Viscoelastic Emergent Gravity: Quantum Dissipation and Attenuation of Gravitational Waves

Using the non-observation of gravitational-wave amplitude attenuation in the binary neutron star merger GW170817 over 40 Mpc (with waveform amplitude consistency at the ~1% level, we infer a relaxation time \( \tau \) ≥ 3.2 × 1023 s \( \tau \)for a viscoelastic extension of General Relativity (GR) that incorporates quantum dissipative corrections via the fluctuation--dissipation theorem (FDT). In the weak-field linearized limit, this framework yields damped gravitational waves with an amplitude decay rate \( \Gamma \) ≈ ω2 / 2\( \tau \)c for angular frequency ω, although such damping is extremely weak given the enormous lower bound on \( \tau \). Einstein's equations are recovered as \( \tau \to \infty \) (zero dissipation limit). This viscoelastic emergent gravity model is consistent with current gravitational-wave propagation tests and provides a phenomenological avenue to include quantum irreversibility in gravity without conflict with observations. We also introduce a hybrid description in which a quantum mediator (coherent, unitary) coexists with a dissipative viscoelastic reservoir obeying fluctuation--dissipation. This allows a regime-dependent prediction: gravitationally mediated entanglement appears when the coherent coupling, set by the nonlocal phase \( \Delta \phi(G, m, r, \delta, t) \), overcomes reservoir-induced dephasing, while the channel becomes effectively entanglement-breaking when dissipation dominates. We provide numerical maps of the entangling frontier in realistic parameter space (mesoscopic masses, micron separations, second-scale evolution), together with updated GW-propagation bounds that continue to imply negligible intrinsic damping. We also discuss a purpose-built computing architecture where a strong engineered reservoir intentionally enforces rapid collapse, distinct from the universal hybrid description.