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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 mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
Thus, the mass in the formula = is the relativistic mass. For a particle of ... Where m > 0 and p = 0, this equation again expresses the mass–energy equivalence E = m.
Once this mass difference, called the mass defect or mass deficiency, is known, Einstein's mass–energy equivalence formula E = mc 2 can be used to compute the binding energy of any nucleus. Early nuclear physicists used to refer to computing this value as a "packing fraction" calculation.
Also, Poincaré is the first to describe the relativistic velocity-addition formula – implicitly in his publication and explicitly in his letter to Lorentz. 1905 – Albert Einstein publishes his special theory of relativity, including the mass–energy equivalence that would be later written as E = mc 2.
This contradicts the mass–energy equivalence formula, which requires the relation = / without the 4 ⁄ 3 factor, or in other words, four-momentum doesn't properly transform like a four-vector when the 4 ⁄ 3 factor is present.
Some of the tests of the equivalence principle use names for the different ways mass appears in physical formulae. In nonrelativistic physics three kinds of mass can be distinguished: [14] Inertial mass intrinsic to an object, the sum of all of its mass–energy. Passive mass, the response to gravity, the object's weight.