Lightning is the electric breakdown of air by strong electric fields (from electric potential energy to mechanical energy of the random motion of air molecules (heat), and to light).

For other uses of "energy" see Energy.

In physics and other sciences, energy (from the Greek ενεργός, energos, "active, working")^[1] is a concept, a quantifiable attribute of physical systems. It is not an object or a substance, but it is quantifiable in a way such that it cannot be created or destroyed. The units used to quantitate energy are the same as those used to define work in physics. Many forms of energy are defined in the natural sciences, e.g. kinetic energy, potential energy, electrical energy; chemical energy etc.; any one of them can be transformed into another form, often through a process that involves mechanical work. However, the transformation from one form to another is not always total, it is limited by the second law of thermodynamics. A fraction of the energy remains in the form of thermal energy in many such transformations. Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... This article or section needs additional references or sources to facilitate its verification. ... In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and characterization of universal laws which govern matter, energy, space, and time. ... Part of a scientific laboratory at the University of Cologne. ... A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in language or symbology, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships between them. ... Quantifiability is the degree to which a thing can be quantified, such as via measaurement or precise description in mathematics and science. ... An attribute is the following: Generally, an attribute is an abstraction characteristic of an entity In database management, an attribute is a property inherent in an entity or associated with that entity for database purposes. ... A physical system is a system that is comprised of matter and energy. ... A physical body is an object which can be described by the theories of classical mechanics, or quantum mechanics, and experimented upon by physical instruments. ... Look up substance in Wiktionary, the free dictionary. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... Electrical energy can refer to several closely related things. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... In physics and engineering,energy transformation often termed as energy conversion, is any process of transforming one form of energy to another. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ... 1. ...

Definitions

Energy, in physics, can be defined as the amount of work a physical system can do on another.^[2] In this way, energies such as gravitational energy, electric energy, and elastic energy can be defined from the work done by different types of forces. Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... A physical system is a system that is comprised of matter and energy. ... Energy of two or more masses (or other forms of energy-momentum) gravitationally interacting with each other. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... The elastic energy is the energy which causes or is released by the Elastic distortion of a solid or a fluid. ... In physics, force is an influence that may cause a body to accelerate. ...

Some textbooks^[3] prefer to introduce energy without relying on prior definitions of force, work, or momentum.

Historical perspective

Main articles: Timeline of thermodynamics, statistical mechanics, and random processes and History of Physics

Thomas Young - the first to use the term "energy" in the modern sense.

The concept of energy emerged out of the idea of vis viva, which Leibniz defined as the product of the mass of an object and its velocity squared; he believed that total vis viva was conserved. To account for slowing due to friction, Leibniz claimed that heat consisted of the random motion of the constituent parts of matter — a view shared by Isaac Newton, although it would be more than a century until this was generally accepted. In 1807, Thomas Young was the first to use the term "energy", instead of vis viva, in its modern sense.^[4] Gustave-Gaspard Coriolis described "kinetic energy" in 1829 in its modern sense, and in 1853, William Rankine coined the term "potential energy." A timeline of events related to thermodynamics, statistical mechanics, and random processes. ... The known history of physics is thought to have begun around 2400 BC, when members of the Harappan civilization used shell objects to serve as compasses for measuring the angles of the sky. ... Image File history File links Download high resolution version (921x1152, 226 KB) This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years or less. ... Image File history File links Download high resolution version (921x1152, 226 KB) This image is in the public domain because its copyright has expired in the United States and those countries with a copyright term of life of the author plus 100 years or less. ... There have been several well-known people named Thomas Young, including: Thomas Young, 16th century archbishop of York Thomas Young, M.A., Master of Jesus College, Cambridge 1644-50 Thomas Young (1773-1829), scientist Thomas Young VC, the recipient of the Victoria Cross Thomas Young, the Baptist Evangelist from Piedmont... Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ... Sir Isaac Newton, (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist, regarded by many as the greatest figure in the history of science. ... Thomas Young, English scientist // Young belonged to a Quaker family of Milverton, Somerset, where he was born in 1773, the youngest of ten children. ... Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... Gaspard-Gustave de Coriolis or Gustave Coriolis (May 21, 1792–September 19, 1843), mathematician, mechanical engineer and scientist born in Paris, France. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... William John Macquorn Rankine (July 2, 1820 - December 24, 1872) was a Scottish engineer and physicist. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ...

The development of steam engines required engineers to develop concepts and formulas that would allow them to describe the mechanical and thermal efficiencies of their systems. Engineers such as Sadi Carnot, physicists such as James Prescott Joule, mathematicians such as Émile Clapeyron and Hermann von Helmholtz , and amateurs such as Julius Robert von Mayer all contributed to the notion that the ability to perform certain tasks, called work, was somehow related to the amount of energy in the system. The nature of energy was elusive, however, and it was argued for some years whether energy was a substance (the caloric) or merely a physical quantity, such as momentum. A steam engine is a heat engine that makes use of the thermal energy that exists in steam, converting it to mechanical work. ... In physics, mechanical efficiency is the effectiveness of a machine and is defined as Efficiency is often indicated by a percentage, the efficiency of an ideal machine is 100%. Due to the fact that energy cannot emerge from nothing and the Second law of thermodynamics which states that the quality... The thermal efficiency () is a dimensionless performance measure of a thermal device such as an internal combustion engine, a boiler, or a furnace, for example. ... Sadi Carnot Nicolas Léonard Sadi Carnot (June 1, 1796 - August 24, 1832) was a French mathematician and engineer who gave the first successful theoretical account of heat engines, the Carnot cycle, and laid the foundations of the second law of thermodynamics. ... James Joule - English physicist James Prescott Joule, FRS (December 24, 1818 – October 11, 1889) was an English physicist, born in Sale, Cheshire. ... Emile_Clapeyron Benoit Paul Émile Clapeyron (February 26, 1799 - January 28, 1864) was an French engineer and physicist, considered as one of the founders of thermodynamics. ... Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist. ... Julius Robert von Mayer. ... The caloric theory is an obsolete scientific theory that heat consists of a fluid called caloric that flows from hotter to colder bodies. ... In classical mechanics, momentum (pl. ...

