Changes

'''E=mc&sup2;''' asserts that the energy ('''E''') in an unmoving particle is equal to the square of the [[speed of light]] ('''c&sup2;''') times the [[mass]] ('''m''') of that particle.<ref>"Energy and mass are linked in the most famous relationship in physics: E = mc&sup2;. (The energy content of a body is equal to the mass of the body times the speed of light squared.)" [https://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|E&sup2;=(mc&sup2;)&sup2;+(pc)&sup2;]], 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=mc&sup2;'' 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=mc&sup2;''' asserts that the energy ('''E''') in an unmoving particle is equal to the square of the [[speed of light]] ('''c&sup2;''') times the [[mass]] ('''m''') of that particle.<ref>"Energy and mass are linked in the most famous relationship in physics: E = mc&sup2;. (The energy content of a body is equal to the mass of the body times the speed of light squared.)" [https://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|E&sup2;=(mc&sup2;)&sup2;+(pc)&sup2;]], 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=mc&sup2;'' from first principles have failed.<ref name="wvarticles">Five lectures at Wikiversity.  The 4th one purports to derive the formula, using the assumptions in the "What the Equation Means" section.

*[https://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]

*[https://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]

*[https://en.wikiversity.org/wiki/Special_relativity/momentum Lecture 2]

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 &quot;convert&quot; 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 &quot;convert&quot; 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]].

Physicists have never been able to unify light with matter,<ref>Quantum Electrodynamics describes how matter interacts with matter, and 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=mc&sup2; 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>

[[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=mc&sup2; 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=mc&sup2;''' has never yielded anything of value and it has often been used as a redefinition of &quot;[[energy]]&quot; 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>[https://www.pbs.org/wgbh/nova/physics/legacy-of-e-equals-mc2.html Peter Tyson ''The Legacy of E=mc&sup2;'']  October 11, 2005. PBS ''NOVA''.</ref>

The claim that '''E=mc&sup2;''' has never yielded anything of value and has often been used as a redefinition of &quot;[[energy]]&quot; 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>[https://www.pbs.org/wgbh/nova/physics/legacy-of-e-equals-mc2.html Peter Tyson ''The Legacy of E=mc&sup2;'']  October 11, 2005. PBS ''NOVA''.</ref>

The [[Theory of Relativity]] has never been able to mathematically derive '''E=mc&sup2;''' 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 E₀=mc&sup2;'', 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 [[Theory of Relativity]] has never been able to mathematically derive '''E=mc&sup2;''' 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 E₀=mc&sup2;'', 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 has acquired something of a "cult" status.  In the USA, the popular ''[[Twilight Zone]]'' series featured '''E=mc&sup2;''' 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.

The equation has acquired something of a "cult" status.  In the USA, the popular ''[[Twilight Zone]]'' series featured '''E=mc&sup2;''' 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&mdash;both serious scientists and science popularizers&mdash;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>[https://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc&sup2;''], Nov 10, 2005, NOVA</ref>

Many science writers&mdash;both serious scientists and science popularizers&mdash;have at various times written their own explanations 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>[https://www.pbs.org/wgbh/nova/physics/ancestors-einstein.html David Bodanis ''Ancestors of E=mc&sup2;''], Nov 10, 2005, NOVA</ref>

In 2005 The PBS NOVA series also asked 10 physicists to describe the equation in layman's terms.<ref>[https://www.pbs.org/wgbh/nova/einstein/experts.html Lexi Krock, David Levin (editors) ''E=mc&sup2; explained'', June, 2005. PBS ''NOVA'']</ref>  Here is a sample of five of the statements:

In 2005 The PBS NOVA series also asked 10 physicists to describe the equation in layman's terms.<ref>[https://www.pbs.org/wgbh/nova/einstein/experts.html Lexi Krock, David Levin (editors) ''E=mc&sup2; explained'', June, 2005. PBS ''NOVA'']</ref>  Here is a sample of five of the statements:

Kinetic energy is actual visible energy, that is, energy of things that are in motion.  It's the energy of a thrown baseball.  Radiation (for example, light) also counts as kinetic energy&mdash;it's the motion of photons.  Light carries energy, force, and momentum.  The force carried by light is not as obvious as the force of a thrown baseball, but it is there.  The force of sunlight has been proposed for long-term space travel.  It is also the force that causes the [[Pioneer anomaly]] and the force that makes a comet's tail stream away from the Sun.

