Today’s concept of time traces back to Einstein’s theory of special relativity (SR). In SR, he shows how inertial systems relate to each other. In general relativity (GR), he considers gravitation a property of curved spacetime. Here we prove: Einstein makes two mistakes in his concept of time. (1) He claims that clocks in a system K’ could synchronize at any instant with clocks in K, where K’ moves relative to K. If they did, they would have no clockwork. (2) He assigns variables of time to K’ (or else K) instead of assigning them to the measuring observer. Mislead by SR, Einstein makes a third mistake: In GR, he selects again an indefinite metric. Our “Euclidean relativity” (ER) is based on a Euclidean metric. We postulate: (1) In Euclidean spacetime (ES), all energy is moving radially away from an origin at the speed of light. (2) The laws of physics have the same form in each reality (projection of ES to an observer’s 3D space). (3) All energy is “wavematter” (electromagnetic wave packet and matter in one). Previous ER models run into paradoxes as they conceive of ES as reality. We show: The Lorentz transformation in SR is recovered in ER; gravitation relates to a rotation; ER is compatible with quantum mechanics. Einstein’s mistakes in SR have no measurable consequence, but GR is only an approximation for individual observers. We solve 12 fundamental mysteries, like today’s Hubble constant, dark energy, wave–particle duality, and quantum entanglement.