Editing Conservation of energy (section)

==History==
{{further|History of energy}}
{{More citations needed section|date=November 2015}}
[[Ancient philosophy|Ancient philosophers]] as far back as [[Thales of Miletus]] {{circa}}&nbsp;550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy" (for example, Thales thought it was water). [[Empedocles]] (490–430 BCE) wrote that in his universal system, composed of [[Classical element|four roots]] (earth, air, water, fire), "nothing comes to be or perishes";<ref>{{cite journal|last=Janko|first=Richard|title=Empedocles, "On Nature"|journal=Zeitschrift für Papyrologie und Epigraphik|year=2004 |volume=150 |pages=1–26|url=http://ancphil.lsa.umich.edu/-/downloads/faculty/janko/empedocles-nature.pdf }}</ref> instead, these elements suffer continual rearrangement. [[Epicurus]] ({{circa}} 350 BCE) on the other hand believed everything in the universe to be composed of indivisible units of matter—the ancient precursor to 'atoms'—and he too had some idea of the necessity of conservation, stating that "the sum total of things was always such as it is now, and such it will ever remain."<ref>{{cite book|last=Laertius|first=Diogenes|title=Lives of Eminent Philosophers: Epicurus|url=https://www-loebclassics.com/view/diogenes_laertius-lives_eminent_philosophers_book_x_epicurus/1925/pb_LCL185.569.xml?result=1&rskey=YoU4V6}}{{Dead link|date=March 2021 |bot=InternetArchiveBot |fix-attempted=yes }}. This passage comes from a letter quoted in full by Diogenes, and purportedly written by Epicurus himself in which he lays out the tenets of his philosophy.</ref>

In 1605, the Flemish scientist [[Simon Stevin]] was able to solve a number of problems in statics based on the principle that [[perpetual motion]] was impossible.

In 1639, [[Galileo Galilei|Galileo]] published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height to which a moving body ascends on a frictionless surface does not depend on the shape of the surface.

In 1669, [[Christiaan Huygens]] published a brief account on his laws of collision. Among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their [[linear momentum|linear momenta]] as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental.<ref>{{Cite journal |last=Erlichson |first=Herman |date=1997-02-01 |title=The young Huygens solves the problem of elastic collisions |url=https://pubs.aip.org/aapt/ajp/article-abstract/65/2/149/1054978/The-young-Huygens-solves-the-problem-of-elastic?redirectedFrom=fulltext |journal=American Journal of Physics |volume=65 |issue=2 |pages=149–154 |doi=10.1119/1.18659 |bibcode=1997AmJPh..65..149E |issn=0002-9505}}</ref> In his ''[[Horologium Oscillatorium]]'', Huygens gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of perpetual motion. His study of the dynamics of pendulum motion was based on a single principle, known as [[Evangelista Torricelli|Torricelli's Principle]]: that the [[Center of mass|center of gravity]] of a heavy object, or collection of objects, cannot lift itself. Using this principle, Huygens was able to derive the formula for the [[Center of percussion|center of oscillation]] by an "energy" method, without dealing with forces or torques.<ref>{{Cite journal |last=Erlichson |first=Herman |date=1996-05-01 |title=Christiaan Huygens' discovery of the center of oscillation formula |url=https://pubs.aip.org/aapt/ajp/article-abstract/64/5/571/1045484/Christiaan-Huygens-discovery-of-the-center-of?redirectedFrom=fulltext |journal=American Journal of Physics |volume=64 |issue=5 |pages=571–574 |doi=10.1119/1.18156 |bibcode=1996AmJPh..64..571E |issn=0002-9505}}</ref>

[[File:Gottfried Wilhelm Leibniz.jpg|thumb|150px|[[Gottfried Leibniz]]]]
Between 1676 and 1689, [[Gottfried Leibniz]] first attempted a mathematical formulation of the kind of energy that is associated with ''motion'' (kinetic energy). Using Huygens's work on collision, Leibniz noticed that in many mechanical systems (of several [[mass]]es ''m<sub>i</sub>'', each with [[velocity]] ''v<sub>i</sub>''),
:<math>\sum_{i} m_i v_i^2</math>

was conserved so long as the masses did not interact. He called this quantity the ''[[vis viva]]'' or ''living force'' of the system. The principle represents an accurate statement of the approximate conservation of [[kinetic energy]] in situations where there is no friction. Many [[physicist]]s at that time, including [[Isaac Newton]], held that the [[conservation of momentum]], which holds even in systems with friction, as defined by the [[momentum]]:

:<math>\sum_{i} m_i v_i</math>

was the conserved ''vis viva''. It was later shown that both quantities are conserved simultaneously given the proper conditions, such as in an [[elastic collision]].

