John Carlos Baez on Nostr: wrote: "I'm desperately trying to reconcile the large and the small scales. After all ...

wrote: "I'm desperately trying to reconcile the large and the small scales. After all there has to be a continuous transition between them in the course of a free fall. At large scale, the observer sees the ships in front of him piling up at the horizon. Eventually, the observer gets close to the horizon. What does he see then? Do the piled up ships start suddenly slipping through the horizon?"

As you say, there has to be continuous transition between the large-scale and small-scale behavior. I agree that it's tricky to think about this if you don't use any math. But there's no need for desperation.

First, don't imagine anything "sudden" - that goes against the continuity.

Second, don't imagine the horizon as a location in space, where things get "bunched up", because it's not! It's a lightlike surface. When your starship crosses it, you see a bunch of ships on the horizon that are further and further away, and further back in time.... which is, by the way, just how you *always* see a bunch of things lined up. I think this is what you really need to ponder, and as always the Penrose diagram is your friend.

You can learn a lot from the case of 2 ships, one in front of the other. 11 hours ago, in my frame of references, Greg Egan (npub12cu…d38p) solved that case:

https://mathstodon.xyz/@gregeganSF/113564919547422793