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''E=mc²''
Energy refers to kinetic energy of motion, or radiated energy.
Energy refers to kinetic energy of motion, or radiated energy.
*E=mc² is not about gravity or gravitational mass.
*''E=mc²'' is not about gravity or gravitational mass.
*E=mc² is not about light, or other electromagnetic radiation, except insofar as it is a form of energy.
*''E=mc²'' is not about light, or other electromagnetic radiation, except insofar as it is a form of energy.
*E=mc² is not about nuclear power ''per se''. It applies everywhere.
*''E=mc²'' is not about nuclear power ''per se''. It applies everywhere.
*E=mc² is not about where the power of the atomic bomb comes from, though the physicists developing atomic power and atomic bombs were completely familiar with it.
*''E=mc²'' is not about where the power of the atomic bomb comes from, though the physicists developing atomic power and atomic bombs were completely familiar with it.
A little calculation will show that E=mc² is dimensionally correct. So, for example, in [[SI]] units (also called MKS units), E is in [[Joule]]s, m in [[kilogram]]s, and c in [[meter]]s per second. In [[CGS]] units or units of the [[US Customary System of Units|US Customary System]] ([[pound]]s and [[foot|feet]]) it is also dimensionally correct, as long as the units are used consistently. Physicists, when they are really into theory, sometimes like to use "natural units", which are calibrated so that ''c'' is dimensionless and has the value 1. <!-- We won't do that.-->
A little calculation will show that ''E=mc²'' is dimensionally correct. So, for example, in [[SI]] units (also called MKS units), E is in [[Joule]]s, m in [[kilogram]]s, and c in [[meter]]s per second. In [[CGS]] units or units of the [[US Customary System of Units|US Customary System]] ([[pound]]s and [[foot|feet]]) it is also dimensionally correct, as long as the units are used consistently. Physicists, when they are really into theory, sometimes like to use "natural units", which are calibrated so that ''c'' is dimensionless and has the value 1. <!-- We won't do that.-->
In any normal units, the value of c, the speed of light, is enormous, its square even more so. This means that E=mc² equates an extremely tiny amount of mass with an extremely large amount of energy. This gives the equation some of its mystique. <!--We will attempt to dispel that mystique, and explain just what the equation means.-->
In any normal units, the value of c, the speed of light, is enormous, its square even more so. This means that ''E=mc²'' equates an extremely tiny amount of mass with an extremely large amount of energy. This gives the equation some of its mystique. <!--We will attempt to dispel that mystique, and explain just what the equation means.-->
E=mc² is a meaningless though working, almost nonsensical though often applied, e.g., in nuclear physics, statement that purports to relate all matter to energy and light.<ref>The equation claims that the total energy ''E'' of a body in all forms is equal to that body's mass ''m'' multiplied by the square of the speed of light ''c''. </ref> In fact, no theory has successfully unified the laws governing mass (''i.e.'', gravity) with the laws governing light (''i.e.'', electromagnetism). Simply put, E=mc² is [[liberal]] claptrap.
''E=mc²'' is a meaningless though working, almost nonsensical though often applied, e.g., in nuclear physics, statement that purports to relate all matter to energy and light.<ref>The equation claims that the total energy ''E'' of a body in all forms is equal to that body's mass ''m'' multiplied by the square of the speed of light ''c''. </ref> In fact, no theory has successfully unified the laws governing mass (''i.e.'', gravity) with the laws governing light (''i.e.'', electromagnetism). Simply put, ''E=mc²'' is [[liberal]] claptrap.
[[Biblical Scientific Foreknowledge]] predicts that a unified theory of all the laws of physics is impossible, because light and matter were created at different times, in different ways, as described in the [[Book of Genesis]].
[[Biblical Scientific Foreknowledge]] predicts that a unified theory of all the laws of physics is impossible, because light and matter were created at different times, in different ways, as described in the [[Book of Genesis]].
[[Mass]] is a measure of an object's inertia, and is directly related to the force of [[gravity]]. 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 [[Biblical Scientific Foreknowledge]].
[[Mass]] is a measure of an object's inertia, and is directly related to the force of [[gravity]]. 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 [[Biblical Scientific Foreknowledge]].
