Why should space-time have an overall shape...?

Question

Why should space-time have an overall shape, such as being positively curved (like a sphere), negatively curved (like a saddle), or flat (like a perfect plane)?

Answer 1

Great question! Shape is a word used by us 3 dimensional beings to describe polygons and polyhedrons. The world "shape" breaks down when we try to apply it to 4 dimensional objects known as polychorons. Yet, the General Theory of Relativity tells us that our universe is a polychoron, since it exists in space-time; so how can we describe its shape?

Through analogy we can get some idea of why space-time must have a 4 dimensional shape. Although we 21st century people are very comfortable with the notion that our Earth is a sphere and that we live on its surface, when you really get down to it, our day to day lives are lived in 2 dimensions (except when we go to work in our office buildings and skyscrapers). We prefer to represent places on earth using two dimensional paper, and it works just fine.

In the same way, we represent our universe in 3 dimensions, using solar system models with little globes, and especially using computer models, like Celestia, that show a 3d universe as seen through a "window" of our computer screen.

But how can we represent the 4 dimensional space-time that is described by General Relativity? We mostly use pictures of flat x/y grids being dimpled and bent around objects of large gravitational force like stars and black holes; but these grids really represent cubic 3 dimensional grids, and we just don't have brains capable of adding a 4th dimension to show the dimples as they really are! The only way to detect such dimples would be by watching a clock face from outside the observer frame of reference: the clock would be measured to be moving slower in the vicinity of extremely massive objects.

So when we say 4d space-time is curved, we say it because the math says it is so, but we can't really go any further in describing its shape, except through analogy: As the 2d surface of our planet Earth curves into its 3d spherical shape, so our 3d universe must curve into its 4d super-polyhedral polychoronal shape, whatever it is.

It's complicated.

Answer 2

Why do you think it would not? If it is real and physical, it must have dimensions of some sort. Once you say that, space-time has a shape, even if it is not constant. No matter what convolutions you claim, no matter whether it is shaped like a perfect sphere or a nightmare of a porcupine, if it has dimensions, it has shape. Saying one says the other. Space time in a given region is theorized to be distorted by gravity. So shape might well be governed by nearby stars and/or black holes and all sorts of stuff in between. Between galaxies, where stars are VERY few and VERY far between, there is no gravity to distort space-time so it can be much flatter.

Answer 3

It is not that space-time has a shape which we humans have declared. It is that the universe is either positively, negatively, or non-curved as a simplified definition of its condition. It is somewhat similar to stating that something is either an animal, vegetable, or mineral.

The other answers address what is specifically meant by the various conditions of curvature of apace-time.

Answer 4

It does not have to be, it is easier for us to understand it better this way. We are unable to comprehend space-time in anything other than 3-dimensional.

If we could understand it in say a, 4th demensional aspect, think of the possibilities that your mind could understand.

Answer 5

Because this relates to the expansions, contraction or steady state theory of the universe.