Quantum Gravity with Particle Curvature Without Space Curvature

We propose an operational µτ-approach to gravity on a flat background: the gravitational interaction is interpreted as a universal retuning of the particle scale (µ) and the rate of internal clocks (τ). Quanta of space possess real and imaginary parts. The size of each quantum of space is equal to the size of the Universe and has a Möbius topology. Tensor perturbations (gravitons) propagate along the imaginary parts of the space quanta and, upon intersecting their real parts, induce coherent changes of µ ,τ in all fields. In the weak-field regime, the theory reproduces the classical tests of GR (PPN up to 1PN order, lensing, Shapiro delay, equality of EM and GW speeds); in the strong-field regime, it predicts small 2PN deviations, possible “echoes” in black-hole ringdown, and a weak scalar polarization. Within a single framework, several “dark” effects are described simultaneously: dark matter as a BH-bound imaginary-geometric response (including Bullet Cluster–type cases), dark energy as the sum of a vacuum component and the growth of space quanta, and baryon asymmetry as a consequence of a two-sheeted (Möbius-like) topology. The theory preserves causality and local Lorentz invariance, is formulated as an EFT with controlled corrections, and provides sharp observational tests for nearfuture experiments.