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DanArmak comments on What makes you YOU? For non-deists only. - Less Wrong
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I don't see any reason to privilege the thread of consciousness - I'm confident it doesn't actually work the way you're supposing. My personal instinct is that I at every instant am identical to this particular configuration of particles, and given that such a configuration of particles will persist after the experiment (though on the other side of the world), it doesn't seem particularly as if I've been killed in any permanent way. (I'm fairly sure I couldn't collect on my estate, for example.) Sure, it's risky, but if sufficient safeguards are in place, it's teleporting, as pengvado said (?).
A note: even if I hadn't had this instinct before, the idea of a persistent and real thread of consciousness is brought into doubt in a number of ways by Daniel Dennett's revolutionary work, Consciousness Explained. My copy is on my shelf at home at the moment, but Dennett explains several instances in which the naive perception of consciousness is shown to be unreliable. I don't think it's a valid marker to use to identify identity.
(Besides, what of spells of unconsciousness? Should someone whose thread of consciousness is interrupted be considered to have been literally killed and reborn as a facsimile?)
How do you think it does work? That is, are you suggesting there is a thread of consciousness that sometimes works differently from how I've experienced it so far? I haven't seen a good model so far.
I've read Dennett's book. It does a good job of deconstructing and disproving existing models, but I don't remember that it proposed a good new model, just some interesting ideas and pointers.
Meanwhile, your model:
has its own share of problems. For instance, you have no idea how many configurations identical or epsilon-similar to yours exist elsewhere at any given moment. You can't know when they're created or destroyed or modified. How can you not privilege the pattern-instance that right now is posting on LW, if you have no idea if it's the only instance or one of a million, the others being clones I just created in my basement?
Okay, I'll grant you that I privilege the one I am at the moment, but the nine hundred ninety nine thousand nine hundred and ninety nine duplicates will each privilege themselves - and if I knew that they would be created in advance, I would be concerned for what they would experience for the same reason I care about any other future experience of mine.