William Thomson (Lord Kelvin) amalgamated all of these laws into the laws of thermodynamics, which aided in the rapid development of explanations of chemical processes using the concept of energy by Rudolf Clausius, Josiah Willard Gibbs and Walther Nernst. It also led to a mathematical formulation of the concept of entropy by Clausius, and to the introduction of laws of radiant energy by Jožef Stefan. William Thomson, Archbishop of York, has the same name as this man. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 – August 24, 1888), was a German physicist and mathematician. ... Josiah Willard Gibbs (February 11, 1839 New Haven – April 28, 1903 New Haven) was one of the very first American theoretical physicists and chemists. ... Walther Nernst. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Radiant energy is the energy of electromagnetic waves. ... Joseph Stefan (Slovene Jožef Stefan) (March 24, 1835 – January 7, 1893) was a Slovene physicist, mathematician and poet. ...

During a 1961 lecture^[3] for undergraduate students at the California Institute of Technology, Richard Feynman, a celebrated physics teacher and Nobel Laureate, said this about the concept of energy: The California Institute of Technology (commonly referred to as Caltech)[1] is a private, coeducational university located in Pasadena, California, in the United States. ... Richard Phillips Feynman (May 11, 1918 – February 15, 1988; surname pronounced ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... The Nobel Prizes (pronounced no-BELL or no-bell) are awarded annually to people who have done outstanding research, invented groundbreaking techniques or equipment, or made outstanding contributions to society. ...

Since 1918 it has been known that the law of conservation of energy is the direct mathematical consequence of the translational symmetry of the quantity conjugate to energy, namely time. That is, energy is conserved because the laws of physics do not distinguish between different moments of time (see Noether's theorem). Conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms (for instance, friction turns kinetic energy into thermal energy). ... Translation is an activity comprising the interpretation of the meaning of a text in one language — the source text — and the production, in another language, of a new, equivalent text — the target text, or translation. ... Sphere symmetry group o. ... Conjugate can be: in mathematics in terms of complex numbers, the complex conjugate; more generally see conjugate element (field theory). ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...

Energy in various contexts

The concept of energy and its transformations is extremely useful in explaining and predicting most natural phenomena. The direction of transformations in energy (what kind of energy is transformed to what other kind) is often directed by entropy (energy spread) considerations, since in practice all energy transformations are permitted on a small scale, but certain larger transformations are not permitted because it is statistically unlikely that energy or matter will randomly move into more concentrated forms or smaller spaces. Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...

The concept of energy is often used in almost all fields of science. For example, in Chemistry, Biology, Geology and Meterology The exact context of various natural phenomena associated with these transformations varies from one natural science to another. A phenomenon (plural: phenomena) is an observable event, especially something special (literally something that can be seen from the Greek word phainomenon = observable). ...

Regarding applications of energy concept

Energy is subject to a strict global conservation law; that is, whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant ^[5] In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...

• The total energy of a system can be subdivided and classified in various ways. For example, it is sometimes convenient to distinguish potential energy (which is a function of coordinates only) from kinetic energy (which is a function of coordinate time derivatives only). It may also be convenient to distinguish gravitational energy, electrical energy, thermal energy, and other forms. These classifications overlap; for instance thermal energy usually consists partly of kinetic and partly of potential energy.
• The transfer of energy can take various forms; familiar examples include work, heat flow, and advection, as discussed below.
• The word "energy" is also used outside of physics in many ways, which can lead to ambiguity and inconsistency. The vernacular terminology is not consistent with technical terminology. For example, the important public-service announcement, "Please conserve energy" uses vernacular notions of "conservation" and "energy" which make sense in their own context but are utterly incompatible with the technical notions of "conservation" and "energy" (such as are used in the law of conservation of energy).^[6].

In classical physics energy is considered a scalar quantity, canonical conjugate to time. In special relativity energy is also a scalar (although not a Lorentz scalar but a time component of the energy-momentum 4-vector).^[7] In other words, energy is invariant with respect to rotations of space, but not invariant with respect to rotations of space-time (= boosts). System (from Latin systēma, in turn from Greek systēma) is a set of entities, real or abstract, comprising a whole where each component interacts with or is related to at least one other component and they all serve a common objective. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... For a non-technical overview of the subject, see Calculus. ... In physics and other sciences, energy (from the Greek ενεργός, energos, at work) is a concept, a quantifiable attribute of physical systems. ... Classical physics is physics based on principles developed before the rise of quantum theory, usually including the special theory of relativity and general theory of relativity. ... A scalar may be: Look up scalar in Wiktionary, the free dictionary. ... A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... In physics a Lorentz scalar is a scalar which is invariant under a Lorentz transformation. ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ... In relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space, whose components transform like the space and time coordinates (t, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). ... Space has been an interest for philosophers and scientists for much of human history. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ... The Lorentz transformation (LT), named after its discoverer, the Dutch physicist and mathematician Hendrik Antoon Lorentz (1853-1928), forms the basis for the special theory of relativity, which has been introduced to remove contradictions between the theories of electromagnetism and classical mechanics. ...

