E = mc2 Mass–energy equivalence

In physics, mass–energy equivalence is the concept that the mass of an object or system is a measure of its energy content. For instance, adding 25 kilowatt-hours (90 megajoules) of any form(s) of energy to any object increases its mass by 1 microgram.
A physical system has a property called energy and a corresponding property called mass; the two properties are equivalent in that they are always both present in the same (i.e. constant) proportion to one another. Mass–energy equivalence arose originally from special relativity, as developed by Albert Einstein, who proposed this equivalence in 1905 in one of his Annus Mirabilis papers entitled "Does the inertia of an object depend upon its energy content?"The equivalence is described by the famous equation:

where E is energy, m is mass, and c is the speed of light. Thus, this mass–energy relation states that the universal proportionality factor between equivalent amounts of energy and mass is equal to the speed of light squared. This also serves to convert units of mass to units of energy, no matter what system of measurement units is used.
If a body is stationary, it still has some internal or intrinsic energy, called its rest energy. Rest mass and rest energy are equivalent and remain proportional to one another. When the body is in motion (relative to an observer), its total energy is greater than its rest energy. The rest mass (or rest energy) remains an important quantity in this case because it remains the same regardless of this motion, even for the extreme speeds or gravity considered in special and general relativity; thus it is also called the invariant mass.
On the one hand, the equation E = mc² can be applied to rest mass (m or m₀) and rest energy (E₀) to show their proportionality as E₀ = m₀c².
On the other hand, it can also be applied to the total energy (E_tot or simply E) and total mass of a moving body. The total mass is also called the relativistic mass m_rel as it is not significantly greater than the rest mass until the speed approaches that of light, where special relativity should be used in order to describe the motion. Therefore, the total energy and total mass are related by E = m_relc².
Thus, the mass–energy relation E = mc² can be used to relate the rest energy to the rest mass, or to relate the total energy to the total mass. To instead relate the total energy or mass to the rest energy or mass, a generalization of the mass–energy relation is required: the energy–momentum relation.
E = mc² has frequently been used as an explanation for the origin of energy in nuclear processes, but such processes can be understood as simply converting nuclear potential energy, without the need to invoke mass–energy equivalence. Instead, mass–energy equivalence merely indicates that the large amounts of energy released in such reactions may exhibit enough mass that the mass loss may be measured, when the released energy (and its mass) have been removed from the system. For example, the loss of mass to an atom and a neutron, as a result of the capture of the neutron and the production of a gamma ray, has been used to test mass–energy equivalence to high precision, as the energy of the gamma ray may be compared with the mass defect after capture. In 2005, these were found to agree to 0.0004%, the most precise test of the equivalence of mass and energy to date. This test was performed in the World Year of Physics 2005, a centennial celebration of Einstein's achievements in 1905.

Einstein was not the first to propose a mass–energy relationship (see the History section). However, Einstein was the first scientist to propose the E = mc² formula and the first to interpret mass–energy equivalence as a fundamental principle that follows from the relativistic symmetries of space and time.

Einstein: mass–energy equivalence
Albert Einstein did not formulate exactly the formula E = mc² in his 1905 Annus Mirabilis paper "Does the Inertia of an object Depend Upon Its Energy Content?"; rather, the paper states that if a body gives off the energy L in the form of radiation, its mass diminishes by L/c². (Here, "radiation" means electromagnetic radiation, or light, and mass means the ordinary Newtonian mass of a slow-moving object.) This formulation relates only a change Δm in mass to a change L in energy without requiring the absolute relationship.

Objects with zero mass presumably have zero energy, so the extension that all mass is proportional to energy is obvious from this result. In 1905, even the hypothesis that changes in energy are accompanied by changes in mass was untested. Not until the discovery of the first type of antimatter (the positron in 1932) was it found that all of the mass of pairs of resting particles could be converted to radiation.

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