The entangled particles in some sense remain right next to each other, even as they’re separated in what we think of as space and time.
But the connection between the particles may be something other than the hyperdimensional spaces we’ve imagined.
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.