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Strilanc comments on Open thread, 24-30 March 2014 - Less Wrong Discussion
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Here's a cute/vexing decision theory problem I haven't seen discussed before:
Suppose you're performing an interference experiment with a twist: Another person, Bob, is inside the apparatus and cannot interact with the outside world. Bob observes which path the particle takes after the first mirror, but then you apply a super-duper quantum erasure to Bob so that they remember observing the path of the particle, but they don't remember which path it took. Thus, at least from your perspective, the superposed versions of Bob interfere, and the particle always hits detector 2. (I can't find the reference for super-duper quantum memory erasure, probably because it's behind a paywall. Perhaps (Deutsch 1996) or (Lockwood 1989).)
Suppose that after Bob makes their observation, but before you observe Bob, you offer to play a game with Bob: If the particle hits detector 2, you give them $1; but if it hits detector 1, they give you $2. Before the experiment ran, this would have seemed to Bob like a guaranteed $1. But during the experiment, it seems to Bob that the game has expected value -$.50. What should Bob do?
If it seems unfair to wipe Bob's memory, there's an equivalent puzzle in which Bob doesn't learn anything about the particle's state, but the particle nevertheless becomes entangled with Bob's body. In that case, the super-duper quantum erasure doesn't change Bob's epistemic state.
My grasp of quantum physics is rudimentary; please let me know if I'm completely wrong.
I disagree that Bob's expected value drops to -0.5$ during the experiment. If Bob is aware that he will be "super-duper quantum memory erased", then he should appropriately expect to receive 1$.
There may be more existential dread during the experiment, but the expectations about the outcome should stay the same throughout.
Ok, User:Manfred makes the same point here. It implies that at any point, heretofore invisible worlds could collide with ours, skewing the results of experiments and even leaving us with no future whatsoever (although admittedly with probability 0). Would you agree with that?
No, I don't think that's likely at all.
Worlds only interfere when they evolve into the same state. Because the state space is exponentially large, only worlds that are already almost-equivalent to our world are likely to "collide with us".
If you've based a decision on some observation, worlds where that observation didn't happen are not almost-equivalent. They differ in trillions (note: massive underestimate) of little ways that would all need to be corrected simultaneously, lest the differences continue to compound and push things even further apart. Their contributions to the branch we're in is negligible.
Your thought experiment used a "super duper quantum eraser", but in reality I don't think such a thing is actually possible. The closest analogue I can think of is a quantum computer, but those prevent decoherence/collapse. They don't undo it.