View source for On Physical Lines of Force/Part IV/What became of the vortices

{{DISPLAYTITLE:What became of the vortices}}
''[[On Physical Lines of Force]] → [[On Physical Lines of Force/Part IV|Part IV]] → Aftermath''

== 1865: the field without the machine ==

Maxwell read ''A Dynamical Theory of the Electromagnetic Field'' to the Royal Society on '''8 December 1864'''; it was published in the ''Philosophical Transactions'', vol. 155 (1865), pp. 459–512.

The cells are gone. The idle wheels are gone. What remains is a set of equations for a field, justified by general dynamical reasoning — the medium has energy, some kinetic and some potential; write down the Lagrangian; the equations follow — with no picture of what the medium is made of.

The results survive the demolition unchanged. The displacement current is still there. The wave equation is still there, and this time it is derived directly from the field equations rather than through the elasticity of a cell wall, which is why it is the 1865 derivation and not the 1862 one that stands in modern textbooks.

== 1873: the Treatise ==

In ''A Treatise on Electricity and Magnetism'', Part IV, Chapter XXI is "Magnetic Action on Light", and Article 822 still develops "the hypothesis of molecular vortices". Maxwell had not thrown the model away. Article 831 gives his settled verdict:

<blockquote>
The theory proposed in the preceding pages is evidently of a provisional kind, resting as it does on unproved hypotheses relating to the nature of molecular vortices, and the mode in which they are affected by the displacement of the medium.
</blockquote>

He adds that coincidences with experiment carry much less scientific value in a speculative theory of this kind than in his electromagnetic theory of light, which makes no claims about molecular constitution.

Article 831 also contains his own dating of the earlier work:

<blockquote>
A theory of molecular vortices, which I worked out at considerable length, was published in the Phil. Mag. for March, April, and May, 1861, Jan. and Feb. 1862.
</blockquote>

Notice what the ''Treatise'' keeps and what it drops. The general vortex machinery of Parts I to III is not used to derive the field equations any more. But the rotational account of magneto-optical rotation — the physics of [[On Physical Lines of Force/Part IV/The six results|Part IV]] — is still there eleven years later. '''Part IV's physical idea outlived the machinery that produced it.'''

== How historians read the retreat ==

The standard telling is a straightforward one: Maxwell built a mechanical model, extracted what he needed, recognised it was untenable, and abandoned it for an abstract field theory. Pelosi and Selleri put it that way — in 1861–62 Maxwell "resorted to a purely mechanical view, using the concept of 'molecular vortices'", while "In his 1865 paper the mechanical analogy was abandoned in favour of a more abstract concept, that describes an 'electromagnetic field' that pervades all space."

'''Bruce Hunt has argued that this overstates it''', on a point of reading that matters for anyone quoting the paper. Writing in ''Historical Studies in the Natural Sciences'' (2015), Hunt observes that the famous "may appear somewhat awkward" passage

<blockquote>
has often been cited as evidence that Maxwell regarded his entire vortex model as "awkward," "provisional and temporary," and frankly unrealistic. But in fact Maxwell used such terms only about the idle wheel particles… not the vortices themselves.
</blockquote>

On Hunt's reading, Maxwell thought the vortices were probably real and offered only the idle wheels as a device. The change of approach after 1863 owes less to disillusionment than to Maxwell's work on '''electrical standards for the British Association''', which pushed him toward an engineering habit of mind: relations between measurable quantities first, mechanisms second.

Both readings are consistent with the ''Treatise'': Maxwell keeps the vortices where they earn their keep, in the magneto-optical chapter, and stops using them where the field equations can stand on their own.

== What was scaffolding and what was building ==

{| class="wikitable"
! built on the vortex model !! survived it?
|-
| the magnetic stress tensor || yes — [[On Physical Lines of Force/Modern derivations/The Maxwell stress tensor|still standard]]
|-
| the magnetic energy density || yes
|-
| the vector potential as electromagnetic momentum || yes
|-
| the motional term <math>\mathbf{v}\times\mathbf{B}</math> || yes
|-
| '''the displacement current''' || yes — [[On Physical Lines of Force/Modern derivations/The displacement current|the term everything depends on]]
|-
| '''light as an electromagnetic wave''' || yes — rederived in 1865 without the model
|-
| the elasticity of the cells || no
|-
| the idle-wheel particles as electricity || no
|-
| rotation of polarized light by ether angular momentum || no, but the ''rotational character'' of magnetism, yes
|}

The general lesson is worth stating carefully, because it is easy to state badly. The point is '''not''' that being wrong is a good way to do physics. It is that a mechanical picture can be a reliable instrument for finding relations that outlast it — ''provided its author keeps track of which parts are secure and which are provisional''. Maxwell did that explicitly, in print, at every stage: [[On Physical Lines of Force/Part II|three levels of confidence]] named in a single sentence at the opening of Part II; the idle wheels labelled provisional the moment they were introduced; the sphericity of the cells conceded as an idealisation; and the velocity-of-light inference offered as something he "can scarcely avoid" rather than something he had proved.

The scaffolding came down. It had been erected by someone who knew it was scaffolding.

== Where this edition stops ==

This wiki follows the paper and its immediate sequels to 1873. It does not cover the experimental confirmation of electromagnetic waves, the reformulation of Maxwell's equations into modern vector form by Heaviside and Gibbs, or the twentieth-century developments. The [[On Physical Lines of Force/Chronology|chronology]] marks the boundary.

For the modern statements of everything the paper established, see [[On Physical Lines of Force/Modern derivations|From 1861 to today]].

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''Previous: [[On Physical Lines of Force/Part IV/The six results|The six results]] · [[On Physical Lines of Force|Back to the contents]]''

''Plain-language versions: [[On Physical Lines of Force/Explainers/A wrong model that produced right answers|A wrong model that produced right answers]] · [[On Physical Lines of Force/Explainers/What came after|What came after]]''