Founding Physics on a Mathematical Background Reality

Physics makes two questionable assumptions: (1) Distant galaxies are accelerating relative to Earth. (2) Entangled objects are spatially separated from each other. Why questionable? Acceleration relative to Earth has never been observed in a single galaxy. Observers perceive entangled objects as spatially separated, yet 3D space is relative. We show that physical realities are projections of a mathematical background reality: 4D Euclidean space (ES). In Euclidean relativity (ER), all objects move through ES at the speed C. There is no time coordinate in ES. All action is due to a monotonically increasing, absolute, external evolution parameter θ. An observer experiences two projections of ES as space and time. The axis of his current 4D motion is his proper time τ. Three orthogonal axes form his 3D space x₁, x₂, x₃. His physical reality is his spacetime x₁(ϑ), x₂(ϑ), x₃(ϑ), τ(ϑ), where τ is a natural time coordinate and θ converts to absolute parameter time ϑ. Without gravity, his spacetime is Minkowski-like. As in general relativity (GR), gravity in ER is the curvature of spacetime. Since coordinates in GR are merely labels, the Einstein field equations also hold in systems that use τ as the time coordinate. ER predicts time’s arrow, relativistic effects, galactic motion, the Hubble tension, and entanglement. Remarkably, ER manages without cosmic inflation, expanding space, dark energy, and non-locality. ER tells us: (1) Distant galaxies maintain their recession speeds. (2) From their perspective, entangled objects have never been spatially separated, yet their proper time flows in opposite 4D directions.