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How are mass and energy related in Einstein’s theory of relativity?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

In Albert Einstein’s theory of special relativity, mass and energy are considered the same physical entity and are interconvertible. This relationship is expressed by the equation:12

$E = m c^{2}$

In this formula, E represents energy, m is the rest mass of an object, and c is the speed of light.13

The equation demonstrates that even when a particle is at rest, it possesses "rest mass energy" equal to $m c^{2}$ . In physical processes such as nuclear fission or nuclear fusion, the total mass of the system can change; the difference in mass is converted into kinetic energy or binding energy. Consequently, the law of conservation of mass is incorporated into the broader law of conservation of energy, as the total energy and momentum remain constant throughout such transformations. While it was once common to discuss a "velocity-dependent mass," modern physics emphasizes the invariant rest mass, as the concept of variable mass can lead to confusion.3