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Mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. This is expressed quantitatively using the special relativity equation:

E=mc²

where:

• E = energy equivalent to the mass (J)
• m = mass (kg)
• c = speed of light (m.s^-1)

This equation is a mathematical by-product of calculation of relativistic work required to accelerate a body. The conversion factor c² is 89.88 PJ/kg = 21.48 Mt TNT per kg = 149.3 pJ/u = 931.5 MeV/u.

If the energy in the equation is rest energy then the mass must be rest mass or invariant mass.

Contents 1 Conservation of mass and energy 2 Fast moving object 3 See also 4 External links

With the concept of mass-energy equivalence, we combine together the conservation of mass and the conservation of energy, allowing mass to be converted to forms of active energy (such as kinetic energy, heat or light) while still retaining mass. (However, if the system is not closed, such energy can be lost along with its associated mass.) Conversely, active energy in the form of kinetic energy or radiation can be converted to particles which have rest mass. The total amount of mass and energy in a closed system (as seen by a single observer) remains constant. Energy cannot be created or destroyed, and in all of its forms, trapped energy exhibits mass. In relativity theory, mass and energy are two forms of the same thing, and neither one appears without the other.

A fast-moving object moving at near to the speed of light cannot be accelerated to, or faster than, the speed of light, regardless of how much energy we put into the system. As we apply a constant force on such an object, and hence do work on the object, its speed does not appear to increase by the amount specified by E_kinetic = 1/2 mv². Instead, the energy provided to it continues to appear as mass, even as the rate of velocity increase nearly stops. The object's relativistic mass increases, in what is known as mass dilation. The relativistic mass of an object is expressed as a function of its relative speed to that of light.

As discussed more fully in mass in special relativity, the relativistic mass which appears associated with a single fast-moving object is an observer-dependent quantity, and the part of it which is associated with a single object's kinetic energy is just as observer-dependent as the kinetic energy itself. In this case, either one may be made to disappear entirely, by proper choice of inertial frame. For this reason, mass in special relativity is usually chosen to be rest mass or invariant mass, which is a quantity which is not frame-dependent. There is no part of invariant mass for single objects which depends on kinetic energy. In contrast, although a part of the invariant mass for systems of objects may depend on the kinetic energy of some of the objects in the system, this part of the mass is not observer-dependent, and cannot be made to disappear by choice of observers, since it is already defined as that energy which is present in the particular inertial frame where the contribution of kinetic energy to invariant mass is minimized (the COM frame). See invariant mass for more.

• Albert Einstein
• Mass defect
• Mass in special relativity
• Special relativity
• Energies per unit mass
• Henri Poincare
• Olinto De Pretto

• Stanford Encyclopedia of Philosophy entry
• Dual origin of E=mc²