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'''E=mc²''' asserts that the energy ('''E''') in an unmoving particle is equal to the square of the [[speed of light]] ('''c²''') times the [[mass]] ('''m''') of that particle.<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 [[E^2=(mc^2)^2+(pc)^2|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 4th one derives the formula, using the assumptions in the "What the Equation Means" section.
'''E=mc²''' asserts that the energy ('''E''') in an unmoving particle is equal to the square of the [[speed of light]] ('''c²''') times the [[mass]] ('''m''') of that particle.<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 [[E^2=(mc^2)^2+(pc)^2|E²=(mc²)²+(pc)²]], where '''p''' represents momentum,<ref>https://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 4th one derives the formula, using the assumptions in the "What the Equation Means" section.
*[http://en.wikiversity.org/wiki/Special_relativity/space,_time,_and_the_Lorentz_transform Lecture 1]
*[https://en.wikiversity.org/wiki/Special_relativity/space,_time,_and_the_Lorentz_transform Lecture 1]
*[http://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]
*[https://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]
*[http://en.wikiversity.org/wiki/Special_relativity/energy Lecture 3]
*[https://en.wikiversity.org/wiki/Special_relativity/energy Lecture 3]
*[http://en.wikiversity.org/wiki/Special_relativity/E_%3D_mc%C2%B2 Lecture 4]
*[https://en.wikiversity.org/wiki/Special_relativity/E_%3D_mc%C2%B2 Lecture 4]
*[http://en.wikiversity.org/wiki/Special_relativity/spacetime_diagrams_and_vectors Lecture 5]</ref> [[Politics|Political]] pressure, however, has since made it impossible for anyone pursuing an academic career in [[science]] to even question the validity of this nonsensical [[equation]]. ''Simply put, E=mc² is [[liberal claptrap]]''.
*[https://en.wikiversity.org/wiki/Special_relativity/spacetime_diagrams_and_vectors Lecture 5]</ref> [[Politics|Political]] pressure, however, has since made it impossible for anyone pursuing an academic career in [[science]] to even question the validity of this nonsensical [[equation]]. ''Simply put, E=mc² is [[liberal claptrap]]''.
The formula asserts that the mass of an object, at constant energy, magically varies precisely in inverse proportion to the square of a change in the speed of light over time,<ref>http://www.livescience.com/29111-speed-of-light-not-constant.html</ref> which violates [[conservation of mass]] and disagrees with commonsense.<ref>The formula asserts that the mass of an object has energy associated with it, even when it is not moving (p=0). The formula asserts a relationship between the rest mass of an object, its energy and the speed of light. According to the formula, the apparent mass of an object depends on its energy and so [[conservation of mass]] is not satisfied. Instead, relativity proposes that the total energy of a [[closed system]] is conserved, when we "convert" the masses into energies using this formula.</ref>
The formula asserts that the mass of an object, at constant energy, magically varies precisely in inverse proportion to the square of a change in the speed of light over time,<ref>http://www.livescience.com/29111-speed-of-light-not-constant.html</ref> which violates [[conservation of mass]] and disagrees with commonsense.<ref>The formula asserts that the mass of an object has energy associated with it, even when it is not moving (p=0). The formula asserts a relationship between the rest mass of an object, its energy and the speed of light. According to the formula, the apparent mass of an object depends on its energy and so [[conservation of mass]] is not satisfied. Instead, relativity proposes that the total energy of a [[closed system]] is conserved, when we "convert" the masses into energies using this formula.</ref>
The equation is extremely famous, and just as extremely misunderstood, in popular culture. Among the more outlandish claims are statements to the effect that "E=mc² holds the secret of the atomic bomb."<ref>Not so. The energy of the atomic bomb comes not from E=mc², but from the tension between the electrostatic force and the strong nuclear force. E=mc² simply meant that the fission products from the [[Little Boy|Hiroshima]] bomb weighed 0.7 grams less than the original Uranium.</ref>
The equation is extremely famous, and just as extremely misunderstood, in popular culture. Among the more outlandish claims are statements to the effect that "E=mc² holds the secret of the atomic bomb."<ref>Not so. The energy of the atomic bomb comes not from E=mc², but from the tension between the electrostatic force and the strong nuclear force. E=mc² simply meant that the fission products from the [[Little Boy|Hiroshima]] bomb weighed 0.7 grams less than the original Uranium.</ref>
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [http://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [https://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
The equation has acquired something of a "cult" status. In the USA, the popular ''[[Twilight Zone]]'' series featured '''E=mc²''' prominently, giving the equation greater currency with the public. The song ''[[Albert Einstein|Einstein]] A Go-Go'' by the band Landscape had a similar effect in the UK in the 1980s. The equation was the title of a single by ''Big Audio Dynamite'' in 1985, and an album by Mariah Carey in 2008. Some movies have been themed on this equation.<ref>http://www.imdb.com/title/tt0322120/?ref_=fn_tt_tt_2, http://www.imdb.com/title/tt0116160/?ref_=fn_tt_tt_1</ref> The equation, along with a picture of a mushroom cloud and a picture of [[Albert Einstein]], were featured on the front cover of an issue of ''Time'' magazine in 1946. All of this is disappointing when one considers how few people actually understand what the equation is saying.
