On Action at a Distance (Browne)

by Walter Raleigh Browne

Read November 13, 1880

THE object of this paper is partly historical, partly critical. In discussing what is called "Action at a Distance," the statement is frequently made that Newton was of opinion that " nobody who possessed a competent faculty of thinking" could possibly imagine such a thing to exist. The writer wishes, first, to show historically that this is by no means an accurate representation of Newton-s views, and, secondly, to consider critically whether the repudiation of " action at a distance," which is now certainly common, is, after all, justified by the facts of the universe.

In the first place, Newton's words, contained in the Third Letter to Bentley, are as follows :—" That gravity should be innate, inherent, and essential to matter, so that one body may act on another body at a distance through a vacuum, without the mediation of any thing else by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to fixed laws ; but whether this agent be [72] material or immaterial I have left to the consideration of my readers."

Now, in speaking of this passage, it is- usual to quote the first of these sentences only, and omit the second ; and yet it is obvious that the second is intended to explain and define the sense of the first. Read by the light of the second, it seems perfectly clear that all which is denied in the first is the possibility of gravity being an inherent property of matter, in the sense in which hardness, inertia, &c. may be considered as properties. What Newton might seem to have had in his mind was the coarse materialism of Democritus and Lucretius, which held that all the phenomena of the universe were due to the mere motions and clashings of its ponderable atoms. This at least, he would hold, was disproved by his discoveries, because to defend it by assuming an occult property of matter, which could extend to a distance, was absurd. All, however, which he really says is that one body cannot, uncaused, act on another at a distance. In the second sentence he expressly uses, not indeed the word Cause, but the much stronger word Agent; and he distinctly contemplates the possibility of this agent being, not material, but immaterial. It seems clear, therefore, that he is thinking of nothing less than of denying that action at a distance may, as a matter of fact, exist. Indeed, when we consider that this passage occurs, not in a mathematical work, but in a letter expressly treating of the relation between the discoveries of science and the doctrines of theology, and when we remember the strong theological views which he is known to have held, it seems impossible to doubt that he would have been perfectly contented to acquiesce in the immaterial nature of the agent of gravity ; though, no doubt, he would have been perfectly open to consider any reasonable hypothesis of a material agent which might have been placed before him.

Having thus attempted to restore the true sense of this famous passage, the writer will go on to consider, in the second place, how far the conception of Action at a distance actually merits the condemnation it has received. It seems desirable to commence with a definition, and to lay down the consequences which flow from it in general, before proceeding to consider particular cases. [73]

Definition.— "By the term 'Action at a distance' is meant that direct action takes place between two bodies, separated from each other by a finite distance, without the intervention of any other body whatever."

Now if action at a distance does not exist, then the only direct way in which one body (A) can act upon another (B) is by coming into absolute contact with it; and the only indirect ways in which it can act upon it are two, viz. either by projecting a third body from contact with itself into contact with B, or by diverting some third body which, if not diverted, would have come into contact with B.

If action at a distance does not exist, all the actions between all the bodies of the universe must be explicable, by impact, on one of these three hypotheses. If any phenomenon takes place which cannot be so explained, then action at a distance does exist. It may be added that, if it is shown to exist in any one instance and at any distance, there is no probability against its existence in any other instance and at any other distance. It is no less wonderful, and no more wonderful, that two bodies should act on each other across the hundred millionth of an inch, than that they should act on each other across a hundred million of miles. In fact it is easy to conceive a creature so large, or so small, that the difference between these two distances would appear to it quite insignificant.

Let us now take the above three hypotheses and see whether all the actions in the universe can be explained by them.

First, as to the direct impact of one interacting body A upon another B. This may no doubt explain certain obvious eases, as the stoppage of a falling body when it reaches the earth ; but it is equally obvious that there are many others, such as gravity, magnetism, fact, it will be granted that in these and many other cases there is an apparent action between bodies at a distance; and our business is to see whether it is real or apparent only.

Secondly, with reference to the projection of other bodies from A against B. It is clear that the actions thus produced can be actions of repulsion only: therefore this principle cannot explain any case of attraction. Moreover the power by which A is able to project these bodies against B itself requires explanation. If they have previously been at rest in [74] relation to A, then A can only project them by some innate explosive power totally different from impact. And if any one suggests that the bodies have previously been in motion with respect to A, and that they are projected by elastic reaction from A, then he must be asked to give an explanation of elasticity from impact only, and without introducing action at a distance. In any case it seems clear that this principle will not carry us very far in explaining the actions of the universe.

