How can 3-dimensional space be curved in a 2-dimensional plane cut through it?
In trying to explain general relativity to the lay public, writers often describe spacetime as being like a rubber sheet, which is distorted by large, massive objects sitting on it. They suggest the orbital motion of planets can be thought of as frictionless circular rolling in the “gravitational well” produced by the massive object. Further, they suggest gravity itself is nothing but this well. When dropped above a massive object, things fall into the well or depression in space. But this analogy doesn’t work. First, it depends on gravity to operate, so how can it then explain how gravity operates? Second, following this model, an apple held above the earth and dropped wouldn’t fall straight down, it would follow curved spacetime to where Earth’s pole was sitting upon the runner sheet. Am I right in assuming that this explanation of general relativity is an oversimplification that just breaks down on close inspection? How can you envision 3 dimensional space as a 2 distorted single plane or geodesic shape?