I saw this explanation on another ELI5 and it was really nice so I shall use it here;
Let us imagine 4 evenly spaced objects in space, A, B, C, and D. Here is a visual representation:
A-B-C-D
Now I shall expand space (every dash becomes 4 dashes)
A——B——C——D
From the point of view of object A, object B has only moved away by 3 additional dashes. However, object C has moved away by 6 additional dashes, and object D has moved away by 9 dashed! For object B, it is A and C that has moved by 3 dashes, and D that has moved 6.
So it seems the farther an object is in space, the faster it seems to move away.
For the atoms in our bodies and other such objects, they are very very close to each other. They do move apart while space expands, but the distance they move is very very small, and they immediately come together due to the electromagnetic force, gravity, etc.
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