Horizon - Einstein's Equation Of Life And Death - [2005-01-27]
On September 27 1905 Annalen der Physik published a fourth paper, "Does the Inertia of a Body Depend Upon Its Energy Content?", in which Einstein developed an argument for arguably the most famous equation in the field of physics: E = mcÂ². Einstein considered the equivalency equation to be of paramount importance because it showed that a massive particle possesses an energy, the "rest energy", distinct from its classical kinetic and potential energies.
The paper is based on James Clerk Maxwell's and Heinrich Rudolf Hertz's investigations and, in addition, the axioms of relativity, as Einstein states,
The results of the previous investigation lead to a very interesting conclusion, which is here to be deduced.The previous investigation was based "on the Maxwell-Hertz equations for empty space, together with the Maxwellian expression for the electromagnetic energy of space ..."The laws by which the states of physical systems alter are independent of the alternative, to which of two systems of coordinates, in uniform motion of parallel translation relatively to each other, these alterations of state are referred (principle of relativity).
The equation sets forth that energy of a body at rest (E) equals its mass (m) times the speed of light (c) squared, or E = mcÂ².
If a body gives off the energy L in the form of radiation, its mass diminishes by L/cÂ². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion thatThe mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 Ã— 1020, the energy being measured in ergs, and the mass in grammes.[...]If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.
The mass-energy relation can be used to predict how much energy will be released or consumed by nuclear reactions; one simply measures the mass of all constituents and products and multiplies the difference by c2. The result shows how much energy will be released or consumed, usually in the form of light or heat. When applied to certain nuclear reactions, the equation shows that an extraordinarily large amount of energy will be released, much larger than in the combustion of chemical explosives, where the mass difference is hardly measurable at all. This explains why nuclear weapons produce such phenomenal amounts of energy, as they release binding energy during nuclear fission and nuclear fusion, and also convert a much larger portion of subatomic mass to energy.