Yes, everything is relative, but as all frames are equivalent, that makes them absolute as well.
Seeing how relative and absolute are sort of completely opposite, I can see how that would make them equivalent.
Spork wrote that some professors do not think that the treadmill is a frame of reference, and that is because they are right.
They are indeed right; a treadmill is an object, not a frame of reference, nor as some people seem to think some people think, a fan.
Moving objects are not different frames.
Also correct. Objects are indeed not frames.
They are objects moving in the same frame.
That, or they are objects moving in different frames.
There is no
the Newtonian frame.
What your statements above illustrate, humber, is that you should familiarize yourself with reference frames and co-ordinate transformations. A frame of reference is just what it's called; it is a vantage point from which one describes the physics of some phenomenon. You can describe the cart in a frame of reference fixed to the cart, or one fixed to the earth, or one that is fixed to Uranus. The point is, if the cart works in one reference frame, it will work in all others. The treadmill illustrates in a convenient way that it works in a reference frame fixed to the cart.
Most of the things you say above are impossible to say if you understand this. I don't think it is shameful in any way that you don't, but your reluctance to learn
is. You insist that you are put through paces that if followed, will lead you (with arithmetic) to the conclusion that the cart works. There is a reason for this.