A healthier stochastic semiclassical gravity: world without Schr\"{o}dinger cats

Semiclassical gravity couples classical gravity to the quantized matter in meanfield approximation. The meanfield coupling is problematic for two reasons. First, it ignores the quantum fluctuation of matter distribution. Second, it violates the linearity of the quantum dynamics. The first problem can be mitigated by allowing stochastic fluctuations of the geometry but the second problem lies deep in quantum foundations. Restoration of quantum linearity requires a conceptual approach to hybrid classical-quantum coupling. Studies of the measurement problem and the quantum-classical transition point to the solution. It is based on a postulated mechanism of spontaneous quantum monitoring plus feedback. This approach eliminates Schr\"{o}dinger cat states, takes quantum fluctuations into account, and restores the linearity of quantum dynamics. Such a captivating conceptionally `healthier' semiclassical theory exists in the Newtonian limit, but its relativistic covariance hits a wall. Here we will briefly recapitulate the concept and its realization in the nonrelativistic limit. We emphasize that the long-known obstacles to the relativistic extension lie in quantum foundations.