Feynman preferred the term ‘magnetic moment’ for a reason found in Page 14-8, Volume II of the Feynman Lectures on Physics. The electrical analog of the magnetic dipole moment is called the electric dipole moment. It arises wherever and whenever the center of the electric charge density distribution differs from the center of mass of a particle. The result would be a twisting force similar to a torque as the particle moves in an electric field. Not surprisingly, the standard model of elementary particles experimentally proved that the electric dipole moment of an electron is practically zero to a very high degree of precision. On the contrary, the same very high degree of experimental accuracy proved that the magnetic dipole moment of the electron can never be zero. In general, magnetic dipole moment is a measureable physical property for all fermions. This property is related to the orbital and spin magnetic moment of every particle whether electrically charged or electrically neutral. Experimentally, it exists where and when a turning force (torque) is observed as the particle passes through a uniform magnetic field. In scalar notations: m=T/B where m is the magnetic dipole moment, T is the torque, and B is the magnetic flux density. Equivalently, if a conducting coil of N turns with cross section area A carrying an electric current I then m=NIA implying that NIA=T/B or T=NIAB. In vector notations, the vector torque T is given by the cross product of vector m and vector H, T=m×H where H is the magnetic field intensity. This m is properly defined as the magnetic dipole moment. Alternatively, m can be defined as the electromagnetic moment then T=m×B where B is the vector magnetic flux density. These raise the question for the existence of two distinct T or m?

By simply defining a scalar product T·T, it becomes equivalent to the square of energy E². Since B=mH where m is the permeability of the medium then E²=m(m×H)·(m×H) represents a quantum of the zero-point energy fluctuation. The fluctuations formed from the infinitely many distinct alignments of m and H. If m and H are orthogonal then E² is a maximum. If m and H are antiparallel or parallel then E² is a minimum. However, expanded using Lagrange’s identity E²=m[(m·m)(H·H)-(m·H)(m·H)]=m[(m·H)(m·H)-(m·m)(H·H)]. If (m·m)(H·H) is identically zero then E²=±m(m·H)(m·H) representing distinct quantum states of zero-point energies. Nonetheless, (m·m)(H·H) vanishes iff either these distinct m and m or H and H are orthogonal. This augmented the cross product implication by simply using the facts that the magnitude of m×H is given by |m||H|sinq and the magnitude of m·H is given by |m||H|cosq. However, sin²q+cos²q=1 implying that the sum of E² is absolutely coordinate free and measuring the continuous angular displacements is unnecessary in the infinitesimal domain of the space-time continuum.