M3. Newton’s Third Law: Its Formulation, Its Significance

Newton phrased his third law of mechanics in this way:

To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.¹

In modern terminology, the same statement would
 be rendered: “For every force in nature there is always an equal and opposite force; or the mutual forces of two bodies upon each other are always equal in magnitude and opposite in direction.” The first half of Newton’s statement of the third law says that all of nature’s forces come in balanced pairs, equal and opposite. The second half of the statement explains that the equal and opposite forces exist between any pair of interacting bodies, and then goes on to emphasize the vector nature of the law. Why Newton chose to use the word “action” instead of the word “force” is not certain²—perhaps to let “action” summarize both the idea of “force” and the idea of “change of momentum,” perhaps only for the linguistic reason that “action” has a convenient opposite, “reaction,” and “force” does not. In any case, it is adequate to state Newton’s third law as a law of equal and opposite forces. In its most compact form, as an equation, the law may be written

F_AB = –F_BA.

In words: The force exerted by object B on object A is equal and opposite to the force exerted by object A on object B. Note that the third law requires for its application two (or more) interacting bodies. The first and second laws can be phrased in terms of single bodies.

An important point to appreciate about Newton’s third law is its generality, a generality springing from what it does not say. It does not say anything about motion. It does not say anything about forces on object A arising from any source other than object B.
 It does not say anything about the kind of force exerted by A on B or B on A. It is a completely general statement about forces in nature, independent of their strength, their source, their kind, or their effect. One cannot, for instance, learn the strength or even the direction of the gravitational force exerted by the Earth on a book from Newton’s third law. That knowledge comes from a particular law of force, the law of universal gravitation. The third law states only that the force of the Earth on the book, whatever its strength, whatever its nature, is balanced by an opposite force of the book on the Earth. Moreover, it leaves open the possibility that as yet undiscovered forces may act between bodies. If they do, and if Newton’s third law remains valid, the new forces, too, must come in equal and opposite pairs. When Newton formulated the third law, only the gravitational force was understood quantitatively. Later electric and magnetic forces were found to obey the third law. Ordinary contact forces, basically electric in nature, conform to the same law. In the subatomic domain, the strong and weak interactions have been found to be consistent with the law of momentum conservation, which may be considered to be a modern synthesis of Newton’s first and third laws.

---

---

⇐ PREVIOUS ESSAY | NEXT ESSAY ⇒