Comment Re:Linearization (Score 1) 553
Here's the part that I find interesting. The whole gravity/space-time curvature is merely an abstraction of gravity into a new dimension.
Ancient people's idea of gravity was simple. Stuff goes down.
Then people figured out that the earth's surface is curved, and "down" didn't work anymore. The new theory of gravity said that stuff moves toward other stuff, and the earth is a big blob of stuff that all our little stuff moves toward. Kinda simple, but you don't have the nice, straight, linear sort of system. You've got a radial one, and other planets and stars have their own gravity fields that pull stuff toward them, and it's a bit more complex.
So, with this notion of mass curving the surface of space/time in some higher dimension, we envision space/time as a sort of elastic surface. Mass sinks into the surface, and smaller mass will "roll" into the depression caused by the larger mass. Why does the "mass" roll downhill? Well, there's the kicker: this higher dimension apparently has its own sort of gravity, and, like the ancients' theory, it's nice and straight: it always goes down!
That's not actually true. Take a square apiece of paper. Draw a straight line parallel with one side in the middle. Then tear the paper perpendicular to the line from one side to the line. Now pull one side of the tear over the other. See how the paper bends into a cone? That's what gravity does. It causes "space" to not be flat just like that. However, look what happened to your line. Now it curves around toward the direction of your tear. So it is the geometry of the paper that causes the gravity. It isn't about anything rolling downhill, or about there being another type of gravity pulling everything down a rubber sheet. Instead, the shape of surface causes anything going in a straight line to be deflected towards that tear. And why does your object tend to go in a straight line? Because of Newton's first law, of course!