At the start of the first iteration, under both interpretations, the probability of surviving the experiment is 50%, as given by the squared norm of the wave function. At the start of the second iteration, assuming the Copenhagen interpretation is true, the wave function has already collapsed; thus, if the experimenter is already dead, there is a 0% chance of survival for any further iterations. However, if the many-worlds interpretation is true, a superposition of the live experimenter necessarily exists (as also does the one who dies). After every iteration only one of the two experimenter superpositions – the live one – is capable of having any sort of conscious experience. Putting aside the philosophical problems associated with individual identity and its persistence, we may assert that, under the many-worlds interpretation, the experimenter, or at least a version of them, continues to exist through all of their superpositions where the outcome of the experiment is that they live. In other words, we may say that a version of the experimenter survives all iterations of the experiment, whichever its number. Since the superpositions where a version of the experimenter lives occur by quantum necessity (again, under the many-worlds interpretation), it follows that their survival, after any realizable number of iterations, is physically necessary; hence, the notion of quantum immortality.
