The idea that two entangled particles share a wave function seems at least problematic. The ontological state of the wave function is an open problem but I think you can&#x27;t get away with thinking of them as independent entities that can associate with and unassociate from particles. It is probably more like there is one very complex wave function for the entire universe and we can only sometimes get away with thinking of it as the product of the wave function of a system we are interested in and the wave function of all the rest, the environment.<p>But even disregarding this, there seems to be a need to propagate something through space. The wave function of the entangled pair could be spread out in space and when Alice performs a measurement on her particle you have to notify the wave function at Bob&#x27;s place that it should also change.<p>You could also try to imagine that the entire wave function for the two entangled particles is not spread out in space and located next to Alice which makes it easier to imagine how the entire wave function could change at once. But now how does Bob&#x27;s particle know that the far away wave function changed in order to behave appropriately? We still have to propagate that notification over to Bob. And what if Bob decides to perform the measurement instead of Alice but the wave function is sitting around at Alice&#x27;s place?<p>There is some inherent nonlocality in quantum mechanics and the effects of measurements have to propagate through space even when they can not be used to exchange classical information. One idea that I find really interesting is ER = EPR [1] by Susskind. The idea is vaguely that entanglement determines locality, i.e. two things are close together if they are entangled, especially two entangled and spatially separated particles are connected by a wormhole and therefore actually remain close together all the time. This would make spooky actions at a distance a lot less spooky because it would mean that you can never really separate entangled particles. It would probably also mean that the topology of space is actually extremely complex and only superficially looks like Euclidean three dimensional space.<p>[1] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;ER%3DEPR" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;ER%3DEPR</a>