Rules:
*You can teleport into and out of it at will
*It has a couple of plug sockets and can connect to internet from the region you teleported in from
*You can take objects and people with you
*As already stated, it is (3m)^3 (3m*3m*3m). The walls are plain plaster with a light in the middle of the ceiling. The pocket dimension is topologically toroidal, so if there weren’t walls and a ceiling/floor (which you can actually destroy) you would loop if you went more than 3m in any direction. Gravity, then, is artificial and can be altered to anywhere from 0 to 2g from a dial on the wall.
Edit: additional specifications
*You can only teleport out to where you teleported in from.
*Time proceeds at the same rate inside the pocket dimension
*There is an eject button for those inside to get out if something happens to you
You can transmit something, but it has a noise added to it. To decode it, you need to send the readings to the other end, via normal means. Basically, the receiver can tell, in hindsight, that a message was sent, but only once its other half has been received via normal means. The best you can do is get a timestamp of when the message was sent, as well as a message channel that is impossible to intercept.
The problem comes when QM meets relativity. With instant communication, you can send information into its own past. E.g. A and B are 2 planets. C is a ship, passing planet B at relativistic speeds. Planet A sends a message to B, over the FTL link. B then sends it to C, over a normal link. C, finally sends it back to A over FTL. Due to the ‘tilt’ of C’s light cone, the “now” of A-C is behind the “now” of A-B. This allows for paradoxical situations. The maths of Relativity implies that you can’t form a closed time loop like this. Such behaviours tend to imply some deeper rule, even if we haven’t found its cause yet.
Quantum mechanics has a lot of strangeness. It also seems to play fast, but not loose with causality. E.g. objects can move backwards in time, but still obey causality. Others can be smeared over time space, but still collapse to a causality obeying state. Etc
I so wish we could experiment with this to see where it actually breaks down