation - Solutions of the Schrödinger equation

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There are several ways to derive Snell's Law, and therefore the Angle of Refraction. The first way it was discovered was by an application of Fermat's principle which states that a light wave must take a path that is an extremum in time subject to the constraints present. Normally this is translated into "Light will always take the quickest path it can." From this principle, and using a bit of differential calculus, Snell’s Law can be derived thus leading to the Angle of Refraction. If one looks into the meaning of Fermat’s principle, ot ...

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Angle of refraction, Angle of refraction - Derivation and Meaning of the Angle of Refraction, Angle of refraction - Results the Angle of Refraction

Read more here: » Angle of refraction: Encyclopedia II - Angle of refraction - Derivation and Meaning of the Angle of Refraction

The Kaluza-Klein theory is striking because it has a particularly elegant presentation in terms of geometry. In a certain sense, it looks just like ordinary gravity in free space, except that it is phrased in five dimensions instead of four. Kaluza-Klein theory - The Einstein equations. The equations governing ordinary gravity in free space can be obtained from an action, by applying the variational principle to a certain action. Let M be a (pseudo-)Riemannian manifold, which may be taken as the spa ...

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Kaluza-Klein theory, Kaluza-Klein theory - Overview, Kaluza-Klein theory - Space-Time-Matter theory, Kaluza-Klein theory - Geometric interpretation, Kaluza-Klein theory - The Einstein equations, Kaluza-Klein theory - The Maxwell equations, Kaluza-Klein theory - The Kaluza-Klein geometry, Kaluza-Klein theory - Commentary and generalizations

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Linear - Linear functions. In mathematics, a linear function f(x) is one which satisfies the following two properties (but see below for a slightly different usage of the term): Additivity property (also called the superposition property): f(x + y) = f(x) + f(y). This says that f is a group homomorphism with respect to addition. Homogeneity property: f(αx) = Î ...

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Linear, Linear - Mathematics, Linear - Linear functions, Linear - Linear polynomials, Linear - Physics, Linear - Electronics, Linear - Military tactical formations, Linear - Music

Read more here: » Linear: Encyclopedia II - Linear - Mathematics

Although it is known that the nucleon is made from three quarks, as of 2005, it is not known how to solve the equations of motion for QCD. Thus, the study of the low-energy properties of the nucleon are performed by means of models. The only first-principles approach available is to attempt to solve the equations of QCD numerically, using lattice QCD. This requires complicated algorithms and very powerful supercomput ...

See also:

Nucleon, Nucleon - The proton, Nucleon - The neutron, Nucleon - Antinucleons, Nucleon - Quark model classification, Nucleon - Models of the nucleon

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His greatest work was with electricity. In 1821, soon after the Danish chemist, Hans Christian Ørsted discovered the phenomenon of electromagnetism, Davy and William Hyde Wollaston tried but failed to design an electric motor. Faraday, having discussed the problem with the two men, went on to build two devices to produce what he called electromagnetic rotation: a continuous circular motion from the circular magnetic force around a wire. A wire extending into a pool of mercury with a magnet placed inside would rotate around the magnet if cha ...

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Michael Faraday, Michael Faraday - Early career, Michael Faraday - Scientific career, Michael Faraday - Miscellaneous, Michael Faraday - Quotations

Read more here: » Michael Faraday: Encyclopedia II - Michael Faraday - Scientific career

While for most units the difference between cgs and SI is a mere power of 10, the differences in electromagnetic units are considerable; so much so that formulas for physical laws need to be changed depending on what system of units one uses. In SI, electric current is defined via the magnetic force it exerts and charge is then defined as current multiplied with time. In one variant of the cgs system, electrostatic units (esu), charge is defined via the force it exerts on other charges, and current is then defined as charge per time. One consequence of this ...

See also:

Centimetre gram second system of units, Centimetre gram second system of units - Electromagnetic units

Read more here: » Centimetre gram second system of units: Encyclopedia II - Centimetre gram second system of units - Electromagnetic units

The identity of the original inventor of radio, at the time called wireless telegraphy, is contentious. The key invention for the beginning of "wireless transmission of data using the entire frequency spectrum" [spark-gap radio] has been attributed to both Nikola Tesla, Guglielmo Marconi, and Alexander Popov. History of radio - Radio's prehistory 19th century. In 1820, Hans Christian Ørsted discovered the relationship between electricity and magnetism in a very simple experiment. He demonstrated that a wi ...

