Wiki:
(...) Woodward states there is no violation of momentum conservation in Mach effects:
If we produce a fluctuating mass in an object, we can, at least in principle, use it to produce a stationary force on the object, thereby producing a propulsive force thereon without having to expel propellant from the object. We simply push on the object when it is more massive, and pull back when it is less massive. The reaction forces during the two parts of the cycle will not be the same due to the mass fluctuation, so a time-averaged net force will be produced. This may seem to be a violation of momentum conservation. But the Lorentz invariance of the theory guarantees that no conservation law is broken. Local momentum conservation is preserved by the flux of momentum in the gravity field that is chiefly exchanged with the distant matter in the universe.
If we produce a fluctuating mass in an object, we can, at least in principle, use it to produce a stationary force on the object, thereby producing a propulsive force thereon without having to expel propellant from the object. We simply push on the object when it is more massive, and pull back when it is less massive. The reaction forces during the two parts of the cycle will not be the same due to the mass fluctuation, so a time-averaged net force will be produced. This may seem to be a violation of momentum conservation. But the Lorentz invariance of the theory guarantees that no conservation law is broken. Local momentum conservation is preserved by the flux of momentum in the gravity field that is chiefly exchanged with the distant matter in the universe.