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 5th Dimension - hypothesis

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“ Scientifically grounded Hypothesis on the Existence of a physical fifth Dimension”

For euclidean space a transfer of the equation for a circle x2 + y2 = R2 and the equation for the surface of a sphere  x2 + y2 + z2 = R2 to four spatial dimensions is done:

                                           x2 + y2 + z2 + u2 = R2 .

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 p2 R3 . 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.