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
That’s one of the things we are looking for with particle accelerators, like CERN.
Quantum Mechanics is ridiculously accurate, within its domain. However, it doesn’t predict, or allow for General Relativity.
GM is ridiculously accurate, within its domain, but doesn’t allow for quantum mechanics.
Therefore we know both must be wrong (or at least incomplete).
Unfortunately the overlap is when gravitational forces become significant on quantum scales. There’s 4 ways to study this.
We can pack a ridiculous amount of energy into a tiny space, in a controlled manner. This is the best method. We also can’t do it.
We can pack a ridiculous amount of energy into a tiny space, in an uncontrolled, brute force manner. We can then hope to get lucky, or do it enough to beat the odds. This is what particle accelerators like CERN do. We can’t control what hits when accurately, but we can do enough collisions that 1 in a trillion is useful, then sift through the data looking for it.
We can use tricks to ‘stretch’ the quantum realm. This method is limited, but interesting. Gravity wave detectors effectively do this. They can use a laser to create an effect quantum object measured in meters or more.
We can look for places where quantum gravity is dominant, and see what happens. This is what things like the web space telescope are good for. We can look closely at black holes, and neutron stars, and see what they do to space time. Unfortunately, we are also stuck with whatever the universe happens to have done.
In short, the problem is being chipped at. It’s painfully slow, and buried in ever more complex maths, but it’s being done. I would love to see this “solved” in my lifetime. It’s unlikely, but could happen.