Quote by Acut
@Riad
There's a counterexample. Just imagine 3 charged masses aligned (named 1, 2 and 3. 2 is the central one). Suppose charge of 1 = charge of 3, and distance 12 = distance 23. Than 1 will exert in 2 a force, but only 1 will be displaced.
You don't need to impose that those point masses have the same mass nor that they are equal. Just use Newton's definition F=dp/dt, and use Newton's third law in order to find that, regardless of the properties of thoses masses, or the quantity of bodies under study, we will always have conservation of momentum.
In fact, you should start backwars: conservation of momentum always holds (even in relativity or quantum mechanics), but there are situations in which Newton's third law doesn't apply. So you can't really use Newton's third law to find cons. of momentum, but use cons. of momentum from Newton's third law.

I can not quite get you.. if you move 1 then 3 moves also otherwise you have the center of mass (of the three) moving without an ext. force involved. It seems to me that if it is possible to negate this ballanced displacement idea, then momentum is not conserved.. note that all events are taking the same time period dt so velocity would be the same as momentum. The most interesting thing about this idea is that it can be used to justify the second and third laws of Newton and it can even explain inertia.. since to move one mass forward you need to push another back.. so that the sum of sum(distance x mass)= zero.