The difference in this case is that the object has 0 momentum and the portal doesn’t impart its momentum to the cube because you can’t collide with the portal. There is no force acting on the object to make it move.
That is not how either relativity or momentum work. The cube is still inert and the portal’s movement would have no effect on it unless it has some acting force that pushes it when passing through. Even if the exit portal was moving, the cube would remain stationary unless it had nothing to rest upon and gravity pulled it down.
The difference in this case is that the object has 0 momentum and the portal doesn’t impart its momentum to the cube because you can’t collide with the portal. There is no force acting on the object to make it move.
Of course it has momentum relative to the portal.
That is not how either relativity or momentum work. The cube is still inert and the portal’s movement would have no effect on it unless it has some acting force that pushes it when passing through. Even if the exit portal was moving, the cube would remain stationary unless it had nothing to rest upon and gravity pulled it down.