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'''E=mc²''' asserts that the energy ('''E''') which makes up the [[matter]] in an unmoving object particle is equal to the square of the [[speed of light]] ('''c²''') times the [[mass]] ('''m''') of that bodyparticle.<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.)" [httphttps://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>httphttps://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.*[httphttps://en.wikiversity.org/wiki/Special_relativity/space,_time,_and_the_Lorentz_transform Lecture 1]*[httphttps://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]*[httphttps://en.wikiversity.org/wiki/Special_relativity/energy Lecture 3]*[httphttps://en.wikiversity.org/wiki/Special_relativity/E_%3D_mc%C2%B2 Lecture 4]*[httphttps://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>
Physicists have never been able to unify light with matter<ref>Quantum Electrodynamics describes how matter interacts with matter, the standard model of particle physics describes how matter (fermions) interact with bosons (force carriers) for the electromagnetic, strong and weak forces. To date, no theory has been proven to unify gravity with electromagnetism.</ref>despite more than a billion-dollars-worth of attempts, and it is likely impossible to ever do so.<ref>Much of 20th century physics has centered around the interactions between photons (light) and fermionic matter, and much more than a billion dollars has been spent on this. But that doesn't imply that they have been "unified".</ref> [[Biblical Scientific Foreknowledge]] predicts that there is no unified theory of light and matter because they were created at different times, in different ways, as described in the [[Book of Genesis]].
[[Mass]] is a measure of an object's inertia, in other words its resistance to acceleration. In contrast, the intrinsic [[energy]] of an object (such as an [[atom]]) is a function of electrostatic charge and other non-inertial forces, having nothing to do with gravity. Declaring the object's energy to be a function of inertia rather than electrostatics is an absurd and impossible attempt to unify the forces of nature, contrary to the accepted view (as predicted by [[Biblical Scientific Foreknowledge]]) that the forces of nature have not been unified. Liberal scientists assert the formula E=mc² is not limited to nuclear reactions; it applies to chemical reactions and even to the energy stored in a compressed spring.<ref>http://www.newton.dep.anl.gov/askasci/phy99/phy99140.htm</ref>
The claim that '''E=mc²''' has never yielded anything of value and it has often been used as a redefinition of "[[energy]]" for pseudo-scientific purposes by non-scientific journals. Claims can be found not only on liberal, second-tier college websites but at those of [[Baylor]] and the [[MIT]] that the equation is used in [[nuclear power]] generation and [[nuclear weapon]]s ([[nuclear fusion]] and [[nuclear fission]]) and about [[antimatter]].<ref>[http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/E=mcsquared/index.html John D. Norton ''Einstein for everyone - E=mc²''], Department of History and Philosophy of Science University of Pittsburgh</ref><ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html Rod Nave ''HpyerPhysics - Relativistic Energy''], Georgia State University</ref><ref>[httphttps://www.pbs.org/wgbh/nova/physics/legacy-of-e-equals-mc2.html Peter Tyson ''The Legacy of E=mc²''] October 11, 2005. PBS ''NOVA''.</ref>
The [[Theory of Relativity]] has never been able to mathematically derive '''E=mc²''' from first principles,<ref name="wvarticles"/> and a physicist observed in a peer-reviewed paper published in 2011 that "Leaving aside that it continues to be affirmed experimentally, a rigorous proof of the mass-energy equivalence is probably beyond the purview of the special theory."<ref>[http://adsabs.harvard.edu/abs/2011AmJPh..79..591H Eugene Hecht: ''How Einstein confirmed E<sub>0</sub>=mc²'', American Journal of Physics, Volume 79, Issue 6, pp. 591-600 (2011)]</ref> Nevertheless, Robert Dicke - one of the most accomplished American-born physicists and experimental physicists in history - found it unlikely that the equivalence was wrong.<ref>R. H. Dicke "The Theoretical Significance of Experimental Relativity", Gordon and Breach, 1964</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|
*"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). [httphttps://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>httphttps://www.imdb.com/title/tt0322120/?ref_=fn_tt_tt_2, httphttps://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>[httphttps://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc²''], Nov 10, 2005, NOVA</ref>
In 2005 The PBS NOVA series also asked 10 physicists to describe the equation in layman's terms.<ref>[httphttps://www.pbs.org/wgbh/nova/einstein/experts.html Lexi Krock, David Levin (editors) ''E=mc² explained'', June, 2005. PBS ''NOVA'']</ref> Here is a sample of five of the statements:
{{cquote|''It's something that doesn't happen in your kitchen or in everyday life.''|||[[Neil deGrasse Tyson]], Astrophysicist, American Museum of Natural History}}{{cquote|''When an object emits light, say, a flashlight, it gets lighter.''|||Sheldon Glashow, Theoretical Physicist and Nobel Laureate, Boston University}}{{cquote|''Things that seem incredibly different can really be manifestations of the same underlying phenomena.''|||Nima Arkani-Hamed, Theoretical Physicist, Harvard University}}{{cquote|''You can get access to parts of nature you have never been able to get access to before.''|||Lene Hau, Experimental Physicist, Harvard University}}{{
cquote|''It certainly is not an equation that reveals all its subtlety in the few symbols that it takes to write down.''|||Brian Greene Theoretical Physicist Columbia University}}
Hundreds of years of research by chemists (and, before that, the alchemists) worked out the potential energies that are characteristic of various substances, and that the potential and kinetic energies are accurately converted from one to the other, leading to the principle of conservation of total energy.