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History of radio, History of radio - Origins and developments, History of radio - Radio's prehistory 19th century, History of radio - Wireless beginnings, History of radio - Radio communication, History of radio - Radio factory, History of radio - Spark-gap wireless telegraphy 1896–1920, History of radio - Audio broadcasting 1915–Present, History of radio - Radio broadcasting beginnings, History of radio - FM radio, History of radio - 20th century developments, History of radio - Telex on Radio, History of radio - 21st century development, History of radio - Exotic technologies, History of radio - Television

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In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor (or by defining a frame field). The curvature tensor of this manifold and associated quantities such as the Einstein tensor Gab, are well-defined even in the absence of any physical theory, but in general relativity they acquire a physical inte ...

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Electrovacuum solution, Electrovacuum solution - Mathematical definition, Electrovacuum solution - Invariants, Electrovacuum solution - Einstein tensor, Electrovacuum solution - Eigenvalues, Electrovacuum solution - Rainich conditions, Electrovacuum solution - Test fields, Electrovacuum solution - Examples

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The Einstein field equation, when fully written out as a sytem of partial differential equations, takes the form of a rather complicated system of coupled, nonlinear partial differential equations. As such, in general, it is very hard to solve. Nonetheless, several effective techniques for obtaining exact solutions are available. The simplest involves imposing symmetry conditions on the metric tensor, such as stationarity (symmetry under time translation) or axisymmetry (symmetry under rotation about some symmetry axis). With s ...

See also:

Exact solutions in general relativity, Exact solutions in general relativity - Introduction, Exact solutions in general relativity - Difficulties with the definition, Exact solutions in general relativity - Types of exact solution, Exact solutions in general relativity - Constructing solutions, Exact solutions in general relativity - Existence of solutions, Exact solutions in general relativity - Global stability theorems, Exact solutions in general relativity - The positive energy theorem, Exact solutions in general relativity - Examples

Read more here: » Exact solutions in general relativity: Encyclopedia II - Exact solutions in general relativity - Constructing solutions

The state space of certain quantum systems can be spanned with a position basis. In this situation, the Schrödinger equation may be conveniently reformulated as a partial differential equation for a wavefunction, a complex scalar field that depends on position as well as time. This form of the Schrödinger equation is referred to as the Schrödinger wave equation. Elements of the position basis are called position eigenstates. We will consider only a single-particle system, for which each position eigenstate may be deno ...

See also:

Schrödinger equation, Schrödinger equation - Time-independent Schrödinger equation, Schrödinger equation - Schrödinger wave equation, Schrödinger equation - The wavefunction, Schrödinger equation - Operators in the position basis, Schrödinger equation - Non-relativistic Schrödinger wave equation, Schrödinger equation - Probability currents, Schrödinger equation - Solutions of the Schrödinger equation

Read more here: » Schrödinger equation: Encyclopedia II - Schrödinger equation - Schrödinger wave equation

When accelerated motion is involved, there are phenomena that will allow an observer to establish a zero point, there are phenomena that determine a preferred reference frame. For example the case of rotation: the astronomer Schwarzschild had noted that in the solar system the lines connecting the aphelia and perihelia of the planets do not rotate with respect to each other and with respect to the background of the fixed stars (apart from an unexplained precession of the perihelion of Mercury). Also it could be seen from astronomical observa ...

See also:

Principle of relativity, Principle of relativity - Galilean relativity, Principle of relativity - Special relativity, Principle of relativity - General relativity, Principle of relativity - references and links

Read more here: » Principle of relativity: Encyclopedia II - Principle of relativity - General relativity

The Einstein field equation, when fully written out as a sytem of partial differential equations, takes the form of a rather complicated system of coupled, nonlinear partial differential equations. As such, in general, it is very hard to solve. Nonetheless, several effective techniques for obtaining exact solutions are available. The simplest involves imposing symmetry conditions on the metric tensor, such as stationarity (symmetry under time translation) or axisymmetry (symmetry under rotation about some symmetry axis). With s ...