Energy transfer

Because energy is strictly conserved and is also locally conserved (wherever it can be defined), it is important to remember that by definition of energy the transfer of energy between the "system" and adjacent regions is work. A familiar example is mechanical work. In simple cases this is written as: Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ...

ΔE = W             (1)

if there are no other energy-transfer processes involved. Here ΔE  is the amount of energy transferred, and W  represents the work done on the system.

More generally, the energy transfer can be split into two categories:

ΔE = W + Q             (2)

where Q  represents the heat flow into the system.

There are other ways in which an open system can gain or lose energy. If mass if counted as energy (as in many relativistic problems) then E must contain a term for mass lost or gained. In chemical systems, energy can be added to a system by means of adding substances with different chemical potentials, which potentials are then extracted (both of these process are illustrated by fueling an auto, a system which gains in energy thereby, without addition of either work or heat). These terms may be added to the above equation, or they can generally be subsumed into a quantity called "energy addition term E" which refers to any type of energy carried over the surface of a control volume or system volume. Examples may be seen above, and many others can be imagined (for example, the kinetic energy of a stream of particles entering a system, or energy from a laser beam adds to system energy, without either being either work-done or heat-added, in the classic senses).

ΔE = W + Q + E             (3)

Where E in this general equation represents other additional advected energy terms not covered by work done on a system, or heat added to it.

Energy is also transfered from potential energy (E_p) to kinetic energy (E_k) and then back to potential energy constantly. This is referred to as conservation of energy. In this closed system, energy can not be created or destroyed, so the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

E_pi + E_ki = E_pf + E _kf

The equation can then be simplified further since E_p = mgh (mass times acceleration due to gravity times the height) and E_k = 1/2 mv² (half times mass times velocity squared). Then the total amount of energy can be found by adding E_p + E_k = E_total.

Energy and the laws of motion

The Hamiltonian

The total energy of a system is sometimes called the Hamiltonian, after William Rowan Hamilton. The classical equations of motion can be written in terms of the Hamiltonian, even for highly complex or abstract systems. These classical equations have remarkably direct analogs in nonrelativistic quantum mechanics.^[8] In physics and mathematics, Hamiltons equations is the set of differential equations that arise in Hamiltonian mechanics, but also in many other related and sometimes apparently not related areas of science. ... Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematician, physicist, and astronomer who made important contributions to the development of optics, dynamics, and algebra. ...

The Lagrangian

Another energy-related concept is called the Lagrangian, after Joseph Louis Lagrange. This is in some ways even more fundamental than the Hamiltonian, and can be used to derive the equations of motion.^[specify] In simple cases the Lagrangian can be written as kinetic energy minus potential energy. A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... Joseph-Louis Lagrange, comte de lEmpire (January 25, 1736 – April 10, 1813; b. ...

Usually Lagrange formalism is mathematically more convenient than Hamilton one for non-conservative systems (like systems with friction).

Energy and thermodynamics

According to the second law of thermodynamics, work can be totally converted into heat, but not vice versa. The first law of thermodynamics simply asserts that energy is conserved,^[9] and that heat is included as a form of energy transfer. A commonly-used corollary of the first law is that for a "system" subject only to pressure forces and heat transfer (e.g. a cylinder-full of gas), the change in energy of the system is given by: The second law of thermodynamics is an expression of the universal law of increasing entropy. ... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin in Canberra, Australia. ...

,

where the first term on the right is the heat transfer, defined in terms of temperature T and entropy S, and the last term on the right hand side is identified as "work" done on the system, where pressure is P and volume V (the negative sign is because we must compress the system to do work on it, so that the volume change dV is negative). Although the standard text-book example, this is very specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection, and because it depends on temperature. The most general statement of the first law — i.e. conservation of energy — is valid even in situations in which temperature is undefinable. Fig. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ...

Energy is sometimes expressed as:

,

which is unsatisfactory^[6] because there cannot exist any thermodynamic state functions W or Q that are meaningful on the right hand side of this equation, except perhaps in trivial cases.

Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential. At two points in the oscillation cycle it is entirely kinetic, and alternatively at two other points it is entirely potential. Over the whole cycle, or over many cycles net energy is thus equally split between kinetic and potential. This is called equipartition principle - total energy of a system with many degrees of freedom is equally split between all these degrees of freedom. In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ... Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. ... It has been suggested that this article or section be merged with Scalar potential. ... A cycle (Latin cyclus, from Greek kuklos meaning circle) is anything round, in the physical sense (e. ... In classical statistical mechanics, the equipartition theorem is a general formula that allows average energies of many physical systems to be calculated as a function of temperature. ... The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ...

This principle is vitally important to understanding the behavior of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. This concept is also related to the second law of thermodynamics which basically states that when an isolated system is given more degrees of freedom (places where energy may be stored), energy spreads evenly over all allowed degrees (without distinction between "new" and "old" degrees). Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Look up distribution in Wiktionary, the free dictionary. ... The second law of thermodynamics is an expression of the universal law of increasing entropy. ...

