The difference, called a mass defect, is a measure for the strength of the bond between the four nucleons: the greater the mass defect, the stronger the energy needed to pry the nucleons apart.Įveryday matter is given its stability by chemical bonds between its atoms and/or molecules. The mass of a helium nucleus is thus a bit less than two times the proton mass plus two times the mass of a neutron. ![]() Mass of bound system = sum of masses of its parts – (binding energy)/c 2. If you apply E=mc 2 (or more precisely the inverse formula m=E/c 2 giving the mass m corresponding to a given energy E) to our energy equation above, this gives a straightforward result: The relativistic mass of a bound system is somewhat smaller than the sum of the masses of its constituent parts, namely According to Einstein, to every energy there corresponds a mass, and to every mass there can be assigned a corresponding energy. ![]() Physicists call the “energy needed to split the object apart” its binding energy.Įnter Einstein and his famous equivalence of energy and (relativistic) mass, expressed in the most famous of all physics formulae: E=mc 2. We can also move the expended energy to the right side of the equation, which leaves us withĮnergy of the composite object = sum of the energies of its parts – energy needed to split the object apart.Īt least as far as energies are concerned, this shows that the composite object (in physics lingo: the “bound system”) is less than the sum of its parts. Thus, we must have:Įnergy of the composite object + energy expended to split it up = sum of the energies of the separate parts after the split In particular the total energy before and after the split of a composite object into its parts must be the same. Energy, says a fundamental law of physics, is conserved. But energy doesn’t spontaneously come into existence or vanish. In the language of physics: You need to do some work, invest some energy to pry the constituents apart against the forces that keep them together. On the contrary, splitting a stable object into its constituents takes some effort. For instance, the nucleus of a helium atom does not spontaneously split into the two protons and two neutrons that are its constituents: If a composite object is stable, that is tantamount to saying it won’t spontaneously decay into its component parts. The key to this phenomenon is called binding energy. But, perhaps somewhat surprisingly, for those quantities, the whole is commonly less than the sum of its parts. ![]() Is the whole the sum of its parts? As far as simple physical quantities like mass and energy are concerned, the answer is a definite no. Why Einstein’s famous formula tells us that the whole, as far as mass is concerned, is often less than the sum of its parts An article by Markus Pössel
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