The magnetic moment of an electron is symbolized as g and is called the “g-factor.”
The magnetic moment is the degree to which the electron is influenced by an external magnetic field, for example, the field of a nearby bar magnet. An electron is influenced by an external magnetic field because the electron, itself, generates a magnetic field. It does so due to its electrical field and its spin. Physicists have long known that a spinning electrical field creates a magnetic field. In the 1920’s when physicists detected a new property that was responsible for the magnetism exerted by electrons, they assumed the electron must be spinning. They called the new property “spin.” Only later, did their calculations indicate that the electron could not possibly be spinning in the sense that a top does.
Nevertheless, the term “spin” continues in use. It is convenient to think of it as some kind of rotation, regardless of physical impossibility. So, in keeping with this convention, the electron can be thought of, metaphorically, as spinning on its axis. As it spins, the axis changes its angle. This is called “precession” of the axis. The magnetic moment of an electron is determined by the speed at which the angle of the axis changes.
The calculation of the magnitude of the magnetic moment of the electron holds a special place in the achievements of quantum physics. It has been calculated to 13 decimal places. But this is not what is so remarkable. What’s remarkable is the extent of agreement between the calculated figure and the measured figure. The magnitude of the magnetic moment of an electron has been measured repeatedly in experiments done over the last century. The calculated and measured magnitudes agree to 13 digits after the decimal point.
The measured and the calculated magnitude of the magnetic moment is 2.00231930436182. The Nobel Laureate physicist, Richard Feynman, said, in 1985, that the accuracy of this calculation is: “the equivalent of measuring the distance from Los Angeles to New York, a distance of over 3,000 miles, to within the width of a human hair.” Since 1985, measurements have been refined as have the calculated using the equations of Quantum Field Theory. Now the accuracy is equivalent of “measuring the distance from the Earth to the Moon to within the width of a human hair.” * This degree of accuracy tells physicists that Quantum Field Theory describes reality.
*Source: On-line article by Dan Styer, “Calculation of the anomalous magnetic moment of the electron,” June 21, 2012 http://www2.oberlin.edu/physics/dstyer/StrangeQM/Moment.pdf