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Eliezer_Yudkowsky comments on Time turners, Energy Conservation and General Relativity - Less Wrong
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This is nothing compared to the impossibility of Time-Turners given MWI, which is of course a given. I've been assuming that HPMOR runs on collapse QM.
What if a time turner functions like this:
The Time Turner, unknown to you and hours prior to any spinning, creates a near-duplicate of you (and itself) somewhere in the world
The Time Turner contrives for you to end up end up exactly like the duplicate it created, n hours later, and then compels you to turn itself (like ComedTea compels you to drink it).
On being turned, the TIme Turner destroys you and itself.
Another attempt to reduce the probability mass of this fantasy world?
I think it fits best with a transactional form, actually. Time-turners just provide alternate routes for the transactions over their length, and you get a self-consistent outcome.
Hmm. Now I want to see what happens if you try to do a quantum interference experiment involving a time-turner. Good luck getting the phase to stay coherent over an hour, including the process of time-turning, though.
My prediction: "QB ABG ZRFF JVGU GVZR"
Hmm, I don't see how MWI would be interfering with time-turners. If anything, you can model a time-turner as spawning a new world at the destination point in the past, if you are willing to overlook the mass non-conservation issue. Unwinding a directed cyclic graph into a tree would also resolve the grandfather paradox and the "don't mess with time" message-in-a-bottle.
Isn't "resolving the grandfather paradox" the whole reason for the impossibility of Time-Turners (as opposed to generic time machines)? HP and HPMoR time travel seems to be of the Novikov variety, which isn't what you'd observe if trips into the past aren't constrained to reproduce previously-observed history. In HP you can't kill your grandfather because you didn't kill your grandfather (exact mechanism to be handwaved later). In MWI/spawning time travel you can kill your grandfather, and then that new history just won't produce another baby you.
Right. In general, spawning time travel is paradox-free, that's why I am not clear on why "the impossibility of Time-Turners given MWI". Presumably if you already spawn uncountable numbers of worlds all the time, it's not a big deal to spawn one more.
You can certainly postulate a physics that's both MWI and contains something sorta like Time-Turners except without the Novikov property. The problem with that isn't paradox, it just doesn't reproduce the fictional experimental evidence we're trying to explain. What's impossible is MWI with something exactly like Time-Turners including Novikov.
(Nods.)
I am ignorant on these topics, but isn't Novikov consistency predicated on QM? In that the "actual" paradox-free world is produced by a sum-over-histories? What about MWI prevents this?
Sorry if this is an incredibly stupid question.
Novikov consistency is synonymous with Stable Time Loop, where all time travelers observe the same events as they remember from their subjectively-previous iteration. This is as opposed to MWI-based time travel, where the no paradox rule merely requires that the overall distribution of time travelers arriving at t0 is equal to the overall distribution of people departing in time machines at t1.
Yes, Novikov talked about QM. He used the sum-over-histories formulation, restricted to the subset of histories that each singlehandedly form a classical stable time loop. This allows some form of multiple worlds, but not standard MWI: This forbids any Everett branching from happening during the time loop (if any event that affects the time traveler's state branched two ways, one of them would be inconsistent with your memory), and instead branches only on the question of what comes out of the time machine.
Hmm. So if, say, I committed quantum suicide, then traveled back, I wouldn't have any special information about the result of the RNG. Most of me would still end up in worlds where I died; God's dice get re-rolled every time round. No extra math to prevent paradoxes; although it still looks like Novikov for non-quantum events.
Whereas under standard Novikov Consistency, I'm restricted to the worlds where I survived, because otherwise I came from nowhere. In fact, the universe is restricted to those worlds; there are only worlds where I survived and came back and worlds where I died and didn't. Thus, no Everett branching. Right.
The degree to which the difference would be observable depends on the amount of quantum variance in your life, I guess.