Newton's Third Law of Motion
//Bead panel from a baby carrier//, Bahau people. Borneo 19th century, 35 x 28 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
Bead panel from a baby carrier, Bahau people. Borneo 19th century, 35 x 28 cm. From the Teo Family collection, Kuching. Photograph by D Dunlop.
The third law of motion from Isaac NewtonXlink.png is about a balance between the forces of cause and effect. It has been translated as

"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."1

This has something in common with the ancient Indian idea of karmaXlink.png a key concept in Hindu, Jain, Buddhist, Tao, Shinto and Sikh philosophies. It is also similar to Western aphorisms like 'what goes around comes around'. And surely Newton himself would have heard the words "for whatsoever a man soweth, that shall he also reap"2 from a contemporaneous English translation of the Jewish and Christian texts. But Newton's third law is more than just a vague claim of cosmic balance. It has a mathematically precise expression in terms of two compound atoms called $\mathbf{A}$ and $\mathbf{B}$ that have an interaction with each other by exchanging another particle called $\sf{X}$. The interaction begins when $\mathbf{A}$ emits $\sf{X}$ which causes the effect of $\sf{X}$ being absorbed into $\mathbf{B}$ after an elapsed time of $\Delta t$. The forces on $\mathbf{A}$ and $\mathbf{B}$ due to this interaction are found by substituting their changes of momentum $\Delta \bar{p}$ discussed earlier into the definition of force to obtain

$\begin{align} \overline{F} ^{\mathbf{A}} \equiv \frac{ \Delta \bar{p} ^{\mathbf{A}} }{ \Delta t } = \frac{ - \bar{p}^{ \sf{X}} }{ \Delta t } \end{align}$and$\begin{align} \overline{F} ^{\mathbf{B}} \equiv \frac{ \Delta \bar{p} ^{\mathbf{B}} }{ \Delta t } = \frac{ \, \bar{p}^{ \sf{X}} }{ \Delta t } \end{align}$

so that

$\overline{F} ^{ \mathbf{A}} = - \, \overline{F} ^{ \mathbf{B}}$

The force of the cause is of equal size and in the opposite direction to the force of the effect. These quantities are measureable. And for WikiMechanics, they are well defined in terms of sensation.

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