IEEE IMS 2015 celebrates Maxwell’s fundamental equations for electro-magnetic phenomenon that were almost lost to the world.

By Hamilton Carter, Senior Editor, Semi IP Systems

It’s their second 150^{th} birthday really. Perhaps for something as monumental as James Clerk- Maxwell’s big four equations, in order to celebrate properly, one should celebrate for two years. Maxwell presented his groundbreaking work to the Royal Society in December of 1864. His work wasn’t published, however, until January of 1865. So, last year we celebrated the introduction of his equations and this year we’re celebrating their subsequent publication.

IMS 2015 dedicated an entire session to talks on the history of Maxwell’s equations. NASA’s Dr. Bob Scully and Dr. James C. Rautio, of Sonnet Software presented two of the talks. Dr. Scully focused more on the ‘what’ of the equations pointing out the mechanical origins of Maxwell’s work while Dr. Rautio focused more on the ‘who’ and ‘how’ of the story. Dr. Rautio did the voices for several of the characters in his presentation, and explained how Fitzgerald, Heaviside and others saved Maxwell’s seminal work just as it was slipping into obscurity.

Dr. Scully pointed out that when Maxwell wrote down his original work on the subject, it wasn’t the four vector valued equations we’re familiar with. Instead, his initial treatment, using quaternion notation was a set of 20 coupled differential equations. Presented in this way, the accomplishment doesn’t pale as it usually does when compared to Einstein’s 16 differential equations for general relativity. Then again though, Einstein’s equations are also non-linear.

Dr. Scully’s presentation covered the early historical development of Maxwell’s thought processes. Maxwell went with quaternion notation both because vector notation didn’t exist yet, and because his dear friend Peter Guthrie Tait suggested it. In his initial models, Maxwell maintained that the magnetic field was represented by vortices. The rotation of these vortices represented their angular momentum and was denoted as the magnetic field strength. His theory modeled the luminiferous aether, (the substance then hypothesized to be responsible for the propagation of electromagnetic fields; it has since been abandoned), as a perfectly elastic non-lossy substance. His development of the displacement current, the phenomena responsible for AC conduction across capacitors, and the bane of freshman physics students the world over, was necessary to avoid energy loss in the aether due to shear stress. Maxwell’s mechanical model contained the magnetic and electric fields as part of the same system. The magnetic field contained the kinetic energy of the system and the electric field, the potential energy.

Dr. Rautio used Bruce Hunt’s “The Maxwellians” as source material. He pointed out that Maxwell’s equations were almost lost to obscurity. The equations in their original form weren’t well-understood by the scientific masses. Incredibly, (from our modern perspective), few people were certain there were any good applications for them. In the late 1800’s the equations were rescued by a rather disparate group of researchers that included Fitzgerald, and Heaviside. Fitzgerald, the first to champion the resurrection of the equations, was soon joined by Heaviside. Heaviside would go on to co-develop the vector notation that made the equations more accessible to the masses.

As a final aside, if you’re a physics history buff you might recognize Fitzgerald’s name as being associated with the special relativistic length contractions that ultimately came to bear Lorentz’s name. When asked about the origin of Fitzgerald’s association, the speaker noted that after Heaviside presented the original derivation showing that the electric field of a particle contracts in the direction parallel to its motion, Fitzgerald, reasoning that electrons provide the spacing between atoms, hypothesized that the material itself would contract in the direction of its motion.