Oscillators, phonons, and photons

In an ensemble of unsynchronized oscillators, the average energy is spread equally between kinetic and potential.

In a solid, thermal energy (often referred to as heat) can be accurately described by an ensemble of thermal phonons that act as mechanical oscillators. In this model, thermal energy is equally kinetic and potential. 1. ...

In ideal gas, potential of interaction between particles is essentially delta function - thus all of the energy is kinetic.

Because an electrical oscillator (LC circuit) is analogous to a mechanical oscillator, its energy must be, on average, equally kinetic and potential. It is entirely arbitrary whether the magnetic energy is considered kinetic and the electrical energy considered potential, or vice versa. That is, either the inductor is analogous to the mass while the capacitor is analogous to the spring, or vice versa.

1. By extension of the previous line of thought, in free space the electromagnetic field can be considered an ensemble of oscillators, meaning that radiation energy can be considered equally potential and kinetic. This model is useful, for example, when the electromagnetic Lagrangian is of primary interest and is interpreted in terms of potential and kinetic energy.
2. On the other hand, in the key equation m²c⁴ = E² − p²c², the contribution mc² is called the rest energy, and all other contributions to the energy are called kinetic energy. For a particle that has mass, this implies that the kinetic energy is 0.5p² / m at speeds much smaller than c, as can be proved by writing E = mc² √(1 + p²m ^{− 2}c ^{− 2}) and expanding the square root to lowest order. By this line of reasoning, the energy of a photon is entirely kinetic, because the photon is massless and has no rest energy. This expression is useful, for example, when the energy-versus-momentum relationship is of primary interest.

The two analyses are entirely consistent. The electric and magnetic degrees of freedom in item 1 are transverse to the direction of motion, while the speed in item 2 is along the direction of motion. For non-relativistic particles these two notions of potential versus kinetic energy are numerically equal, so the ambiguity is harmless, but not so for relativistic particles. Radiant energy is the energy of electromagnetic waves. ...

Work and virtual work

Main articles: Mechanics, Mechanical work, Thermodynamics, and Quantum mechanics

Work is roughly force times distance. But more precisely, it is Mechanics (Greek ) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Fig. ...

This says that the work (W) is equal to the integral (along a certain path) of the force; for details see the mechanical work article. In physics, force is an influence that may cause a body to accelerate. ... Mechanical work is a force applied through a distance, defined mathematically as the line integral of a scalar product of force and displacement vectors. ...

Work is frame dependent. For example, consider a ball being hit by a bat. In the center-of-mass reference frame, the bat does no work on the ball. But, in the reference frame of the person swinging the bat, considerable work is done on the ball. Refers to reference frame dependance. ...

Quantum mechanics

In quantum mechanics energy is defined in terms of the energy operator as a time derivative of the wave function. A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...

As the Schrödinger equation (which equates energy operator to full energy of a particle or a system) describes the space- and time-dependence of quantum mechanical systems and bound systems the solution of this equation is discrete (a set of permitted states, each characterized by an energy level). In quantum wave mechanics energy is related to the frequency of the wave by the Planck equation E = hν (where h is the Planck's constant and ν the frequency). In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... A quantum mechanical system can only be in certain states, so that only certain energy levels are possible. ... The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ... This article is about Planck, the German physicist. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...

Relativity

According to special relativity, rest mass is a part of total energy^[7] as can be seen from the relativistic equation relating mass, energy and momentum of a body: The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

m²c⁴ = E² − p²c²,

where

m is the mass,

c is the speed of light,

E is the energy, and

p is the 3-dimensional momentum.

This equation is a mathematical by-product of calculation of relativistic work to accelerate a body (=calculation of relativistic kinetic energy). A line showing the speed of light on a scale model of Earth and the Moon The 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. It is the speed of all electromagnetic radiation... The kinetic energy of an object is the extra energy which it possesses due to its motion. ...

For example, consider electron-positron annihilation, in which the rest mass of individual particles is destroyed, but the inertia equivalent of the system of the two particles (its invariant mass) remains (since all energy is associated with mass), and this inertia and invariant mass is carried off by photons which individually are massless, but as a system retain their mass. This is a reversible process - the inverse process is called pair creation - in which the rest mass of particles is created from energy of two (or more) annihilating photons. e- redirects here. ... The first detection of the positron in 1932 by Carl D. Anderson The positron is the antiparticle or the antimatter counterpart of the electron. ... The invariant mass or intrinsic mass or proper mass or rest mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference. ... Pair production is a nuclear physics process which occurs where a high-energy photon, generally interacting with an atomic nucleus, produces a particle and an antiparticle. ...

In general relativity,^[7] the stress-energy tensor serves as the source term for the gravitational field, in rough analogy to the way mass serves as the source term in the non-relativistic Newtonian approximation.

It is a common misconception to assert that energy is "equivalent" to mass. It would be more accurately to state that energy has inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.

That misconception presumably arises from trying to reconcile the conservation law with a pre-20th-century definition of energy. In the modern view, the rest energy (aka mass) is included in the definition of energy. Therefore the relevant conservation law is as simple as can be: E is conserved.

Measurement

There is no absolute measure of energy. Rather energy is measured in terms of the transition of a system from one state into another.

