Conditional on Many-Worlds being true, Bob expects to survive with 100% probability. Conditional on Copenhagen being true, Bob expects to survive with only 0.01% probability. So if Bob exits the box alive, this is strong evidence for him in favor of Many-Worlds.
I disagree that Many-Worlds and Copenhagen give any different predictions for Bob here. The expected value of the observable (is Bob Alive) is not only the same for Alice, and also remains the same (i.e. 1) when conditionalized on Bob’s still having experiences.
A chain of thought experiments connecting regular conditional probability to quantum suicide:
Thought experiment 1:
Imagine Bob buys a quantum lottery ticket and hires an unstoppable kidnapper to put him in a red room later the same day if he won the lottery, and in a blue room if he lost.
Regardless of which theory of quantum mechanics he prefers, Bob should expect to most likely experience losing the lottery, but conditional on waking up in a red room the next day, the probability that he won the lottery is 100%.
Thought experiment 2:
Same as above, except the unstoppable kidnapper is now an unstoppable assassin who kills him if he lost. I say: this doesn’t change the probability of what he experiences at the time of winning the lottery, or the conditional probability of what he remembers given that he is in a red room/alive the next day.
Thought experiment 3:
Same as above, except replace the quantum lottery and the assassin with a quantum suicide machine. If it kills him, the machine first momentarily shines a blue light on Bob. Again, same probabilities/conditional probabilities.
Thought experiment 4:
Same as above, except no blue light. The only thing this changes is what Bob expects to experience in the moment, not what he should expect conditional on still having experiences later.
I disagree that Many-Worlds and Copenhagen give any different predictions for Bob here. The expected value of the observable (is Bob Alive) is not only the same for Alice, and also remains the same (i.e. 1) when conditionalized on Bob’s still having experiences.
A chain of thought experiments connecting regular conditional probability to quantum suicide:
Thought experiment 1:
Imagine Bob buys a quantum lottery ticket and hires an unstoppable kidnapper to put him in a red room later the same day if he won the lottery, and in a blue room if he lost.
Regardless of which theory of quantum mechanics he prefers, Bob should expect to most likely experience losing the lottery, but conditional on waking up in a red room the next day, the probability that he won the lottery is 100%.
Thought experiment 2:
Same as above, except the unstoppable kidnapper is now an unstoppable assassin who kills him if he lost. I say: this doesn’t change the probability of what he experiences at the time of winning the lottery, or the conditional probability of what he remembers given that he is in a red room/alive the next day.
Thought experiment 3:
Same as above, except replace the quantum lottery and the assassin with a quantum suicide machine. If it kills him, the machine first momentarily shines a blue light on Bob. Again, same probabilities/conditional probabilities.
Thought experiment 4:
Same as above, except no blue light. The only thing this changes is what Bob expects to experience in the moment, not what he should expect conditional on still having experiences later.