There can’t be infinite deceleration,

I realise I should have been more specific.
Considering the pusher as a point object, deceleration of the pusher be infinite. Just another simplification so that you don’t have to calculate what would happen to all the speeds in between.

You said unfoldable not non-compressible. Your fault.

This is a nice example that also makes me think more questions.

• Will the hole punching be forward or backward?
• Assuming infinite deceleration, for an observer on the other end of the barn, will the barn be punched through, before or after the pole-pusher has stopped?
• For the pole-pusher, will the barn be punched through, before or after it has stopped?

Gets more interesting

The only time any information can be encoded onto entangled particles is when they’re created.

If that were the case, then we aren’t really doing FTL communication, unless we manage to entangle them at a distance. No?

OIC, it’s still useful if we want to make a secret key and send it somewhere. Then both sides can take a reading sometime in the future and they can then use whatever cluster of entangled particles they saw, as the symmetric key.