Secret wrote:I've thought of that before but so far no one have detected the higher dimensional thickness [...]
But the point is that we can't
detect that thickness, because we have no access to it.
Imagine a 2D world formed by plastic polygonal shapes trapped between two sheets of glass. Each polygonal shape is a perfect prism, so it has no evidence of any 3D features as far as its sides are concerned. The shapes can only interact with each other by their boundaries, because they are trapped between the glass sheets. Even though the shapes themselves may have quite a large thickness, say 1cm, but because they are confined by the glass, and because their sides have no 3D features, it is impossible for them to detect any 3D features at all. As far as they're concerned, the universe only exists in 2D, even though in reality they have quite a lot of 3D thickness.
Of course, this illusion of 2D remains as long as the radius of the prisms are relatively large compared to their thickness. If you have a very thin cylinder, for example, say its thickness is 1cm like everything else, but its radius is 0.001mm. Then there's a small chance that when it collides with something else, it may fall over sideways so that now it's no longer standing vertically between the two sheets of glass, but is rolling around. It's still confined, but now it starts to show some "odd features" because now its radius becomes its "thickness" and its thickness becomes its length. If two such cylinder collide, they may still bounce off each other like before, but they can also roll over each other or one can lie on top of the other. This will cause "strange effects" from the shapes' 2D point of view. They still have no way of measuring the "strange thickness" of the fallen cylinders, but they will observe that they have strange properties that are different from other non-fallen objects.
This is interesting because as long as the radius is not too far below the 3D thickness of the object, then it behaves "normally", but once its radius becomes too small, it has the risk of "falling over" and acquiring strange properties. So there is a size scale at which things start to turn strange (i.e., 3D effects start to show up). Does this remind you of the real world?
Macroscopic objects behave "normally", but once you get down past a certain size, things start to act strangely. Conceivably, this is because objects smaller than a certain size starts to exhibit extra-dimensional properties.
And indeed, this is the idea behind "curled up" dimensions and string theory. When the object is big enough, you don't see anything strange because only their 3D properties are manifested. They are too big to "fall over" in the extra, confined dimensions. But when things get small enough, then the effects of the additional dimensions start to show up. Now they can "fall over" in the extra dimensions, and when we try to interpret the effects from our 3D-centric point of view, we find them really strange. But if we interpret them as the effect of having extra dimensions to "fall" or "rotate" in, then a lot of these effects become quite mundane. That's one of the neat things about string theory.