Thirdly, we have the principle that A may stop certain other bodies, which would otherwise have impinged upon B. This principle, as is well known, was applied by Le Sage to explain the facts of gravitation.^[1] His hypothesis was that showers of "extramundane particles " are sweeping through space equally in all directions, and that a fraction of these, being intercepted by A and B, urge those two bodies towards each other. This hypothesis is encumbered with a large number of arbitrary assumptions; and the latest supporter of the theory, Mr. S. Tolver Preston,^[2] presents it under a greatly modified form. He supposes the solar system to be immersed in an impalpable gas, the particles of which have a mean length of free path greater than the distance through which gravity has been observed to hold (greater, therefore, than the distance between the Sun and Neptune), and which tend to bring together, by the resultant of their impacts upon them, any two bodies within that range. It is not proposed in this paper to attempt an exhaustive discussion of this theory; but were it left as an unquestioned explanation of gravitation, it might be thought a strong presumption that all other actions were to be explained on the same principle. It may therefore be remarked that it is encumbered by very serious difficulties. In addition to those put forward by Dr. Croll and others, the following may be suggested:—

(1) Mr. Tolver Preston founds his theory on the late Prof. Maxwell's proof,^[3] that "a self-acting adjustment goes on among a system of bodies or particles in free collision, such that the particles are caused to move equally in all directions, [75] this being the condition requisite to produce equilibrium of pressure".^[4] Now this equilibrium of pressure, and the theory based upon it, may be perfectly true for all known gases. But all such gases are under certain conditions, which need not hold universally; in especial they are bounded in some way. The atmosphere, which is the freest gas we can observe directly, is bounded by the earth on one side and space on the other, and is prevented from passing into space by the action of gravity. But we have no right whatever to assume such a boundary for interstellar space, or to assume that a gas filling such a space would have equilibrium of pressure. The probability would seem to be the other way; for any disturbance in such a gas would tend to propagate itself in all directions for ever. In any case, Maxwell's results must be proved, not assumed, to hold for this gravity-gas, as it may be termed.

(2) Another difficulty in the theory is the enormous degree of porosity which it postulates for solid bodies. To fix our ideas, suppose that, in any unit of surface of a solid, one millionth part only is occupied by the really solid part (i. e. the part which would stop the particles of the gravity-gas) of the molecules composing that surface. Then it is obvious that a layer of such molecules a few millions thick would be practically certain to stop the whole of the gravity-particles impinging upon it. No arrangement of the molecules one behind the other will get over this, because the gravity-particles are assumed to come in all directions at once. Now such a layer would certainly be no more than a small fraction of an inch in thickness. And yet it is absolutely necessary for the theory (in order to explain how gravity varies as mass) to suppose that these gravity-particles pass through the 16,000 miles of the earth's diameter, under the enormous density, pressure, and temperature which must exist in the interior, without having more than a very small proportion of their number stopped in the passage. The difficulty is rendered the greater when we remember that, ex hyp., these attenuated molecules cannot act on each other at a distance, in producing the various [76] phenomena of solid bodies, but only in one of the three modes of direct impact enumerated above.

(3) Another difficulty arises from the fact that the heavenly bodies are not found to experience any perceptible resistance whatever in passing through this gravity-gas. It is clear that if a body be in motion in the midst of a shower of such particles coming equally from all directions, it will receive a greater number of blows on its front surface, and a less number on its rear surface, than if it were at rest; and consequently its motion will be retarded. The only way of surmounting this difficulty is to suppose that the heavenly bodies, in relation to the gravity-gas, are practically at rest; in other words, that the velocity of the gravity-particles is practically indefinite compared with that of the heavenly bodies. Since in the case of Mercury, for instance, this latter velocity is about thirty miles per second, it is clear that the velocity of the gravity-particles must be something altogether beyond calculation; and then, since the effect of the collisions is, after all, very limited, the mass of the particles must be assumed correspondingly small. Hence our conception of the gravity-gas must practically be that of an indefinite number of indefinitely small particles moving in all directions with indefinitely high velocities—a conception from which it hardly seems safe to draw any definite conclusion whatever.