Methods

The methods for the measurement of energy often deploy methods for the measurement of still more fundamental concepts of science, viz. mass, distance, radiation, temperature, time, electric charge and electric current. Various meters Measurement is the estimation of a physical quantity such as length, temperature, or time. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... Radiation as used in physics, is energy in the form of waves or particles. ... Fig. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Electric current is the flow (movement) of electric charge. ...

A Calorimeter - An instrument used by physicists to measure energy

Conventionally the technique most often employed are calorimetry, in thermodynamics that relies on the measurement of temperature: a thermometer or a bolometer for measurement of intensity of a radiation. Wikipedia does not have an article with this exact name. ... Wikipedia does not have an article with this exact name. ... A calorimeter is a device used for calorimetry, the science of measuring the heat of chemical reactions or physical changes as well as heat capacity. ... The world’s first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in various chemical changes; calculations which were based on Joseph Black’s prior discovery of latent heat. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... It has been suggested that List of temperature sensors be merged into this article or section. ... Rendition of an imaging bolometer from Los Alamos National Laboratory A bolometer is a device for measuring incident electromagnetic radiation. ...

Units

Main article: Units of energy

Through the history of science energy has been expressed in several different units, e.g. ergs and calorie. At present, the accepted unit of measurement for energy is the SI unit of energy joule. Wikipedia does not yet have an article with this exact name. ... An erg is the unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, symbol erg. Its name is derived from the Greek word meaning work. The erg is a small unit, equal to a force of one dyne exerted for a distance of one... A calorie is a unit of measurement for energy. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The joule (IPA pronunciation: or ) (symbol: J) is the SI unit of energy. ...

Kinetic and potential energy

Main articles: Kinetic energy, Potential energy, Electromagnetic radiation, Photon, and Thermal energy

Classical kinetic energy is due to motion of a body, or particles within it (subject to length-scale restrictions, as discussed below). The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... It has been suggested that this article or section be merged with light. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... 1. ... This article or section is in need of attention from an expert on the subject. ...

Classical potential energy is due to the position of an object relative to other objects. This form of energy can be positive or negative, depending on whether it is work done on an object by a force, or work done by the object against a force. Negative energy is a thus a mathematical construct in reference to another system. Each of the fundamental interactions of nature can be linked to a kind of potential energy. Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... In physics, force is an influence that may cause a body to accelerate. ... Negative energy can refer to several concepts: Energy in any system below an arbitrarily defined level (called reference level, ground state, or zero level). ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ...

These notions of potential and kinetic energy depend on a notion of length scale. For example, one can speak of macroscopic potential and kinetic energy, which do not include thermal potential and kinetic energy. Also what is called chemical potential energy (below) is a macroscopic notion, and closer examination shows that it is really the sum of the potential and kinetic energy on the atomic and subatomic scale. Similar remarks apply to nuclear "potential" energy and most other forms of energy. This dependence on length scale is non-problematic if the various length scales are decoupled, as is often the case ... but confusion can arise when different length scales are coupled, for instance when friction converts macroscopic work into microscopic thermal energy.

– ^[10]

Forms of energy

Heat, a form of energy, is partly potential energy and partly kinetic energy.

In the context of natural sciences, energy can be in any of several different forms: thermal, chemical, electrical, radiant, nuclear etc. Some basic textbooks broadly groups all these forms of energy into two broad categories:^[11] kinetic energy and potential energy. However, some forms of energy resist such easy classification, as is the case with light energy. Other familiar types of energy (such as heat in most circumstances) are a varying mix of both potential and kinetic energy. Download high resolution version (1600x1163, 240 KB) Wikipedia does not have an article with this exact name. ... Download high resolution version (1600x1163, 240 KB) Wikipedia does not have an article with this exact name. ... In physics, heat, symbolized by Q, is defined as transfer of thermal energy [1] Generally, heat is a form of energy transfer associated with the different motions of atoms, molecules and other particles that comprise matter when it is hot and when it is cold. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... 1. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Electrical energy can refer to several closely related things. ... Radiant energy is the energy of electromagnetic waves. ... Nuclear energy is energy released from the atomic nucleus. ...

Gravitational potential energy

Gravitational potential energy is the work of gravitational force during rearrangement of mutual positions of interacting masses - say, when masses are moved apart (such as when a crate is lifted), or closer together (as when a meteorite falls to Earth). If the masses of the objects are considered to be point masses, this work (thus the gravitational potential energy) is equal to Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ...

where

m and M are the two masses in question,

r is the distance between them,

G is the gravitational constant.

According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

Electric potential energy

Electric potential energy is the work of electric forces during rearrangement of positions of charges (usually versus some reference configuration of the same charges - say, charges at infinite distance from each other). This energy results in chemical potential energies (energy required to break chemical bonds, or obtained from forming them). Energy per unit of electric charge is called potential. Chemical potentials can be seen directly in the electrical potentials of electrochemical cell (grouped in batteries), and fuel cells. The energy released in lightning, from burning a liter of fuel oil, or from using an amount of electrical power from an electrical-wiring system, are all common examples of extracting work from rearrangement of charges, which is stored beforehand as electromagnetic potential energy. Spatially it is stored in the electric field surrounding charges. Quantitatively, electromagnetic potential energy is: The electric potential energy of a body is its potential energy due to electric effects, neglecting other forces (such as gravity). ... A demonstration electrochemical cell setup resembling the Daniell cell. ... A fuel cell is an electrochemical device similar to a battery, but differing from the latter in that it is designed for continuous replenishment of the reactants consumed; i. ... It has been suggested that optical field be merged into this article or section. ...

where

q and Q are the electric charges on the objects in question,

r is the distance between them,

ε₀ is the electric constant of a vacuum.

