Q1. If John disappears instantaneously at time t1 and is reconstructed at time t2 with exactly the same atomic arrangement, is John's consciousness in that new body?
Q2. If the answer to Q1 is yes, what if two new bodies were reconstructed at t2 instead of one? Which is "myself" from John's point of view?
I heard a discussion of this issue which made a useful comparison - that brains are not clockwork but more like a steam engine, with information as a 'working fluid'. That is, we are not just the infrastructure which can be in a stable or frozen condition, instead we are something dynamic, a constantly updating state integrating many ongoing processes. So you say atom arrangement, fine. But also currents & waves moving through us.
Human resuscitation is a very interesting area, with a lot of recent progress. There are indications humans may be able to hibernate, lowering core body-temperature & other bodily processes including mental activity, to dramatically decrease calorie consumption. Maybe if we can understand more about how to safely shut down this might help. They are talking about using this state for space travel, and for surgery.
I feel until we get closer to understanding brains & making analogues, we are just giving opinions. You should note atomic-fidelity is not required for cellular-scale organisation, but also that we likely need to understand ongoing processes not just momentary states.
As a Buddhist, the idea identity is a process not a state or essence separate to processes, is very familiar. Who is 'really' who would be about legal definitions, custom, and emerging practices to deal with real tensions in practice. In a very real sense we can be only loosely connected to who we used to be in our own lives - the continuity might be greater for onlookers like parents, than something we experience ourselves..
I think you are confused by some familiar terms like mind, memory, intellect, personality, consciousness etc. Any way I believe your question is about consciousness.
Atomic arrangement would affect your intellect; but not your consciousness.
Answer to Q 1:
Yes. Consciousness would be the same.
Since it is incomparable, it is illogical to say big consciousness or small consciousness. Time may affect memories, personality etc. But TIME DOES NOT AFFECT CONSCIOUSNESS. The number or arrangements of atoms also does not affect consciousness. It is incomprehensible. Verse 13:16 implies to consciousness.
Are you in an unconscious sate when you are in deep sleep? What is the difference between John's consciousness and yours while both of you are in deep sleep?
You needn't ponder too much. What change happens to a patient's consciousness after brain surgery? Does he run away from his relatives after the surgery...? What would happen to his consciousness if one of his kidneys is removed or transplanted? So, if you wish you can believe that his consciousness is there. (I don't wish to correct your belief.)
Any way the changes may happen in his memories due to the change in the arrangements of atom...it is clear from the above instance.
Answer to Q2:
If two new bodies were reconstructed, both of them would claim that he himself is John. Normally nobody would/can say, "I am he himself; not myself." Each one wouldn't give up his own identity. (I didn't forget Tat tvam asi.)