Modern pop culture would have us believe that there is such a thing as the 4th spatial dimension. And yes it's easily shown that $n$ dimensions is possible using math alone and 3 just happens to be our specific case. But as far as modern science goes, how confident are we that there are more than 3 spatial dimensions? Are there currently any accepted theories that rely on a 4th spacial dimension? (I'm particularly interested in this answer) I was provoked when I looked up how at the quantum level particles seem to pop in and out of existence. A simple write off that pop culture uses is that these particles are just "passing through" our 3D space as they travel fully through their higher dimensions. Is there much of a consensus on this?
Also please let's avoid discussion of time being the 4 dimension if at all possible. I'm speaking of space only.