March 11, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with the ER=EPR conjecture?

Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. In other words, there exists a natural duality between spacetime and branchtime, with connections between distinct points in the spacetime causal graph (which correspond to Einstein–Rosen bridges) behaving in a fundamentally similar way to connections between distinct points in the multiway evolution graph (which correspond to quantum entanglements).

More precisely, a formal statement of the ER=EPR conjecture is that the Bekenstein–Hawking entropy of a pair of entangled black holes is equivalent to their entanglement entropy. If Hawking radiation effects occur as a result of branch pairs that fail to reconverge as a consequence of disconnections in the multiway causal graph, the ER=EPR conjecture is really just a rather elementary statement about the geometry of branchtime (in other words, it states that the natural distance metric in branchtime is the entanglement entropy of pairs of microstates, which one can prove directly from the properties of the Fubini–Study metric tensor).