Quantum Backreaction and Wave-Particle Duality in Curved SpacetimeExploring Quantum Wavefunction Evolution Under Spacetime Curvature and Backreaction Effects

Wave-particle duality remains a cornerstone of quantum mechanics, yet its behavior in strongly curved spacetime is not fully understood. We present a novel formalism embedding quantum wavefunctions within the evolving spacetime metric, incorporating backreaction effects from gravitational perturbations. By modifying the Schrödinger equation to include quantum curvature terms, we derive a generalized Klein-Gordon equation that predicts phase distortions in wavefunctions near black holes and during inflationary epochs. These modifications suggest that quantum wave coherence is influenced by the local curvature tensor, leading to observable effects in interferometric experiments. We propose experimental validation using atom interferometry and quantum optics, where these curvature-induced quantum effects should manifest as measurable phase shifts. Additionally, we discuss implications for quantum computing in curved spacetime, where decoherence mechanisms would be fundamentally altered.

Key Predictions:

* Wavefunction distortion near black holes: Quantum interference experiments near strong gravity sources will reveal nontrivial phase shifts.

* Quantum metrology applications: Atomic clock precision is affected by local spacetime fluctuations.

* Curvature-induced decoherence: Quantum computing systems require novel error correction strategies in high-curvature regimes.