(4) The last-mentioned difficulty leads to another, viz. to fix the relations between the gravity-gas and the luminiferous aether. They cannot be the same; for Mr. Tolver Preston and Prof. Maxwell have shown^[5] that the velocity of propagation of a wave in such a gas = √(5)/3 x the velocity of the gas-particles. Since the velocity of waves in the aether is about 180,000 miles per second, this would give the velocity of the particles themselves = about 130,000 miles per second— a velocity immensely below what is required to account for the fact of non-resistance. But if the aether and the gravity-gas be different bodies, the particles of the latter must be colliding continually with those of the former, as they collide with the molecules of ordinary matter. How is it that no effects due [77] to such collisions are observed ? It would seem likely that they would assume the shape of a diffused glow of light and heat, growing more and more intense as the translatory motion of the gravity-particles was turned into vibratory motion of the tether-particles. It is needless to say that nothing in the least resembling this takes place.

We will here leave the discussion of Le Sage's impact theory, as explaining the particular case of gravitation, and go on to inquire how the same, or any other impact theory, can explain some other phenomena of the universe. We will first take those of cohesion.

Cohesion.— To fix our ideas, let us take the case of a square bar of good wrought iron or mild steel, 1 foot long and 1 square inch in area. Then the following two facts, amongst others, have to be accounted for:—

(a) The extension of the bar as a whole (and therefore the extension of the mean distance between the successive layers of its molecules) by 1/1000 of its length is sufficient to produce between the successive sections of the bar a stress of tension ( taking the form of an attraction between the sections) of about 15 tons, say 8000 times the attraction exercised by the earth upon the whole bar when placed in contact with it.

(b) The contraction of the bar through the same relative distance is sufficient to produce between the sections a stress of compression (taking the form of a repulsion between the sections) also of 15 tons or thereabouts.

Can these two facts be explained on any of the three impact theories, which we have shown to be the only possible ones? It seems almost sufficient to ask the question; but it may be well to take them in order.

(1) Can the facts be explained on the hypothesis of direct contact between the molecules ? Were this true, it would be impossible to produce any contraction of the bar without forcing two solid bodies into the same space. It is obvious that it will not do to suggest that the contraction may be in the molecules themselves ; for then we have only to transfer the inquiry to the particles composing those molecules. Are these particles themselves in contact or not ? If they are not, they cannot keep the bar together ; if they are, they cannot be compressed. Again, if the molecules are spherical, or of any [78] other regular shape whatever, they cannot oppose any resistance to separation, i. e. there can be no tensional stress. The only way out of this seems to be to conceive them shaped something like burrs, and holding on to each other by hooks. This is altogether contrary to the vortex-atom and all other known theories of molecules. Moreover such burr-like molecules must hold to each other somewhat loosely; and a certain amount of extension would be necessary (as in the case of a slack chain) before any resistance was experienced. But no such slackness has been observed with the most delicate instruments ; and we have seen that an extension of 1/1000 is sufficient to produce an enormous resistance. For these and the like reasons the hypothesis of direct contact is inadmissible.

(2) Can the facts be explained on the hypothesis of particles projected from the molecules of one section against those of the next ? Now it is clear that any effect due to this cause will be merely an effect of repulsion. Consequently the end section of the bar will be repelled from that next to it, and will fly off; another body brought into contact with the bar will be repelled by it, &c. For these and the like reasons this hypothesis is inadmissible.

(3) Can the facts be explained on the same hypothesis as that of Le Sage, viz. of independent particles flying through space and intercepted by the molecules of the bar ? In the first place, it is clear that these cannot be the particles of the gravity-gas ; for if these pass through the earth without having more than a small proportion stopped, it is clear that the number intercepted by an inch of iron will be infinitesimal. We should have to conceive, therefore, a separate atmosphere for each solid body, and an atmosphere the effects of which are many thousand times as great as that of the gravity-gas. But, further, let us assume this atmosphere, and consider what will happen when the bar is extended. An}- one section will be removed to a greater distance from the next, and its sheltering influence will be diminished in the inverse ratio of the squares of the distances. Consequently the effect of extension will be to diminish the attraction between the sections; whereas the actual effect is enormously to increase it. For these and the like reasons this third and last hypothesis is also inadmissible. [79]

The two latter hypotheses, and any combination of them, labour under a further and fatal disadvantage, viz. that the cohesion of the bar would be different in different parts. Thus in whatever way the flying particles are supposed to move, it is evident by symmetry that the central section will be solicited in one direction precisely as much as in another; hence the slightest pull will cause the bar to part in the middle.

