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In cosmology and astronomy the phenomena of stars , nova , supernova , quasars and gamma-ray bursts are the universe's highest-output energy transformations of matter.
All stellar phenomena including solar activity are driven by various kinds of energy transformations. Energy in such transformations is either from gravitational collapse of matter usually molecular hydrogen into various classes of astronomical objects stars, black holes, etc.
The nuclear fusion of hydrogen in the Sun also releases another store of potential energy which was created at the time of the Big Bang.
At that time, according to theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements.
This meant that hydrogen represents a store of potential energy that can be released by fusion. Such a fusion process is triggered by heat and pressure generated from gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into sunlight.
In quantum mechanics , energy is defined in terms of the energy operator as a time derivative of the wave function.
The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics.
The Schrödinger equation describes the space- and time-dependence of a slowly changing non-relativistic wave function of quantum systems.
The solution of this equation for a bound system is discrete a set of permitted states, each characterized by an energy level which results in the concept of quanta.
In the case of an electromagnetic wave these energy states are called quanta of light or photons. When calculating kinetic energy work to accelerate a massive body from zero speed to some finite speed relativistically — using Lorentz transformations instead of Newtonian mechanics — Einstein discovered an unexpected by-product of these calculations to be an energy term which does not vanish at zero speed.
He called it rest energy : energy which every massive body must possess even when being at rest. The amount of energy is directly proportional to the mass of the body:.
For example, consider electron — positron annihilation, in which the rest energy of these two individual particles equivalent to their rest mass is converted to the radiant energy of the photons produced in the process.
In this system the matter and antimatter electrons and positrons are destroyed and changed to non-matter the photons. However, the total mass and total energy do not change during this interaction.
The photons each have no rest mass but nonetheless have radiant energy which exhibits the same inertia as did the two original particles. This is a reversible process — the inverse process is called pair creation — in which the rest mass of particles is created from the radiant energy of two or more annihilating photons.
In general relativity, 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.
Energy and mass are manifestations of one and the same underlying physical property of a system. This property is responsible for the inertia and strength of gravitational interaction of the system "mass manifestations" , and is also responsible for the potential ability of the system to perform work or heating "energy manifestations" , subject to the limitations of other physical laws.
In classical physics , energy is a scalar quantity, the 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.
Energy may be transformed between different forms at various efficiencies. Items that transform between these forms are called transducers.
Examples of transducers include a battery, from chemical energy to electric 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 electric generator ; or a heat engine , from heat to work.
Examples of energy transformation include generating electric energy from heat energy via a steam turbine, or lifting an object against gravity using electrical energy driving a crane motor.
Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object.
If the object falls to the ground, gravity does mechanical work on the object which transforms the potential energy in the gravitational field to the kinetic energy released as heat on impact with the ground.
Our Sun transforms nuclear potential energy to other forms of energy; its total mass does not decrease due to that in itself since it still contains the same total energy even if in different forms , but its mass does decrease when the energy escapes out to its surroundings, largely as radiant energy.
There are strict limits to how efficiently heat can be converted into work in a cyclic process, e. However, some energy transformations can be quite efficient.
The direction of transformations in energy what kind of energy is transformed to what other kind is often determined by entropy equal energy spread among all available degrees of freedom considerations.
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.
Energy transformations in the universe over time are characterized by various kinds of potential energy that has been available since the Big Bang later being "released" transformed to more active types of energy such as kinetic or radiant energy when a triggering mechanism is available.
Familiar examples of such processes include nuclear decay, in which energy is released that was originally "stored" in heavy isotopes such as uranium and thorium , by nucleosynthesis , a process ultimately using the gravitational potential energy released from the gravitational collapse of supernovae , to store energy in the creation of these heavy elements before they were incorporated into the solar system and the Earth.
This energy is triggered and released in nuclear fission bombs or in civil nuclear power generation. 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 or other losses, the conversion of energy between these processes would be perfect, and the pendulum would continue swinging forever.
This is referred to as conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other.
This can be demonstrated by the following:. Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed.
It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence.
In different theoretical frameworks, similar formulas were derived by J. Part of the rest energy equivalent to rest mass of matter may be converted to other forms of energy still exhibiting mass , but neither energy nor mass can be destroyed; rather, both remain constant during any process.
Conversely, the mass equivalent of an everyday amount energy is minuscule, which is why a loss of energy loss of mass from most systems is difficult to measure on a weighing scale, unless the energy loss is very large.
Examples of large transformations between rest energy of matter and other forms of energy e. Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes.
An irreversible process is one in which energy is dissipated spread into empty energy 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 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 randomisation in a crystal.
As the universe evolves in time, more and more of its energy becomes trapped in irreversible states i. 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 through a heat engine , or be transformed to other usable forms of energy through the use of generators attached to heat engines , grows less and less.
The fact that energy can be neither created nor be destroyed is called the law of conservation of energy. In the form of the first law of thermodynamics , this states that a closed system 's energy is constant unless energy is transferred in or out by work or heat , and that no energy is lost in transfer.
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.
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.
While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in heat engines the second law of thermodynamics states that the system doing work always loses some energy as waste heat.
This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the available energy. Mechanical and other forms of energy can be transformed in the other direction into thermal energy without such limitations.
Richard Feynman said during a lecture: . There is a fact, or if you wish, a law , governing all natural phenomena that are known to date.
There is no known exception to this law — it is exact so far as we know. The law is called the conservation of energy.
It states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens.
It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.
Most kinds of energy with gravitational energy being a notable exception  are 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.
This law is a fundamental principle of physics. As shown rigorously by Noether's theorem , the conservation of energy is a mathematical consequence of 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. This is because energy is the quantity which is canonical conjugate to time.
This mathematical entanglement of energy and time also results in the uncertainty principle - it is impossible to define the exact amount of energy during any definite time interval.
The uncertainty principle should not be confused with energy conservation - rather it provides mathematical limits to which energy can in principle be defined and measured.
Each of the basic forces of nature is associated with a different type of potential energy, and all types of potential energy like all other types of energy appears as system mass , whenever present.
For example, a compressed spring will be slightly more massive than before it was compressed. Likewise, whenever energy is transferred between systems by any mechanism, an associated mass is transferred with it.
In quantum mechanics energy is expressed using the Hamiltonian operator. On any time scales, the uncertainty in the energy is by.
In particle physics , this inequality permits a qualitative understanding of virtual particles which carry momentum , exchange by which and with real particles, is responsible for the 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.
Energy transfer can be considered for the special case of systems which are closed to transfers of matter.
The portion of the energy which is transferred by conservative forces over a distance is measured as the work the source system does on the receiving system.
The portion of the energy which does not do work during the transfer is called heat. Examples include the transmission of electromagnetic energy via photons, physical collisions which transfer kinetic energy , [note 5] and the conductive transfer of thermal energy.
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Energy is treated in a number of articles. For the development of the concept of energy and the principle of energy conservation, see principles of physical science ; mechanics ; thermodynamics ; and conservation of energy.
For the major sources of energy and the mechanisms by which the transition of energy from one form to another occurs, see coal ; solar energy ; wind power ; nuclear fission ; oil shale ; petroleum ; electromagnetism ; and energy conversion.
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