In recognition of FQXi of Doomsday week, suppose the world ended tomorrow. In particular, suppose that, as discussed in Kate Becker's fun article, we live in a 'false vacuum', that can decay to a lower energy state. The decay would take the form of a bubble of 'true' vacuum that grows at the speed of light, smashing into us with enormous energy without warning, annihilating everything we hold dear (even, perhaps, our beloved local laws of physics). Seems pretty noticeable.
But bubble formation is a quantum process, and we should think about what this means. Suppose we take a big region including both us and the bubble's formation location, and describe it as a quantum system with some set of states, interacting with its environment. When 'the bubble nucleates', it is something like a quantum measurement, and we can say that our quantum system is in a state containing something like a decohered superposition of our region with the bubble, and our region without the bubble. What we would mean by 'the bubble hits us' is that we find that we are in the branch of the wavefunction in which the bubble has, indeed, formed. But (unless we adhere to an interpretation in quantum mechanics in which the usual Schrodinger equation is actually violated), the other branch is still there too, at least mathematically.
Now suppose we adhere to the 'Many Worlds' interpretation, in which there is some sense in which both branches are supposed to be 'equally real'. I then must think of something like an ensemble of equally-real Anthonys, some of which get smashed by bubbles and some of which do not. And with each of these is a corresponding reader (you) that either gets smashed or not, perhaps a fraction of a second earlier or later. Now again I ask the question: if the world ends tomorrow, would you notice? Unless there is some aspect of awareness completely independent of your instantly-incinerated physical body, I can see no sensible meaning to 'you notice the bubble destroying you.' On the other hand, there are plenty of copies of you in the ensemble -- those with no bubble -- that go merrily along with their lives. Presumably the day after tomorrow 'you' are simply one of those, and 'I' am one of the corresponding surviving Anthonys. In short, how could we say with any confidence that we do *not* live in an unstable false vacuum? (An attempt to answer this using statistical arguments concerning what the 'survivors' would see was given by Max and Nick Bostrom in this paper, check it out.)
This "quantum immortality" line of thought (which I first realized some time ago after reading Mad Max's quantum suicide paper, though I'm sure I was not the first to realize) is disturbing enough that it is natural to wonder which one of its assumptions we can most easily discard. You might choose to believe that you have a non-corporeal -- and hence bubble-proof -- immortal soul that can nonetheless meaningfully notice that you have died. This might be fun to believe but I have not had much luck doing so myself. More obviously, you might choose to throw out the Many Worlds interpretation (which you my have already thought was nuts, and this just confirms it). But consider this: suppose the Universe is infinite, which is all the rage in inflationary cosmology and in any case seems a plausible cosmological possibility. Then it seems that we can define an (infinite) ensemble of regions that are identical except for the nucleation or non-nucleation of a bubble. In fact, I'm pretty sure -- as Max & I recently convinced ourselves -- that an ensemble can be defined that is *exactly* equivalent to the quantum mechanical one describing an individual system in the Many World interpretation. Thus even if you think a single measurement in some particular place has just one outcome, the net effect (in an infinite universe) precisely echoes what happen in Many Worlds: "cosmological immortality".
And you didn't notice that the world ended as you read that last sentence.