In spite of what Einstein discovered about the equivalence of mass and energy expressed by the elegantly simple equation: ��=����, it does not explain the reason why energy is quantized on the left but the mass is not quantized on the right. Since this equation is symmetrical, it is also true that ����=�� and similarly it does not explain why the mass is not quantized on the left but the energy is quantized on the right. Einstein discovered this in 1905. However, in 1847, 58 years earlier, Hermann Ludwig Ferdinand von Helmholtz (1821-94) made the discovery of the symmetric law of energy conservation and introduced the concept of free energy defined as the internal energy of any irreversible thermodynamic system minus the product of absolute temperature and entropy. If he is alive today, certainly he could give a plausible explanation. Unfortunately, he died 6 years prior to Max Planck’s discovery of energy quantization in 1900. Moreover, it is likely that Helmholtz was one of the remaining 19th century’s self-satisfied scientists and was of the opinion that the work of later investigators would be merely to make measurements to the next decimal place. He believed then that science is finally completed by two foundations: Newton’s and Maxwell’s physics of the continuous.

Unbeknown to him and others is the fact that the square of ��=���� gives the square of energy as ��=����. This is the second addend to the total relativistic energy: ��=����+����. If linear momentum �� is zero then ��=���� and if the rest mass �� is zero then ��=��/�� as exact momentum of light. For ��=ℎ�� (Planck’s quantum) then ��=ℎ/��, both given as postulates of every quantum theory. Still, these failed to explain the possibility of mass quantization for the case where both ��=0 and ��=0. This last possibility can give a complete understanding of the truth of energy conservation if and only if there is a quantum theory of space-time as the integrability of squares of zero-point energies representing the quantum vacuum fluctuations of all virtual particles whose existence first verified in 1958’s experiments to detect the Casimir effect. The truth – energy by itself is not completely conserved but the square of energy is.