By examining the history of interactions which occured between the two states.
Well, yes, but what are you looking for when you do the examination?
That is, OK, you examine the history, and you think “Well, I observe X, and I don’t observe Y, and therefore I conclude identity was preserved.” What I’m trying to figure out is what X and Y are.
Before walking into the machine, what experience do you expect to have after: (1) walking back out or (2) waking up on Mars?
Well, yes, but what are you looking for when you do the examination?
That is, OK, you examine the history, and you think “Well, I observe X, and I don’t observe Y, and therefore I conclude identity was preserved.” What I’m trying to figure out is what X and Y are.
Both.