# On Action at a Distance

On Action at a Distance, is an article by James Clerk Maxwell which appeared in Nature (Mar 6, 1873) Vol VII, Issue 175. It was also published, with minor changes, both in the Proceedings of the Royal Institution of Great Britain Vol. VII. 1876, and in Vol. 2, The Scientific Papers of James Clerk Maxwell in 1890. The article is a discussion of scientific and mathematical investigations relating to the concepts of action at a distance, Michael Faraday's lines of force, and the luminiferous aether. Maxwell was personally responsible for much of the related research.

## Quotes

• I must ask you to go over very old ground, and to turn your attention to a question which has been raised again and again ever since man began to think.
• The question is that of the transmission of force. We see 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?
• The mode in which Faraday was accustomed to look at phenomena of this kind differs from that adapted by many modern inquirers, and my special aim will be to enable you to place yourselves at Faraday's point of view, and to point out the scientific value of that conception of lines of force which, in his hands, became the key to the science of electricity. ...
• Why... should we not admit that the familiar mode of communicating motion by pushing and pulling... is the type and exemplification of all action between bodies, even in case in which we can observe nothing between...
• Here for instance is a kind of attraction which Professor Guthrie has made us familiar. A disk is set in vibtration, and is then brought near a light suspended body, which immediately begins to move towards the disk as if by an invisible cord. ...Sir W. Thomson has pointed out that in a moving fluid the pressure is least where the velocity is greatest. The velocity of the vibratory motion of the air is greatest near the disk. Hence the pressure of the air on the suspended body is less on the side nearest the disk... the body yields to the greater pressuire, and moves toward the disk.
The disk, therefore, does not act where it is not. It sets the air next to it in motion by pushing it, this motion is communicated to more and more distant portions of the air in turn, and thus the pressure on opposite sides of the suspended body rendered unequal, and it moves toward the disk in consequence of excess pressure. The force is therefore the force of the old school—a case of vis a tergo—a shove from behind.
• The advocates of the doctrine of action at a distance, however... say... Do we not see an instance of action at a distance in the case of a magnet... Besides this, Newton's law of gravitation... asserts not only that the heavenly bodies act ... across immense intervals of space... on one another with precisely the same force as if the strata beneath which each is buried [were] non-existant. If any medium takes part... it must surely make some difference whether the space... contains nothing but this medium, or whether it is occupied by the dense matter of the earth or of the sun.
• But the advocates... maintain that even when the action is apparently the pressure of contiguous portions of matter... that a space always intervenes between... that so far from action at a distance being impossible, it is the only kind of action which ever occurs, and that the favorite old vis a tergo... exists only in the imagination of schoolmen.
• The best way to prove that when one body pushes another it does not touch it, is to measure the distance between... Here are two glass lenses, one of which is pressed against another... By means of an electric light... a series of coloured rings is formed on the screen... first observed and first explained by Newton. The particular colour of any ring depends on the distance between the surfaces... [W]hat we call optical contact is not real contact. Optical contact indicates only that the distance between... is much less than a wavelength... Now it is possible to bring two pieces of glass so close together, that... they will adhere together so firmly, that when torn asunder the glass will break... Thus... bodies begin to press against each other whilst still at a measurable distance, and that even when pressed together with great force they are not in absolute contact...
Why, then, say the advocates... should we continue to maintain the doctrine, founded only in the rough experience of a pre-scientific age, that matter cannot act where it is not, instead of admitting that all... contact essential to action were in reality cases of action at a distance... too small to be measured...
• [A]s for those who introduce ætherial, or other media... without any direct evidence... or any clear understanding of how the media work... the less these men talk about their philosophical scruples about admitting action at a distance the better.
• The progress of science in Newton's time consisted in getting rid of the celestial machinery with which generations of astronomers had encumbered the heavens, and thus "sweeping cobwebs off the sky."
Though the planets had already got rid of their crystal spheres, they were still swimming in the vortices of Descartes. Magnets were surrounded by effluvia, and electrified bodies by atmospheres, the properties of which resembled in no respect those of ordinary effluvias and atmospheres.
• When Newton demonstrated that the force which acts on each of the heavenly bodies depends on its relative position with respect to the other bodies, the new theory met with violent opposition by the advanced philosophers... who described the doctrine of gravitation as a return to the exploded method of explaining everything by occult causes, attractive virtues, and the like.
... To determine the mode in which their mutual action depends on their relative positions was a great step in science, and this Newton asserted he had made.
• But so far was Newton from asserting that bodies really act... over a distance, independently of anything in between them, that in a letter to Bentley... quoted by Faraday... he says:—"It is inconceivable that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact, as it must do if gravitation, in the sense of Epicurus, be essential and inherent in it... That gravity should be innate, inherent, and essential to matter, so that one body can act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe that no man who has in philosophical matters a competent faculty of thinking can ever fall into it."
• Accordingly, we find in his Optical Queries, and in his letters to Boyle, that Newton had very early made the attempt to account for gravitation by means of the pressure of a medium, and that the reason he did not publish these investigations "proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature."