The equation has acquired something of a "cult" status. In the USA, the popular ''[[Twilight Zone]]'' series featured '''E=mc²''' prominently, giving the equation greater currency with the public. The song ''[[Albert Einstein|Einstein]] A Go-Go'' by the band Landscape had a similar effect in the UK in the 1980s. The equation was the title of a single by ''Big Audio Dynamite'' in 1985, and an album by Mariah Carey in 2008. Some movies have been themed on this equation.<ref>https://www.imdb.com/title/tt0322120/?ref_=fn_tt_tt_2, https://www.imdb.com/title/tt0116160/?ref_=fn_tt_tt_1</ref> The equation, along with a picture of a mushroom cloud and a picture of [[Albert Einstein]], were featured on the front cover of an issue of ''Time'' magazine in 1946. All of this is disappointing when one considers how few people actually understand what the equation is saying.
A number of science writers—both serious scientists and science popularizers—have at various times written their own explanation of the equation. Some of these are helpful; many are not. One of the better ones, though not without its share of nonsense, is a NOVA series by the [[Public Broadcasting Service]]<ref>[http://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc²''], Nov 10, 2005, NOVA</ref>
A number of science writers—both serious scientists and science popularizers—have at various times written their own explanation of the equation. Some of these are helpful; many are not. One of the better ones, though not without its share of nonsense, is a NOVA series by the [[Public Broadcasting Service]]<ref>[http://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc²''], Nov 10, 2005, NOVA</ref>
This experiment is not one of the ones usually cited as validating E=mc². That was not its goal. The generally accepted important tests of this equation are the measurements of alpha decay energies, described above.
This experiment is not one of the ones usually cited as validating E=mc². That was not its goal. The generally accepted important tests of this equation are the measurements of alpha decay energies, described above.
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> The award was for ''"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>
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>[https://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> The award was for ''"their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles."''<ref>[https://www.nobelprize.org/nobel_prizes/physics/laureates/1951/# Nobel Prize Organization]</ref>
Verifying E=mc² was not the goal of the experiment, and the Nobel prize was awarded for the transmutation itself, not any verification of the equation. This experiment could not have proved any general truth to the equation, since it was a test of just one specific reaction. But data from this experiment was consistent with the equation for the particular transmutation involved.
Verifying E=mc² was not the goal of the experiment, and the Nobel prize was awarded for the transmutation itself, not any verification of the equation. This experiment could not have proved any general truth to the equation, since it was a test of just one specific reaction. But data from this experiment was consistent with the equation for the particular transmutation involved.
==A Topical Example: Speed of Extremely Energetic Neutrinos==
==A Topical Example: Speed of Extremely Energetic Neutrinos==
Here is another example of the use of this formula in physics calculations. In 2011 there were [http://www.theguardian.com/science/2011/sep/22/faster-than-light-particles-neutrinos?newsfeed=true reports] that high-energy neutrinos had been observed traveling at a speed faster than the speed of light in an experiment at the Gran Sasso laboratory in Italy. Specifically, they seemed to have arrived at the detector 60 nanoseconds faster than light would have. Relativity doesn't allow that, and, since neutrinos have nonzero (but incredibly tiny) mass, they aren't even supposed to travel ''at'' the speed of light.
Here is another example of the use of this formula in physics calculations. In 2011 there were [https://www.theguardian.com/science/2011/sep/22/faster-than-light-particles-neutrinos?newsfeed=true reports] that high-energy neutrinos had been observed traveling at a speed faster than the speed of light in an experiment at the Gran Sasso laboratory in Italy. Specifically, they seemed to have arrived at the detector 60 nanoseconds faster than light would have. Relativity doesn't allow that, and, since neutrinos have nonzero (but incredibly tiny) mass, they aren't even supposed to travel ''at'' the speed of light.
The mass of a neutrino is about 0.44x10<sup>−36</sup>kilograms. (Normally all of these things are measured in more convenient units such as Giga-electron-Volts, but that makes implicit use of E=mc<sup>2</sup>. If we don't accept that, we have to do the calculations under classical physics, using SI (meter/kilogram/second) units.) The neutrinos were accelerated to an energy of about 17GeV, or .27x10<sup>−8</sup>Joules. If one did not accept relativity and had to use classical physics and the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, one would get v=110x10<sup>12</sup> meters per second. This is about 370,000 times the speed of light, something that scientists would certainly have noticed. In fact, with special relativity, the speed is just under the speed of light, such that the neutrinos should be received at the detector about .26x10<sup>−24</sup> seconds (.26 yoctoseconds) later than the speed of light itself. This is far too small to measure—15 orders of magnitude smaller than the resolution of the GPS signals in the experiment.
The mass of a neutrino is about 0.44x10<sup>−36</sup>kilograms. (Normally all of these things are measured in more convenient units such as Giga-electron-Volts, but that makes implicit use of E=mc<sup>2</sup>. If we don't accept that, we have to do the calculations under classical physics, using SI (meter/kilogram/second) units.) The neutrinos were accelerated to an energy of about 17GeV, or .27x10<sup>−8</sup>Joules. If one did not accept relativity and had to use classical physics and the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, one would get v=110x10<sup>12</sup> meters per second. This is about 370,000 times the speed of light, something that scientists would certainly have noticed. In fact, with special relativity, the speed is just under the speed of light, such that the neutrinos should be received at the detector about .26x10<sup>−24</sup> seconds (.26 yoctoseconds) later than the speed of light itself. This is far too small to measure—15 orders of magnitude smaller than the resolution of the GPS signals in the experiment.