P.S. I found the following interesting paragraph in Bousso et al which considers Susskind’s complementarity proposal. It seems to make a big difference whether you define an observer first (and then consider his causal horizon), or define a causal patch first (together with its horizon) and then consider where the observer might be:
In the traditional discussion of black hole complementarity, one picks an observer and constructs the associated causal patch. It is impossible, by construction, for an observer to leave his own patch. In other words, time cannot end if we live in a causal patch centered on our own worldline. In eternal inflation, however, one first picks a causal patch; then one looks for observers in it. Some of these observers will be closer to the boundary and leave the patch sooner than others, who happen to stay in the patch longer. Equivalently, suppose we do want to begin by considering observers of a given type, such as an observer falling towards a black hole. To compute probabilities, we must average over all causal patches that contain such an observer. In some patches the observer will be initially far from the boundary, in others he will hit the boundary very soon. This yields a probability distribution for the rate at which time ends
If we consider it in “many worlds” terms, then the wave function over the causal patch contains many different branches, and human observers (indeed our whole Milky Way galaxy) get to exist in lots of those branches. But in only a very few of the branches is our galaxy near the centre of the patch and able to continue to survive for 100s of billions of years; in most of the other branches we are somewhere off-centre, and will be smeared out against the horizon very much sooner. The fact that the Milky Way will continue to exist in some branches does not mean we should expect to survive in our branch. This reminds me somewhat of the discussions on quantum suicide.
P.S. I found the following interesting paragraph in Bousso et al which considers Susskind’s complementarity proposal. It seems to make a big difference whether you define an observer first (and then consider his causal horizon), or define a causal patch first (together with its horizon) and then consider where the observer might be:
If we consider it in “many worlds” terms, then the wave function over the causal patch contains many different branches, and human observers (indeed our whole Milky Way galaxy) get to exist in lots of those branches. But in only a very few of the branches is our galaxy near the centre of the patch and able to continue to survive for 100s of billions of years; in most of the other branches we are somewhere off-centre, and will be smeared out against the horizon very much sooner. The fact that the Milky Way will continue to exist in some branches does not mean we should expect to survive in our branch. This reminds me somewhat of the discussions on quantum suicide.