Quantum immortality
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Quantum immortality is the name for the speculation that the Everett many-worlds interpretation of quantum mechanics implies that a conscious being cannot cease to be. The idea is highly controversial.
The idea comes from a variant of the quantum suicide thought experiment. Suppose a physicist standing beside a nuclear bomb tries to detonate it. In almost all parallel universes, the nuclear explosion will vaporize the physicist. However, there is a small set of alternate universes in which the physicist somehow survives. The idea behind quantum immortality is that the physicist is only alive in, and thus able to experience, one of the universes in which a miraculous survival occurs, even though these universes form a small subset of the possible universes. In this way, the physicist would appear, from a personal point of view, to be living forever. There are some parallels with this in the anthropic principle.
An easier to understand example is the one given in quantum suicide where a physicist sits in front of a gun which is triggered, or not triggered, by radioactive decay. With each run of the experiment there is a 50-50 chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct, then at each run of the experiment the physicist will be split into a world in which he lives and one in which he dies. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the physicist will notice that he never seems to die therefore proving himself to be immortal, or at least according to quantum immortality.
Detractors regard this idea as nonsense, and argue that this outcome does not fall out naturally from the many-worlds interpretation of quantum mechanics. They say that in the vast majority of universes, the physicist would cease to exist and therefore the most likely experience of a physicist standing next to a nuclear explosion would be the experience (or lack of experience) of ceasing to exist. The counterargument to this is that lack of experience is not itself an experience.
The critics also argue that the continuity of consciousness, and the possibility of it enduring forever, are actually assumptions in this scenario, and ones with no physical basis. They also claim that the logic of the thought experiment would suggest that a conscious observer can never become unconscious, and therefore can never sleep. A counterargument to this is that the theory does not claim that one can never experience worlds where one loses consciousness, but rather that one can never experience the period of unconsciousness itself. The observer will therefore never experience a world where he dies in his sleep, but if he wakes up again he will simply note that there was a gap in his conscious experience.
Some critics also point out that some hypothetical ultimate fates of the Universe may at some point in the future leave no chance at all for the continuation of life. While perhaps somewhat beyond the scope of the usual arguments regarding quantum immortality, these scenarios are still interesting cases to consider.
Proponents of the idea point out that while it is highly speculative, there is nothing in the notion of quantum immortality that violates the known laws of physics.
Although quantum immortality is motivated by the quantum suicide thought experiment, Max Tegmark, one of the inventors of this experiment, has stated that he does not believe that quantum immortality is a consequence of his work. His argument is that under any sort of normal conditions, before someone dies they undergo a period of diminishment of consciousness, a non-quantum decline (which can be anywhere from seconds to minutes to years), and hence there is no way of establishing a continuous existence from this world to an alternate one in which the person continues to exist.
Some of the science fiction of Greg Egan, particularly his novel Quarantine, uses somewhat similar ideas related to the many-worlds interpretation.