Science fiction: third law broken

Problem

Science fiction: third law broken. What would happen if Newton’s third law stopped holding? In particular, how would the conservation of the centre of mass of an isolated system be affected?

Solution

The conservation of total momentum — and hence the inertial motion of the centre of mass — depends crucially on the third law: it is what guarantees that internal forces occur in equal-and-opposite pairs, cancelling in the sum.

If the third law failed, internal forces would no longer cancel in the vector sum. Then $\frac{\dd \vec P_\text{tot}}{\dd t} = \sum \vec F_\text{internal} \neq \vec 0$ even for an isolated system. The centre of mass could spontaneously accelerate, generating momentum “out of nothing”, with no interaction with the outside. A thruster that pushes itself along by pulling on its own bootstraps would become possible — something the third law forbids.

Links

Topics: Centre of mass Concepts: Newton’s third law · Conservation of momentum Skills: Limiting-case and science-fiction analysis