>One consciousness is simply extinguished forever. The other continues.

If there is one instance of a widely-distributed program installed on a particular computer, and the instance of the program on that particular computer is deleted, but the program continues to exist in identical form on many other computers, then the program continues to exist in spite of the fact that one of its instances has been deleted.

If consciousness is thought of as a process inextricably tied to a particular physical substrate, then our own consciousnesses are constantly being extinguished, and we all die countless 'deaths' every day as the matter in our brains is recycled and replaced.

If, on the other hand, consciousness is viewed as an information process that can be realised on any suitable physical substrate, then extinguishing one instance of consciousness in one particular universe by means of quantum suicide doesn't necessarily mean that that particular consciousness is extinguished forever, as long as an identical instance, or instances, of it continue to exist somewhere in the wavefunction. The Many Worlds Interpretation suggests there may be an infinity of such instances.

There is a tendency to think of these instances as copies, and to think of each such copy of a consciousness as a separate doppelganger existing in some unreachable reality. But if the instances are truly identical in every respect, then Leibniz' principle of the identity of indiscernibles [1] suggests that it might not be right to think of them as being separate: in some deep sense, they're all actually the same single thing.

The philosopher Derek Parfit developed a now-famous thought experiment in the phiolosophy of identity [2] in which he encouraged people to think about a scenario in which a malfunctioning teleporter creates two identical copies of a person, one of which must then be destroyed by the machine. Obviously we tend to sympathise with the 'copy' faced with imminent destruction, and that might lead us to reject the idea that the continuation of a physically identical copy of our self is a sufficient condition for survival.

There is a problem with this thought experiment though, in my view, and quantum suicide is in a sense a type of 'fix' for it. If there is a situation in which two copies of a person exist, and one copy is about to be destroyed, then the two copies are necessarily no longer 'indiscernible' in Leibniz' sense. Parfit's example is actually a striking case of indiscernibility, because at the point at which one of the copies is about to be destroyed, the two copies actually have some very different memories and thoughts. This version of Parfit's thought experiment therefore really involves two similar, but not identical, people, one of whom is about to be killed.

The quantum suicide thought experiment, in contrast, necessarily ensures that no conscious entity ever experiences its own imminent death in the same manner as Parfit's version, because the 'suicide' is designed to take place faster than the brain can process a thought. The other major difference is of course that the 'copies' that survive the suicide are not created by a teleporter, but are a necessary feature of the wavefunction.

An alternative to saying that one consciousness is extinguished forever in quantum suicide would be to say that the single consciousness existing across the 'copies' in the wavefunction no longer has conscious access to events in the universes in which the suicide occurs, but survives in, and continues to have conscious access to, the universes where the suicide does not take place.

It only makes sense to think of one consciousness as having been 'extinguished' if that consciousness is thought of as being inextricably linked to one particular physical substrate. If consciousness is thought of as an information processing pattern that can be instantiated on any suitable substrate, then all that matters is that such a substrate exists somewhere. If the substrate is physically possible, then the Many Worlds Interpretation requires it to exist.

[1] https://en.wikipedia.org/wiki/Identity_of_indiscernibles

[2] https://en.wikipedia.org/wiki/Teletransportation_paradox