Sorry but I have read this question

How exactly does curved space-time describe the force of gravity?

and the answer by joseph f. johnson, where he says:

"Newton did not realise that space-time could be curved and that then the geodesics would not appear to our sight to be straight lines when projected into space alone. That ellipse you see in pictures of planetary orbits? It is not really there of course since the planet only reaches different points of the ellipse at different times...that ellipse is not what the planet really traverses in space-time, it is the projection of the path of the planet onto a slice of space, it is really only the shadow of the true path of the planet, and seems much more curved than the true path really is.

( ¡ The curvature of space-time in the neighbourhood of the earth is really very small ! The path of the earth in space-time would even appear to be nearly straight to an imaginary Euclidean observer who, in a flat five-dimensional space larger than ours, was looking down on us in our slightly curved four dimensional space-time embedded in their world. It's ctct, remember, so the curving around the ellipse gets distributed over an entire light-year, and appears to be nearly straight...and is straight when one takes into account the slight curvature of space-time.)"

My question is, if we see the earth round, is that too because of what he describes? So in 4D, the earth looks flatter? Why does the earth curve spacetime so much seemingly, that it makes the earth look round, and everything falling towards the center? In 4D earth would look like what?

Question#2: Analogy of this to the rings of Saturn. In 4D they would look straight? Since they are just orbitals of rocks around Saturn. There orbitals would look like a straight line in 4D? But if that is true, then they must be allocated along a section only, since it is a finite number of rocks. But then they must have a beginning and an end. So where would that line section start, at which rock?


1 Answer 1


First, the earth looks round because it is round. Take a marble with an incredibly weak gravitational field. It bends space-time around it so little, that it is practically un-observable, yet it still looks round. The earth might very mildly bend the vision line of an observer, but it isn't enough to make a flat object appear round. (In fact it would work the other way if any, making the earth appear slightly flatter)

Second, practically describing what a four-spacial-dimension object looks like is nearly impossible, since we don't even have a word for the fourth dimensional direction (Up/Down, Left/Right, Forward/Back... then what?!?). And trying to visualize it will give you a headache.

What you can do is study how a 2D world compares to our 3D world, and then project those conclusions forward onto how our 3D world compares with a 4D world. I would suggest reading the book Flatland by Edwin A. Abbott, and then watching the movie of the same name.

Here is a quick example. Imagine a 2D world. It would look like a kid's drawing, a large rocky circle for the world with lava at the center. When you (a viewer in 3D space) looks upon this 2D world, you can see EVERYTHING at one glance: the surface, the insides, even the very center! Well this is rather amazing actually, because it means that a 4D viewer could look at earth (assuming it existed in strictly three dimensions), and they would be able to see EVERYTHING at ONE GLANCE. Granted their eyesight might not be able to pick out very much detail if they were far enough away to see the whole world, but they could see the entirety of our world, the whole surface, the mantle, even the very core at just one glance. I am not talking about those cut-out diagrams of the earth's core you see in science books, but the ENTIRE surface, the ENTIRE mantle, the ENTIRE core, EVERYTHING!! (Even the insides of our bodies! Yuck!)

That is just one tiny example of how we look to higher dimensional viewers. If you ever meet one, ask it where to find oil or diamonds :-P


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