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'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.

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's place that it should also change.

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'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's place?

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.

[1] https://en.wikipedia.org/wiki/ER%3DEPR

A wave function as I visualize it, doesn't exist at points it time, it exists over all points in time. Until the box is opened the cat has been alive and been alive the whole time. After collapse only one of those states is left which applies the whole time.

So if it we're possible for entangled particles to have one wave function, collapsing it makes the observed result the one that applies all the time, back to when it got entangled in a pair. I don't see this a communicating anything over distance. It's more like 'communicating' backward in time, but I don't really think that's communicating any more than opening the box communicates back in time to effect an outcome.

Quite right. It is increasingly clear that holographic theories imply 'space' has at least one dimension (spatial degree of freedom) less than we think. The Holographic Principle says a volume only has a possible number of independent states proportional to its surface area (r^2), not its internal volume (r^3). This means that what we think of as a 3D volume, is really a plate of spaghetti, with the number of threads proportional to r^2, but each thread actually corresponding to the same 'place', with instant state changes along its whole non 'length', appearing as non-local correlations to our dimensionally ambitious eyes.

The limitation of the number of threads to r^2 might be because they all have to puncture the surface to create the appearance of a volume in the first place. The theory of Loop Quantum Gravity can even generate a discrete spectrum of area values in response to various meshed (graph) 'edges' puncturing a topological surface. Geometry is quantized.

QM is obviously an incomplete theory, and there is no point repeating the philosophical arguments of the 20th century, ad nauseam. In the 21st century, physicists are beginning to put together new theories of quanta, space, time and gravity that will be a lot more coherent and satisfying, even though we will lose the cherished notion of locality.

The Dining Philosophers should stop arguing over the forks and start to discuss the spaghetti!

P.S. Douglas Adams was right, it's The Great Spaghetti Monster after all.

> But even disregarding this, there seems to be a need to propagate something through space.

That's the problem with QM. So far as we can tell, nothing propagates through space. Even if something did propagate through space, it does so faster than the speed of light. And we know that information travelling faster than the speed of light is impossible. Because if it was possible, we would have causality violations.

i.e. if faster than light travel was possible, the universe would necessarily look very different than it does.

So we have multiple experiments, all of which are true, and which apparently disagree with each other in certain esoteric ways. Since the universe is consistent, we must conclude that the failure is in our understanding, not in the universe.