• The doctrine of direct action at a distance... was first asserted by Roger Cotes, in his preface to the Principia... According to Cotes, it is by experience that we learn that all bodies gravitate. We do not learn in any other way that they are extended, movable, or solid. Gravitation, therefore, has as much right to be considered an essential property of matter...
• And when the Newtonian philosophy gained ground in Europe, it was the opinion of Cotes rather than that of Newton that became most prevalent, till at last Boscovich propounded his theory, that matter is a congeries of mathematical points, each endowed with the power of attracting or repelling the others according to fixed laws. In his world, matter is unextended, and contact is impossible. He did not forget, however, to endow his mathematical points with inertia.
• [I]t was most essential that Newton's method should be extended to every branch of science to which it was applicable—that we should investigate the forces with which bodies act on each other... before attempting to explain how that force is transmitted. No men could be better fitted to apply themselves to the first part of the problem, than those who considered the second part quite unnecessary.
• Accordingly, Cavendish, Coulomb, and Poisson, the founders of the exact sciences of electricity and magnetism, paid no regard to those old notions of "magnetic effluvia" and "electric atmospheres," which had been put forth in the previous century, but turned their undivided attention to the determination of the law of force, according to which electrified and magnetized bodies attract or repel each other. In this way the true laws of these actions were discovered... by men who never doubted that the action took place at a distance, without the intervention of any medium, and who would have regarded the discovery of such a medium as complicating rather than as explaining the undoubted phenomena of attraction.
• 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 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 rotary force, and accordingly many minds were set a-speculating on vortices and streams of æther whirling round the current.
• 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 as a result of a system of push-and-pull forces between the elementary parts of these currents.
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.
• 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.
No man ever more conscientiously and systematically laboured to improve all his powers of mind than did Faraday from the very beginning of his scientific career. But whereas the general course of scientific method then consisted in the application of the ideas of mathematics and astronomy to each new investigation in turn, Faraday seems to have had no opportunity of acquiring a technical knowledge of mathematics, and his knowledge of astronomy was mainly derived from books.
Hence, though he had a profound respect for the great discovery of Newton, he regarded the attraction of gravitation as a sort of sacred mystery, which, as he was not an astronomer, he had no right to gainsay or to doubt, his duty being to believe it in the exact form in which it was delivered to him. Such a dead faith was not likely to lead him to explain new phenomena by means of direct attractions.
Besides this, the treatises of Poisson and Ampère are of so technical a form, that to derive any assistance from them the student must have been thoroughly trained in mathematics, and it is very doubtful is such a training can be begun with advantage in mature years.
• Thus Faraday, with his penetrating intellect, his devotion to science, and his opportunities for experiments, was debarred from following the course of thought which had led to the achievements of the French philosophers, and was obliged to explain the phenomena to himself by means of a symbolism which he could understand, instead of adapting what had hitherto been the only tongue of the learned.
• This new symbolism consisted of those lines of force extending themselves in every direction from electrified and magnetic bodies, which Faraday in his mind's eye saw as distinctly as the solid bodies from which they eminated.
• The idea of lines of force and their exhibition by means of iron filings was nothing new. They had been observed repeatedly, and investigated mathematically as an interesting curiosity of science. But let us hear Faraday himself...
"It would be a voluntary and unnecessary abandonment of most valuable aid if an experimentalist, who chooses to consider magnetic power as represented by lines of magnetic force, were to deny him the use of magnetic filings. By their employment he may make many conditions of the power, even in complicated cases, visible to the eye at once, may trace the varying direction of the lines of force and determine the relative polarity, may observe in which direction the power is increasing or diminishing, and in complex systems may determine the neutral points, or places where there is neither polarity nor power, even when they exist in the midst of powerful magnets. By their use probable results may be seen at once, and many a valuable suggestion gained for future leading experiments."
• Experiment on Lines of Force. In this experiment each filing becomes a little magnet. The poles of opposite names belonging to different filings attract each other and stick together, and more filings attach themselves to the exposed poles, that is, to the ends of the row of filings. In this way the filings, instead of forming a confused system of dots over the paper, draw together, filing to filing, till long fibres of filings are formed, which indicate by their direction the lines of force in every part of the field.
• The mathematicians saw in this experiment nothing but a method of exhibiting at one view the direction in different places of the resultant two forces, one directed to each pole of the magnet; a somewhat complicated result of a simple law of force.
• But Faraday, by a series of steps as remarkable for their geometrical definiteness as for their speculative ingenuity, imparted to his conception of these lines of force a clearness and precision far in advance of that with which the mathematicians could then invest their new formulæ.
• Faraday's lines of force are not to be considered merely as individuals, but as forming a system, drawn in space in a definite manner so that the number of lines which pass through an area, say of one square inch, indicates the intensity of the force acting through the area. Thus the lines of force become definite in number. The strength of a magnetic pole is measured by the number of lines which proceed from it; the electro-tonic state of a circuit is measured by the number of lines which pass through it.
• [E]ach individual line has a continuous existence in space and time. When a piece of steel becomes a magnet, or when an electric current begins to flow, the lines of force do not start into existence each in its own place, but as the strength increases new lines are developed within the magnet or current, and gradually grow outwards, so that the whole system expands from within, like Newton's rings in our former experiment.
