Electron’s mass



Helge Kragh, “Quantum Generations; The History of Physics in the Twentieth Century”

pub. Princeton University Press, 1999, p105.


Chapter 8


The Revolution That Failed




The Concept of Electromagnetic Mass




In 1881, young J. J. Thomson showed that when a charged sphere moves through the ether, it will acquire a kind of apparent mass, analogous to a sphere moving through an incompressible fluid. For a sphere with charge e and radius R, he found the electromagnetically induced mass to be

m’ = 4/15 e2/R2c . This first introduction of electromagnetic mass was later improved by the eccentric British engineer-physicist Oliver Heaviside, who in 1889 derived the expression m’ = 2/3 e2/R2c . Contrary to Thomson, who did not think of the “apparent mass” as real, Heaviside considered it as real as the material mass. It was part of the sphere’s measurable or “effective” mass. A further improvement was obtained by Wilhelm Wien in 1900, in a paper significantly titled “On the Possibility of an Electromagnetic Foundation of Mechanics.” Wien confirmed Heaviside’s expression in the limit of small verlocities and added the important result that the electromagnetic mass would depend on the velocity and differ from Heaviside’s if the velocity approached the velocity of light.



Comment by Ivor Catt, 16oct03.

I do not know whether Kragh has got the history right. Perhaps Mike Gibson could enlighten us. Mike is the best expert on Heaviside’s writings. The historical facts of the matter bear on whether Heaviside should have noticed “The Catt Anomaly”. If Heaviside calculated the electron’s mass in 1889, he was some way on the way to The Catt Anomaly more than a decade before his war started with Miss Way. His published his last book in 1902. However, the above piece from Kragh indicates that Heaviside only had a fixed mass, not a mass that would increase to infinity at the velocity of light, the velocity at which the electric charge would have to travel if it came from the west to deal with “The Catt Anomaly”. Personally, I have never investigated in detail Heaviside’s attitude to the mass of an electron.


The Catt Anomaly is a question about where the electric charge comes from on the lower conductor to terminate the electric flux which exists between the upper and the lower conductor when a TEM step has passed. Dr Neil McEwan says it comes from the west, and does not have to travel at the speed of light. Pepper FRS says it could not come from the west, because it would have to travel at the speed of light [and so have infinite mass].


Heaviside failed to notice “The Catt Anomaly”. I excused him on the grounds that in his time, the electron did not definitely have mass. Kragh (above) appears to contradict this, so that Heaviside should have noticed “The Catt Anomaly”. However, it took me, Catt, decades to notice it.





The battle for the soul of science


Why did Heaviside fail to notice “The Catt Anomaly”.


As I remember, my article Wireless World dec 1982 entitled “The New Bureaucracy” discusses the battle within science/technology between the sacred and the profane, between mathematics and physics.


Like myself, Heaviside bridges the barrier between maths and physics, but this is rare. “The Catt Anomaly” is definitely a straight Physics (as opposed to mathematical) question.


“Maxwell’s Equations” contain no physical forces, and no mass, so they will glibly sail past “The Catt Anomaly”, which is a problem resulting from the mass of electricity, further exacerbated by its increase in mass with speed. Heaviside actually wrote them, piecing together bits and pieces from Maxwell’s Treatise. At that time, and even in Heaviside’s writings, electromagnetism was discussed in a much more confusing, complex way than it is today, when I was able to see “The Catt Anomaly”. Even in my youth, in around 1950, at school, we had two types of electric charge, one being three hundred times as great as the other. Thus, although Heaviside did great work in rationalising the symbolism and procedure for discussing electromagnetism, it was cleaned up further after his death. At school, also, we had both cgs and MKS, and many other complications which have now been disposed of.


Kragh mentions the delay in adding loading coils to telephone wires, so that long distance speech telephony was delayed for decades in England. Heaviside fought this battle, which would have gone even worse for him had he found the fatal flaw in the model for an undersea cable that he had to promote in order to get loading coils introduced.

Ivor Catt   17oct03