Some very precise numbers
The magnetic properties of an electron are characterised by a dimensionless number ge. It is called the ‘gyromagnetic ratio’ and it relates the strength of the magnetic field the electron creates –its ‘dipole moment’– to its angular motion –its ‘spin’. [Sometimes we liken an electron to a spinning top: this is a useful bit of fiction.]
The value of ge can be determined experimentally by spectroscopic studies, which can be carried out with great precision. The value is very close to 2. It is usual to quote the value of ge/2 The result (up to date when this was written!) is
![\[ \frac{g_e}{2} = 1.001 159 652 41 (20) \hspace*{1cm} \mbox{[EXPERIMENT!]} \]](mastermathpng-0.png)
The value of ge can also be worked out on the basis of a theory that combines quantum physics, relativity and electromagnetism (for which you will have to wait until your final year here!). That theory gives
![\[ \frac{g_e}{2} = 1.001 159 652 38 (26) \hspace*{1cm} \mbox{[THEORY!]} \]](mastermathpng-1.png)
The precision of the experimental measurement thus allows a very stringent test of a fundamental theory.