On Fri, Feb 13, 1998 at 05:55:18PM +1000, Mitchell Porter wrote: > 'Quantum suicide' is a ridiculous experiment. Suppose you tried to > kill yourself ten times and failed. What does that prove about the > existence of other universes? > > Tegmark claims that MWI uniquely predicts that an experimenter > who attempts quantum suicide will hear ten clicks - but then says > that in most worlds, the experimenter will be dead before the tenth > attempt. What this boils down to is the assertion that *if* the > experimenter survives, they will have heard ten clicks. *All* the > interpretations agree on that.
I think what Tegmark is saying is that conditional expectation of the experimenter given that MWI is true is that he will hear ten clicks, but his conditional expectation given that MWI is false is that he will hear only a few clicks. So if he hears ten clicks he would conclude MWI is likely to be true. This type of argument relies on a concept I call sensory probability. That is, probability of statements of the following form: "I will perceive x." One could argue that this is the only kind of probability that really matters. (Or maybe it doesn't matter at all. I'm not sure which.) It is certainly very paradoxical. Let me give two examples, simpler than the quantum suicide. 1. An experiment calls for the experimenter to flip a fair coin. A device is set up so that if it lands heads, the experimenter would be killed before perceiving this. What probability should he assign to the statements "I will perceive heads" and "I will perceive tails." 2. An experiment calls for the experimenter to flip a fair coin. A device is set up so that if it lands heads, the experimenter would be duplicated (i.e. a copy would be made of his body) and both copies would witness the result. What probability should he assign to the statements "I will perceive heads" and "I will perceive tails." I think Max would say 0, 1, 2/3, 1/3, respectively. I now suspect there are some serious paradoxes associated with sensory probability, but I need to think about it some more.