Tweedle Dum & Tweedle Dee

Here is a thought experiment.Consider a machine that can duplicate theposition and state of atoms - a people duplicator.Another machine having the capacity to transmit matter, perhaps byconverting it into radiation first.A human being is 'duplicated' and simultaneously transmitted together with his duplicate into a room.The room itself is the inside of a sphere so that all directions look thesame. There are no windows and no objects in the room.The room floats free in space far from any other matter so there is no gravity, ie. no up or down direction.Now imagine the person and his duplicate materialising in the room, one behind the other like they were part of a queue for the bus.The one at the 'head of the queue' would see the blank walls of the room. The one behind him would see the back of this other figure.Perhaps the one behind might tap his duplicate on the shoulder who would turn around and then a conversation would ensue between the original and his duplicate.Although one is a duplicate of the other they are able to hold a two way conversation because when they materialised in the room their experiences became different one experienced the wall visually whereas the other experienced the back of a head.But if the machine that transported them into the room had materialised themfacing each other so that when they became aware of their surroundings they saw exactly the same things what then?I think that because there is no different experience for either of them they would continue to do and say exactly the same thing for all time. They could never hold a two way conversation because the initial symmetry of their experience cannot be broken .Is there anything they could do so as to avoid spending forever in a Tweedle Dum Tweedle Dee existence.?