Kinetic energy is actual visible energy, that is, energy of things that are in motion.  It's the energy of a thrown baseball.  Radiation (for example, light) also counts as kinetic energy&mdash;it's the motion of photons.  Light carries energy, force, and momentum.  The force carried by light is not as obvious as the force of a thrown baseball, but it is there.  The force of sunlight has been proposed for long-term space travel.  It is also the force that causes the [[Pioneer anomaly]] and the force that makes a comet's tail stream away from the Sun.

Potential energy is the other kind&mdash;"hidden" energy.  It can become kinetic energy, or vice-versa.  A wound up spring, a charged battery, a stretched rubber band, a mixture of gasoline and air, an explosive, and a radioactive atom, all have potential energy.  It's what is needed to make the principle of conservation of energy work.  That is, when kinetic energy comes into existence, it's because potential energy was converted into kinetic energy.  The wound-up spring of a clock has potential energy, that runs down over time, being converted into the kinetic energy of the ticking sound.  A battery has potential energy that runs down when it provides electricity to make things move.  Various chemical substances have characteristic amounts of potential energy, that may be converted to or from kinetic energy when chemical reactions occur.  For example, Sodium and Chlorine have more potential energy than Sodium Chloride.  Explosives have more potential energy than their constituent atoms.  Radioactive atoms have more potential energy than their "daughter" atoms.

Potential energy is the other kind&mdash;"hidden" energy.  It can become kinetic energy, or vice-versa.  A wound-up spring, a charged battery, a stretched rubber band, a mixture of gasoline and air, an explosive, and a radioactive atom, all have potential energy.  It's what is needed to make the principle of conservation of energy work.  That is, when kinetic energy comes into existence, it's because potential energy is converted into kinetic energy.  The wound-up spring of a clock has potential energy, that runs down over time, being converted into the kinetic energy of the ticking sound.  A battery has potential energy that runs down when it provides electricity to make things move.  Various chemical substances have characteristic amounts of potential energy, that may be converted to or from kinetic energy when chemical reactions occur.  For example, Sodium and Chlorine have more potential energy than Sodium Chloride.  Explosives have more potential energy than their constituent atoms.  Radioactive atoms have more potential energy than their "daughter" atoms.

The principle of ''conservation of energy'', universally accepted for well over 100 years, says

The principle of ''conservation of energy'', universally accepted for well over 100 years, says

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&mdash;its mass times c², and changes in potential 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.

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&mdash;its mass times c², and changes in potential 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.

With those preliminaries out of the way, it is possible to give a concise explanation of what the equation means:

With those preliminaries out of the way, it is possible to give a concise explanation of what the equation means:

Now that's way too small to measure for anything other than nuclear reactions, which is why it escaped everyone's notice for so long.  But it has been measured and experimentally verified for nuclear transformations all across the periodic table.

Now that's way too small to measure for anything other than nuclear reactions, which is why it escaped everyone's notice for so long.  But it has been measured and experimentally verified for nuclear transformations all across the periodic table.

:There's an interesting parallel with heat.  Before the rise of thermodynamics, it was believed that heat was a "substance".  That substance was called "caloric".  When heat travels from one body to another, what was really happening was presumed to be a transfer of caloric.  Much effort was put into measuring the mass of this mysterious "substance".  It was always found to be zero, and we now know that what is actually being transferred is thermal energy.  So it is not unheard-of to assign mass to intangible properties.

