I frequently hear people say that the universe is based off of a 4th-dimensional space-time continuum. As a result, it could hypothetically do things like loop on itself if you went in one direction long enough. However, people often point out that the 4th dimension is not time, but rather an independent spacial dimension. At the same time though, they might talk about how the 4th dimension actually is time in the space-time continuum, which makes no sense to me at all. Is the 4th dimension time in the space-time continuum, or something else?
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This often comes up in the context of trying to explain how objects move through space, and especially how gravity works to cause smaller (less massive) objects to “fall” toward larger objects.
Picture a 2D world in which “space” consists of a flat sheet of stretchy material, like a trampoline.
You place a really heavy object (your mom, perhaps) in the center of the trampoline. Then you place a small ball, like a marble, off to one side. What happens when you let go? It rolls inward toward the center.
Why does the ball roll toward the middle? From our perspective, because we are living in three visible spatial dimensions, we can see that it is because the presence of a heavy object in the middle of the trampoline is curving the fabric of “space” (the trampoline), which causes the ball to roll “downhill” even though nothing is obviously pushing it that direction.
But the ball only exists in 2D; from its perspective it looks like the trampoline is still flat, because it only knows about the directions forward/backward, and left/right. It has no idea what “up/down” means. But it still rolls in toward the middle, and we, as 3 dimensional beings, can see that it is because the fabric of the 2D world the ball is living in is curved.
Our 3D world is similar. When you put a big object in 3D space, it curves the fabric of space time in a very similar way. It creates a curvature in an unseen 4th dimension, that creates an apparent force of gravity, pulling other objects toward it. Just like your mom standing on the trampoline causes the ball to roll “downhill” toward her because the trampoline is curved due to her mass, the Earth existing in our 3D space causes us to fall “downhill” toward it because space is curved due to its mass.
We just can’t see that curvature because, like with the ball, it exists in an “extra” dimension that is outside of what we are capable of perceiving directly. But, like the ball, we can still tell that the curvature is there, because we feel its effects (gravity).
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