The discipline of electromagnetism grew out of the growing realisation in the nineteenth century that electricity and magnetism were first of all related and then part of a single unified phenomenon.
Once Oersted had noticed that a changing electric field, such as switching a circuit on or off, affected a compass needle, and it was further discovered that a changing magnetic field, such as moving a magnet, induced a brief current in a circuit, electromagnetism became the hottest topic in physics. Faraday provided a systematic and codified set of experimental results, and then the mathematical physicists set to work to provide the definitive model.
This page will deconstruct the work of James Clerk Maxwell, looking both at his exceptional mathematical model and his flawed mechanical explanation, and suggesting how the latter might be improved.
Maxwell’s vortex model
Maxwell’s eventual success stemmed directly from his 1861 paper 'On Physical Lines of Force' in the London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, where he suggested that the magnetic field lines might be vortices in an underlying fluidic ether. Like most physicists at that time, who thought mechanistically, he considered that light was a wave and that it therefore required a medium of propagation, a substance in which the waves occurred. He co-opted this ‘luminiferous medium’ as the background material that also carried electromagnetic effects, and he invoked the low pressure areas at the heart of his imagined vortices as providing suction that we observe as magnetic attraction.
In was in this 1861 paper that Maxwell also introduced the crucial idea of an ‘electric displacement’.
Bringing the maths together
The equations of electromagnetism originally numbered 20, as written by Maxwell, but these have been reduced to four by combining the x, y and z directions together into single formulae by using the notation of vectors.
Maxwell wasn’t the only one working on this problem, and his four equations are also known individually as Gauss’s law (or Gauss’s flux theorem), Gauss’s law for magnetism, Faraday’s law of induction and Ampère’s circuital law. There is additionally a Lorentz force law, not one of Maxwell’s equations.
You can see the mathematics on this external site.
The set of five (or twenty-one) equations can be arrived at by collecting enough data and then finding the mathematics that fits. I call this ‘pure’ mathematical modelling, as it takes no interest in the underlying physical causes and effects. Maxwell wanted to achieve something more. Several decades later, Max Planck would initiate quantum theory with his discovery, through initially pure mathematical modelling, that light was emitted and absorbed in separate, finite amounts, ‘quanta’. On receiving the Nobel Prize, Planck said:
‘But even if the radiation formula should prove to be absolutely accurate it would after all be only an interpolation formula found by happy guesswork, and would thus leave one rather unsatisfied. I was, therefore, from the day of its origination, occupied with the task of giving it a real physical meaning’.i
Maxwell clearly felt the same way.
Daring to reinterpret Maxwell
Maxwell’s attempt to interpret electromagnetism physically, as the effect of motion within a fluid (the ‘luminiferous medium’ or ‘ether’) didn’t work in a number of ways, and I will offer an alternative hydrodynamic interpretation, a ‘modified Maxwell model’ here.
The first step is to interpret Maxwell’s ‘electric displacement’, now known as displacement current, as an actual physical displacement of fluid vortices, making it clear that this ‘strain’ (forced displacement from equilibrium) does not require a solid ether.
More controversial is to contradict Maxwell’s interpretation of electricity. In 1861, Maxwell wrote:
‘according to our hypothesis, an electric current is represented by the transference of the moveable particles interposed between the neighbouring vortices.’ii
I cannot see any good argument or evidence for this, and so suggest instead a more radical and far simpler idea, that electric field strength and magnetic field strength are two different ways of measuring the same vortex. Magnetic field places a value on the rotation, while electric field gives a figure for the reduction in effect with distance from the centre of rotation.
(This allocates a different direction to the magnetic field of a current carrying wire from that currently assumed, but this does not seem to create any serious problems.)
This requires that we distinguish electric current from magnetic field. The powerful similarities between the two were the starting point for Einstein’s famous 1905 paper on special relativity, called ‘On the Electrodynamics of Moving Bodies’, and described succinctly by Sir James Jeans as ‘electricity and magnetism become electricity at rest and electricity in motion.’iii
In this new physical interpretation of Maxwell, therefore, it is suggested, somewhat tentatively, that electric current is a vortex motion about the centre of the current carrying wire, transmitting purely rotational energy, while magnetic field lines are also vortices (Maxwell’s vortices) with an additional motion along the vortex. We might think of this as a ‘vortex streamer’.
The nature of light
The final and most controversial change is to the interpretation of Maxwell's most radical contribution to quantum theory, the ‘transverse electromagnetic wave’ or TEM.
Maxwell’s derivation of the TEM is fairly short and almost purely mathematical. What he shows is that the equations he has derived from his hydrodynamic model of electromagnetism, and specifically from his magnetic vortices, will sustain transverse waves, ripples in the vortices, that travel at light speed.
He concludes that these are therefore light, and I am certain that this conclusion is wrong.
There are two observations that suggest strongly that Maxwell was incorrect in this assertion. Firstly, electromagnetic fields and hence magnetic vortices do not appear to occupy all of space, and certainly do not connect us to distant stars and galaxies. Secondly, they are often curvilinear, and are clearly not followed by light, which is famous for travelling in straight lines.
Modern theory has already reinterpreted Maxwell, taking his mathematics as showing that electric fields produce magnetic fields and vice versa, rendering the composite self-sustaining.
Robert Millikan, in his seminal ‘oil drop’ paper, found this idea bizarre:
‘This hypothesis may well be called reckless, first because an electromagnetic disturbance which remains localised in space seems a violation of the very conception of an electromagnetic disturbance, and second because it flies in the face of the thoroughly established facts of interference.’iv
It is therefore my suggestion that Maxwell’s rippling vortices transfer naturally their motion to Maxwell’s fluidic ether, and the resulting pressure waves are what we see as light. This suggestion has potentially profound consequences, and is the link between the analysis of this site and the more speculative ideas of Esau James.
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i. Max Planck, 1858 – 1947, 1919 Nobel Prize address, The Origin and Development of the Quantum Theory.
ii. J C Maxwell, London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, fourth series, March 1861, page 285
iii. Sir James Jeans: The Mathematical Theory of Electricity and Magnetism (5th Edn.) (CUP, 1933) page 3
iv. R.A. Millikan, 1868 – 1953, A Direct Photoelectric Determination of Planck’s ‘h’, Physical Review 7 (1916) page 355