I think you might be over-thinking this.@atmasphere I doubt it, I'm quite ok with physics and I apply it to the situation.
You got most of this right, right up until your conclusion. Think about a generator, one with no load and one with a load, which will be harder to turn? By your logic above (if I’m reading it right) somehow the loaded generator is easier to turn, which certainly isn’t going to happen.
Seems you did not understand what I wrote: lower R presents obviously more breaking force, opposing the stylus movement. This is the electromagnetic induction law in action: the current (flowing through R) creates the magnetic field that opposes the stylus movement. This force behaves like ~f/R.
I think where you’re getting into trouble is the idea that the output goes down with reduced R load, which it does. The problem is: a certain amount of energy is used to make the stylus move. Where does that energy go? It is of course applied to the input load of the preamp in the form of a voltage. Now if you decrease the voltage by reducing the R load value, where is that same energy going? The Law of energy conservation says it has to go somewhere! It does not just ’vanish’. It is dissipated in the load and also by the cartridge coils themselves, both in the form of heat.Just to be precise, the energy is not presented in a form of a voltage because voltage alone cannot perform work. The energy is presented in a form of a heat, dissipated in the combined resistance of the circuit (R_load, the coil DCR, the cables etc), caused by the induced voltage applied to the resistance. This is ok. The question is so what? To speak of energy conservation, you have to look at all the forces acting on the stylus:
- the driving force, coming from the diamond tracking a rotating, modulated groove, say at freq. f; this force is the source of all the energy flows- the restoring force of the suspension- various damping forces, including the electromagnetic one ~f/R
In a simple case of a linear suspension, you can solve it (for the speed of the stylus as the signal is proportional to it) and you will see that the movement has two components:
1) the transient, exponentially decaying self oscillations of the stylus; the frequency is the usual cart-tonearm combo but decreased due to the electromagnetic damping; the decay time is inv. proportional to the damping so ~R in the EMF part
2) the steady state, the forced movement with the freq. f, dictated by the tracked groove;this is the signal we want; the amplitude of this movement will have an R dependence too
The only *qualitative* change in R can happen is in the 1st, spurious part. Lowering the R changes the suspension character from underdamped to critically damped to overdamped. But this is not the signal we are trying to get! This is an artefact added to the real signal of freq. f.
Of course if the motor is so weak that the stylus tracing a HF track into low R will make it slow, we are in trouble but let's assume a healthy TT design.
But I think you will find if you do some measurements that the output does not go down as fast as it appears you are thinking. This is because the stock 47K load is easy to drive and the output of the cartridge will stay pretty constant until the load is decreased to some point below 10x the impedance of the cartridge; IOW probably less than 100 ohms.
I suspect you are trying to describe a behavior of the 1/R function. Yes, far from zero it flattens out so changes say 1k to 47k can be negligible, but the closer to zero the steeper the changes.
Summarizing, you seem to selectively use the bits of the whole picture of the stylus motion and draw conclusions from them, like the fact that lower R changes the compliance, but you completely neglect that there is a very strong driving force here coming from the rotating platter, and this is the force setting the stylus into the motion.