(This comment is a reply to another branch of this discussion as well.)
Yes, God will be able to see that there is a you that survived the process and went on to live the life of Riley. But whether or not you will be able to see that is a very open question
I disagree. To keep things simple, let's suppose that the bullet, if it hits, really will kill the participant with practically 100% certainty and will do so practically immediately (I'll come to this a bit later). In that case the only outcome the participant can expect to experience, and that they will experience with certainty, is that the gun didn't fire. This is exactly what happens if you take the mortal's-eye-view; God, as you mentioned, will notice that elsewhere in the multiverse, the participant did get hit. Now, whether the participant cares about their loved ones or the copies that die in the attempt is a matter of preferences, but if we're simply talking about which outcome to experience, this is how it goes, I think.
Note that playing quantum roulette successfully depends crucially on the speed with which you can kill yourself. Trying to play by slitting your wrists, for example, doesn't work because once you see that your wrists are slit you can't roll that back. So the success of the enterprise depends entirely on killing yourself fast enough that you don't become aware of your imminent and (in the relevant branches of the multiverse) unavoidable death. How fast is fast enough? Well, that is (literally!) the sixty-four-million-dollar question. Unless you have an answer that you are very confident is the correct one, it seems to me like an imprudent risk to take.
With this I agree, which is why I think the quantum Russian roulette or quantum suicide scenarios are mostly interesting as a thought experiment, as they're intended to be. But there are practical situations that are somewhat analogous: think, for example, about a terminally ill patient who faces an almost certain death within several days. Should they expect to survive or continue to experience things, and if so, in what way? My understanding is that according to quantum mechanics, there are all kinds of weird scenarios with non-zero probability that make "survival" possible, such as simply surviving one more day indefinitely despite all odds, being miraculously cured, or maybe being resurrected by a hyper-advanced future civilization in a simulation. Note that, in principle, this probably applies to any possible life-and-death situation.
I used the word "experience" a number of times there, which brings me to a point you made in another comment:
Notice (!) that when you start to talk about "noticing" things you are tacitly bringing consciousness into the discussion, which is a whole 'nuther can o' philosophical worms.
I don't think this can of worms is that bad. We have a pretty good grasp of what it means to be conscious, even if we can't define it exactly; and also we're (at least I am) pretty confident that it's a purely physical phenomenon with nothing supernatural and thus subject to the laws of QM. I think that's enough. Where it does get a bit problematic is when we're talking about scenarios like the one with the terminally ill patient; presumably there's also a possibility that the patient's consciousness degrades until it no longer makes sense to call them conscious, since there's probably no clear line anywhere separating conscious and non-conscious in this way. (This might also imply that if we should expect to die, we should expect to do so by very slow decay, like patients with Alzheimer's, which doesn't sound too good to me.)
I agree with most of what you say. Consciousness is not supernatural. But it is still problematic because:
the only outcome the participant can expect to experience, and that they will experience with certainty
"Only outcome you can experience" is not quite the same thing as "Will experience with certainty." Let's go back to the case where you survive in both branches. The outcome you do experience is the only outcome that you can experience. The trick is that this is really two statements disguised as one. After the event there...
I was asked to write up a pithy summary of the upshot of this paper. This is the best I could manage.
One of the most remarkable features of the world we live in is that we can make measurements that are consistent across space and time. By "consistent across space" I mean that you and I can look at the outcome of a measurement and agree on what that outcome was. By "consistent across time" I mean that you can make a measurement of a system at one time and then make the same measurement of that system at some later time and the results will agree.
It is tempting to think that the reason we can do these things is that there exists an objective reality that is "actually out there" in some metaphysical sense, and that our measurements are faithful reflections of that objective reality. This hypothesis works well (indeed, seems self-evidently true!) until we get to very small systems, where it seems to break down. We can still make measurements that are consistent across space and time, but as soon as we stop making measurements, then things start to behave very differently than they did before. The classical example of this is the two-slit experiment: whenever we look at a particle we only ever find it in one particular place. When we look continuously, we see the particle trace out an unambiguous and continuous trajectory. But when we don't look, the particle behaves as if it is in more than one place at once, a behavior that manifests itself as interference.
The problem of how to reconcile the seemingly incompatible behavior of physical systems depending on whether or not they are under observation has come to be called the measurement problem. The most common explanation of the measurement problem is the Copenhagen interpretation of quantum mechanics which postulates that the act of measurement changes a system via a process called wave function collapse. In the contemporary popular press you will often read about wave function collapse in conjunction with the phenomenon of quantum entanglement, which is usually referred to as "spooky action at a distance", a phrase coined by Einstein, and intended to be pejorative. For example, here's the headline and first sentence of the above piece:
This sort of language is endemic in the popular press as well as many physics textbooks, but it is demonstrably wrong. The truth is that measurement and entanglement are actually the same physical phenomenon. What we call "measurement" is really just entanglement on a large scale. If you want to see the demonstration of the truth of this statement, read the paper or watch the video or read the original paper on which my paper and video are based. Or go back and read about Von Neumann measurements or quantum decoherence or Everett's relative state theory (often mis-labeled "many-worlds") or relational quantum mechanics or the Ithaca interpretation of quantum mechanics, all of which turn out to be saying exactly the same thing.
Which is: the reason that measurements are consistent across space and time is not because these measurements are a faithful reflection of an underlying objective reality. The reason that measurements are consistent across space and time is because this is what quantum mechanics predicts when you consider only parts of the wave function and ignore other parts.
Specifically, it is possible to write down a mathematical description of a particle and two observers as a quantum mechanical system. If you ignore the particle (this is a formal mathematical operation called a partial trace of an operator matrix ) what you are left with is a description of the observers. And if you then apply information theoretical operations to that, what pops out is that the two observers are in classically correlated states. The exact same thing happens for observations made of the same particle at two different times.
The upshot is that nothing special happens during a measurement. Measurements are not instantaneous (though they are very fast ) and they are in principle reversible, though not in practice.
The final consequence of this, the one that grates most heavily on the intuition, is that your existence as a classical entity is an illusion. Because measurements are not a faithful reflection of an underlying objective reality, your own self-perception (which is a kind of measurement) is not a faithful reflection of an underlying objective reality either. You are not, in point of metaphysical fact, made of atoms. Atoms are a very (very!) good approximation to the truth, but they are not the truth. At the deepest level, you are a slice of the quantum wave function that behaves, to a very high degree of approximation, as if it were a classical system but is not in fact a classical system. You are in a very real sense living in the Matrix, except that the Matrix you are living in is running on a quantum computer, and so you -- the very close approximation to a classical entity that is reading these words -- can never "escape" the way Neo did.
As a corollary to this, time travel is impossible, because in point of metaphysical fact there is no time. Your perception of time is caused by the accumulation of entanglements in your slice of the wave function, resulting in the creation of information that you (and the rest of your classically-correlated slice of the wave function) "remember". It is those memories that define the past, you could even say create the past. Going "back to the past" is not merely impossible it is logically incoherent, no different from trying to construct a four-sided triangle. (And if you don't buy that argument, here's a more prosaic one: having a physical entity suddenly vanish from one time and reappear at a different time would violate conservation of energy.)