The above trains of reasoning are not long, and rest on undoubted facts; and the writer has not been able to discover any flaw in them. But unless some such flaw, and a fatal one, be discovered, it must be held to be demonstrated that the phenomena of cohesion cannot be explained except on the hypothesis of action at a distance.

Magnetism.— Of the many difficult cases presented by the phenomena of electricity, it will be sufficient to cite one of the simplest. When an ordinary iron magnet is brought near a piece of iron, the latter is attracted to it. Now the first impact hypothesis is here inadmissible, because the bodies are not in contact; and the second, because the effect is one of attraction, not of repulsion. Thus the only possible explanation of this fact, apart from action at a distance, is by supposing that the magnet intercepts a proportion of a shower of particles which would otherwise impinge equally in all directions upon the iron. It is of course possible to imagine a " magnetism- gas," different again from both the "gravity-gas " and the " cohesion-gases," to which this would apply; but the writer has not been able to imagine any property, consistent with the principle of impact, which could be given to the magnet, such as to make it intercept these particles, when the same magnet, before being magnetized, would be unable to do so—and also such as would make it intercept the particles flying towards a piece of iron, and not to intercept the particles flying towards a similar piece of brass.

Vibrations.— Any thing like the vibration of a molecule about a central position (which is the fundamental idea in explaining Heat, Light, and all undulatory movements) seems to be impossible on this theory. For a molecule, once started, is in the position of a free projectile through space, and will continue to move in a straight line until it accidentally strikes against some other molecule which may be moving in any [80] other direction. Hence it is obvious that the chance of the molecule ever coming back to its original position is indefinitely small. This applies especially to the case of the aether, the particles of which are comparable to those of the gravity-gas.

The above are a few very simple cases, in which it seems certainly difficult to avoid the conclusion that action at a distance must necessarily exist. And if it exists in these cases, then, as already remarked, it becomes at least probable that it may exist in other cases, such as gravity, where the evidence is not so clear. In conclusion it may be asked, therefore, what real reason is there why this hypothesis of action at a distance should not be admitted. To some minds it seems to present itself in the light of a theory which it is a priori difficult, if not impossible, to believe. But Physics has nothing to do with mental impressions; and in the history of the Inductive Sciences there are many well-known instances, where a priori notions of this kind have seriously hindered the advance of knowledge. It is evident that the progress of science in any direction must be towards certain universal and final facts, beyond which she cannot go. On the one theory, the ultimate fact in the ease of gravity is enunciated in a very simple law of force, connecting together all ponderable bodies. On the other theory, the ultimate facts are apparently enunciated in the laws of impact between elastic bodies (which also involve the conception of force), and in the statement of the fundamental conceptions and results of the Kinetic Theory of Gases, assumed to hold for an exceedingly rare gas pervading all space. The writer submits that, a priori, one of these theories is as likely as the other—but that both must be judged by the test of their accordance with known facts, and by that test alone must be accepted or condemned.

On the general comparison of the two views, as to their power of explaining facts, one remark may perhaps be allowed. It will not, probably, be denied that, if we only knew the exact laws of any action whatever between bodies, we could at once explain it on the hypothesis that these bodies are made up of centres of force, each possessing position and inertia, and acting on the other centres according to laws which it would be [81] easy, or at least possible, to determine. It certainly cannot be said at present that we could equally explain any action by the mere laws of impact, even if we include in them those of elasticity. So long as these two statements hold, it seems more in accordance with the cautious spirit of true science to maintain the old theory, than unreservedly to adopt the new one.

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1. Sir W. Thomson, Phil. Mag. May 1873.
2. Phil. Mag. Sept. 1877, Nov. 1877, Jan. 1878.
3. S. Tolver Preston, Phil. Mag. Sept. 1877.
4. I have, unfortunately, failed to verify the reference to this paper of Prof. Maxwell's, given by Mr. Tolver Preston, and therefore can speak of it only from his description.
5. S. Tolver Preston, Phil. Mag. June 1877.