General Relativistic Wormhole Connections from Planck-Scales and the ER = EPR Conjecture

Abstract: Einstein's equations of general relativity (GR) can describe the connection between events within a given hypervolume of size $L$ larger than the Planck length $L_P$ in terms of wormhole connections where metric fluctuations give rise to an indetermination relationship that involves the Riemann curvature tensor. At low energies (when $L \gg L_P$), these connections behave like an exchange of a virtual graviton with wavelength $\lambda_G=L$ as if gravitation were an emergent physical property. Down to Planck scales, wormholes avoid the gravitational collapse and any superposition of events or space--times become indistinguishable. These properties of Einstein's equations can find connections with the novel picture of quantum gravity (QG) known as the ``Einstein--Rosen (ER)=Einstein--Podolski--Rosen (EPR)'' (ER = EPR) conjecture proposed by Susskind and Maldacena in Anti-de-Sitter (AdS) space--times in their equivalence with conformal field theories (CFTs). In this scenario, non-traversable wormhole connections of two or more distant events in space--time through Einstein--Rosen (ER) wormholes that are solutions of the equations of GR, are supposed to be equivalent to events connected with non-local Einstein--Podolski--Rosen (EPR) entangled states that instead belong to the language of quantum mechanics. Our findings suggest that if the ER = EPR conjecture is valid, it can be extended to other different types of space--times and that gravity and space--time could be emergent physical quantities if the exchange of a virtual graviton between events can be considered connected by ER wormholes equivalent to entanglement connections.