I've already discussed in the other thread why travel in the Antarctic is prohibitive (ignoring the natural conditions). Would you just like me to follow you to every thread you bring this up and answer it again and again?
If the plane is infinite, where would you expect it to "collapse" to?
You know I love you John! And I suggested sending something without a human, like a drone, to do the job, so risks to life and limb are negligible. A plane will fly over Antarctica just fine, the only problem is that if anything goes wrong, there's almost literally no one to come and help you. As happened recently. But a drone could do the job just fine. And who would know you'd done it? There's no one monitoring 99% of the airspace. Or, if there were, you'd have hard evidence of a conspiracy, which would be amazingly cool and/or scary to learn about. I know I'd be changing my mind about a great many things.
Physics suggests an infinitely massive object would collapse pretty much instantly into a black hole due to gravity. Our continued existence argues this isn't the case. Unless we are operating under the assumption of Universal Acceleration, which has its own set of quandaries.
Most planes take 3 hours to reach their destinations which I've shown are far away from the edge. A drone would presumably take much longer, and this isn't even to the edge. This raises a huge set of other issues, but I suppose its worth looking into.
Where do you think it would collapse to?
Why do you think that an infinite plane would not have equal force pulling on each point due to the equal amount of matter to its left, right, north, south, and so on? The pull from particles aligned at 0 deg would balance out those from 180 and 90 from 270. And so on for each angle.
That's a solid point, and one I hadn't thought through completely.
An infinite solid "plane" of some arbitrary thickness wouldn't collapse due to gravity for the reasons you said. I had fun reasoning it out!
However, it seems to me that, for a uniform plane of relatively even thickness, gravity would behave strangely. On an infinite plane, gravity would pull in many directions, but these would largely cancel out, and downward pull would win out.
However, as gravity scales with distance and mass, gravity would be theoretically be
greater at the tops of mountains, as there is more mass directly below you, correct? I'm not sure, I keep running into problems with where the center of mass would be. I guess it would depend on the size of the mountain and how thick the plane might be.
This is counter to what we actually observe, as gravity pulls LESS hard at the tops of mountains, as we get farther from the earth's center of mass. But again, I've been wrong before.
With the plane thing, longer distances are an engineering problem. Those aren't hard TOO hard to solve. Carry more fuel on a more efficient device. Or just use a rocket and make it a one-way trip. We can already send rockets to the other side of the world, we could just aim it the opposite way and send it over Antarctica. My (joking) motto is, "If brute force doesn't work, you just aren't using enough."