I have a question about quantum physics. Suppose Bob is in state |Bob>, the rest of Bob's Everett branch is in state |rest>, and the universe is in state |u>, one of whose summands is |Bob>|rest>. How should Bob make predictions?
Determine |b'>, the successor state to |Bob>|rest>. Then the expectation of observable o is .
Determine |u'>, the successor state to |u>. Then the expectation of observable o is .
Theory 1 leads to the paradox I described in last week's open thread. Two users helpfully informed me that theory 1 is not what MWI says; MWI is more like theory 2. But theory 2 predicts that Bob will probably vanish! One could restrict to worlds that contain Bob, but that would imply quantum immortality.
Am I hopelessly confused? Does MWI imply that there is no continuity of experience? Has anyone ever proposed theory 1?
But theory 2 predicts that Bob will probably vanish!
I don't think it does. The probability current is locally conserved. So |u'> has to give a high probability to some world very close to Bob's, i.e. one with a continuous evolution of him in it.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.