Imagine a system made of 4 pieces, each of mass m. Einstein pointed out that the total mass of the system should be Mc2 = ℰ + 4mc2
Here ℰ is the total internal
energy of the system, the sum of the kinetic and potential
energies of the 4 particles. But for systems in nature, the
size of an atomic nucleus or larger, the total internal energy
of a bound system is negative. Notice that this means
that M is less than 4m! Physicists define the
binding energy of a system as B = -ℰ, so that B
is the work it would take to disassemble the system
completely. Example: suppose each particle
has a mass of 10 MeV/c2, and the mass of the system
is measured to be 30 MeV/c2. What is the
binding energy of the system? ℰ = Mc2 - 4mc2 = 30
MeV - 40 MeV = -10 MeV. It would take 10 MeV of work to
pull the system apart.