One thing has always really bothered me about general relativity (probably due to gaps in my understanding). As I understand it, any object with mass distorts spacetime around it – a common analogy is to imagine an object on an elastic sheet: the sheet bends under the weight of the object (a nice graphic of this is at the top of this page).
Here’s the difficulty I’m having: in order to bend or distort something, you have to apply a force to it. So if the Sun (or other massive object) distorts nearby spacetime, that means the Sun must somehow apply a force to spacetime itself. I have a hard time wrapping my head around that – how does having mass allow an object exert a force on space itself?
Or am I thinking about this in the wrong way?