A possible connection between quantum mechanics and spacetime

Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the uncertainty of spacetime for the particle. Summarizing all possible trajectories in conventional path integral quantum mechanics can be transformed into the summation of all possible spacetime metrics. Furthermore, we emphasize that in conventional quantum gravity, it is possible that the classical matter fields correspond to quantum spacetime. We argue that this is not quite reasonable and propose a new path integral quantum gravity model based on the new interpretation of wave-particle duality. In this model, the aforementioned drawback of conventional quantum gravity naturally disappears.

💡 Research Summary

The paper proposes a novel reinterpretation of wave‑particle duality as a manifestation of spacetime‑structure uncertainty for microscopic particles. Starting from the familiar path‑integral formulation of quantum mechanics, the authors argue that each trajectory summed over in the Feynman integral can be regarded as a geodesic in some curved spacetime. Because any physically allowed curve can be embedded as a geodesic of an appropriately chosen metric, the set of all possible trajectories is equivalent to the set of all possible spacetime metrics. By introducing a functional mapping (F