How does one model 4D gravity? Consider the 3D to 2D analogy. If the 2D person lived on a planet, that would be a circle. Then 2 planets orbiting each other wou

How does one model 4D gravity? Consider the 3D to 2D analogy. If the 2D person lived on a planet, that would be a circle. Then 2 planets orbiting each other would appear to the 2D person as two line segments oscilating up and down (because the 2D person cannot see the entire circle, just the edge view). Based on the velocity of oscillation and the separation of the line segments, a 2D newton could come up with an analogous law of gravition with an inverse square relation. But if two 3d planets were orbiting transversely through the 2D plane of our inhabitants, the 2D person would see two separate line segments growing and shrinking although the line segments could maintain a constant distance of separation. The velocity of growing and shrinking would be changing even though their separation was constant. Extending this analogy to our universe makes me wonder if our calculation that the universe is expanding is just an illusion. Rather, at astronomical distances, our universe could be traversing 4 dimensions. And what we perceive as an accelerating expansion of the universe is just motion into the 4th dimension. And if we could travel into that dimension, we might be able to get to places that appear far away but are actually not. Though it sounds far fetched, it also might explain the stuff that is postulated to happen at the quantum scale-where quantum fluctuations are postulated to occur. The only thing we would need to be able to do is to 'coordinate' the fluctuations of lots of adjacent voxels of space. And then we could wander through 4D space.