"New physics needs new mathematics" is a demand that has been formulated for a long time in order to finally be able to connect relativity theory and quantum physics mathematically. The reason why this has not been possible so far is revealed for the first time on the basis of misunderstandings in vector calculus and in quaternion calculus. Their former pioneers Hermann Grassmann and William Rowan Hamilton described their "new science" almost simultaneously around 1843. However, their mathematical systems differed fundamentally from each other, although they both dealt with the same (electromagnetic) domain of expansion "Q-4". Now a sustainable enhancement in the sciences is on the horizon. If the two mathematical systems are combined with a new understanding of the imaginary, a holistic calculation system will emerge that will bring our universe together into a holistic universal whole. That the development of mathematical laws and operations is only possible with a new interpretation of the imaginary represents a central thesis, which is elaborated in the book "absolut imaginär" (2022/ 03). The two newly introduced, purely imaginary domains of existence "i-1" and "i-0" play a special role in this context. Both can be traced back to the original explanations by Hermann Grassmann and William Rowan Hamilton. But only the last leads to the reinterpretation of an imaginary holism and thereby forms the key element of a New Physics. In this way, the mechanism of physical entanglement finally receives its long-awaited, missing mathematical element.