“ Scientifically grounded Hypothesis on the Existence of a physical fifth Dimension”
For euclidean space a transfer of the equation for a circle x^{2} + y^{2} = R^{2} and the equation for the surface of a sphere x^{2} + y^{2} + z^{2} = R^{2} to four spatial dimensions is done:
x^{2} + y^{2} + z^{2} + u^{2} = R^{2} .
Analogous to the surface of a sphere one receives a curved three-dimensional (riemannean) space which is unlimited and cyclic. In all directions of this space one gets back to the starting point after moving a distance of n * 2 p R. This space is finite, because its volume is 2 p^{2} R^{3} . With time as another dimension in this "surface of a four-dimensional sphere" we receive a metric which is similar to the cosmological Robertson - Walker - Model. |