The film Upside Down showed a fiction movie where 2 planets of gravities exists within a fairly short distance. One may also assume that all parts of one planet is parallel to the other, which means if you look up anywhere on the planet A, you would see planet B in an opposite gravity. If this phenomenon will abide all our laws that we know of, how would the two worlds look like? (Deliver a sketch on how this 2 worlds(planets) would most likely look like. (i.e. two pizzas facing each other vertically))
You could look at a solid sphere within a hollow sphere, a bit like this image I stole from google:
The red sphere is actually basically a thin outer shell, the blue sphere is solid through, and there is empty space between them.
One world would have it's people walk around on the inside of the red line, another on the outside of the blue line. I think you'd have to have artificial lights.
A hollow sphere by itself would have zero gravity within the hollow well. So the red world wouldn't exert any gravitational forces on the blue world.
I think that the blue world would have a gravitational effect on the red world. You might be able to counter this by having the red world constantly spinning to provide a countering centrifugal force. It isn't actually gravity, but it would feel like it to those walking in the red world.
I tried googling the physics of this idea, but got swamped by a whole heap of unrelated material, so it might be completely implausible.
Two spheres meet at a point, not all over. A universe of plates rather than spheres would need more rules than simply two charges of mass. You could contrive those rules to make it come out however you wanted: there is not a natural elaboration that produces anything like that movie.
That was not the only thing wrong. Taking that as a given as well as the three rules presented in the opening sequence, air is obviously immune from the compatibility law, and perhaps so is water which can sometimes switch charges on its own to produce the "upside-down rain". People drank opposite drinks and did not explode. The stamps fro the other side were taped to strings and the long-time contact did not make it catch fire. Neither did the aircraft wreck that had blocks of opposite rock chained to its structure: it stayed inert even after the wreckage was long decayed. So the rules are only applied when convenient for the plot, which is not a good worldbuilding exercise.
A long time ago I read a short story with similar gravity, abord a space habitat. Natural gravity worked normally on both polization-trated forms of matter. But on the habitat they saved space by having occupents on both sides (floor and ceiling) of living quarters.
Thatnis (1) constructed, and (2) is a box made from normal matter that contains polarized matter, and (3) the directed gravity is supplied outside of that structure.
So scale that up to a planet-sized engineering concept, like a stacked-plate world. Why stop with 2? Maybe there are more layers to be discovered. There is no compatibility issue but matter of each kind can get mixed together. Maybe there is some way to encourage separation to remain, to keep it going over long time periods. Maybe the two facing layers are populated with different types of life from different home planets, with different chemistries?
There is no physical law that would account for different instances of atoms having different gravity charges.
Maybe matter is attracted to whichever plate it's near, rather than being of two different kinds. Then you just need to control the warping of spacetime to produce such a field.