In 1687, [[Isaac Newton]] published his ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]'', which set out his [[Newton's laws of motion|laws of motion]]. It was organized around the concept of force and momentum. However, the researchers were quick to recognize that the principles set out in the book, while fine for point masses, were not sufficient to tackle the motions of rigid and fluid bodies. Some other principles were also required.

By the 1690s, Leibniz was arguing that conservation of ''vis viva'' and conservation of momentum undermined the then-popular philosophical doctrine of [[interactionist dualism]]. (During the 19th century, when conservation of energy was better understood, Leibniz's basic argument would gain widespread acceptance. Some modern scholars continue to champion specifically conservation-based attacks on dualism, while others subsume the argument into a more general argument about [[causal closure]].)<ref>{{cite journal |last1=Pitts |first1=J. Brian |title=Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter |journal=Foundations of Science |date=September 2021 |volume=26 |issue=3 |pages=559–584 |doi=10.1007/s10699-020-09657-1|pmid=34759713 |pmc=8570307 }}</ref>

[[File:Daniel Bernoulli 001.jpg|thumb|left|150px|[[Daniel Bernoulli]]]]

The law of conservation of vis viva was championed by the father and son duo, [[Johann Bernoulli|Johann]] and [[Daniel Bernoulli]]. The former enunciated the principle of [[virtual work]] as used in statics in its full generality in 1715, while the latter based his ''[[Hydrodynamica]]'', published in 1738, on this single vis viva conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the [[Bernoulli's principle]], which asserts the loss to be proportional to the change in hydrodynamic pressure. Daniel also formulated the notion of [[Work (physics)|work]] and efficiency for [[hydraulic]] machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas.

This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the [[D'Alembert's principle]], [[Lagrangian mechanics|Lagrangian]], and [[Hamiltonian mechanics|Hamiltonian]] formulations of mechanics.
 
[[File:Emilie Chatelet portrait by Latour.jpg|thumb|right|150px|[[Emilie du Chatelet]]]]

[[Émilie du Châtelet]] (1706–1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by [[Willem 's Gravesande]] in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy—as indicated by the quantity of material displaced—was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height from which the balls were dropped, equal to the initial potential energy. Some earlier workers, including Newton and Voltaire, had believed that "energy" was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped. In classical physics, the correct formula is <math>E_k = \frac12 mv^2</math>, where <math>E_k</math> is the kinetic energy of an object, <math>m</math> its mass and <math>v</math> its [[speed]]. On this basis, du Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to consider it in different forms (kinetic, potential, heat, ...).<ref name=Hagengruber>Hagengruber, Ruth, editor (2011) ''Émilie du Chatelet between Leibniz and Newton''. Springer. {{ISBN|978-94-007-2074-9}}.</ref><ref name=Arianrhod>{{cite book|last1=Arianrhod|first1=Robyn|title=Seduced by logic : Émilie du Châtelet, Mary Somerville, and the Newtonian revolution|date=2012|publisher=Oxford University Press|location=New York|isbn=978-0-19-993161-3|edition=US|url=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9444991}}</ref>

[[Engineer]]s such as [[John Smeaton]], [[Peter Ewart]], {{interlanguage link|Carl Holtzmann|de||ar|كارل هولتزمان}}, [[Gustave-Adolphe Hirn]], and [[Marc Seguin]] recognized that conservation of momentum alone was not adequate for practical calculation and made use of Leibniz's principle. The principle was also championed by some [[chemist]]s such as [[William Hyde Wollaston]]. Academics such as [[John Playfair]] were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the [[second law of thermodynamics]], but in the 18th and 19th centuries, the fate of the lost energy was still unknown.

Gradually it came to be suspected that the heat inevitably generated by motion under friction was another form of ''vis viva''. In 1783, [[Antoine Lavoisier]] and [[Pierre-Simon Laplace]] reviewed the two competing theories of ''vis viva'' and [[caloric theory]].<ref>Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat", ''Académie Royale des Sciences'' pp.&nbsp;4–355</ref><ref>{{cite journal |last1=Guerlac |first1=Henry |title=Chemistry as a Branch of Physics: Laplace's Collaboration with Lavoisier |journal=Historical Studies in the Physical Sciences |date=1976 |volume=7 |pages=193–276 |doi=10.2307/27757357 |url=https://online.ucpress.edu/hsns/article-abstract/doi/10.2307/27757357/47949/Chemistry-as-a-Branch-of-Physics-Laplace-s?redirectedFrom=fulltext |access-date=24 March 2022 |publisher=University of California Press|jstor=27757357 }}</ref> [[Benjamin Thompson|Count Rumford]]'s 1798 observations of heat generation during the [[Boring (manufacturing)|boring]] of [[cannon]]s added more weight to the view that mechanical motion could be converted into heat and (that it was important) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). ''Vis viva'' then started to be known as ''energy'', after the term was first used in that sense by [[Thomas Young (scientist)|Thomas Young]] in 1807.