In use of electrical energy from an electrical wiring system, or from a chemical battery, the electric potential energy available per amount of electric charge moved (which in turn is given by electric current multiplied by time), is represented by the electrical potential difference (measured in volts) between the conductors. Thus, when one ampere flows for one second across a potential of one volt, one joule of energy is made available from the electrical potential. The force which provides for the work that is done, is provided to the charge by an electrical field. The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ... The electric potential energy of a body is its potential energy due to electric effects, neglecting other forces (such as gravity). ... Current can be measured by a galvanometer, via the deflection of a magnetic needle in the magnetic field created by the current. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ...

Magnetic energy

Energy can also be stored in a magnetic field. Certain particles having spinning charge generate magnetic field in their vicinity. Electric current in superconducting magnetic energy storage generates strong magnetic field which has energy associated with it - and thus electromagnet can be used to store energy. Since magnetic field is simply relativistic part of electric field, magnetic energy is closely related to electric energy. Variable magnetic field generating variable electric field results in transfer of energy (thus, of power) by an electrical transformer. In physics, a magnetic field is an pseudovector field that traces out solenoidal lines of force in and around closed electric circuits and bar magnets. ... The terms spin and SPIN have several meanings, including those primarily discussed as spinning: For spin in sub-atomic physics, see spin (physics) For the stalled aircraft maneuver or any of several forms of loss of control in aircraft, see spin (flight) For the periodical, see Spin Magazine For the... Superconducting magnetic energy storage (SMES) uses superconductivity - the ability of certain materials to conduct electricity without resistance - to store electrical energy. ... Look up Power in Wiktionary, the free dictionary. ... Three-phase pole-mounted step-down transformer. ...

Thermal potential energy

Potential thermal energy is the part of thermal energy which is not made up of kinetic thermal energy, and is thus stored as electric potential energy. This potential electrical part of thermal energy is stored in "deformation" of atomic bonds during thermal motion of atoms (as atoms oscillate around their position of equilibrium, they not only have kinetic energy of motion, but also a potential energy of displacement from equilibrium). This type of potential energy is a significant portion (about half) of thermal energy for strongly-bonded systems (solids and liquids), with the rest of thermal energy in such systems being the kinetic energy of the atoms. 1. ...

In monoatomic gas, however, the potential part of thermal energy is a smaller fraction of thermal energy in gases (as gas molecules practically do not interact with each other) - thus almost all their thermal energy is kinetic.

In multiatomic gases vibrational energy has its potential part U=nkT/2 where n is the number of vibrational degrees of freedom. The phrase degrees of freedom is used in three different branches of science: in physics and physical chemistry, in mechanical and aerospace engineering, and in statistics. ...

Each existing degree of freedom in physical system (say, gas molecule) contributes equal amount kT/2 into total thermal energy.

Chemical potential energy

Potential chemical energy of an object is the energy which may potentially be liberated as a result of transformations of chemical substances. In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Water and steam are two different forms of the same chemical substance A chemical substance is any material with a definite chemical composition, no matter where it comes from. ...

The change in chemical potential energy in the course of a chemical transformation depends on the parameters like temperature, pressure and concentration. It is equal to the difference between the energy content of the product substances and that of the reactants. Energy is involved in breaking or making of chemical bonds. Some energy can be released as a result of rearrangement of bonds between atoms of a chemical substance (or a mixture thereof) only if the energy in the reactant chemical substances is more than that in product substances. Water and steam are two different forms of the same chemical substance A chemical substance is any material with a definite chemical composition, no matter where it comes from. ...

Elastic potential energy

Potential elastic energy is the energy stored in the elastic intermolecular bonds. Elastic energy is actually of several types: it is sometimes a kind of electric potential energy (as in metal springs), and in these cases energy is released as charged atoms which have been compressed are allowed to move apart. However, in other cases (such as compressed ideal gas) the potential energy is not stored as electric, but rather is stored as a kinetic energy of moving atoms. The elastic energy is the energy which causes or is released by the Elastic distortion of a solid or a fluid. ...

In the ideal case of a metal spring described by Hooke's Law, the stored elastic energy is equal to:

where

k is the spring constant, dependent on the individual spring,

x is the deformation of the object.

Nuclear potential energy

Nuclear potential energy, along with electric potential energy, provides the energy released from nuclear fission and nuclear fusion processes. The result of both these processes are nuclei in which strong nuclear forces bind nuclear particles more strongly and closely. Weak nuclear forces (different from strong forces) provide the potential energy for certain kinds of radioactive decay, such as beta decay. The energy released in nuclear processes is so large that the relativistic change in mass (after the energy has been removed) can be as much as several parts per thousand. Nuclear energy is energy released from the atomic nucleus. ... The electric potential energy of a body is its potential energy due to electric effects, neglecting other forces (such as gravity). ... For the generation of electrical power by fission, see Nuclear power plant An induced nuclear fission event. ... The deuterium-tritium (D-T) fusion reaction is considered the most promising for producing fusion power. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ...