• Thus every line of force preserves its identity during the whole course of its existence, though its shape and size may be altered to any extent.
• [E]very question relating to the forces acting on magnets or currents, or to the induction of currents in conducting circuits, may be solved by the consideration of Faraday's lines of force. In this place they can never be forgotten. By means of this new symbolism, Faraday defined with mathematical precision the whole theory of electro-magnetism, in language free from mathematical technicalities, and applicable to the most complicated and simplest cases.
• He observed that the motion which the magnetic and electric force tends to produce is invariably such a to shorten the lines of force and allow them to spread out laterally from each other. He thus preserved in the medium a state of stress, consisting of a tension, like that of a rope, in the direction of the lines of force, combined with a pressure in all directions at right angles to them.
• This is quite a new conception of action at a distance, reducing it to a phenomenon of the same kind as that action at a distance which is exerted by means of the tension of ropes and the pressure of rods.
• When the muscles of our bodies are excited... the fibres tend to shorten themselves and at the same time expand laterally. A state of stress is produced in the muscle, and the limb moves. This explanation of muscular action is by no means complete...
• For similar reasons we may regard Faraday's conception of a state of stress in the electro-magnetic field as a method of explaining action at a distance by means of the continuous transmission of force, even though we do not know how the state of stress is produced.
• [O]ne of Faraday's most pregnant discoveries, that of the magnetic rotation of polarised light, enables us to proceed... Of two circularly polarised rays of light, precisely similar in configuration, but rotating in opposite directions, that ray is propagated with greater velocity which rotates in the same direction as the electricity of the magnetizing current.
• It follows... as Sir W. Thomson has shewn by strict dynamical reasoning, that the medium when under the action of magnetic force must be in a state of rotation... [i.e.,] that small portions of the medium, which we may call molecular vortices, are rotating, each on its own axis, the direction of this axis being that of the magnetic force.
• Here, then, we have an explanation of the tendency of the lines of magnetic force to spread out laterally and to shorten themselves. It arises from the centrifugal force of the molecular vortices.
• We have thus found that there are several different kinds of work to be done by the electro-magnetic medium if it exists. We have also seem that magnetism has an intimate relation to light, and we know that there is a theory of light which supposes it to consist of the vibrations of a medium. How is this luminiferous medium related to our electro-magnetic medium?
• [E]lectro-magnetic measurements have been made from which we can calculate by dynamical principles the velocity of propagation of small magnetic disturbances in the supposed electro-magnetic medium.
This velocity is great, from 288 to 314 millions of metres per second... Now the velocity of light, according to Foucault's experiments, is 298... But if the luminiferous and the electro-magnetic media occupy the same place, and transmit disturbances at the same velocity, what reason have we to distinguish the one from the other? By considering them as the same, we avoid at least the reproach of filling space twice over with different kinds of æther.
• [T]he only kind of electro-magnetic disturbance which can be propagated through a non-conducting medium is a disturbance transverse to the direction of propagation, agreeing... with what we know about that disturbance which we call light.
• [T]he electro-magnetic theory of light will agree in every respect with the undulatory theory, and the work of Thomas Young and Fresnel will be established on a firmer basis than ever, when joined with that of Cavindish and Coulomb by the key-stone of the combined sciences of light and electricity—Faraday's great discovery of the electro-magnetic rotation of light.
• The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has seen fit to fill with the symbols of the manifest order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity. It extends unbroken from star to star; and when a molecule of hydrogen vibrates in the dog-star, the medium receives the impulses of these vibrations; and after carrying it in its immense bosom for three years, delivers them in due course, regular order, and full tale into the spectroscope of Mr Huggins, at Tulse Hill.
• But the medium has other functions and operations besides bearing light from man to man, and from world to world, and giving evidence of the absolute unity of the metric system of the universe. Its minute parts may have rotatory as well as vibratory motions, and the axis of rotation form those lines of magnetic force which extend in unbroken continuity into regions which no eye has seen, and which, by their action on our magnets, are telling us in language not yet interpreted, what is going on in the hidden underworld from minute to minute and from century to century.
• And these lines must not be regarded as mere mathematical abstractions. They are the directions in which the medium is exerting a tension like that of a rope, or rather, like that of our own muscles. The tension of the medium in the direction of the earth's magnetic force is in this country one grain weight on eight square feet. In some of Dr Joule's experiments, the medium has exerted a tension of 200 lbs. per square inch.
• But the medium, in virtue of the very same elasticity by which it is able to transmit undulations of light, is also able to act as a spring. When properly wound up, it exerts a tension, different from the magnetic tension, by which it draws oppositely electrified bodies together, produces effects through the length of telegraph wires, and when of sufficient intensity, leads to the rupture and explosion called lightning.
• These are some of the already discovered properties of that which has been called vacuum, or nothing at all. They enable us to resolve several kinds of action at a distance into actions between contiguous parts of a continuous substance. Whether this resolution is of the nature of explication or complication, I must leave to the metaphysicians.