[[File:Gaspard-Gustave de Coriolis.jpg|thumb|150px|[[Gaspard-Gustave Coriolis]]]]

The recalibration of ''vis viva'' to

:<math>\frac {1} {2}\sum_{i} m_i v_i^2</math>

which can be understood as converting kinetic energy to [[Work (thermodynamics)|work]], was largely the result of [[Gaspard-Gustave Coriolis]] and [[Jean-Victor Poncelet]] over the period 1819–1839. The former called the quantity ''quantité de travail'' (quantity of work) and the latter, ''travail mécanique'' (mechanical work), and both championed its use in engineering calculations.

In the paper ''Über die Natur der Wärme'' (German "On the Nature of Heat/Warmth"), published in the {{Lang|de|[[Zeitschrift für Physik]]}} in 1837, [[Karl Friedrich Mohr]] gave one of the earliest general statements of the doctrine of the conservation of energy: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called ''Kraft'' [energy or work]. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others."

===Mechanical equivalent of heat===
A key stage in the development of the modern conservation principle was the demonstration of the ''[[mechanical equivalent of heat]]''. The [[caloric theory]] maintained that heat could neither be created nor destroyed, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.

In the middle of the eighteenth century, [[Mikhail Lomonosov]], a Russian scientist, postulated his corpusculo-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid.

In 1798, Count Rumford ([[Benjamin Thompson]]) performed measurements of the frictional heat generated in boring cannons and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt.

[[File:SS-joule.jpg|thumb|left|130px|[[James Prescott Joule]]]]

The mechanical [[equivalence principle]] was first stated in its modern form by the German surgeon [[Julius Robert von Mayer]] in 1842.<ref>von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in ''Annalen der Chemie und Pharmacie'', '''43''', 233</ref> Mayer reached his conclusion on a voyage to the [[Dutch East Indies]], where he found that his patients' blood was a deeper red because they were consuming less [[oxygen]], and therefore less energy, to maintain their body temperature in the hotter climate. He discovered that [[heat]] and [[mechanical work]] were both forms of energy, and in 1845, after improving his knowledge of physics, he published a monograph that stated a quantitative relationship between them.<ref>Mayer, J.R. (1845). ''Die organische Bewegung in ihrem Zusammenhange mit dem Stoffwechsel. Ein Beitrag zur Naturkunde'', Dechsler, Heilbronn.</ref>

[[File:Joule's Apparatus (Harper's Scan).png|thumb|right|[[James Prescott Joule|Joule]]'s apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.]]

Meanwhile, in 1843, [[James Prescott Joule]] independently discovered the mechanical equivalent in a series of experiments. In one of them, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate.  He showed that the [[gravitational energy|gravitational potential energy]] lost by the weight in descending was equal to the [[internal energy]] gained by the water through [[friction]] with the paddle.

Over the period 1840–1843, similar work was carried out by engineer [[Ludwig A. Colding]], although it was little known outside his native Denmark.

Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition.

{{For|the dispute between Joule and Mayer over priority|Mechanical equivalent of heat: Priority}}

In 1844, the Welsh scientist [[William Robert Grove]] postulated a relationship between mechanics, heat, [[light]], [[electricity]], and [[magnetism]] by treating them all as manifestations of a single "force" (''energy'' in modern terms). In 1846, Grove published his theories in his book ''The Correlation of Physical Forces''.<ref>{{cite book | author=Grove, W. R. | title=The Correlation of Physical Forces | url=https://archive.org/details/correlationphys06grovgoog | location=London | publisher=Longmans, Green | year=1874 | edition=6th }}</ref> In 1847, drawing on the earlier work of Joule, [[Nicolas Léonard Sadi Carnot|Sadi Carnot]], and [[Émile Clapeyron]], [[Hermann von Helmholtz]] arrived at conclusions similar to Grove's and published his theories in his book ''Über die Erhaltung der Kraft'' (''On the Conservation of Force'', 1847).<ref>{{cite web|title= On the Conservation of Force|url=http://www.bartleby.com/30/125.html|publisher=Bartleby|access-date= 6 April 2014}}</ref> The general modern acceptance of the principle stems from this publication.

