It bothers me too, why? because it's circular reasoning: acceleration can't explain acceleration.
> Would it help if the sheet were in a centrifuge?
No, for the same reason. (You're imagining a tube-shaped membrane?)
To make it worse, it's developing a wrong idea that hides the right and deeply strange idea: when an object passes a mass and its path seems to deflect what's really happening is that the object is moving in a straight line the whole time and space itself is curved. (The situation is actually a little stranger than that, but I'm no physicist so I won't try to explain any further.)
As a sibling points out, it’s not explanatory as much as a visualization. Or if it explains something it’s not gravity itself but a less familiar kind of geometry and a new concept of straightness where sometimes the shortest path is what we’d usually think of as curved. Seems fine. Little chance of understanding gravity until you can grasp the prerequisite concepts you’re going to describe it with.
And anyway explaining gravity v2 in terms of v1’s first approximation isn’t that strange when recursive definitions are going to play a part in lots of higher education anyway. When you’re a kid, 5 is just a concept useful to describe every instance of 5 apples, but later, a number N is perhaps best understood as the successor of N-1.
Gravity is one of the fundamental forces, there's no recursion in it's definition, indeed we don't "define" it we describe it.
The actual description of gravity isn't hard to understand, it's just really strange. There is no good reason to introduce confusing and intrinsically incorrect models.
> There is no good reason to introduce confusing and intrinsically incorrect models.
Well, teaching is the usual reason, otherwise physics with trig would all just wait for calculus, and calculus wouldn't get covered before real analysis, etc. Incorrect, or more charitably "useful, prerequisite, & intentionally not rigorous" models are a pretty standard tool for walking students closer to real understanding. Clearly no one is proposing trampolines and bowling balls models because they are expecting to win a Nobel.
> The actual description of gravity isn't hard to understand, it's just really strange.
Hmm, Einstein thought it was pretty hard, and I didn't know that you and Witten had finished quantum gravity or the other latest and greatest.
> Gravity is one of the fundamental forces, there's no recursion in it's definition, indeed we don't "define" it we describe it.
Unpacking this to a first approximation it actually sounds like you're looking for The Truth instead of useful models, that you always know Truth when you see it, that you don't believe that apparently different descriptions can result in formally equivalent stuff. I'm also guessing that you might be strongly inside a "only cares about math because physics" camp whereas I sympathize more with "only cares about physics because math". Lots of interesting conversations in there, but it'll all just be philosophy at that point anyway and you probably wouldn't like it.
Why though? Would it help if the sheet were in a centrifuge?