For more than a century, the claim that '''E=mc²''' has never yielded anything of value. Often it seems to be used as a redefinition of "[[energy]]" for pseudo-scientific purposes, as by the [[lamestream media]]. There have been attempts to find some justification for the equation in already understood processes involved in [[nuclear power]] generation and [[nuclear weapon]]s, and in the speculation about [[antimatter]].<ref>[http://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 energy released in matter/antimatter annihilations corresponds to E=mc<sup>2</sup>; for example the annihilation of an electron and a positron (each with rest energy of 0.511 mega electron volts according to E=mc<sup>2</sup>) results in the release of two [[gamma ray]] [[photon]]s, which each have energy 0.511 mega electron volts.<ref>[http://www.lbl.gov/abc/Antimatter.html Lawrence Berkeley National Laboratory] ''The ABC of Nuclear Science''</ref>
For more than a century, the claim that ''E=mc²'' has never yielded anything of value. Often it seems to be used as a redefinition of "[[energy]]" for pseudo-scientific purposes, as by the [[lamestream media]]. There have been attempts to find some justification for the equation in already understood processes involved in [[nuclear power]] generation and [[nuclear weapon]]s, and in the speculation about [[antimatter]].<ref>[http://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 energy released in matter/antimatter annihilations corresponds to E=mc<sup>2</sup>; for example the annihilation of an electron and a positron (each with rest energy of 0.511 mega electron volts according to E=mc<sup>2</sup>) results in the release of two [[gamma ray]] [[photon]]s, which each have energy 0.511 mega electron volts.<ref>[http://www.lbl.gov/abc/Antimatter.html Lawrence Berkeley National Laboratory] ''The ABC of Nuclear Science''</ref>
The [[Theory of Relativity]] has never been able to mathematically derive '''E=mc²''' from first principles, 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>
The [[Theory of Relativity]] has never been able to mathematically derive ''E=mc²'' from first principles, 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>
It has been known for a long time that radiation has a mass equivalence, which was correctly derived by [[Henri Poincare]] in 1904,<ref>[http://www.opticsinfobase.org/josa/abstract.cfm?uri=josa-42-8-540 Herbert E. Ives ''Derivation of the Mass-Energy Relation''], JOSA, Vol. 42, Issue 8, pp. 540-543 (1952)</ref> but the equation '''E=mc²''' makes a claim far beyond that limited circumstance:
It has been known for a long time that radiation has a mass equivalence, which was correctly derived by [[Henri Poincare]] in 1904,<ref>[http://www.opticsinfobase.org/josa/abstract.cfm?uri=josa-42-8-540 Herbert E. Ives ''Derivation of the Mass-Energy Relation''], JOSA, Vol. 42, Issue 8, pp. 540-543 (1952)</ref> but the equation ''E=mc²'' makes a claim far beyond that limited circumstance:
{{cquote|The equality of the mass equivalent of radiation to the mass lost by a radiating body is derivable from Poincaré’s momentum of radiation (1900) and his principle of relativity (1904).|||Herbert Ives, 1952}}
{{cquote|The equality of the mass equivalent of radiation to the mass lost by a radiating body is derivable from Poincaré’s momentum of radiation (1900) and his principle of relativity (1904).|||Herbert Ives, 1952}}
== Description for the layman ==
== Description for the layman ==
Ten top physicists were asked to describe in laymen's terms '''E=mc²''':<ref>[http://www.pbs.org/wgbh/nova/einstein/experts.html Lexi Krock, David Levin (editors) ''E=mc² explained''], June, 2005. PBS ''NOVA''. </ref>{{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}}{{
Ten top physicists were asked to describe in laymen's terms ''E=mc²'':<ref>[http://www.pbs.org/wgbh/nova/einstein/experts.html Lexi Krock, David Levin (editors) ''E=mc² explained''], June, 2005. PBS ''NOVA''. </ref>{{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}}
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}}
== History of '''E=mc²''' ==
== History of ''E=mc²'' ==
The [[liberal]] [[Public Broadcasting Service]] explained the history of ''E=mc²'' for its NOVA series as follows:<ref>[http://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc²''], NOVA, Nov 10, 2005</ref>
The [[liberal]] [[Public Broadcasting Service]] explained the history of '''E=mc²''' for its NOVA series as follows:<ref>[http://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc²''], NOVA, Nov 10, 2005</ref>