In 1850, the Scottish mathematician [[William Rankine]] first used the phrase ''the law of the conservation of energy'' for the principle.<ref>William John Macquorn Rankine (1853) "On the General Law of the Transformation of Energy," ''Proceedings of the Philosophical Society of Glasgow'', vol. 3, no. 5, pages 276-280; reprinted in: (1) ''Philosophical Magazine'', series 4, vol. 5, no. 30, [https://books.google.com/books?id=3Ov22-gFMnEC&pg=PA106 pages 106-117] (February 1853); and (2) W. J. Millar, ed., ''Miscellaneous Scientific Papers: by W. J. Macquorn Rankine'', ... (London, England: Charles Griffin and Co., 1881), part II, [https://archive.org/stream/miscellaneoussci00rank#page/203/mode/1up pages 203-208]: "The law of the ''Conservation of Energy'' is already known—viz. that the sum of all the energies of the universe, actual and potential, is unchangeable."</ref>

In 1877, [[Peter Guthrie Tait]] claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the ''[[Philosophiae Naturalis Principia Mathematica]]''. This is now regarded as an example of [[Whig history]].<ref>{{cite book
|title=On the shoulders of merchants: exchange and the mathematical conception of nature in early modern Europe
|first1=Richard W. |last1=Hadden |publisher=SUNY Press
|year=1994 |isbn=978-0-7914-2011-9 |page=13
|url=https://books.google.com/books?id=7IxtC4Jw1YoC}}, [https://books.google.com/books?id=7IxtC4Jw1YoC&pg=PA13 Chapter&nbsp;1, p.&nbsp;13]
</ref>

===Mass–energy equivalence===
{{Main|Mass–energy equivalence}}
{{More citations needed section|date=November 2015}}
Matter is composed of atoms and what makes up atoms. Matter has [[rest mass|''intrinsic'' or ''rest'' mass]]. In the limited range of recognized experience of the nineteenth century, it was found that such rest mass is conserved. Einstein's 1905 theory of [[special relativity]] showed that rest mass corresponds to an equivalent amount of ''rest energy''. This means that ''rest mass'' can be converted to or from equivalent amounts of (non-material) forms of energy, for example, kinetic energy, potential energy, and electromagnetic [[radiant energy]]. When this happens, as recognized in twentieth-century experience, rest mass is not conserved, unlike the [[mass in special relativity|''total'' mass]] or ''total'' energy. All forms of energy contribute to the total mass and total energy.

For example, an [[electron]] and a [[positron]] each have rest mass.  They can perish together, converting their combined rest energy into [[photon]]s which have electromagnetic radiant energy but no rest mass.  If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total ''mass'' nor the total ''energy'' of the system will change.  The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Likewise, non-material forms of energy can perish into matter, which has rest mass.

Thus, conservation of energy (''total'', including material or ''rest'' energy) and [[conservation of mass]] (''total'', not just ''rest'') are one (equivalent) law. In the 18th century, these had appeared as two seemingly-distinct laws.

===Conservation of energy in beta decay===
{{Main|Beta decay#Neutrinos}}
The discovery in 1911 that electrons emitted in [[beta decay]] have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus.<ref>{{cite book |last1=Jensen |first1=Carsten |year=2000 |title=Controversy and Consensus: Nuclear Beta Decay 1911-1934 |url=https://www.springer.com/birkhauser/physics/book/978-3-7643-5313-1 |publisher=Birkhäuser Verlag |isbn=978-3-7643-5313-1 }}</ref><ref>{{cite journal |bibcode= 1978PhT....31i..23B |doi=10.1063/1.2995181 |title=The idea of the neutrino |journal=Physics Today |volume=31 |issue=9 |pages=23–8 |year=1978 |last1=Brown |first1=Laurie M. }}</ref> This problem was eventually resolved in 1933 by [[Enrico Fermi]] who proposed the correct [[Fermi's interaction|description of beta-decay]] as the emission of both an electron and an [[antineutrino]], which carries away the apparently missing energy.<ref>
{{cite journal
 |last=Wilson |first=F. L.
 |year=1968
 |title=Fermi's Theory of Beta Decay
 |url=http://microboone-docdb.fnal.gov/cgi-bin/RetrieveFile?docid=953;filename=FermiBetaDecay1934.pdf;version=1
 |journal=[[American Journal of Physics]]
 |volume=36 |issue=12 |pages=1150–1160
 |bibcode= 1968AmJPh..36.1150W
 |doi= 10.1119/1.1974382
}}</ref><ref>
{{cite book
 |last=Griffiths |first=D.
 |year=2009
 |title=Introduction to Elementary Particles
 |edition=2nd |pages=314–315
 |publisher=Wiley
 |isbn=978-3-527-40601-2
}}</ref>