Physics
Mass Energy Equivalence
Mass-energy equivalence, described by Einstein's famous equation E=mc^2, states that mass and energy are interchangeable and can be converted into each other. This concept revolutionized physics by showing that mass can be considered a form of energy and vice versa, leading to developments in nuclear energy, particle physics, and cosmology.
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10 Key excerpts on "Mass Energy Equivalence"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 2 Mass-Energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measu- rement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distance'^2/'time'^2)'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of ________________________ WORLD TECHNOLOGIES ________________________ thermodynamics. Mass–energy equivalence does not imply that mass may be ″converted″ to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences.
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- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 2 Mass–energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('dista-nce' 2 /'time' 2 )'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of ________________________ WORLD TECHNOLOGIES ________________________ thermodynamics. Mass–energy equivalence does not imply that mass may be converted to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created or destroyed.
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- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 8 Mass-Energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distance'^2/ 'time'^2)'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a ________________________ WORLD TECHNOLOGIES ________________________ restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass– energy equivalence does not imply that mass may be ″converted″ to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 1 Mass–energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distan-ce'^2/'time'^2)'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a ________________________ WORLD TECHNOLOGIES ________________________ restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass–energy equivalence does not imply that mass may be ″converted″ to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. In physics, mass must be differentiated from matter, a more poorly defined idea in the physical sciences.
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- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 4 Mass–Energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set ________________________ WORLD TECHNOLOGIES ________________________ equal to 1 ('distance'/'time'), and the formula becomes the identity E = m'('distance' 2 / 'time' 2 )'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass–energy equivalence does not imply that mass may be converted to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy are both conserved separately in special relativity, and neither may be created or destroyed.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 2 Mass–energy Equivalence 3-meter-tall sculpture of Einstein's 1905 E = mc 2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept the total internal energy E of a body at rest is equal to the product of its rest mass m and a suitable conversion factor to transform from units of mass to units of energy. If the body is not stationary relative to the observer then account must be made for relativistic effects where m is given by the relativistic mass and E the relativistic energy of the body. Albert Einstein proposed mass–energy equivalence in 1905 in one of his Annus Mirabilis papers entitled Does the inertia of a body depend upon its energy-content? The equivalence is described by the famous equation where E is energy, m is mass, and c is the speed of light in a vacuum. The formula is dimensionally consistent and does not depend on any specific system of measurement units. For example, in many systems of natural units, the speed (scalar) of light is set equal to 1 ('distance'/'time'), and the formula becomes the identity E = m '('distance' 2 / 'time' 2 )'; hence the term mass–energy equivalence. The equation E = mc 2 indicates that energy always exhibits mass in whatever form the energy takes. Mass–energy equivalence also means that mass conservation becomes a restatement, or requirement, of the law of energy conservation, which is the first law of thermodynamics. Mass–energy equivalence does not imply that mass may be converted to energy, and indeed implies the opposite. Modern theory holds that neither mass nor energy may be destroyed, but only moved from one location to another. Mass and energy ________________________ WORLD TECHNOLOGIES ________________________ are both conserved separately in special relativity, and neither may be created or des-troyed.
eBook - ePub- Francisco Fernflores(Author)
- 2017(Publication Date)
- Momentum Press(Publisher)
CHAPTER 3
CONTEMPORARY DEBATES AND INSIGHTSThere tend to be two types of discussions in the contemporary physics literature about Einstein’s mass–energy relation. First, there are more historically focused discussions among physicists, and historians and philosophers of physics, concerning whether or not Einstein ever really correctly derived the direct proportionality between mass energy codified in his famous equation, and if he did, when he did. Although we have already appealed to some of this work, in this chapter we wish to examine some of this literature for inevitably it contributes to a more clear understanding of Einstein’s influential result.The other type of discussion in the contemporary literature straddles two issues: (1) How should the relativistic mass–energy relation be taught? and (2) What is the best way to understand what it means to say that mass is “converted” into energy (or vice versa) or that mass and energy are “equivalent?” Papers that address these questions have tended to appear in journals such as the American Journal of Physics and the European Journal of Physics , i.e., journals that are primarily aimed at physics educators in higher education.In this chapter, we will examine some key contributions to this literature, because we are seeking philosophical clarity concerning the meaning and use of expressions involving both the “conversion” and “equivalence” of mass and energy. Note, for instance, that although talk of “converting” mass into energy is fairly common, not only in presentations of science for the layperson but also in physics education, one seldom hears physicists talk about energy being “converted” into mass. Similarly, one does, from time to time, still find the odd physicists (or scientist or philosopher more generally) talking about matter
