Today’s concepts of space and time trace back to Albert Einstein’s theories of relativity. In special relativity, he derives relations of how a “moving observer” experiences space and time with respect to an “observer at rest”. In general relativity, he derives relations of how mass and energy are affecting space and time. Both theories have been very successful, but fail to solve fundamental mysteries such as competing values of the Hubble constant, dark energy, the wave–particle duality, and quantum entanglement. Here we show that this failure is due to prioritizing a “system at rest”: In Einstein’s relativity, there is no superordinate reference frame that would treat objects at rest and moving objects alike. We replace Minkowski spacetime with Euclidean spacetime (ES) and claim that reality is formed by projecting ES to 3D space. Alternative models of Euclidean relativity run into geometric paradoxes as they claim reality to be in ES. Our theory profits from two new concepts: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). In Cartesian ES coordinates, it is not predefined for all objects alike which axial distance relates to time. Time is a subordinate quantity: covered distance divided by the speed of light. Wavematter is a generalized concept of energy: Each object is wave from an external view, but matter from its internal view. Length contraction, time dilation, acceleration, and gravitation are geometric effects. We even derive a Theory of Everything in ES. Matching the symmetry simplifies physics.