Does the apple fall towards the earth or does the earth move up to the apple?

Question

Does an apple fall towards the earth or does the earth move towards the earth?...but if this is true then in the opposite side of the world would have to move towards them as well.

Answer 1

A 1kg body has a weight of ~9.81 newtons, and if you drop it from a height of 5 metres it takes about 1 second to fall. It also attracts Earth with a force of 9.81 newtons.

In 1 second, 9.8 newtons will accelerate Earth through a distance of $8.213 \times 10^{-25}$ metres, about a billionth of the radius of a proton. Assuming no other objects are falling towards Earth at the same time. ;)

I used this string in Google to do that calculation:
.5*(1 second)^2*(9.81 newtons)/(mass of earth)

Answer 2

Does an apple fall towards the earth or does the earth move towards the earth?.

Neither.

Puny humans cannot see what is really going on. They see a universe that appears to be three-dimensional and for some reason see the second hand on their watch always moving forward but never realizing that's important. So when an apple breaks free of the tree, from a human's perspective they see it fall towards the Earth and ask themselves whether the apple is falling to the ground or vice-versa.

But we aliens can see the reality, that the universe is four-dimensional and neither object is "moving to" the other. In fact, both objects are moving in free fall, it's just that the shortest path from today to tomorrow lies in different directions for the apple and the Earth and those directions happen to intersect. So from our perspective the apple never does anything interesting at all, it's not suddenly "falling", that was its natural state all along. But first the tree and then the ground are harshing its buzz.