A classic

Copied from the other post:

It would violate relativity if it was A, though right? For example, one of the important thought experiments of relativity is that if you are in a sealed room, you cannot identify whether or not the room is stationary or has some velocity.

But if portals worked like the way they do in A, couldn't you could devise an experiment? Suppose there are two scenarios, one where the room is moving with some velocity, let's say 1 m/s downwards that is orthogonal to the floor and ceiling. No gravity, no friction, etc. Then you can have two portals, one that is pointed orthogonal to the room's velocity (so, mounted on one of the walls), and another portal that is mounted on the ceiling. Then, hold a table with a companion cube on it like in the diagram in the post, and ram it upwards at a speed of 1 m/s so the cube goes through the portal in the ceiling.

Then if the room is moving, then the table you are holding is stationary, because the room is traveling downwards at 1 m/s and you are moving the table upwards at 1 m/s, so the cube would just plop out of the second portal with no velocity. But if the room was stationary, then the table you are holding is moving, so it would go out of the second portal at 1 m/s in an orthogonal direction. So you can tell if your room is moving or not based on that, whether or not the block plops out of comes out at velocity 1 m/s.

So it must be B, in both cases (table stationary and portal moving, or table moving and portal stationary) the cube must fly out at velocity v. This way, there is no difference. It could be interpreted as the moving portal transferring its momentum somehow to the block.

Of course, we are assuming principles of physics apply to fictional portal that does not exist, so this might just be wrong.

Momentum is conserved with respect to the reference frame. In the new reference frame, the cube is moving quickly. It has no momentum on the platform, and has significant momentum after passing through the portal with high velocity. The apparent lack of conservation of momentum is due to the two reference frames being different.

It's like there are two superimposed identical universes, but one is stationary wrt the cube, and the other is moving wrt the cube. In the first universe, the cube has no momentum. In the second universe, the cube has high momentum. "Falling into" the second universe out of the first one would make it look like the cube manifested with significant momentum, even though it was at rest in its original universe.

There is no actual "paradox," except in the sense that this result may be unintuitive. (It's like how one-boxing Newcomb is objectively correct, but the premise breaks some assumptions in some of the usually-applicable math due to the impossible conditions.)

You should add the image and clarify that Yes is "B" while No is "A".

@Shemetz Done!