Wormhole and Entanglement (Non-)Detection in the ER=EPR Correspondence

TL;DR

This paper demonstrates that, consistent with quantum mechanics, there is no observable in general relativity capable of unambiguously detecting the presence of a wormhole, aligning with the undetectability of entanglement in quantum theory.

Contribution

It proves that wormholes cannot be unambiguously detected by any measurement in general relativity, preserving the quantum mechanical property of entanglement undetectability within ER=EPR.

Findings

No measurement can definitively detect a wormhole in general relativity.

Wormhole detection is fundamentally unobservable, mirroring entanglement undetectability.

Supports the consistency of ER=EPR with quantum mechanics.

Abstract

The recently proposed ER=EPR correspondence postulates the existence of wormholes (Einstein-Rosen bridges) between entangled states (such as EPR pairs). Entanglement is famously known to be unobservable in quantum mechanics, in that there exists no observable (or, equivalently, projector) that can accurately pick out whether a generic state is entangled. Many features of the geometry of spacetime, however, are observables, so one might worry that the presence or absence of a wormhole could identify an entangled state in ER=EPR, violating quantum mechanics, specifically, the property of state-independence of observables. In this note, we establish that this cannot occur: there is no measurement in general relativity that unambiguously detects the presence of a generic wormhole geometry. This statement is the ER=EPR dual of the undetectability of entanglement.