An interesting fact is that, normally, one considers only ''changes'' in potential energy; one doesn't need an absolute scale. A rock at the top of a hill has more potential energy than after it rolls to the bottom of the hill, but the energy at the bottom isn't necessarily zero. We could dig a hole and let it roll down farther, with its energy going negative. Only changes matter. Now it turns out that, once one accepts the implications of E=mc², one ''could'' assign an absolute potential energy to something—its mass times c², and changes in potential emergy energy would work out correctly because of the mass changes. But that isn't necessary, and, in any case, it would require accepting E=mc² and would therefore be getting ahead of the story.
The 1932 Cockcroft-Walton experiment, described in more detail below, 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">See [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 [Quantitative Analysis of a few parts per millionAlpha Decay]].
==Alleged Experimental verification--the Cockcroft-Walton experimentThe Rainville test==In 1932 English physicist John Cockcroft and Irish physicist Ernest Walton performed Perhaps the first artificial nuclear transmutation of nuclei, for which they were awarded the 1951 [[Nobel Prize]] in physics -- '''''but not for any most precise direct empirical verification of E=mc²mc<sup>2</sup> was done in 2005 by Simon Rainville ''et. al.'''.<ref>[http://www.nobelprizenature.orgcom/nobel_prizesnature/physicsjournal/laureatesv438/1951n7071/cockcroft-lecturefull/4381096a.pdf John D. Cockroft ''Experiments on the interaction of highhtml Nature 438, 1096-speed nucleons with atomic nuclei''1097 (22 December 2005)], Nobel Lecture, Dec 11, 1951doi:10.1038/4381096a; Published online 21 December 2005</ref> The award was for ''article states that "their pioneer work on the transmutation Einstein's relationship is separately confirmed in two tests, which yield a combined result of atomic nuclei by artificially accelerated atomic particles.1−"Delta;''<ref>[http:mc²//wwwE=(−1.nobelprize4±4.org/nobel_prizes/physics/laureates/1951/# Nobel Prize Organization]4)×10<sup>−7</refsup> , indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described."
==The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]]==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>[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. But analysis of 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 does in fact verify was consistent with the equation for the particular transmutation involved.
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==
==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 [httphttps://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.
Later [http://news.sciencemag.org/2012/02/official-word-superluminal-neutrinos-leaves-warp-drive-fans-shred-hope%E2%80%94barely?ref=hp reports] started to resolve the mystery, and it is now accepted that the neutrinos behaved properly. But a BBC reporter made the incorrect statement that [httphttps://www.bbc.co.uk/news/science-environment-17364682 the neutrinos travelled at precisely light speed]. This was a simple misstatement, by .26 yoctoseconds.
The issue was discussed at length at Conservapedia.<ref>http://www.conservapedia.com/Talk:Main_Page/Archive_index/102#Faster_than_light_neutrinos</ref><ref>http://www.conservapedia.com/Talk:Main_Page/Archive_index/102#The_final_nail_in_the_coffin_of_relativity.3F</ref><ref>http://www.conservapedia.com/Talk:Main_Page/Archive_index/102#Another_Blow_to_Relativity</ref><ref>http://www.conservapedia.com/Talk:Main_Page/Archive_index/109#Neutrinos_now_obey_speed_limit</ref><ref>http://www.conservapedia.com/Talk:Main_Page/Archive_index/111#Neutrinos</ref>
*[[Logical Flaws in E=mc²]]
*[[Essay:Rebuttal to Logical Flaws in E=mc²]]
*[[Quantitative Analysis of Alpha Decay]]
*[[E^2=(mc^2)^2+(pc)^2]]
<references />
[[Category:Relativity]]
[[Category:Laws of Physics]]
[[Category:Physics]]
