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. (The trick is that if
the potential energy between constituents approaches a
constant as r approaches infinity, we set that constant to
zero.) 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.