:There's an interesting parallel with heat.  Before the rise of thermodynamics, it was believed that heat was a "substance".  That substance was called "caloric".  When heat travels from one body to another, what was really happening was presumed to be a transfer of caloric.  Much effort was put into measuring the mass of this mysterious "substance".  It was always found to be zero, and we now know that what is actually being transferred is thermal energy.  So it is not unheard of to assign mass to intangible properties.

The nonzero mass of potential energy, and the equation E=mc², were determined on theoretical grounds, before any experimental observations were made.  The logic of this follows from these assumptions:

The nonzero mass of potential energy, and the equation E=mc², were determined on theoretical grounds before any experimental observations were made.  The logic of this follows from these assumptions:

#Galilean and Newtonian mechanics.

#Galilean and Newtonian mechanics.

Because the change in mass arising from a given release of energy is so small (<math>1/c^2</math>, which 1.11 x 10⁻¹⁷ kilograms per joule), it is essentially impossible to check this equation for normal processes.  For example, a flashlight battery loses about 1 picogram of mass when it discharges, and the resultant atoms from the detonation of 1 kilogram of TNT weigh 47 nanograms less than the TNT.  Even if all the particles of smoke and gas could be collected reliably, the difference couldn't be detected.

Because the change in mass arising from a given release of energy is so small (<math>1/c^2</math>, which 1.11 x 10⁻¹⁷ kilograms per joule), it is essentially impossible to check this equation for normal processes.  For example, a flashlight battery loses about 1 picogram of mass when it discharges, and the resultant atoms from the detonation of 1 kilogram of TNT weigh 47 nanograms less than the TNT.  Even if all the particles of smoke and gas could be collected reliably, the difference couldn't be detected.

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.

Measuring the effect requires processes 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.<ref name=einstein1905b/>

Einstein touched on this possibility in his original 1905 paper.<ref name=einstein1905b/>

::<math>{}_{86}^{222}\mathrm{Rn}\,\rightarrow\, {}_{84}^{218}\mathrm{Po}\, +\, {}_2^4\mathrm{He}</math>

::<math>{}_{86}^{222}\mathrm{Rn}\,\rightarrow\, {}_{84}^{218}\mathrm{Po}\, +\, {}_2^4\mathrm{He}</math>

Accurate ways of measuring speed of a charged particle, by deflecting it in a magnetic field, had been developed by then, so that, by very painstaking observation and measurement, it was determined that the first alpha particle (Helium nucleus) had an energy of 4.78 MeV and the second an energy of 5.49 Mev.  This confirmed E=mc² up to the accuracy of the measurements.  The equation, along with knowledge of isotope mixes, now explained why the atomic weights appearing in the periodic table were nearly integers, but not exactly so.

Accurate ways of measuring speed of a charged particle, by deflecting it in a magnetic field, had been developed by then, so that, by very painstaking observation and measurement, it was determined that the first alpha particle (Helium nucleus) had an energy of 4.78 MeV and the second an energy of 5.49 Mev.  This confirmed E=mc² up to the accuracy of the measurements.  The equation, along with knowledge of isotope mixes, now explains why the atomic weights appearing in the periodic table were nearly integers, but not exactly so.

Around 1925, the development of the mass spectrograph, by Francis Aston, made it possible to measure atomic weights to extreme precision.

Around 1925, the development of the mass spectrograph, by Francis Aston, made it possible to measure atomic weights to extreme precision.

