Mass-Energy Equivalence (E = mc²)

The equation does not say that mass turns into energy. It says that mass is energy — one of its forms, written in a different unit, with $c^2$ doing the same job that 1000 does when converting kilometres to metres. A stationary object of mass $m$ possesses energy $mc^2$ simply by existing, and the statement runs both ways: heat a brick and it becomes fractionally more massive, compress a spring and the same, charge a battery and the same. Those increases are real and utterly unweighable, because $c^2 \approx 9 \times 10^{16}$ J/kg means one joule of stored energy weighs $1.1 \times 10^{-17}$ kg. The exchange rate is what hid the relation from three centuries of careful chemistry.

Run a gram through it. $0.001 \times (3 \times 10^{8})^2 = 9 \times 10^{13}$ J, or 90 TJ, which is 25 GWh — about one day's output from a large power station. No process available to us releases anything close to all of it. Uranium fission liberates roughly 0.09% of the fuel's mass as energy; hydrogen fusion, the Sun's process, manages about 0.7%; and burning petrol releases something like one part in $10^{10}$, which is precisely why the mass deficit never showed up on a chemist's balance. The Sun radiates $3.8 \times 10^{26}$ W, so dividing by $c^2$ it is shedding about 4.3 million tonnes of mass every second — and has been for four and a half billion years without exhausting a rounding error of its total.

It did not come from nuclear physics. Einstein published it in September 1905 as a three-page afterthought to the special relativity paper, under the title "Does the inertia of a body depend upon its energy content?", and the argument is a thought experiment: a body emits two equal pulses of light in opposite directions, so its momentum is unchanged, but analysed from a moving frame the bookkeeping only balances if the body's mass has dropped by the emitted energy divided by $c^2$. He wrote it as $m = L/V^2$. Radioactivity was mentioned only as a place the effect might one day be large enough to detect; the weapons and the reactors were four decades away and no part of the intention.

Now the corrections, and there are several worth making. Nothing "becomes energy" in a reactor. In fission no matter disappears; the fragments simply have less mass than the original nucleus because they are more tightly bound, and the difference departs as kinetic energy and radiation. Energy was conserved at every instant — the accounting moved from one column to another. Mass is not a fuel being consumed. Second, $E = mc^2$ is the special case for a body at rest. The full statement is $E^2 = (pc)^2 + (mc^2)^2$, and a moving body has energy $\gamma mc^2$. That $\gamma$ is where "relativistic mass" came from, and the convention has been abandoned deliberately: it encourages the belief that mass grows with speed, which it does not. Mass is an invariant, identical in every frame; what grows is energy and momentum. Third, and most surprising: almost none of your own mass is the mass of your constituent quarks. A proton's mass comes overwhelmingly from the kinetic and binding energy of the gluon field inside it, with the three valence quarks contributing on the order of 1%. Read the equation from right to left and it is the reason you weigh what you weigh. Finally, a system's mass is not the sum of its parts' masses — a sealed box of hot gas is measurably heavier than the same box cold.