Cartridge Loading and Compliance Laws

I understand the need to keep the system resonance out of the audible frequency band and footfall band. But why would a low mass arm be useful in doing that. I would have thought that the idea was to keep the arm from moving in sympathy with the stylus, and a higher inertial would accomplish that. In fact, if we could maintain a ridgid mount of the cartridge body, and only allowed the stylus to move in response to the groove modulations, wouldnt that be the perfect set up, no losses due to the arm moving in the same direction as the stylus or gains for that matter when the arm moves opposite to the stylus. So wouldnt a high mass arm accomplish that goal better than a low mass arm, even with a high compliance cartridge.

No. Because your model does not hold true in real life. In real life, the tonearm must permit the cartridge to trace the groove from outside to inside, and so it cannot be fixed in space, which is where your model falls short. In real life, the cantilever has to move the effective mass of the cartridge body and the arm wand up to the pivot point. The cantilever of a high compliance cartridge would be more prone to flex in response to the need to move this mass in addition to its need to flex in response to groove modulations, with a high mass tonearm vs a low mass one. This could produce a low level signal that is not part of the music signal, i.e., distortion. The best simple analogy I know is to think of a high mass arm as a truck and a low mass arm as a sports car. Have you ever seen a truck with bad shocks (high compliance/low damping) when it travels over a bump? It will be set into harmonic motion by the bump more easily than will a sports car with much smaller, higher compliance shocks, because the latter has so much less mass. Conversely, really hard shocks (low compliance) on a sports car will knock your teeth out. Even this model has flaws, I admit, but I hope I made my point.

I wonder would using lighter cartridge screws help if your arm were a little heavy and cart a little light compliance wise? Or would that make things even worse or with cart screws does it even matter really?

I have seen these really light aluminum and plastic cartrdge screws before and of course steel or stainless steel ones. Someone told me before that these little screws can affect the sound, how though I am not really sure.

Lighter screws are definitely better because that mass is at the farthest point from the pivot. So that affects the inertia of the tonearm. Aluminum screws are preferred for both less weight and the non-magnetic properties. Don't use plastic screws. Plastic creeps, ie. stretches, and you won't be able to maintain the torque with plastic screws.

Lewn,
To use your truck/sports car analogy however, a truck would be less likely to be knocked off its straight path than a sports car hitting the same bump. I dont know that the analogy works because the tonearm is not moving, and therefore has no momentum inertia of its own, only its fixed inertia as an impediment to motion. But since I dont want the tonearm to move relative to the stylus, why wouldnt that be better. Dont we want to keep the headshell/cartridge/stylus relationship fixed except for those movement in the stylus that correspond to the vinyl groove. Why would we want the tonearm to move? And if it did at the same rate as the stylus, which of course it can't, wouldnt that result in no sound at all. Isnt it the movement of the stylus and coil assembly relative to a fixed magnet what produces the sound. And if that fixed magnet moved the same as the stylus/coil, no sound would be reproduced.