- Martinus J G Veltman(Author)
- 2003(Publication Date)
- World Scientific(Publisher)
In fact, the energy increases less sharply with momentum, and for very high values of the momentum the energy becomes proportional to it. (Energy approximately equals momen-tum times c , the speed of light.) A typical case is shown in the next figure, with the dashed line showing the non-relativistic case, the solid curve the relativistically correct relation. kinetic energy 0 Momentum Relativ. The quantitatively minded reader may be reminded of the equa-tions quoted in Chapter 1. In particular there is the relation between energy and momentum, plotted in the next figure: 2 2 2 c m p c E + = . or, using the choice of units such that c = 1: 2 2 2 m p E + = . 129 E N E R G Y, M O M E N T U M A N D M A S S -S H E L L Another important fact is the Einstein equation E = mc 2 . This very famous equation can be deduced in a number of ways, none of which is intuitively appealing. This equation tells us that even for a particle at rest the energy is not zero, but equal to its mass multiplied with the square of the speed of light. In particle physics this equation is a fact of daily life, because in inelastic processes, where the set of secondary particles is different from the primary one, there is no energy conservation unless one includes these rest-mass energies in the calculation. As the final particles have generally masses different from the primary ones, the mass-energy of the initial state is in general different from that of the final state. In fact, the first example that has already been discussed extensively is neutron decay; this decay is a beautiful and direct demonstration of Einstein’s law, E = mc 2 . Indeed it is in particle physics that some very remarkable aspects of the theory of relativ-ity are most clearly demonstrated, not just the energy-mass equa-tion. Another example is the lifetime of unstable particles, in particular the muon.
- John R. Fanchi, John R. Fanchi, (Authors)
- 2013(Publication Date)
- Academic Press(Publisher)
CHAPTER NINE Mass–Energy Transformations The notion of quantized energy introduced in the previous chapter is useful for objects moving at speeds that are much less than the speed of light in vacuum. In such a nonrelativistic system, it is possible to treat matter and energy as distinct physical quantities. Scientists have learned, however, that objects moving close to the speed of light obey a different set of rules. The quantum theory had to be extended to the relativistic domain: a domain where the distinction between matter and energy disappears. The most widely accepted theory of elementary particle physics is rel-ativistic quantum theory, and the standard model of elementary particle physics is the quark model. The quark model is the modern day equivalent of Democritus’ atomic theory. An observation that is central to relativistic quantum theory is that energy can be converted into mass, and mass can be converted into energy. We encountered mass–energy transformations in our discussion of solar energy. Solar energy is generated by mass–energy transformations that occur in nuclear fusion reactions inside a star. The con-version of mass to energy is a mechanism at work in stars, nuclear weapons, and nuclear reactors. In this chapter, we acquire a more sophisticated understanding of mass–energy transformations and nuclear reactions by becoming familiar with relativistic quantum theory and the quark model. First, we begin with an introduction to relativity. 9.1 EINSTEIN’S RELATIVITY The concept of relativity was around long before Albert Einstein pub-lished his first paper on relativity in 1905. Relativity is concerned with how the motion of an observer influences the observer’s determination of the relationships between physical quantities. The idea is quite simple. Suppose we are moving in a spaceship at half the speed of light relative to Max, an observer standing still on the ground. The speed of light is 251
eBook - PDFHypersymmetry
Physics of the Isotopic Field-Charge Spin Conservation
- György Darvas(Author)
- 2020(Publication Date)
- De Gruyter(Publisher)
Even in 1921, Einstein himself wrote (p. 783): “ If an amount of energy E be given to a body, the internal mass of the body increases by an amount E/c 2 . ” (Emphasis by me – G.D.) This indicates that – at least in the first period – even the father of the idea was not certain about the na-ture of this statement. Von Laue (1911 and 1955) emphasised the restricted validity of Einstein ’ s E = mc 2 too. He realised at an early stage that it holds only in static sys-tems and in which pressure vanishes. In any other case neither the energy (left side), nor the mass (at the right side) cannot be handled as homogenous, indivisible properties. A recent another approach to make a distinction between forms of masses is discussed by Calmet and Kuntz (2017): According to them a few observed phenom-ena “ suggest that there is a new form of matter that does not shine in the electro-magnetic spectrum. Dark matter is not accounted for by either general relativity or the standard model of particle physics. While a large fraction of the high energy community is convinced that dark matter should be described by yet undiscovered new particles, it remains an open question whether this phenomenon requires a modification of the standard model or general relativity. Here we want to raise a slightly different question namely whether the distinction between modified gravity or new particles is always clear. ” They showed that this is not always the case. My comment here is to refer to the mass of the dion, mentioned in Section 11.3.14. E.P.J. de Haas referred (de Haas, 2004a, 2005) to an early assumption by G. Mie (1912a, 1912b, 1913) concerning the transformation of the masses. The papers pub-lished by Mie contributed to the elaboration of the gravitational theory under prep-aration at that time.
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