Science fiction: instantaneously variable mass

Problem

Science fiction: instantaneously variable mass. Imagine a particle suddenly doubling its own mass while keeping the same velocity. What happens to the centre of mass of the system (particle + the rest of the universe)?

Solution

The centre of mass is the average of the positions weighted by the masses. If a particle suddenly doubles its mass, its weight in the average increases: the centre of mass would instantaneously jump towards the enlarged particle, with nothing actually having moved.

Worse: keeping the same velocity but with double the mass, its momentum $m\vec v$ would double, and so the total momentum of the system would grow out of nothing, violating conservation: $\ev{\vec P_\text{tot} \text{ would increase} \Rightarrow \text{conservation violated}}$ It is precisely to avoid these paradoxes that mass is a conserved quantity: it cannot appear or disappear, and the centre of mass of an isolated system cannot make jumps.

Links

Topics: Centre of mass Concepts: Centre of mass · Conservation of momentum Skills: Limiting-case and science-fiction analysis