{{cquote|Over time, [[physicist]]s became used to multiplying an object's mass by the square of its [[velocity]] (mv²) to come up with a useful indicator of its energy. If the velocity of a ball or rock was 100 mph, then they knew that the energy it carried would be proportional to its mass times 100 squared. If the velocity is raised as high as it could go, to 670 million mph, it's almost as if the ultimate energy an object will contain should be revealed when you look at its mass times c squared, or its mc².}}
{{cquote|Over time, [[physicist]]s became used to multiplying an object's mass by the square of its [[velocity]] (mv²) to come up with a useful indicator of its energy. If the velocity of a ball or rock was 100 mph, then they knew that the energy it carried would be proportional to its mass times 100 squared. If the velocity is raised as high as it could go, to 670 million mph, it's almost as if the ultimate energy an object will contain should be revealed when you look at its mass times c squared, or its mc².}}
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:
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:
Probably the best empirical verification of '''E=mc<sup>2</sup>''' was done in 2005 by Simon Rainville et al., as published in ''Nature''<ref>[http://www.nature.com/nature/journal/v438/n7071/full/4381096a.html Simon Rainville, James K. Thompson, et. al ''World Year of Physics: A direct test of E=mc²''] Nature 438, 1096-1097 (22 December 2005)] doi:10.1038/4381096a; Published online 21 December 2005</ref>, as the authors write in their abstract:
Probably the best empirical verification of ''E=mc²'' was done in 2005 by Simon Rainville et al., as published in ''Nature''<ref>[http://www.nature.com/nature/journal/v438/n7071/full/4381096a.html Simon Rainville, James K. Thompson, et. al ''World Year of Physics: A direct test of E=mc²''] Nature 438, 1096-1097 (22 December 2005)] doi:10.1038/4381096a; Published online 21 December 2005</ref>, as the authors write in their abstract:
{{cquote|Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1−Δmc²/E=(−1.4±4.4)×10<sup>−7</sup>, 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.}}
{{cquote|Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1−Δmc²/E=(−1.4±4.4)×10<sup>−7</sup>, 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.}}
==A Famous Example -- Nuclear Fission of Uranium==
==A Famous Example -- Nuclear Fission of Uranium==
For most types of physical interactions, the masses of the initial reactants and of the final products match so closely that it is essentially impossible to measure any difference. But for nuclear reactions, the difference is measurable. That difference is related to the energy absorbed or released, described by the equation E=mc². (The equation applies to '''all''' interactions; the fact that nuclear interactions are the only ones for which the mass difference is measurable has led people to believe, wrongly, that E=mc² applies only to nuclear interactions.)
For most types of physical interactions, the masses of the initial reactants and of the final products match so closely that it is essentially impossible to measure any difference. But for nuclear reactions, the difference is measurable. That difference is related to the energy absorbed or released, described by the equation ''E=mc²''. (The equation applies to '''all''' interactions; the fact that nuclear interactions are the only ones for which the mass difference is measurable has led people to believe, wrongly, that ''E=mc²'' applies only to nuclear interactions.)
The [[Theory of Relativity]] played no role in this work, but later tried to retrofit the theory to the data in order to explain the explain the observed mass changes. Here is the most famous example of the mass change.
The [[Theory of Relativity]] played no role in this work, but later tried to retrofit the theory to the data in order to explain the explain the observed mass changes. Here is the most famous example of the mass change.
|}
|}
The mass of the Uranium atom is 235.04393, and the sum of the masses of the products is 234.866503. The difference is .177427 amu, or, using the E=mc² equation, 165 million electron volts. (The generally accepted value for the total energy released by Uranium fission, including secondary decays, is about 200 million electron volts.)
The mass of the Uranium atom is 235.04393, and the sum of the masses of the products is 234.866503. The difference is .177427 amu, or, using the ''E=mc²'' equation, 165 million electron volts. (The generally accepted value for the total energy released by Uranium fission, including secondary decays, is about 200 million electron volts.)
