But the connection between the particles may be something other than the hyperdimensional spaces we've imagined.
Either we have higher dimensions which "short circuit" distance and time as they appear to us in our reference frame or we don't have a good handle on what distance and time really are on their most fundamental level.
Our mental constructs and measurements of them could be more of an illusion than not, brought about because of the spacial and temporal reference frame we are tied to, locked in to.
Like quantum mechanics, we'd have a cook book for it, but it wouldn't make common sense.
And it may take a new type of mathematics.
But I bet the human race comes up with a solution, as long as we don't destroy ourselves in the meantime!