Nuclear particles like protons and neutrons are not destroyed(law of conservation of energy) in fission and fusion processes (except in beta minus and beta plus decay or electron capture decay), but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun, also called solar energy, is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million metric tons of solar matter per second into light, which is radiated into space. In this system, the light itself retains the inertia equivalent of this mass, and indeed the mass itself (as a system) and represents 4 million tons per second of electromagnetic field, moving into space. The Sun is the star at the center of the Solar System. ... Solar power describes a number of methods of harnessing energy from the light of the sun. ... The Sun is the star at the center of the Solar System. ...

Transformations of energy

Main article: Energy conversion

One form of energy can often be readily transformed into another with the help of a device- for instance, a battery, from chemical energy to electrical energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electrical generator. Similarly, in the case of a chemical explosion, chemical potential energy is transformed to kinetic energy and thermal energy in a very short time. Yet another example is that of a pendulum. At its highest points the kinetic energy is zero and the gravitational potential energy is at maximum. At its lowest point the kinetic energy is at maximum and is equal to the decrease of potential energy. If one (unrealistically) assumes that there is no friction, the conversion of energy between these processes is perfect, and the pendulum will continue swinging forever. In physics and engineering, energy conversion is any process of converting energy from one form to another. ... In chemistry, a chemical bond is the force which holds together atoms in molecules or crystals. ... Electrical energy can refer to several closely related things. ... This article or section does not cite any references or sources. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... A Siemens steam turbine with the case opened. ... Electrical energy or Electromagnetic energy is a form of energy present in any electric field or magnetic field, or in any volume containing electromagnetic radiation. ... “Dynamo” redirects here. ... This article is concerned solely with chemical explosives. ... In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... 1. ... Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... Friction is the force that opposes the relative motion or tendency toward such motion of two surfaces in contact. ... Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ...

Energy can be converted into matter and vice versa. The mass-energy equivalence formula E = mc², derived independently by Albert Einstein and Henri Poincaré,^{[citation needed]} quantifies the relationship between mass and rest energy. Since c² is very large relative to ordinary human scales, the conversion of mass to other forms of energy can liberate tremendous amounts of energy, as can be seen in nuclear reactors and nuclear weapons. Conversely, the mass equivalent of a unit of energy is minuscule, which is why loss of energy from most systems is difficult to measure by weight, unless the energy loss is very large. Examples of energy transformation into matter (particles) are found in high energy nuclear physics. This article or section does not cite any references or sources. ... 15ft sculpture of Einsteins 1905 E = mc² formula at the 2006 Walk of Ideas, Germany In special relativity, the mass-energy equivalence usually expressed as E = mc² is the concept that there is an energy equivalence to any mass. ... Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... Jules TuPac Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [][1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... Nuclear physics is the branch of physics concerned with the nucleus of the atom. ...

In nature, transformations of energy can fundamentally classed into two kinds: those that are thermodynamically reversible, and those that are thermodynamically irreversible. A reversible process in thermodynamics is one in which no energy is dissipated into empty quantum states available in a volume, from which it cannot be recovered into more concentrated forms (fewer quantum states), without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, conversion of energy from one type of potential field to another, is reversible, as in the pendulum system described above. In processes where heat is generated, however, quantum states of lower energy, present as possible exitations in fields between atoms, act as a reservoir for part of the energy, from which it cannot be recovered, in order to be converted with 100% efficiency into other forms of energy. In this case, the energy must partly stay as heat, and cannot be completely recovered as usable energy, except at the price of an increase in some other kind of heat-like increase in disorder in quantum states, in the universe (such as an expansion of matter, or a randomization in a crystal). A reversible process (or reversible cycle if the process is cyclic) , in thermodynamics, is a process that can be reversed by means of infinitesimal changes in some property of the system (Sears and Salinger, 1986). ... Movie Poster for Irréversible Irréversible (2002, France) is a film written, directed, edited, and photographed by Gaspar Noé. It is considered to be one of the most controversial and disturbing films ever made, due to its explicit on-camera depiction of rape and a vengeful murder. ... In thermodynamics, a reversible process (or reversible cycle if the process is cyclic) is a process that can be reversed by means of infinitesimal changes in some property of the system. ...

As the universe evolves in time, more and more of its energy becomes trapped in irreversible states (i.e., as heat or other kinds of increases in disorder). This has been referred to as the inevitable thermodynamic heat death of the universe. In this heat death the energy of the universe does not change, but the fraction of energy which is available to do work, or be transformed to other usable forms of energy, grows less and less. The heat death is a possible final state of the universe, in which it has reached maximum entropy. ... The heat death is a possible final state of the universe, in which it has reached maximum entropy. ...

Law of conservation of energy

Main article: Conservation of energy

Energy is subject to the law of conservation of energy. According to this law, energy can neither be created (produced) nor destroyed itself. It can only be transformed. Conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms (for instance, friction turns kinetic energy into thermal energy). ...

Most kinds of energy (with gravitational energy being a notable exception)[1] are also subject to strict local conservation laws, as well. In this case, energy can only be exchanged between adjacent regions of space, and all observers agree as to the volumetric density of energy in any given space. There is also a global law of conservation of energy, stating that the total energy of the universe cannot change; this is a corollary of the local law, but not vice versa.^[3][6] Conservation of energy is the mathematical consequence of translational symmetry of time (=indistinguishability of time intervals taken at different time)^[12] - see Noether's theorem. Conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms (for instance, friction turns kinetic energy into thermal energy). ... A translation slides an object by a vector a: Ta(p) = p + a. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ... Noethers theorem is a central result in theoretical physics that shows that a conservation law can be derived from any continuous symmetry. ...

