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When I read philosophy treatments of the teleportation paradox and related subjects like swampman, they seem to focus primarily on drawing analogies to various entirely different scenarios (particularly the Ship of Theseus). I don't have any objection to analogies, as a form of argument, but it seems that no one is interested in the physics of the original situation. In particular, I don't understand why no one ever makes an argument similar to the following:

We have two events: a dematerialization, and a materialization. They do not coincide in space-time. That means we can use relativity of simultaneity to divide the scenario into a number of cases:

  1. The events are separated by a spacelike interval. They appear to be simultaneous in some reference frame, but appear to happen in some order in another reference frame, and the opposite order in a third frame. It also means they are causally independent of one another, so that one event could fail to occur without affecting the other. From the perspective of the person dematerialized, there is no difference between a teleporter and a suicide box, because the materialization is an independent event unrelated to the dematerialization.
  2. The events are separated by a timelike interval. They have a fixed order in every reference frame, and while we may construct reference frames to minimize the interval between them, we cannot make it arbitrarily short. There is a lower bound on the amount of time that elapses between the events in any given reference frame. So either there is a period of time in which both people exist, or a period of time in which neither exists. Clearly, if they both exist simultaneously they must be different people. If neither exists, it seems a stretch to claim that either one of them is "alive" at that point in time.
  3. The events are separated by a lightlike interval. This is the limiting case between spacelike and timelike, and therefore requires perfect timing and positioning to achieve exactly. It shares all properties with the timelike case except for the lower bound on the interval between events. That is, we may construct reference frames in which the interval between events is any nonzero period of time, but they still always happen in the same order and never appear to be exactly simultaneous. It still looks like the two people must be distinct from one another for this to make sense in any particular reference frame, and regardless it seems questionable whether such perfect timing can be realized.

(This argument is not meant to be correct or incorrect. It is meant to illustrate the kind of argument that I have not observed in the literature. Other such arguments might focus on, for example, the uncertainty principle, the observer effect, and so on.)

Am I just totally missing the point of this philosophical problem? I realize that the above reasoning seems to have very little to do with philosophy of mind, but if the original can be reformulated so as to avoid this argument, the refined problem might be more interesting (insofar as it might reveal some aspect of the problem which was less evident in the original). If it cannot, then perhaps it is not a real problem in the first place. So... why aren't physical considerations brought up?

Or do they bring this up all the time, and I'm just ignorant of the literature?

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Discussions of philosophical issues can often benefit from taking into account what we know about physics. In this case this may not be as pronounced because the teleportation paradox is more about semantics and folk intuitions in psychology, than about physics. Since semantic conventions and folk intuitions are mostly based on "intuitive physics", which is at best Newtonian, and in some aspects pre-Newtonian (think of intuitions about inertia), relativity and quantum mechanics are rarely brought up. Also behind it is anxiety over "teleporting souls", which is even less about physics. Gallois' Metaphysics of Identity gives a comprehensive discussion of the related philosophical issues.

Basically, the question is if the "continuity of self" or "self-sameness" is preserved across the teleportation events, and the problem, as I see it, comes from mixing the first and the third person perspectives in interpreting the said continuity or sameness. See How does one bring mind and matter into a single ontology that accounts for subconscious mind? on other troubles with such mixing. Will the teleported body(ies) "feel" continuous with the original (first person)? Under what circumstances and for what reasons should we treat the teleported body/person as "the same" (third person)? We have no way of answering the former without actually doing the deed and asking, and the latter is a question of semantic conventions, which require publicly, and hence empirically, accessible criteria. It is there that the spatiotemporal contiguity, the ship of Theseus, etc., come in.

Does relativistic perspective change things? Let us take the timelike case as the most plausible. The import of relativity seems to be that there must be a time leg between de- and re- materialization. But that can be done already in the Newtonian context simply by making the re-materialization machine wait before it does the re-materialization. This suggests that contiguity might not always be a good criterion for self-sameness, but it was always seen as pragmatic and empirically opportunistic symptom, rather than the "essence" of it, for a similar issue with causation see discussion in When trying to identify causality, do we assume "nearness" between cause and effect? And it tells us nothing about the "feelings". So we still have nothing concerning the first person perspective, and are still open to suggestions on the third person one.

Perhaps, quantum mechanics could contribute more. Kane, who is a philosopher well versed in it, made an interesting point about a related question of "acting differently in the same circumstances" as a definition of "free action". Assuming that the brain can channel micro-quantum indeterminacy into macroscopic events, as say the Geiger counter does, this "definition" becomes dubious (not that we could create "the same circumstances" any more than teleport bodies). In Responsibility, Luck, and Chance Kane writes:

"Suppose two agents had exactly the same pasts up to the point where they were faced with a choice between distorting the truth for selfish gain or telling the truth at great personal cost. One agent lies and the other tells the truth... Where events are indeterminate, as are the efforts they were making, there is no such thing as exact sameness or difference of events in different possible worlds. Their efforts were not exactly the same, nor were they exactly different, because they were not exact."

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