The equivalence of mass and energy

Einstein showed that mass and energy are equivalent. Energy can be converted into mass, and mass into energy. They are related by Einstein s equation  

The loss of mass associated with the production of energy is significant only in nuclear reactions. Energy and matter are always considered to be separately conserved in chemical reactions. 

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This example illustrates another result of the theory of relativity, namely, the equivalence of mass and energy. Rewriting the Iasi equation. 

In this book the value of A is given in energy units rather than units of mass, which is possible because of the equivalence of mass and energy expressed in Einstein s... 

Einstein published a mathematical equation to express the equivalency of mass and energy. The equation is... 

Now Tm going to tell you about a strange concept that s necessary for understanding radioactivity and other nuclear reactions. That concept is the equivalence of mass and energy. Mass can transform into energy, and vice versa. This is part of Einstein s theory of special relativity and is the source of that famous equation E = m. Let s apply the theory to the activities you did in the previous section. When the two magnets are apart, we say that they have potential energy due to... 

Einstein s theory about the equivalence of mass and energy opened the way for finding the real source of the Sun s power, namely nuclear reaction, or - more precisely - nuclear fusion. 

The equivalence of mass and energy explains the otherwise puzzling fact that the mass of an atom is always less than the sum of the masses of its constituent particles. For example, the helium-4 atom consists of two protons, two neutrons, and two electrons, giving the following sum ... 

As in wave mechanics, the simulation of chemical phenomena by number theory is characterized by the appearance of integers, in this case associated with chemical structures and transformations. An obvious conclusion is that the elementary units of matter should be viewed as wave structures rather than point particles, which is consistent with the first appearance of matter in curved space-time. Even 3D wave packets behave in a manner convincingly like ponderable matter and rationalize the equivalence of mass and energy in a natural way. There is no compelling reason why this simple model should be concealed with the notion of wave/particle duality and more so on realizing that the wave-like space-time distortions are strictly 4D structures. In response to environmental pressure, an electronic wave packet can shrink to the effective size of an elementary particle or increase to enfold a proton as a spherical standing wave. 

The evidence on which this theory of stellar evolution is based comes not only from known nuclear reactions and the relativistic equivalence of mass and energy, but also from the spectroscopic analysis of the light reaching us from the stars. This leads to the spectral classification of stars, which is the cornerstone of modem experimental astrophysics. The spectroscopic analysis of starlight reveals much information about the... 

Equation 3.5 expresses the very important concept of equivalence of mass and energy. Since the total energy E consists of the rest mass energy plus the kinetic energy, Eq. 3.5 may be rewritten as... 

To retain this result it is foimd that one must make a radical new assumption and introduce the relation E = mc, where mc is what is called the proper energy. The relation imphes an equivalence of mass and energy and suggests at least the formal possibility of their interconversion, since in virtue of its existence a mass has energy as it were stored up in it. 

Einstein showed that it is mass-energy that is conserved one can he converted into the other. This equivalence becomes important in nuclear reactions, discussed in Chapter 19. In ordinary chemical reactions, however, the interconversion of mass and energy is not a significant factor, and we can regard mass and energy as Independently conserved. 

Clearly, the maximum degree of simplification of the problem is achieved by using the greatest possible number of fundamentals since each yields a simultaneous equation of its own. In certain problems, force may be used as a fundamental in addition to mass, length, and time, provided that at no stage in the problem is force defined in terms of mass and acceleration. In heat transfer problems, temperature is usually an additional fundamental, and heat can also be used as a fundamental provided it is not defined in terms of mass and temperature and provided that the equivalence of mechanical and thermal energy is not utilised. Considerable experience is needed in the proper use of dimensional analysis, and its application in a number of areas of fluid flow and heat transfer is seen in the relevant chapters of this Volume. 

Obviously the motions of encounter and of mean free path do not necessarily have any meaning here nor are they needed. On the other hand, the relaxation time x is easy lo define, e.g., as the time taken by sound to travel unit distance, as computed in the equivalent body in equilibrium (equivalent, in having the same total mass and energy in "V"). 

An outstanding example of how these law s are subject to modification was Einstein s elucidation of the mass-energy equivalence ( —me). Before that, the conservation of mass and the conservation of energy were considered to be independently valid. 

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