According to energy conservation law the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. For the physical concepts, see conservation of energy and energy efficiency. ...

This law is a fundamental principle of physics. It follows from the translational symmetry of time, a property of most phenomena below the cosmic scale that makes them independent of their locations on the time coordinate. Put differently, yesterday, today, and tomorrow are physically indistinguishable. A translation slides an object by a vector a: Ta(p) = p + a. ... A pocket watch, a device used to tell time Look up time in Wiktionary, the free dictionary. ...

Because energy is quantity which is canonical conjugate to time, it is impossible to define exact amount of energy during any finite time interval - making it impossible to apply the law of conservation of energy. This must not be considered a "violation" of the law. We know the law still holds, because a succession of short time periods does notaccumulate any violation of conservation of energy. A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. ...

In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by Fig. ... In mathematics, an operator is a function that performs some sort of operation on a number, variable, or function. ...

which is similar in form to the uncertainty principle (but not really mathematically equivalent thereto, since H and t are not dynamically conjugate variables, neither in classical nor in quantum mechanics). In quantum physics, the Heisenberg uncertainty principle, sometimes called the Heisenberg indeterminacy principle, expresses a limitation on accuracy of (nearly) simultaneous measurement of observables such as the position and the momentum of a particle. ...

In particle physics, this inequality permits a qualitative understanding of virtual particles which carry momentum, exchange by which with real particles is responsible for creation of all known fundamental forces (more accurately known as fundamental interactions). Virtual photons (which are simply lowest quantum mechanical energy state of photons) are also responsible for electrostatic interaction between electric charges (which results in Coulomb law), for spontaneous radiative decay of exited atomic and nuclear states, for the Casimir force, for van der Waals bond forces and some other observable phenomena. Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... In classical mechanics, momentum (pl. ... Look up Creation in Wiktionary, the free dictionary. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... This article or section does not cite its references or sources. ... An energy level is a quantified stable energy, which a physical system can have; the term is most commonly used in reference to the electron configuration of electrons, in atoms or molecules. ... The word light is defined here as electromagnetic radiation of any wavelength; thus, X-rays, gamma rays, ultraviolet light, infrared radiation, microwaves, radio waves, and visible light are all forms of light. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... For spontaneous, see Spontaneous bacterial peritonitis Spontaneous combustion Spontaneous emission Spontaneous fission spontaneous generation Spontaneous human combustion Spontaneous Music Ensemble Spontaneous order Spontaneous process Spontaneous reaction Spontaneous remission Spontaneous symmetry breaking This is a disambiguation page: a list of articles associated with the same title. ... In 1948 Dutch physicist Hendrik B. G. Casimir of Philips Research Labs predicted that two uncharged parallel metal plates will be subject to a force pressing them together. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ...

See also

• Activation energy
• Enthalpy
• Energy (chemistry)
• Energy (biology)
• Energy (Earth science)
• Energy (cosmology)
• Energy policy
• World energy resources and consumption
• Free energy
• Interaction energy
• Internal energy
• Negative energy
• Orders of magnitude (energy)
• Power (physics)
• Renewable energy
• Solar radiation
• Entropy
• Thermodynamics
• Units of energy

Image File history File links Portal. ... Image File history File links Portal. ... The sparks generated by striking steel against a flint provide the activation energy to initiate combustion in this Bunsen burner. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... Energy policy is the manner a given entity (often governmental) has decided to address issues of energy production, distribution and consumption. ... World power usage in TW (=1012 Watt), 1980-2004. ... The free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications. ... In physics, interaction energy is the contribution to the total energy that is caused by an interaction between the objects being considered. ... In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... Negative energy can refer to several concepts: Energy in any system below an arbitrarily defined level (called reference level, ground state, or zero level). ... To help compare different orders of magnitude, the following list describes various energy levels between 10−31 joules and 1070 joules. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transferred. ... World renewable energy in 2005 (except 2004 data for items marked* or **). Enlarge image to read exclusions. ... Solar irradiance spectrum at top of atmosphere. ... Ice melting - classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. ... Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dunamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Wikipedia does not yet have an article with this exact name. ...

Notes and references

Other books

• Alekseev, G. N. (1986). Energy and Entropy. Moscow: Mir Publishers. 
• Walding, Richard,  Rapkins, Greg,  Rossiter, Glenn (1999-11-01). New Century Senior Physics. Melbourne, Australia: Oxford University Press. ISBN 0-19-551084-4. 

External links

• A forum discussion among physicsts on the definition of energy
• Conservation of Energy - a chapter from an online textbook
• Work, Power, Kinetic EnergyPDF (399 KiB) on Project PHYSNET
• Freeview video 'Endless Energy' scientists discuss renewable energy. A programme by the Vega Science Trust and the BBC/OU
• What does energy really mean? From Physics World
• Compact description of various energy sources. Energy sources and ecology.
• World Energy Education Foundation
• Glossary of Energy Terms
• International Energy Agency IEA - OECD
• Energy & Environmental Security
• Energy for kids
• Energy riddle and transformations