Some insights
The CCentipede
en français française

Relativity forbids travel at speeds faster than light.  But what about just plain communication?  It has been proposed that quantum entanglement might provide a way to communicate "instantly".  What might the consequences of such a capability be, in a relativistic universe?  Well, let us consider a story -- a parable, if you will.

(Sincere apologies if this little tale "bugs" anyone.)

The Relativistic Centipede -- aka the CCentipede

The CCentipede, which lives in the jungles of Far Pastafooslio, is quite large, with many body segments, and pair of legs on every segment. It walks (er, runs) at a constant speed of 0.867c.

An entomologist -- call her 'E' -- is trying to catch the CCentipede. While standing still in the jungle, 'E' has measured the CCentipede carefully, using advanced instruments such as strings, clocks, measuring sticks, and grad students, and has determined that the beast appears to be exactly 50 feet long. 'E' has constructed a CCentipede trap, consisting of a tunnel which is 50 feet long, with doors at each end. The trap has an additional very special gadget: A Super-C Whizzbang Instantly Entangled Communicator which allows information to be transferred instantly along the length of the tunnel, in the tunnel's own rest frame.
C-centipede trap

Eventually, the CCentipede walks (er, runs) into the tunnel.
CCentipede sees the trap

A sensor senses the very moment that the rear end of the CCentipede enters the trap, and triggers the Super-C Communicator, which sends a pulse down the length of the tunnel, causing both doors to slam shut instantly and simultaneously (in the tunnel's own rest frame). If all goes well, the CCentipede will be trapped in very, very tight quarters.

CCentipede trap with centipede

Note, particularly, that the exit door slams shut at the very moment when the CCentipede's nose is about to exit the trap, and note carefully that this event is experienced by the CCentipede as well as the trap.

BUT ... The CCentipede is a clever creature, and it, too, has a Super-C Whizzbang Instantly Entangled Communicator, which allows it to respond instantly to any stimulus, along the entire length of its body (that is, both instantly and simultaneously in its own rest frame).

In its rest frame, the CCentipede is 100 feet long, and the tunnel is only 25 feet long, due to good ol' Relativity. It sees the tunnel, and dashes into it. But at the moment when its nose is about to leave the trap, as we know, the exit door slams shut. At that instant, the CCentipede's Super-C Communicator springs into action notifying all the CCentipede's legs of the closed door, and it stops instantly, skidding only enough to allow it to shrink gracefully down to its "stationary" length of 100 feet in the tunnel's rest frame.

BUT ... something is wrong ...

... the back end of the CCentipede has not entered the trap when it stops!

CCentipede half in the trap

SO, the trap hasn't been sprung yet.

SO, the doors never closed.

SO, the CCentipede didn't stop after all, and just ran right through the open tunnel.

CCentipede coming through

BUT ... something is wrong ...

The back end of the CCentipede must enter the trap as it runs through, and that triggers the trap, and the doors slam shut.

SO, the CCentipede does see the doors close, and since the event of the exit door closing is in both frames of reference, it really does see the door close before its head leaves the trap, after all.

SO, the CCentipede does stop, after all ...

SO, ... >>>SPZZAPP<<<

At this moment, the sun and clouds disappear, and the sky turns a solid, even, deep blue. Enormous white letters appear, spelling out...


followed by many cryptic hexadecimal runes...

Reconciling special relativity with FTL communication may present challenges.