==The Rainville test==

==The Rainville test==

Perhaps the most precise direct empirical verification of E=mc² was done in 2005 by Simon Rainville ''et. al.''<ref>[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> The article states that &quot;Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1−&Delta;mc²/E=(−1.4±4.4)×10⁻⁷, 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.&quot;

Some argue that perhaps the most precise direct empirical verification of E=mc² was done in 2005 by Simon Rainville ''et. al.''<ref>[http://www.nature.com/nature/journal/v438/n7071/full/4381096a.html Nature 438, 1096-1097 (22 December 2005)] doi:10.1038/4381096a; Published online December 21, 2005</ref> The article asserts that &quot;Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1−&Delta;mc²/E=(−1.4±4.4)×10⁻⁷, 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.&quot;

==The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]]==

==The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]]==

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 ''&quot;their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles.&quot;''<ref>[https://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 ''&quot;their pioneer work on the transmutation of atomic nuclei by artificially accelerated atomic particles.&quot;''<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.

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

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

:::::<math>{}_3^7\mathrm{Li}\, +\, {}_1^1\mathrm{H}\,\rightarrow\,2\, {}_2^4\mathrm{He}</math>

:::::<math>{}_3^7\mathrm{Li}\, +\, {}_1^1\mathrm{H}\,\rightarrow\,2\, {}_2^4\mathrm{He}</math>

The mass of the particles on the left hand side is 8.0263 [[atomic mass units|amu]], the mass on the right hand side ''only'' 8.0077 amu.<ref>Gerard Piel ''The age of science: what scientists learned in the 20th century'', Basic Books, 2001, p. 144-145</ref>  The difference between this masses is  .00186 amu, which results in the following back-of-an-envelope calculation:

The mass of the particles on the left-hand side is 8.0263 [[atomic mass units|amu]], the mass on the right-hand side ''only'' 8.0077 amu.<ref>Gerard Piel ''The age of science: what scientists learned in the 20th century'', Basic Books, 2001, p. 144-145</ref>  The difference between this masses is  .00186 amu, which results in the following back-of-an-envelope calculation:

::::<math>0.00186\,\mathrm{amu} \cdot c^2 = 0.0186 \cdot 1.66 \cdot 10^{-27}\,\mathrm{kg}\cdot\left(3\cdot10^8\,\mathrm{\frac{m}{s}}\right)^2</math>

::::<math>0.00186\,\mathrm{amu} \cdot c^2 = 0.0186 \cdot 1.66 \cdot 10^{-27}\,\mathrm{kg}\cdot\left(3\cdot10^8\,\mathrm{\frac{m}{s}}\right)^2</math>

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=mc&sup2;.  (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=mc&sup2; 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=mc&sup2;.  (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=mc&sup2; applies only to nuclear interactions.)

The [[Theory of Relativity]] played no role in this work, but proponents later tried to retrofit the theory to the data in order to explain the explain the observed mass changes.<ref>Actually, the formula E=mc² was published in 1905, and has not changed since then.  Fission of Uranium was discovered in 1938.  It is not possible that the equation was retrofitted to explain this discovery.</ref>  Here is the most famous example of the mass change.

The [[Theory of Relativity]] played no role in this work, but proponents later tried to retrofit the theory to the data in order to explain the observed mass changes.<ref>Actually, the formula E=mc² was published in 1905 and has not changed since.  Fission of Uranium was discovered in 1938.  It is not possible that the equation was retrofitted to explain this discovery.</ref>  Here is the most famous example of the mass change.

Nuclear fission, which is the basis for nuclear energy, was discovered in experiments by [[Otto Hahn]] and [[Fritz Strassman]], and analyzed by [[Lise Meitner]], in 1938.

Nuclear fission, which is the basis for nuclear energy, was discovered in experiments by [[Otto Hahn]] and [[Fritz Strassman]], and analyzed by [[Lise Meitner]], in 1938.

The mass of a neutrino is about 0.44x10⁻³⁶kilograms.  (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 .27x10⁻⁸Joules.  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=110x10¹² 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 .26x10⁻²⁴ seconds (.26 yoctoseconds) later than the speed of light itself.  This is far too small to measure&mdash;15 orders of magnitude smaller than the resolution of the GPS signals in the experiment.

