A possible connection between quantum mechanics and spacetime

TL;DR

The paper argues that quantum mechanics can be recast as a spacetime-structure uncertainty by transforming the path integral over trajectories into an integral over spacetime metrics $g_{\alpha\beta}$. It extends this spacetime representation from a single particle to general systems and fields, showing that wave–particle duality corresponds to metric uncertainty and that even field configurations can be viewed as arising from different spacetime geometries. Motivated by this viewpoint, it proposes a revised quantum gravity formulation in which only the metric is quantized and matter fields are constrained to be solutions $\varphi = \Phi(g_{\mu\nu})$ of the classical equations, thereby avoiding the problematic interpretation of classical matter as a quantum spacetime. The work highlights a unifying geometric perspective on quantum phenomena and suggests potential links to holographic ideas, while acknowledging unresolved issues in gauge fixing and the precise mathematical implementation of the proposed framework.

Abstract

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 the 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 the 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.

Figures (1)

• Figure 1: Embedding any one trajectory in the path integral \ref{['eq:1.4']} into a curved spacetime where it becomes a geodesic. The red curve in figure \ref{['fig:1']} (a) represents an arbitrary trajectory $X^{\mu}(\tau)$ in the path integral \ref{['eq:1.4']}. Figure \ref{['fig:1']} (b) shows an infinitely thin ribbon where the trajectory $X^{\mu}(\tau)$ acts as a geodesic. Figure \ref{['fig:1']} (c) depicts a two dimensional surface. The ribbon in figure \ref{['fig:1']} (b) is a part of this surface.