See also:

Exact solutions in general relativity, Exact solutions in general relativity - Difficulties with the definition, Exact solutions in general relativity - Types of exact solution, Exact solutions in general relativity - Constructing solutions, Exact solutions in general relativity - Existence of solutions, Exact solutions in general relativity - Global stability theorems, Exact solutions in general relativity - The positive energy theorem, Exact solutions in general relativity - Examples

Read more here: » Exact solutions in general relativity: Encyclopedia II - Exact solutions in general relativity - Constructing solutions

Historically, the first principle of relativity that was formulated was a principle of relativity of uniform motion suggested by the observation that there doesn't seem to be a phenomenon in dynamics that will allow an observer to establish a zero point of velocity, nor a preferred direction. Every choice of a zero point of velocity, a choice necessary in order to perform a calculation, constitutes a choice of reference frame. All reference frames that move with respect to each other with constant velocity and in a straight lin ...

See also:

Principle of relativity, Principle of relativity - Galilean relativity, Principle of relativity - Special relativity, Principle of relativity - General relativity

Read more here: » Principle of relativity: Encyclopedia II - Principle of relativity - Galilean relativity

At the close of the 19th century, the case for atomic theory, that matter was made of particulate objects or atoms, was well established. Electricity, first thought to be a fluid, was understood to consist of particles called electrons, as demonstrated by J.J. Thompson in his experiments with cathode rays. In brief, it was understood that much of nature was made of particles. At the same time, waves were well understood, together with wave phenomena such as diffraction and interference. Light was believed to be a wave, as Thomas Young's double-slit experiment and effects such as Fraunhofer diffraction had cl ...

See also:

Wave-particle duality, Wave-particle duality - History, Wave-particle duality - Huygens and Newton; Earliest theories of light, Wave-particle duality - Fresnel Maxwell and Young, Wave-particle duality - Einstein and photons, Wave-particle duality - De Broglie, Wave-particle duality - Wave nature of large objects, Wave-particle duality - Theoretical review, Wave-particle duality - Applications

Read more here: » Wave-particle duality: Encyclopedia II - Wave-particle duality - History

One particular variant of Kaluza-Klein theory is Space-Time-Matter theory or induced matter theory, chiefly promulgated by Paul Wesson. In this version of the theory, it is noted that solutions to the equation RAB = 0 with RAB the five-dimensional Ricci curvature, may be re-expressed so that in four dimensions, these solutions satisfy Einstein's equations See also:

Kaluza-Klein theory, Kaluza-Klein theory - Overview, Kaluza-Klein theory - Space-Time-Matter theory, Kaluza-Klein theory - Geometric interpretation, Kaluza-Klein theory - The Einstein equations, Kaluza-Klein theory - The Maxwell equations, Kaluza-Klein theory - The Kaluza-Klein geometry, Kaluza-Klein theory - Commentary and generalizations

Read more here: » Kaluza-Klein theory: Encyclopedia II - Kaluza-Klein theory - Space-Time-Matter theory

Similar experiments have since been conducted with neutrons and protons. Among the most famous experiments are those of Estermann and Otto Stern in 1929. Authors of similar recent experiments with atoms and molecules claim that these larger particles also act like waves. A dramatic series of experiments emphasizing the action of gravity in relation to wave-particle duality were conducted in the 1970's using the neutron interferometer. Neutrons, the stuff of atomic nuclei, provide much of the weight of a nucleus and thus of ordinary ma ...

See also:

Wave-particle duality, Wave-particle duality - History, Wave-particle duality - Huygens and Newton; Earliest theories of light, Wave-particle duality - Fresnel Maxwell and Young, Wave-particle duality - Einstein and photons, Wave-particle duality - De Broglie, Wave-particle duality - Wave nature of large objects, Wave-particle duality - Theoretical review, Wave-particle duality - Applications

Read more here: » Wave-particle duality: Encyclopedia II - Wave-particle duality - Wave nature of large objects

The modern, theoretical resolution of the wave-particle paradox is described by the theoretical framework of quantum mechanics. The framework is deep and broad, and it is impossible to give it justice in only a few paragraphs. However, the explanation of wave-particle duality by quantum mechanics can be briefly described as follows. Every particle in nature, be it a photon, electron or atom, is described by a solution to a differential equation, most typically, the Schroedinger equation. The solutions to this equation are known as wav ...

See also:

Wave-particle duality, Wave-particle duality - History, Wave-particle duality - Huygens and Newton; Earliest theories of light, Wave-particle duality - Fresnel Maxwell and Young, Wave-particle duality - Einstein and photons, Wave-particle duality - De Broglie, Wave-particle duality - Wave nature of large objects, Wave-particle duality - Theoretical review, Wave-particle duality - Applications

Read more here: » Wave-particle duality: Encyclopedia II - Wave-particle duality - Theoretical review