Ask a Physicist

I had always thought that there is no up or down in the outer spaces of the Universe. This now seems not to be correct if matter causes curvature and other objects fall towards the curves. What am I forgetting here?
Submitted by Lamonte from Waikiki, Hawaii

Matter does indeed cause curvature, and this curvature is present even out in space. But that's not the same as the notion of up or down.

Sitting at home, you have a clear idea of which way is down. Hold an apple at arm's length and let go. Down is whichever direction it moves. That also happens to be in the direction of the Earth.

Riding the space shuttle in low Earth orbit (with the windows shuttered), you don't have a clear idea of down. If you let an apple go, it stays in mid-cabin where you left it. The curvature is less than at the surface of the Earth, but only by a few percent so that doesn't explain it. The key is that the apple isn't moving relative to you, which is where the everyday idea of down comes from.

Now about those curves: Objects try to follow special curves called geodesics that are as straight as possible given that spacetime itself is curved. In the space shuttle cabin, you are moving on a geodesic, and when you let the apple go it sits there relative to you since it's moving on a neighboring geodesic that's very similar to yours. At home, your geodesic would lead to the center of the Earth, but you are constantly pushed off your geodesic by several thousand miles of rock getting in the way. This gives you a sensation of weight. When you let the apple go it moves (briefly) on a geodesic, which diverges from your curve, and you see it go flying away from your hand until it too encounters the Earth. So you have a well-defined notion of down, which turns out to mean "towards the geodesic I would follow if there weren't all this matter in the way."

That's one of the counter-intuitive conclusions of Einstein's theory: that the idea of down and the sensation of weight are not actually due to gravity, but rather to all the other forces that are responsible for matter. In space there is still some curvature due to distant matter, but with no matter piled up to push you off your geodesic, you don't feel any "down."