The insight that the conversion from Uranium to Barium was caused by complete fission of the atom was made by Lise Meitner in December, 1938. She had the approximate "mass defect" quantities memorized, and so she worked out in her head, using the E=mc² equation, that there would be this enormous release of energy. This release was observed shortly thereafter, and the result is nuclear power and nuclear weapons.
The insight that the conversion from Uranium to Barium was caused by complete fission of the atom was made by Lise Meitner in December, 1938. She had the approximate "mass defect" quantities memorized, and so she worked out in her head, using the ''E=mc²'' equation, that there would be this enormous release of energy. This release was observed shortly thereafter, and the result is nuclear power and nuclear weapons.
==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. Recently there has been quite a controversy over whether neutrinos were observed traveling at a speed faster than light. 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. This very issue came up on the [[Talk:Main_Page#Neutrinos]]. The speeds under discussion were calculated by the use of E=mc<sup>2</sup>.
Here is another example of the use of this formula in physics calculations. Recently there has been quite a controversy over whether neutrinos were observed traveling at a speed faster than light. 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. This very issue came up on the [[Talk:Main_Page#Neutrinos]]. The speeds under discussion were calculated by the use of ''E=mc²''.
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. Using the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, we get v=110x10<sup>12</sup>meters per second. This is about 370,000 times 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=mc²''. 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. Using the classical formula <math>\mathrm{E} = \frac{1}{2}mv^2</math>, we get v=110x10<sup>12</sup>meters per second. This is about 370,000 times the speed of light.
However, the classical formula breaks down at speeds close to <math>c</math>, and indeed, as the speed of a massive object approaches <math>c</math>, the object's kinetic energy approaches <math>+\infty</math>.
However, the classical formula breaks down at speeds close to <math>c</math>, and indeed, as the speed of a massive object approaches <math>c</math>, the object's kinetic energy approaches <math>+\infty</math>.
Several scientists have gone on record stating that the neutrinos, which have mass, travel at precisely the speed of light. If true, this disproves the [[Theory of Relativity]] and the claim that '''E=mc<sup>2</sup>'''. However, it is more likely that those scientists are using language inaccurately. It is impossible to measure the speed of neutrinos precisely. What is meant is the difference between the speed of light and the speed of the neutrinos is too small to measure.
Several scientists have gone on record stating that the neutrinos, which have mass, travel at precisely the speed of light. If true, this disproves the [[Theory of Relativity]] and the claim that ''E=mc²''. However, it is more likely that those scientists are using language inaccurately. It is impossible to measure the speed of neutrinos precisely. What is meant is the difference between the speed of light and the speed of the neutrinos is too small to measure.
==Deducing the Equation From Empirical Observation==
==Deducing the Equation From Empirical Observation==
::*'''In nuclear interactions, there is a small but measurable loss of mass.'''
::*'''In nuclear interactions, there is a small but measurable loss of mass.'''
:By the way, we can clearly see that atomic weights of pure isotopes are not integers, and that it has something to do with the energy released by nuclear disintegration. In retrospect, the formula E=mc² explains the non-integer character of atomic weights.
:By the way, we can clearly see that atomic weights of pure isotopes are not integers, and that it has something to do with the energy released by nuclear disintegration. In retrospect, the formula ''E=mc²'' explains the non-integer character of atomic weights.
Making special cases out of nuclear interaction versus non-nuclear ones is unsatisfactory, of course.
Making special cases out of nuclear interaction versus non-nuclear ones is unsatisfactory, of course.
This sort of inductive approach is a common way that scientific discoveries are made. For example, Newton's law of motion, F=ma, is empirical and backed up by enormous amounts of confirming data.
This sort of inductive approach is a common way that scientific discoveries are made. For example, Newton's law of motion, F=ma, is empirical and backed up by enormous amounts of confirming data.
The formula E=mc² '''could have''' been discovered this way in our alternative universe, but, as stated above, that is not historically how it happened. It was formulated on theoretical grounds in order to obtain conservation of momentum in relativistic interactions, and then confirmed by experiment.
The formula ''E=mc²'' '''could have''' been discovered this way in our alternative universe, but, as stated above, that is not historically how it happened. It was formulated on theoretical grounds in order to obtain conservation of momentum in relativistic interactions, and then confirmed by experiment.
==See also==
==See also==