Semiclassical gravity, where the expectation values of quantum operators are used in conjunction with general relativity, is not necessarily seen as more problematic than the Born rule itself. However, it does introduce certain challenges and open questions when it comes to the consistent formulation of a theory of quantum gravity.
The Born rule in quantum mechanics relates to the calculation of probabilities for measurement outcomes based on the squared magnitudes of probability amplitudes. It provides a consistent framework for predicting the statistical outcomes of quantum measurements. The Born rule is widely accepted and has been extensively confirmed by experiments.
Semiclassical gravity, on the other hand, attempts to incorporate quantum effects into the framework of general relativity. In this approach, the expectation values of quantum operators are used to represent the average behavior of quantum fields or particles in a classical gravitational background. While this approach has been successful in certain situations, such as the prediction of Hawking radiation from black holes, it faces several challenges:
Backreaction: When considering the effects of quantum fields on the background geometry, semiclassical gravity does not fully account for the backreaction of these quantum fields on the spacetime itself. This neglect of the backreaction can lead to inconsistencies and breakdowns of the semiclassical approximation in certain regimes.
Singularity Problem: Semiclassical gravity does not provide a satisfactory resolution to the singularities that arise in general relativity, such as the singularities at the centers of black holes or at the beginning of the universe. These singularities represent breakdowns of classical physics and are expected to require a complete theory of quantum gravity for a proper description.
Consistency with Quantum Mechanics: Semiclassical gravity raises questions about the consistent formulation of a theory that combines quantum mechanics and general relativity. It does not address the fundamental conceptual and interpretational issues that arise in the context of quantum gravity, such as the measurement problem or the need for a unified framework that accounts for both quantum phenomena and the curvature of spacetime.
While semiclassical gravity can provide valuable insights and approximate descriptions in certain regimes, it is seen as an effective low-energy approximation rather than a complete theory of quantum gravity. The search for a more comprehensive theory that fully incorporates quantum effects into the gravitational framework is an active area of research in theoretical physics.