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'''E=mc²''' asserts that the energy ('''E''') which makes up the [[matter]] in an unmoving object is equal to the square of the [[speed of light]] ('''c²''') times the [[mass]] ('''m''') of that body.<ref>"Energy and mass are linked in the most famous relationship in physics: E = mc². (The energy content of a body is equal to the mass of the body times the speed of light squared.)" [http://www.pbs.org/wgbh/nova/physics/einstein-genius-among-geniuses.html Einstein: Genius Among Geniuses] - PBS's NOVA</ref> The complete form, when applied to moving objects, is '''E²=(mc²)²+(pc)²''', where '''p''' represents momentum,<ref>http://www.youtube.com/watch?v=NnMIhxWRGNw</ref> It is a statement that purports to relate all [[matter]] to [[energy]]. In fact, no [[theory]] has successfully unified the [[law]]s governing [[mass]] (''i.e.'', [[gravity]]) with the laws governing light (''i.e.'', [[electromagnetism]]), and numerous attempts to derive '''E=mc²''' from first principles have failed<ref name="wvarticles">Five lectures at Wikiversity. The 4<sup>th</sup> one purports to derive derives the formula - can you determine , using the implicit assumptions in the derivation?"What the Equation Means" section.
*[http://en.wikiversity.org/wiki/Special_relativity/space,_time,_and_the_Lorentz_transform Lecture 1]
*[http://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]
One can verify that, in the non-relativistic limit, the second of those equations converges to the first.
It is this requirement, and some "gedanken experiments" involving conversion between potential and kinetic energy, that lead to E=mc²<ref name="wvarticles"/>. These experiments involve some kind of object that isn't moving (though there might be internal motion that doesn't figure in the experiment) and therefore has no kinetic energy and only potential energy, turning into some things that have kinetic energy. The requirements of strict conservation of total momentum and total energy prove the equation. Einstein's famous derivation<ref name="einstein1905b">[http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?" Albert Einstein, Sept 1905]</ref> involved light instead of tangible objects, but the result is the same.
==History of Experimental Verification==
Measuring the effect requires process that release vastly more energy than ordinary chemical processes. The discovery of Radium and Polonium around 1898 gave a tantalizing hint that there were processes that released far more energy than chemical processes could account for. These elements continuously released measurable heat, and also glowed in the dark.
Einstein touched on this possibility in his original 1905 paper [http:<ref name=einstein1905b//www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"]>.
{{cquote|''It is not impossible that with bodies whose energy content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.''}}It would take more than a decade to develop an understanding of the nuclear process involved. The first thing that was required was accurate knowledge of atomic weights.
Around 1925, the development of the mass spectrograph, by Francis Aston, made it possible to measure atomic weights to extreme precision.
The 1932 Cockcroft-Walton experiment, described in more detail below, brought more publicity started to make the equation famous by confirming it, with reasonable accuracy, for an artificially induced nuclear reaction. (Confirming E=mc<sup>2</sup> was not a goal of the experiment; it was an incidental consequence.) The equation had already been known and understood for many years.
In the decades since, nuclear transmutations have been performed, in particle accelerators, all over the periodic table, observing in detail the properties of various isotopes. These have confirmed E=mc<sup>2</sup> with great precision. Perhaps the most precise test, by Rainville ''et. al.''<ref name="rainville">http://www.nature.com/nature/journal/v438/n7071/full/4381096a.html Nature 438, 1096-1097 (22 December 2005)] doi:10.1038/4381096a; Published online 21 December 2005</ref>, confirmed the equation to an accuracy of a few parts per million.
==Claims of isolated attempts experimental Experimental verification==
In 1932 English physicist John Cockcroft and Irish physicist Ernest Walton performed the first artificial nuclear transmutation of nuclei, for which they were awarded the 1951 [[Nobel Prize]] in physics<ref>[http://www.nobelprize.org/nobel_prizes/physics/laureates/1951/cockcroft-lecture.pdf John D. Cockroft ''Experiments on the interaction of high-speed nucleons with atomic nuclei''], Nobel Lecture, Dec 11, 1951</ref>. ''"their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles"''<ref>[http://www.nobelprize.org/nobel_prizes/physics/laureates/1951/# Nobel Prize Organization]</ref> Like all of the very famous experiments of modern physics, this experiment has been replicated, with modern equipment, hundreds of times, all around the world.
They bombarded [[Lithium]] atoms with [[protons]] having a [[kinetic energy]] less than 1 [[Electron-Volts|MeV]]. The result were two (slightly less heavy) [[alpha particle]]s, for which the [[kinetic energy]] was measured as 17.3 MeV
Accurate measurements and detailed calculations allowed for verifying the theoretical values with an accuracy of ±0.5%. This was the first time a nucleus was artificially split, and thereby the first transmutation of elements using accelerated particles:
==A Famous Example -- Nuclear Fission of Uranium==
