I disagree with your interpretation of the 4th dimension,
my take on dimensions:
1st: x-axis
2nd: xy-axis
3rd: xyz-axis
Now, for the 4th dimension, lets say we had a sphere in the 3rd dimension and measures 1 unit in each direction. The 4th dimension would expand the sphere in all three directions without changing the 1 unit length of the ball. Therefore, the 4th dimension is the ability for expansion of matter. As the observer of this phenomenon, and lets say resistant to this feat, you would see everything in the universe getting larger, but coming closer together. The observed would see everything just as they always have, but would see everything in the universe getting farther away (which could explain the redshift). Dark matter is the matter of the 4th dimension. The vast "emptiness of space" is where the highest quantity of dark matter resides. Therefore, you see the largest expansion of space. Dark matter also resides in the space between your atoms. I believe that there is a link between the 3rd dimension and the 4th dimension.