The mass of a neutrino is about 0.44x10⁻³⁶kilograms.  (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 .27x10⁻⁸Joules.  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=110x10¹² 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 .26x10⁻²⁴ seconds (.26 yoctoseconds) later than the speed of light itself.  This is far too small to measure&mdash;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 [https://www.bbc.co.uk/news/science-environment-17364682 the neutrinos travelled at precisely light speed].  This was a simple misstatement, by .26 yoctoseconds.

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 [https://www.bbc.co.uk/news/science-environment-17364682 the neutrinos traveled 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>

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>

For example, the mass of a TNT molecule is 227.1311 Daltons, or 227.1311 g/mol, which is, for all practical purposes, the same as the mass of its constituent Carbon, Hydrogen, Nitrogen, and Oxygen atoms.  It is essentially impossible to measure the difference.  The principle of conservation of mass is upheld.

For example, the mass of a TNT molecule is 227.1311 Daltons, or 227.1311 g/mol, which is, for all practical purposes, the same as the mass of its constituent Carbon, Hydrogen, Nitrogen, and Oxygen atoms.  It is essentially impossible to measure the difference.  The principle of conservation of mass is upheld.

But when nuclear phenomena are discovered, we notice something different.  The masses of the result particles after an event (e.g. alpha decay, nuclear fission, or artificial transmutation) is measurably less than the masses of the original particle(s).  With the invention of the mass spectrometer around 1920, it became possible to measure atomic weights of various isotopes with great precision.

But when nuclear phenomena are discovered, we notice something different.  The masses of the resulting particles after an event (e.g. alpha decay, nuclear fission, or artificial transmutation) are measurably less than the masses of the original particle(s).  With the invention of the mass spectrometer around 1920, it became possible to measure atomic weights of various isotopes with great precision.

Radium-226 decays into Radon-222 by emission of an alpha particle with an energy of 4.78 MeV.

Radium-226 decays into Radon-222 by emission of an alpha particle with an energy of 4.78 MeV.

Each emitted alpha particle has energy of 4.78 MeV, or 4.78 * .1602 * 10⁻¹⁸ Joules.  The total alpha energy from the decay of 1&nbsp;kg of radium is 2.04 * 10¹² Joules.

Each emitted alpha particle has energy of 4.78 MeV, or 4.78 * .1602 * 10⁻¹⁸ Joules.  The total alpha energy from the decay of 1&nbsp;kg of radium is 2.04 * 10¹² Joules.

Also, Radon-222 decays into Polonium-218 by emission of an alpha particle with an energy of 5.49 MeV.

Also, Radon-222 decays into Polonium-218 by emission of an alpha particle with an energy of 5.49 MeV.

| .00002703&nbsp;kg

| .00002703&nbsp;kg

|}

|}

We plot these, and a few others, not shown, on graph paper, and find to our amazement that the relationship is linear.

We plot these, and a few others, not shown, on graph paper, and find to our amazement that the relationship is linear.

:::*'''In all interactions, there is a loss of mass, equal to <math>\frac{1}{c^2}</math> times the amount of energy released.'''

:::*'''In all interactions, there is a loss of mass, equal to <math>\frac{1}{c^2}</math> times the amount of energy released.'''

We don't have to give the units any more, since everything is now dimensionally correct.

We don't have to give the units anymore, since everything is now dimensionally correct.

::There is a very interesting analogy with the discovery of [[Maxwell's Equations]].  Maxwell found an interesting relationship involving the fundamental constants <math>\epsilon\,</math> and <math>\mu\,</math> appearing in his equations.  Specifically, <math>\epsilon\mu\,</math> has the dimensions of seconds squared divided by meters squared, and that:

::There is a very interesting analogy with the discovery of [[Maxwell's Equations]].  Maxwell found an interesting relationship involving the fundamental constants <math>\epsilon\,</math> and <math>\mu\,</math> appearing in his equations.  Specifically, <math>\epsilon\mu\,</math> has the dimensions of seconds squared divided by meters squared, and that: