Universe being flat and why we can't see or access the space "behind" our universe plane?

I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)]

I described everything on my picture:

So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?

And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?

Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker.

When you're talking about curvature it's important to distinguish between intrinsic and extrinsic curvature. I struggled to find a good summary of the difference: page 6 of this PDF discusses it, or Google for similar articles.

A very common analogy for spacetime curvature is the rubber sheet, and this is an example of extrinsic curvature. We take the two dimensional sheet and deform it in a third dimension to create the curvature. With extrinsic curvature it's entirely reasonable to ask if we could move in the third dimension to see "behind the sheet".

However the spacetime curvature described by general relativity is intrinsic not extrinsic curvature and is not caused by bending the three dimensional space in some hypothetical fourth dimension. So you can't move out of spacetime to see what's behind it.

It's difficult to explain intrinsic curvature, but let's try by going back to the rubber sheet. Suppose you keep the sheet flat, but you grab the sheet at a point and pull the sheet in some direction:

The grid is supposed to show how the sheet has been stretched. The sheet is still 2-D, because we haven't stretched if upwards or downwards, but it's been deformed so that the spacing between grid lines changes. The key think (and the hardest to understand intuitively) is that for Flatlanders living on the sheet the grid lines still look straight. A Flatlander walking along the centre vertical grid line would think they were walking in a straight line, but would actually be moving in a curve.

This type of curvature is what happens in general relativity. It's intrinsic not extrinsic. So to back to your question, you can't move behind the universe because there is no behind to move into. There are only the three spatial and one time dimensions - it's just that they are intrinsically curved.

As far as we know right now, you cant see outside the universe. For that to be possible you'd need some way for information to leave and enter the universe. I'm not aware of anything in physics that allows that. Even in black holes, to the best of my knowledge information and energy are preserved once they go inside.

To the second question: If the universe is "closed" then yes, in theory you can travel in a line and get back to where you started. But, if it's flat(like a plane) then it would be infinite and you just keep going forever. We just dont know for sure what the geometry of the universe is. It's very likely that it's flat and infinite.

• So we can't actually see beyond our 3 dimensions? I heard string theory is studying extra dimensions. If it could work on a small scale, could we also do that on large scale? Commented Oct 27, 2013 at 4:06
• @user31751 Note that the grand majority of our knowledge of the cosmos around us comes through electromagnetic interactions with our instruments, ( including our eyes) and the mathematical modeling we apply to this data. At our present level of understanding and modelling it is not possible to exchange information with an "outside" our four dimensional ( 3 space one time) universe even if it existed. The string dimensions exist everywhere but are curled up and tiny, cannot travel the dimensions of the cosmos, and that is where we are at the moment. The rest is speculation and science fiction Commented Oct 27, 2013 at 5:25
• Thanks Anna. The last question is: Does my picture accurately depict our flat universe? Does the universe appear to be flat, because we are seeing only a fraction of the whole, and the rest in fact could be curved? I want to know if understood things right. Commented Oct 27, 2013 at 6:23
• I'm not up to date on the latest, but I remember that measurements of the Cosmic Microwave Background suggested that the universe is very close to being flat. Intuition tells me that if it seems to be close to flat then it probably is. If that's the case then it's infinite outside of our "observable" universe. As far as String Theory, I believe the additional dimensions are small, at the sub-atomic level. What you want is to be able to see into a large macro-scale dimension... like the ant on the sphere seeing into/out of the sphere. Commented Oct 27, 2013 at 6:57