Isaac Newton On Mutual Actions

In my post Peter and Neal Graneau Explain the Importance of Newton's Third Law and Action-at-a-Distance, I quoted from their book Newton versus Einstein¹:

Since the magnitude of the gravitational attraction was a function of the size of both masses, and their distance of separation, it had to be an effect which both bodies experienced at the same time. To Newton the simultaneity of the gravitational force experienced by both bodies appears to have been self-evident. He lost no time discussing it. [p.35, my emphasis]

Prof. André Assis reminded me that Isaac Newton (1643-1727) himself wrote similarly, referring explicitly to the third Law of Motion, in his A Treatise of the System of the World².

Newton states that the centripetal force attracting a body towards another body around which it is revolving, is the result of mutual action, and so the attractive force is also mutual.

SINCE the action of the centripetal force upon the bodies attracted, is, at equal distances, proportional to the quantities of matter in those bodies, reason requires that it should be also proportional to the quantity of matter in the body attracting. For all action is mutual, and (by the third Law of Motion) makes the bodies mutually to approach one to the other, and therefore must be the same in both bodies. It is true that we may consider one body as attracting, another as attracted: But this distinction is more mathematical than natural. The attraction is really common of either to other, and therefore of the same kind in both.

AND hence it is that the attractive force is found in both. The Sun attracts Jupiter and the other Planets. Jupiter attracts its satellites. And for the same reason, the satellites act as well one upon another as upon Jupiter, and all the Planets mutually one upon another. [pp.37-38, my emphasis]

Newton insists that when two bodies are attracted to each other, there are not two operations taking place, but, rather, one operation between the two terms.

And though the mutual actions of two Planets may be distinguished and considered as two, by which each attracts the other; yet as those actions are intermediate, they do not make two, but one operation between two terms. Two bodies may be mutually attracted, each to the other, by the contraction of a cord interposed. There is a double cause of action, to wit, the disposition of both bodies, as well as a double action in so far as the action is considered as upon two bodies: But as betwixt two bodies it is but one single one. It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun: But it is one action by which the Sun and Jupiter mutually endeavour to approach each the other. By the action with which the Sun attracts Jupiter, Jupiter and the Sun endeavour to come nearer together (by the third Law of Motion) and by the action, with which Jupiter attracts the Sun, likewise Jupiter and the Sun endeavour to come nearer together: But the Sun is nor attracted towards Jupiter by a two-fold action, nor Jupiter by a two-fold action towards the Sun: but it is one single intermediate action, by which both approach nearer together. [pp.38-39, my emphasis]

Newton continues, stating that magnetic attraction acts similarly: two bodies interact in a single action, in which both participate.

Thus iron draws the load-stone, as well as the load-stone draws the iron: For all iron in the neighbourhood of the load-stone draws other iron. But the action betwixt the load-stone and iron is single, and is considered as single by the philosophers. The action of iron upon the load-stone is indeed the action of the load-stone betwixt itself and the iron, by which both endeavour to come nearer together; and so it manifestly appears: For if you remove the load-stone, the whole force of the iron almost ceases.

In this sense it is that we are to conceive one single action to be exerted betwixt two Planets, arising from the conspiring natures of both. And this action standing in the same relation to both, if it is proportional to the quantity of [matter] in the one, it will be also proportional to the quantity of matter in the other. [p.39, my emphasis]

Newton’s Third Law states³:

To any action there is always an opposite and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction. [p.417]

Reading the above quotations from A Treatise of the System of the World, it is clear that Newton understood the Third Law as implying mutual action between bodies. The implication for me is that Newton thought of the entire universe as being interconnected.

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1. Peter Graneau and Neal Graneau. Newton versus Einstein: How Matter Interacts with Matter. New York: Carlton Press, 1993.

2. Isaac Newton. A Treatise of the System of the World. Translated into English. The Third Edition. London: B. Motte and C. Bathurst, 1737.

3. Isaac Newton. The Principia: Mathematical Principles of Natural Philosophy. A New Translation by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz. Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen. University of California Press, 1999.