Michael Faraday and James Clerk Maxwell on Action-at-a-Distance
One of the most fundamental debates in physics is that of action-at-a-distance (actio-in-distans, far-action) vs. local motion (actio-in-contact, near-action). It is a topic that I have addressed in one way or another in several of my previous posts.
With respect to the study of electricity and magnetism, I published the post James Clerk Maxwell Opposes Action-at-a-Distance. Therein, I quoted from the Preface to the First Edition of his A Treatise on Electricity and Magnetism, in which he supported the propagation of forces through Michael Faraday’s fields, against the mostly-German proponents of action-at-a-distance.
In this post, I will look more carefully at some of the writings of Clerk Maxwell (1831-1879) and Faraday (1791-1867) on this topic. In particular, I will argue that neither of the two scientists actually refuted action-at-a-distance.
I begin with Clerk Maxwell’s paper, “On Action at a Distance”1, published in 1873. You can find this paper on Hans G. Schantz’s blog, Fields & Energy: "On Action at a Distance".
In this paper, Clerk Maxwell argues in favour of Faraday’s lines of force. But a careful reading of the paper is in order, as we will see. Clerk Maxwell begins with the following question:
The question is that of the transmission of force. We see that two bodies at a distance from each other exert a mutual influence on each other’s motion. Does this mutual action depend on the existence of some third thing, some medium of communication, occupying the space between the bodies, or do the bodies act on each other immediately, without the intervention of anything else? [p.311]
He examines some examples of apparently remote interaction between objects that can readily be explained through the motion of the air on earth. From this he raises the following question:
Why then should we not admit that the familiar mode of communicating motion by pushing and pulling with our hands is the type and exemplification of all action between bodies, even in cases in which we can observe nothing between the bodies which appears to take part in the action? [p.312]
He then presents the basic arguments of supporters of action-at-a-distance:
The advocates of the doctrine of action at a distance, however, have not been put to silence by such arguments. What right, say they, have we to assert that a body cannot act where it is not? Do we not see an instance of action at a distance in the case of a magnet, which acts on another magnet not only at a distance, but with the most complete indifference to the nature of the matter which occupies the intervening space? If the action depends on something occupying the space between the two magnets, it cannot surely be a matter of indifference whether this space is filled with air or not, or whether wood, glass, or copper, be placed between the magnets.
Besides this, Newton’s law of gravitation, which every astronomical observation tends only to establish more firmly, asserts not only that the heavenly bodies act on one another across immense intervals of space, but that two portions of matter, the one buried a thousand miles deep in the interior of the earth, and the other a hundred thousand miles deep in the body of the sun, act on one another with precisely the same force as if the strata beneath which each is buried had been non-existent. If any medium takes part in transmitting this action, it must surely make some difference whether the space between the bodies contains nothing but this medium, or whether it is occupied by the dense matter of the earth or of the sun. [p.313, my emphasis]
What follows is crucial, because this is the point that I want to emphasize in this post.
But the advocates of direct action at a distance are not content with instances of this kind, in which the phenomena, even at first sight, appear to favour their doctrine. They push their operations into the enemy’s camp, and maintain that even when the action is apparently the pressure of contiguous portions of matter, the contiguity is only apparent—that a space always intervenes between the bodies which act on each other. They assert, in short, that so far from action at a distance being impossible, it is the only kind of action which ever occurs, and that the favourite old vis a tergo [force from behind] of the schools has no existence in nature, and exists only in the imagination of schoolmen. [p.313, my emphasis]
What Clerk Maxwell is putting forward here is the argument that no matter the form of intermediate medium that might be proposed by scientists, in fact there is always some space between the particles of that medium, and so, and that level, there will be action-at-a-distance. This leads naturally to the following conclusion, from the point of view of those advocates:
Why, then, say the advocates of direct action, should we continue to maintain the doctrine, founded only on the rough experience of a pre-scientific age, that matter cannot act where it is not, instead of admitting that all the facts from which our ancestors concluded that contact is essential to action were in reality cases of action at a distance, the distance being too small to be measured by their imperfect means of observation? [pp.314-315, my emphasis]
Notwithstanding his opposition thereto, I claim that Clerk Maxwell in fact argues effectively in favour of action-at-a-distance.
He then moves on to the discovery by Hans Cristian Ørsted (also written Örsted, 1777-1851) that a compass turns when placed next to an electric current:
We have now arrived at the great discovery of Örsted of the connection between electricity and magnetism. Örsted found that an electric current acts on a magnetic pole, but that it neither attracts it nor repels it, but causes it to move round the current. He expressed this by saying that “the electric conflict acts in a revolving manner.”
The most obvious deduction from this new fact was that the action of the current on the magnet is not a push-and-pull force, but a rotatory force, and accordingly many minds were set a-speculating on vortices and streams of æther whirling round the current. [p.317]
However, André-Marie Ampère (1775-1836), was able to demonstrate that Ørsted’s observations could be explained by action-at-a-distance between current elements. This is what Clerk Maxwell writes:
But Ampère, by a combination of mathematical skill with experimental ingenuity, first proved that two electric currents act on one another, and then analysed this action into the resultant of a system of push-and-pull forces between the elementary parts of these currents. [p.317]
So Clerk Maxwell acknowledges Ampère’s impressive results, but, as we will see below, chooses to dismiss them, because, in his opinion, Ampère’s formula is too complex! As a result, Clerk Maxwell chooses to move on to Faraday’s work.
