[colordrops]

I never liked the mattress analogy, because if gravity is the bending of the mattress, what is pulling the ball down the slope?

[zehaeva]

It's just an analogy, you're not supposed to think too deeply about them.

The main take away for a lay person is that _like_ the mattress space is being deformed. That's where the analogy stops. Taking it further, like with all analogies, breaks the analogy.

If the analogy was a perfect one, then it would just be the reason and not an analogy.

My main gripe is how hard for most people it is to extrapolate that deformed mattress into a 3d space.

[colordrops]

I get that, I'm just wondering if there's a more effective analogy. Maybe there isn't.

[twentyfiveoh1]

I am not an expert at all but I believe the rough idea is that in General Relativity, everything follows a geodesic. The straightest possible path through curved spacetime.

They use that to explain why you don't feel acceleration when you jump off a building or out of a plane.

They say you DO feel it when you are standing, because the earth is impeding you and pushing you away from the geodesic you naturally want to follow.

So it is counterintuitive. the standing still person is being accelerated/pushed. The freefall person is free.

John wheeler said "Spacetime tells matter how to move; matter tells spacetime how to curve". I think it explains the circular nature.

Mass curves spacetime, that changes how mass moves , mass moving to a new position changes the curvature, that changes how the mass will move next. The dimple in the mattress staying with the mass.

[hollerith]

You've got it right. Our normal environment is an accelerating reference frame. The resting frame (i.e., free fall) is easier to analyze using physics, but is unfamiliar (indeed tend to feel alarming) to us.

[defaultcompany]

I agree. The analogy is using our intuition of how objects move because of gravity to explain gravity. It has always seemed circular to me. I bet there is a better analogy.