This is a sure sign that I have a crapload of free time. Just hear me out – this is interesting!
Moving in One Dimension
Say there is a universe that lived in just one dimension – on the x-axis. People in it can only move forward and backward. They’re not even aware of the concepts of left/right and up/down. How can we create a world for them where they can always keep moving without coming to any kind of “barrier”?
The solution I came up with was to connect the two ends of a line to form a circle. Problem solved. Though the circle itself is a two dimensional object, the 1-D people are living on its surface blissfully unaware of the fact that there are any extra dimensions below them. If the circle is large enough, they won’t notice the curvature at all!
Moving in Two Dimensions
What if we have another universe made of two dimensions alone? Basically everyone lives on a flat sheet and can move forward/backward and left/right, but not up and down. How can we design a sheet in such a way that they’ll always have space to move around without ever encountering any “edges”? My solution was to make a sphere where everyone lives on its surface. Though a sphere is a 3-D object, the people living on it are unaware of anything other than moving backwards and forwards. Kind of like ants. If the sphere is big enough like maybe the size of a planet, it’ll look flat to them. Sounds familiar eh? :D
Moving in Three Dimensions
Coming to our own universe, we can move up/down, left/right, and front/back. We live in 3-D space. But like the above two, how can we construct a system where we can keep going forever in any direction without encountering any barriers? Any “container” will have boundaries that we bounce off against. But the universe has no conventional boundaries. It’s expanding all the time but there are no “barriers” so to speak. How can this be?
If a one dimensional unlimited space is the surface of a 2-D circle and a two dimensional unlimited space is the surface of a 3-D sphere, can it be possible that an unlimited three dimensional space is the surface of a 4-D object? Just like our 2-D people on a sphere don’t know you can move up or down, we ourselves don’t know about the 4th dimension…it boggles the mind to think about kind of shape it’ll look like. I don’t think we can imagine such a thing.
Can it be possible that an unlimited three dimensional space is the surface of a 4-D object?
Of course we call time the 4th dimension, but it’s not a spatial one. We can only imagine 3-D spatial objects. And yet space itself might be the surface of an immense 4-D structure! Just like when a sphere like a planet is big enough we can’t tell that it’s curved and we see the surface having only two dimensions, if our universe is big enough (and boy it is!) we won’t notice the slight “curvature”. And if we keep going…and going…and going…in any direction, eventually we’ll end up where we started. Or at least I think that’s what will happen.
Whatever this 4-D spatial object is, it’s expanding at an ever increasing pace. Like the spots on a balloon become bigger and bigger as it’s inflated even though they’re not moving. Space itself is expanding – our atoms and molecules are stretching. Difficult to imagine isn’t it?
So what do you think? Can we be living on the surface of some unimaginable 4 dimensional structure?