A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity

Detalhes bibliográficos
Autor(a) principal: Duarte, Sérgio Eduardo Silva
Data de Publicação: 2021
Outros Autores: Lima, Nathan Willig
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/236635
Resumo: Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations.
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spelling Duarte, Sérgio Eduardo SilvaLima, Nathan Willig2022-04-06T04:45:57Z20210031-9120http://hdl.handle.net/10183/236635001127672Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations.application/pdfengPhysics education. Vol. 56, no. 3 (May 2021), 035028, 9p.Teoria da relatividadeRelatividadeMassaEnergiaSpecial theory of relativityRelativityEquivalence relationMassEnergyA simple thought experiment to discuss the mass–energy equivalence in the special theory of relativityEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001127672.pdf.txt001127672.pdf.txtExtracted Texttext/plain19833http://www.lume.ufrgs.br/bitstream/10183/236635/2/001127672.pdf.txt9523762bedd9170bc07ae5e698f9a9c0MD52ORIGINAL001127672.pdfTexto completo (inglês)application/pdf627266http://www.lume.ufrgs.br/bitstream/10183/236635/1/001127672.pdf90df75fd7ad5e1edd13a7e9b9f8e01bdMD5110183/2366352023-07-20 03:36:43.718117oai:www.lume.ufrgs.br:10183/236635Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-07-20T06:36:43Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
title A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
spellingShingle A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
Duarte, Sérgio Eduardo Silva
Teoria da relatividade
Relatividade
Massa
Energia
Special theory of relativity
Relativity
Equivalence relation
Mass
Energy
title_short A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
title_full A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
title_fullStr A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
title_full_unstemmed A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
title_sort A simple thought experiment to discuss the mass–energy equivalence in the special theory of relativity
author Duarte, Sérgio Eduardo Silva
author_facet Duarte, Sérgio Eduardo Silva
Lima, Nathan Willig
author_role author
author2 Lima, Nathan Willig
author2_role author
dc.contributor.author.fl_str_mv Duarte, Sérgio Eduardo Silva
Lima, Nathan Willig
dc.subject.por.fl_str_mv Teoria da relatividade
Relatividade
Massa
Energia
topic Teoria da relatividade
Relatividade
Massa
Energia
Special theory of relativity
Relativity
Equivalence relation
Mass
Energy
dc.subject.eng.fl_str_mv Special theory of relativity
Relativity
Equivalence relation
Mass
Energy
description Einstein’s relation between mass and energy is perhaps the most famous equation of Physics. Despite its simplicity, the meaning of E0 = mc2 is not easy to grasp. Furthermore, its traditional derivations rely either on the integral of momentum, on properties of electromagnetic radiation, or even on the expression for transformation of energy. In the present work, we provide a simple thought experiment with an inelastic collision between two particles observed from two inertial reference frames. We show that for the conservation of relativistic momentum to hold, the mass of the system must increase after the collision. We also show that the increase of mass relates to the loss of kinetic energy according to the equation ∆K = −∆mc2 , which enables us to define the equation for relativistic energy (E = mc2/ p 1 − v 2/c 2 ), rest energy (E0 = mc2 ) and relativistic kinetic energy (K = E − E0). There are two main advantages in this presentation: first, it relies only on simple algebra, not depending on differential calculus and on any property of radiation; second, it leads directly to a comprehensible physical meaning of the relation of equivalence, which can sometimes be too obscure in more formal derivations.
publishDate 2021
dc.date.issued.fl_str_mv 2021
dc.date.accessioned.fl_str_mv 2022-04-06T04:45:57Z
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dc.identifier.issn.pt_BR.fl_str_mv 0031-9120
dc.identifier.nrb.pt_BR.fl_str_mv 001127672
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dc.relation.ispartof.pt_BR.fl_str_mv Physics education. Vol. 56, no. 3 (May 2021), 035028, 9p.
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