Take the BMW/FI. Lift the running car with a fork lift, so the wheels don't spin. Now what? Lower it a little so the wheels
just make contact so as to spin. Now what?
Do things change for the belt observer? No.
Depends on how you step onto the belt, but yes, generally.
No. Stepping on the belt does not alter the relative velocities between cart and surface. You said so yourself above somewhere.
There is no motion between the cart and belt observer. Only when you include other frames can you ascribe motion. That is incorrect.
There is information leakage across frames.
I'm not sure that that means anything, but I'll try to comment. The belt indeed only mimics the surface of the road. However, the fact that there is air above it that isn't travelling with the belt makes that air mimic a breeze at the (negative) speed of the belt.
The belt is a partial and cyclic simulation of the road surface. The belt motor provides the power to move that simulated surface through the air just above the belt, so generating a boundary layer similar to the real thing.
The belt motor provides the necessary work for this, the bearings and other losses, but not motive power. For an F1 car to travel at 300kph in still wind, takes perhaps 600hp.
No. You missed the part where there is now wind my frame of reference, therefore the air has the capacity to blow the cart away from me.
No. Try again.
That is self-generated wind, derived by motion of the cart through still air.
There is no belt motion from this frame, because the belt cannot have motion w.r.t itself, and so no wind. Only the boundary that is attached to the belt is present, though this is notionally dimensionless.
Expansion of the belt, cuts off those views, and you see only what is in that frame. In "beltworld" all the KE's and velocites and so forth are once again normal and Newtonian.
No. This is where you jump from sensible statement into the world of papent nonsense. There is only one frame in which the cart is motionless. In other frames, such as all of them, the cart is, in fact, moving.
The cart is motionless w.r.t the treadmill observer. The correct model is that this observer is on the ground, as in the BMW/F1 observer.
That position is denied to allow the treadmill observer to be at 'windspeed'. This forces the condition that all frames must be internally consistent within that model. The treadmill 'windspeed' observer sees the cart as motionless, and exclusivity so. Forcing that state upon the belt observer, means that the cart is also at rest w.r.t that observer, and at a fixed distance determined by the initial displacement. That is consistent with all other frames, and no motion in any frame.
Seeing how I'm definitely part of "et. al.", I'll assume you won't believe me when I say you're wrong.
Belief is not relevant, H'ethetheth