Momentum conservation in a relativistic engine

In a previous paper we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time-dependent currents, the above analysis led to the suggestion of a relativistic engine. Since the system is affected by a total force for a finite period of time this means that the system acquires momentum, the question then arises if we need to abandon the law of momentum conservation. In this paper we make a detailed calculation and show that any momentum gained by the material part of the system is equal in magnitude and opposite in direction to the momentum gained by the electromagnetic field. Hence the total momentum of the system is conserved.