Hubble Tension and Entanglement—Two Puzzles, One Solution

Physics makes two questionable assumptions: (1) Distant galaxies are accelerating relative to Earth. (2) Entangled objects do not stay together spatially. Why questionable? Acceleration has never been observed in a single galaxy. Observers perceive entangled objects as spatially separated objects, yet 3D space is relative. Here we show: While special and general relativity remain fully valid, additional information is available when we take a 4D Euclidean geometry into account. We calculate relativistic effects (Lorentz factor, gravitational time dilation) from purely geometric considerations and conservation laws. The extra information is helpful for understanding the very distant and the very small. In Euclidean relativity (ER), all objects move through 4D Euclidean space (ES) at the same speed C. Worldlines are parameterized by 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 make up his 3D space x₁, x₂, x₃. His physical reality is the “τ-based spacetime” cτ(ϑ), x₁(ϑ), x₂(ϑ), x₃(ϑ), where the observer’s τ is the time coordinate and the parameter θ is converted into parameter time ϑ. ER predicts the Hubble tension and entanglement. Remarkably, ER manages without cosmic inflation, expanding space, dark energy, and non-locality. ER teaches us: (1) Distant galaxies retain their recession speeds. (2) From their perspective, entangled objects have never been spatially separated, yet their proper time flows in opposite 4D directions.