“Lines of Force” & Maxwell

Reference: A Logical Approach to Theoretical Physics

Michael Faraday (1791 – 1867) came up with a brilliant solution to the problem of “action at a distance” (action across the void) by modeling the space between atoms as lines of force. These lines, when concentrated, formed a center of force that could not be distinguished from the atom. Furthermore, Faraday postulated that these lines of force, extended from the atoms of a material body to the atoms of another material body forming the space between them. These lines of force that formed the space then carried the vibrations of radiative phenomena. Thus, matter and space were but a manifestation of a varying force field. To Faraday, the lines of force replaced the very idea of aether, which was assumed to be of material origin and filling the space.

Maxwell (1831 – 1879) constructed his theory of Electromagnetism based on the inspiration he got from the experimental research of Faraday. He writes in the preface of his major work “A Treatise on Electricity & Magnetism.”¹

Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.

In his correspondence with Faraday, however, Maxwell disagreed with Faraday’s ideas on the conservation of Force, because Faraday’s perspective on force did not agree with Newton’s definition of “force”. Maxwell wrote²:

Now, first, I am sorry that we do not keep our words for distinct things more distinct, and speak of the “Conservation of Work or of Energy” as applied to the relations between the amount of “vis viva” and of “tension” in the world; and of the “Duality of Force” as referring to the equality of action and reaction.

Energy is the power a thing has of doing work arising either from its own motion or from the “tension” subsisting between it and other things.

Force is the tendency of a body to pass from one place to another, and depends upon the amount of change of “tension” which that passage would produce.

Maxwell seems to have tried his best to unlock the mystery of action going on in the medium that Faraday sought, but he did not quite understand what Faraday meant by “force of nature”. Faraday had modeled his lines of forces such that they included the inherent force of substance (inertia) as well the energy due to its activity. He was quite clear in saying that his ideas were an alternative to the aether theory. But Maxwell couldn’t move beyond the view of nature as presented by Newton’s mechanics and the aether theory.

In this excellent article Kevin Brown points out where Maxwell was influenced by the aether theory and diverged from the ideas of Faraday³.

Maxwell’s understanding of the electrical force that exists between charged particles was based on the idea that even the ‘empty space’ of the vacuum is actually permeated with some kind of substance, called the ether, which consists of individual parts that can act as dielectrics… In simple terms, he pictured ordinary empty space, when devoid of any electric field, as consisting of many small pairs of positive and negative charge elements, and in the absence of an electric field the two opposite charges in each pair are essentially co-located, so there is no net change or electric potential observable at any point. If an electric potential is established across some region of this medium (e.g., empty space), it tends to pull the components of each pair apart slightly. Maxwell termed this an electric displacement in the medium. Of course, the constituent parts of the dielectric pairs attract each other, so the electric displacement is somewhat like stretching a little spring at each point in space.

The article goes on to say³,

It’s interesting that this theory, which supposedly denies the intelligibility of distant action, nevertheless ends up invoking (albeit on a very small scale) what appears to be elementary attraction between distinct and separate entities.

According to Maxwell himself³,

The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric or magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced…

Maxwell’s modeled the lines of force along the lines of incompressible fluid⁴. These mathematical lines of force bunched up and spread out in space, but they could not model the substance of space thinning out and thickening up as Faraday’s lines could. It gave the electromagnetic field a mechanical character that maintained its identity rigidly separate from space.

Maxwell’s mathematical model of lines of force did not thicken to coincide with matter or thinned to coincide with space as Faraday had visualized from his extensive and painstaking experimentation.

Maxwell then admitted⁵

If, in order to get rid of the idea of action at a distance, we imagine a material medium through which the action is transmitted, all that we have done is to substitute for a single action at a great distance a series of actions at smaller distances between the parts of the medium, so that we cannot even thus get rid of action at a distance.

Maxwell’s field existed between two oppositely charged material surfaces, or between the positive nucleus and the surrounding electrons in an atom. Maxwell’s electromagnetic field was a special case that depended on the concept of discrete electrical charge. It could not be extended to fill the whole space as Faraday’s lines of force could.

Maxwell was unable to unlock the mystery of action at a distance because he assumed his electromagnetic field to be based on discrete electrical charges. Discreteness implies separation and, thus, action at a distance.

Discrete charge and electromagnetic field may exist in the gamma range of the spectrum where electron’s frequency is found, but we may not assume it to exist throughout the spectrum of light. Visible light does not have charge but it has momentum. It may be possible that momentum (or inertia) has some relation to charge.

Interestingly enough, charge has same dimensions as mass per the dimensional analysis provided by Maxwell⁶.

[M] = [Q] = [L³T ^-2] = Area x acceleration

Charge and mass may be related by the property of inertia. This requires that we should look at the characteristics of inertia more closely.

Thus Faraday’s idea of continuum of substance was never implemented by Maxwell. Maxwell’s electromagnetic field was not the same as Faraday’s field of force. The theory of electromagnetism did not provide a viable solution to the problem of action at a distance.

Faraday’s solution to the problem of “action at a distance” got sidetracked; and the mystery of aether continued.

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