Abstract

This paper introduces and examines the prospects of the recent research in a holographic relation between entanglement and spacetime pioneered by Mark van Raamsdonk and collaborators. Their thesis is that entanglement in a holographic quantum state is crucial for connectivity in its spacetime dual. Utilizing this relation, the paper develops a thought experiment that promises to probe the nature of spacetime by monitoring the behavior of a spacetime when all entanglement is removed between local degrees of freedom in its dual quantum state. The thought experiment suggests a picture of spacetime as consisting of robust nodes that are connected by non-robust bulk spacetime that is sensitive to changes in entanglement in the dual quantum state. However, rather than pursuing the thought experiment in further detail, the credibility of the relation between spacetime and entanglement in this zero entanglement limit is questioned. The energy of a quantum system generally increases when all entanglement is removed between subsystems, and so does the energy of its spacetime dual. If a system is subdivided into an infinite number of subsystems and all entanglement between them is removed, then the energy of the quantum system and the energy of its spacetime dual are at risk of diverging. While this is a prima facie worry for the thought experiment, it does not constitute a conclusive refutation.