Mass–energy equivalence

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame. The two differ only by a multiplicative constant and the units of measurement.[1][2] The principle is described by the physicist Albert Einstein's formula: .[3] In a reference frame where the system is moving, its relativistic energy and relativistic mass (instead of rest mass) obey the same formula.

The formula defines the energy (E) of a particle in its rest frame as the product of mass (m) with the speed of light squared (c2). Because the speed of light is a large number in everyday units (approximately 300000 km/s or 186000 mi/s), the formula implies that a small amount of mass corresponds to an enormous amount of energy.

Rest mass, also called invariant mass, is a fundamental physical property of matter, independent of velocity. Massless particles such as photons have zero invariant mass, but massless free particles have both momentum and energy.

The equivalence principle implies that when mass is lost in chemical reactions or nuclear reactions, a corresponding amount of energy will be released. The energy can be released to the environment (outside of the system being considered) as radiant energy, such as light, or as thermal energy. The principle is fundamental to many fields of physics, including nuclear and particle physics.

Mass–energy equivalence arose from special relativity as a paradox described by the French polymath Henri Poincaré (1854–1912).[4] Einstein was the first to propose the equivalence of mass and energy as a general principle and a consequence of the symmetries of space and time. The principle first appeared in "Does the inertia of a body depend upon its energy-content?", one of his annus mirabilis papers, published on 21 November 1905.[5][6] The formula and its relationship to momentum, as described by the energy–momentum relation, were later developed by other physicists.

  1. ^ Serway, Raymond A.; Jewett, John W.; Peroomian, Vahé (5 March 2013). Physics for scientists and engineers with modern physics (9th ed.). Boston, MA: Brooks/Cole. pp. 1217–1218. ISBN 978-1-133-95405-7. OCLC 802321453.
  2. ^ Günther, Helmut; Müller, Volker (2019), "Einstein 's Energy–Mass Equivalence", in Günther, Helmut; Müller, Volker (eds.), The Special Theory of Relativity: Einstein's World in New Axiomatics, Singapore: Springer, pp. 97–105, doi:10.1007/978-981-13-7783-9_7, ISBN 978-981-13-7783-9, S2CID 209978258, archived from the original on 2021-02-21, retrieved 2020-10-14
  3. ^ Bodanis, David (2009). E=mc2: A Biography of the World's Most Famous Equation (illustrated ed.). Bloomsbury Publishing. preface. ISBN 978-0-8027-1821-1.
  4. ^ Poincaré, H. (1900). "La théorie de Lorentz et le principe de réaction"  [The Theory of Lorentz and The Principle of Reaction]. Archives Néerlandaises des Sciences Exactes et Naturelles (in French). 5: 252–278.
  5. ^ Einstein, A. (1905). "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" [Does the Inertia of a Body Depend Upon its Energy-Content?]. Annalen der Physik (in German). 323 (13): 639–641. Bibcode:1905AnP...323..639E. doi:10.1002/andp.19053231314. ISSN 1521-3889.
  6. ^ Schatel, John. "The 1905 Papers". The 1905 Papers. 2: 172.
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