Yes, I am thinking about what the world would be like if it was flat and infinite, for one there would be infinitely many different cultures as you travel farther and farther. There will be more diplomatic relationships to maintain etc.

It would actually be amazing since you know there is endless landscape out there and you could go on a journey that never ends.

aye, but i there anything? Would it be miles and miles of natural terrain, or does it end up as flat unremarkable terrain

Does the sun behave the same everywhere you go? If you walk in the direction that the sun sets, will you ever get closer?

@RobWatts Yea I guess that's one of the physical impossibilities. But for the sake of argument lets say there is still a day/night cycle and the sun still appears to be revolving around this infinite land

The total gravitational force would be infinite at all points. Squish!

@Oldcat Interestingly, gravity is only infinite if the world is infinite in both directions. If the world has an infinite 'length' but a finte 'width', (assuming finite thickness of our world-sheet), the force of gravity integrated across the infinite length of the world yields a finite sum.

@ckersch Agreed, but I think you mean three directions. Infinite length and width, but finite depth. It would be interesting to calculate the required depth of an infinite plane to simulate Earth normal. Only a small portion of the surrounding land would add to perpendicular gravity.

@Samuel Well, it all would, but further away it wouldn't add much. One interesting effect would be that the gravitational field would extend infinitely far up - there would be no "orbit", no microgravity - if you have an infinite flat sheet, then the entire universe has a gravity vector pointing towards it. I'm not even sure there would be a horizon, since all light would eventually be deflected down somewhere (so you could look up at any angle and see light that came from some large distance away).

@Random832 You're right, an infinite plane has a uniform gravitational field to infinity. Pretty neat. I remember doing the calculation in college for an infinite sheet of charge, but don't think I made that obvious connection to gravity.

As you go farther, the area grows in the same proportion as the gravity for each shrinks, so the total is infinite.

Can someone clarify the word "flat" for me? At first I assumed it was meant that the world is essentially an infinite plane instead of a sphere, but the edit seems to indicate it is still a sphere, just with no bumps or indents.. but there are still mountain ranges, so I don't quite understand.

@Samuel That's what I was expecting at first, but it can only be infinite along one direction. If you do a double integral across radius and angle, you get an extra 'r' term on the top of your integral (i.e. area of a differential unit is d_angle * radius * d_radius). Integrating across 'r' is then the integral of (some constant * r)/r^2, which diverges.

One thing which I remember thinking about after watching Insterstellar is that it is actually physically possible to have a "flat earth" if it covered the throat of a wormhole. It would be topologically spherical, but have zero curvature (you could stand on it and look to one side and see yourself, assuming nothing was in the way). From far above, away from the wormhole, it would look like a sphere (with some light distortion around it). The best part is that on the other side of the "flat planet" you would have the same thing, so that you get two spherical planets connected by their surfaces.

@ckersch Determining the gravitational field of an infinitely wide/long sheet is a common exercise in 1st-year undergraduate physics. The force of gravity will actually be finite, as long as the sheet has a finite depth. The interesting thing is that the force of gravity stays the same no matter how high up off the ground you are (even millions of miles)

So Minecraft style?

@FarazMasroor: Minecraft has limits minecraft.gamepedia.com/World_boundary

@ckersch I think the OP means the world is an infinite plane. I did the math - see my related question and answer.

Which one of my friends are you? I came up with this a few months ago, thinking it's a brilliant setting for a book series or an RPG campaign, told a few friends about it and magically I find it here! I'll delight in reading the answers, I was very curious what people would say because my friends didn't say much :).