In the previous posts, I explained that effective 'probabilities' in an MWI are proportional to the amount (measure) of consciousness that sees the various outcomes. Because this measure need not be a conserved quantity, this can lead to nonclassical selection effects, with 'probabilities' for a given outcome still changing as a function of time even after the outcomes have been observed and recorded. That can lead to an illusion of nonlocality, which can only be properly understood by thinking in terms of the measures directly, as opposed to thinking only in terms of 'probabilities'.
The most extreme example in which it is crucial to think in terms of the measures, rather than 'probabilities' only, is the so-called 'Quantum Suicide' (QS) experiment. Failure to realize this leads to a literally dangerous misunderstanding. The issue is explained at length in my eprint "Many-Worlds Interpretations Can Not Imply 'Quantum Immortality'".
The idea of QS is as follows: Suppose Bob plays Russian Roulette, but instead of using a classical revolver chamber to determine if he lives or dies, he uses a quantum process. In the MWI, there will be branches in which he lives, and branches in which he dies. The QS fallacy is that, as far as he is concerned, he will simply find himself to survive with no ill effects, and that the experiment is therefore harmless to him.
A common variation is for him to arrange a bet, such that he gets rich in the surviving branches only, which would thus seem to benefit him. Of course in the branches where he does not survive, his friends will be upset, and this is often cited as the main reason for not doing the experiment.
That it is a fallacy can be seen in several ways. Most basically, the removal of copies of Bob in some branches does nothing to benefit the copies in the surviving branches; they would have existed anyway. Their measure is no larger than it would have been without the QS - no extra consciousness magically flows into the surviving branches, while the measure in the dead branches is removed. If our utility function states that more human life is a good thing, then clearly the overall measure reduction is bad, just as killing your twin would be bad in a classical case.
It is true that the effective probability (conditional on Bob making an observation after the QS event) of the surviving branches becomes 1. That is what creates the QS confusion; in fact, it leads to the fallacy of "Quantum Immortality" - the belief that since there are some branches in which you will always survive, then for practical purposes you are immortal.
But such a conditional effective probability being 1 is not at all the same as saying that the probability that Bob will survive is 1. Effective probability is simply a ratio of measures, and while it often plays the role we would expect a probability to play, this is not a case in which such an assumption is justified.
We can get at what does correspond for practical purposes to the concept of 'the probability that Bob will survive' in a few equivalent ways. In a case of causal differentiation, it is simple: the fraction of copies that survive is the probability we want, since the initial copy of Bob is effectively a randomly chosen one.
A more general argument is as follows: Suppose Bob makes an observation at 12:00, has a 50% chance QS at 12:30, and his surviving copies make an observation at 1:00. Given that Bob is observing at either 12:00 or 1:00, what is the effective probability that it is 12:00? (Perhaps he forgets the time, and wants to guess it in advance of looking at a clock, so that the Reflection Argument can be used here.) The answer is the measure ratio of observations at 12:00 to the total at both times, which is therefore 2/3.
That is just what we would expect if Bob had a 50% chance to survive the QS: Since there are twice as many copies at 12:00 compared to 1:00, he is twice as likely to make the observation at 12:00.
Most of your observations will be made in the span of your normal lifetime. Thus QI is a fallacy; for practical purposes, people are just as mortal in the MWI as in classical models.
Next up: Early attempts to derive the Born Rule in the MWI
- ▼ September (6)