The formula of Ampère, however, is of extreme complexity, as compared with Newton’s law of gravitation, and many attempts have been made to resolve it into something of greater apparent simplicity.
I have no wish to lead you into a discussion of any of these attempts to improve a mathematical formula. Let us turn to the independent method of investigation employed by Faraday in those researches in electricity and magnetism which have made this Institution one of the most venerable shrines of science. [p.318]
In other words, apart from a criticism that Ampère’s formula is too complex, which in my opinion, it is not, Clerk Maxwell actually offers no strong argument against action-at-a-distance!
So now it is time to have a look at what Faraday wrote. A very useful article was written by Mary B. Hesse, entitled “Action at a Distance in Classical Physics”2.
She writes:
It was in regard to electric induction that Faraday first became convinced that the action was propagated through a medium and not at a distance. His experimental researches led to three conclusions which seemed to point to the existence of an active medium:
(i) The induction of electric charge between conductors across an insulating medium depends quantitatively on the nature of the insulator.
(ii) If the insulator is cut and the parts separated, opposite charges appear on the two separated surfaces.
(iii) The lines of induction are curved, as illustrated by the spark of a discharge, and by experiments showing how the force on a charged ball due to a charged insulator is affected by the presence and shape of intervening conductors, which may make induction “turn a corner.”
Faraday concluded that the insulating medium propagates the electric induction by means of its own particles, each of which is itself a conductor and becomes polarized, one side having a negative charge and the other a positive charge. [p.342]
But did this medium proposed by Faraday imply that there was no action-at-a-distance? This is what Faraday writes3:
As, therefore, in the electrolytic action, induction appeared to be the first step, and decomposition the second (the power of separating these steps from each other by giving the solid or fluid condition to the electrolyte being in our hands); as the induction was the same in its nature as that through air, glass, wax, &c. produced by any of the ordinary means; and as the whole effect in the electrolyte appeared to be an action of the particles thrown into a peculiar or polarized state, I was led to suspect that common induction itself was in all cases an action of contiguous particles*, and that electrical action at a distance (i.e. ordinary inductive action) never occurred except through the influence of the intervening matter. [paragraph 1164, pp.361-362, my emphasis]
Here is the note attached to the phrase “action of contiguous particles”.
* The word contiguous is perhaps not the best that might have been used here and elsewhere; for as particles do not touch each other it is not strictly correct. I was induced to employ it, because in its common acceptation it enabled me to state the theory plainly and with facility. By contiguous particles I mean those which are next.—Dec. 1838. [note to paragraph 1164, p.361, my emphasis]
So, if the particles of the medium do not touch each other, then the situation is exactly as described by Clerk Maxwell above:
that a space always intervenes between the bodies which act on each other. They [the advocates of direct action] assert, in short, that so far from action at a distance being impossible, it is the only kind of action which ever occurs. [Maxwell, p.313, my emphasis]
Mary Hesse continues:
So that ultimately it seems that even this action is at a distance if regarded on the atomic scale. Faraday is explicit about this in correspondence with Dr. R. Hare of Pennsylvania. Dr. Hare had objected that rarefication of the air between conductors does not affect the transmission of electric induction, and that therefore the material medium cannot be essential. He suggested that an imponderable matter should be postulated, so that the polarization of this matter between conductors would “connect the otherwise imperfect chain of causes.” Faraday replies that his use of “contiguous” includes a vacuum in which the particles of air may be separated by distances of the order of half an inch, but he will not commit himself here on the hypothesis of an imponderable aether. [p.342, my emphasis]
She concludes:
Physically, action at a distance on the atomic scale is retained by Faraday, because he regards each particle of the intervening medium as being itself a conductor, and the properties of insulators as arising from the assumption that the conducting particles are not in contact with each other. If they were in contact, there would be no insulators. [p.343, my emphasis]
So, James Clerk Maxwell stated that the advocates of direct action, or action-at-a-distance, argued that at every level of the universe, there is space between the particles at that level, and so interaction therebetween must be at a distance. And this is exactly what Michael Faraday supposed when he proposed a medium in which induction could take place.
My conclusion is that there may well be, at every level of the universe, a medium composed of finer particles, making up a lower level. Should there be a lowest level, then the interactions between particles at that lowest level would have to be action-at-a-distance.
However, as I wrote in Cristiaan Huygens Proposes an Infinite Series of Levels to the Universe, there might not be a lowest level. The implications of this possibility will be dealt with in my next post.
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James Clerk Maxwell. LIV. On Action at a Distance. In James Clerk Maxwell. The Scientific Papers. Volume Two. Edited by W.D. Niven. Dover.
Mary B. Hesse. Action at a Distance in Classical Physics. Isis, 46(4):337-353, Dec. 1955.
Michael Faraday. Experimental Researches in Electricity. Volume 1. London: Richard and John Edward Taylor, 1839.