> I know it sounds hard to believe, but if you're willing to bite the bullet that "the center of the universe" has no physical meaning, then earth can't be not the center of the universe any more than it can be.
I disagree.
The sentence «"the center of the universe" has no physical meaning» requires that Earth can't be at the center of the universe, because there isn't a center for it to be at.
You're still allowed any or many arbitrary zero-points, but that's only the center of a number line, nothing else.
It's basically a semantic issue but I don't think the negation of an undefined proposition is true, I think it is undefined. (Thankfully the universe does not run in JavaScript, where !undefined is true.)
But, Earth.x = 42 (in some arbitrary coordinate space), if I understand correctly there isn't a sub-light coordinate space in this universe where Earth.x = undefined.
That's not the reason why the centre of the universe is undefined.
By analogy, while spherical coordinates are arbitrary, latitude is defined. Arbitrary, but defined.
But the centre of the Earth has an undefined latitude, and a topological subspace consisting of just the surface of the Earth can't hand-wave past that by pointing out that's just a coordinate singularity that can be safely ignored — there isn't a center of the Earth anywhere in that subspace. If the universe is flat and finite (looping), this problem still exists.
And if the universe is unbounded (infinite), that has a different problem because you can't properly define a median of an infinite set[0], so no center exists.
If it just stops suddenly after a certain amount of space, then we get to have a center, but there's no sign of that.
[0] I think. Infinity is easy to get messed up with.
I disagree.
The sentence «"the center of the universe" has no physical meaning» requires that Earth can't be at the center of the universe, because there isn't a center for it to be at.
You're still allowed any or many arbitrary zero-points, but that's only the center of a number line, nothing else.