Special relativity forbids information traveling faster than the speed of light. General relativity does not. Therefore, resolve the Einstein-Podolsky-Rosen paradox by stringing a wormhole between two entangled particles, allowing them to communicate as fast as they need. The size of the wormhole is smaller than we can currently observe.
It is unsettling to think of space as like swiss cheese filled with lots of tiny holes connecting different points superluminally, or of space being crisscrossed by lots of tiny wormhole tunnels, but everything else in quantum mechanics -- and general relativity -- is unsettling also. Most wormholes will be short: entangled particles can't travel very far before hitting something that observes one of them, at which point communication happens through the wormhole, and the wormhole becomes no longer necessary, so we assume it dissipates by some unknown mechanism. Or, if there are entangled particles flying around for long distances in a nearly perfect vacuum, then, because it is a vacuum, there's nothing in the region that will "care" that there's a long wormhole in the area.
How small can wormholes be? Is there a relationship between the size of a wormhole and how much, or how quickly, information may be transmitted through it? What interaction would such tiny wormholes have with surrounding matter? Currently there exists no theory of quantum gravity, but in the future, there may be an experimentally supported one, which in turn could disprove this theory.
Holding the mouth of a wormhole open requires negative matter. Future subatomic particle experiments may disprove whether entangleable particles are composed in part of negative matter, in a way similar to how mesons are composed of both matter and antimatter.
Inspired by the Conway Kochen Free Will Theorem, which makes the assumption of no superluminal communication between particles.
Update: this idea is ER=EPR.
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