section_path: In relativity/Special relativity
section_name: Special relativity
paragraph_text: Special relativity
  
  In some frameworks of special relativity, physicists have used different definitions of the term. In these frameworks, two kinds of mass are defined: rest mass (invariant mass), and relativistic mass (which increases with velocity). Rest mass is the Newtonian mass as measured by an observer moving along with the object. Relativistic mass is the total quantity of energy in a body or system divided by c. The two are related by the following equation:
  
  where γ {\displaystyle \gamma } is the Lorentz factor:
  
  The invariant mass of systems is the same for observers in all inertial frames, while the relativistic mass depends on the observer's frame of reference. In order to formulate the equations of physics such that mass values do not change between observers, it is convenient to use rest mass. The rest mass of a body is also related to its energy E and the magnitude of its momentum p by the relativistic energy-momentum equation:
  
  So long as the system is closed with respect to mass and energy, both kinds of mass are conserved in any given frame of reference. The conservation of mass holds even as some types of particles are converted to others. Matter particles (such as atoms) may be converted to non-matter particles (such as photons of light), but this does not affect the total amount of mass or energy. Although things like heat may not be matter, all types of energy still continue to exhibit mass. Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy appear without the other.
  
  Both rest and relativistic mass can be expressed as an energy by applying the well-known relationship E = mc, yielding rest energy and "relativistic energy" (total system energy) respectively:
  
  The "relativistic" mass and energy concepts are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum. Because the relativistic mass is proportional to the energy, it has gradually fallen into disuse among physicists. There is disagreement over whether the concept remains useful pedagogically.
  
  In bound systems, the binding energy must often be subtracted from the mass of the unbound system, because binding energy commonly leaves the system at the time it is bound. The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped. For example, the binding energy of atomic nuclei is often lost in the form of gamma rays when the nuclei are formed, leaving nuclides which have less mass than the free particles (nucleons) of which they are composed.
  
  Mass–energy equivalence also holds in macroscopic systems. For example, if one takes exactly one kilogram of ice, and applies heat, the mass of the resulting melt-water will be more than a kilogram: it will include the mass from the thermal energy (latent heat) used to melt the ice; this follows from the conservation of energy. This number is small but not negligible: about 3.7 nanograms. It is given by the latent heat of melting ice (334 kJ/kg) divided by the speed of light squared (c ≈ 9 × 10 m /s).