uberwensch.bsky.social
like if Just Some Guy was a girl
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me @ March 1st
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yeah...
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one last point: once we've conceded to relativize our 'particle' notion to dectectors, it opens the possibility that different answers to these questions (and different particle content) can be assigned by differently characterized detectors. this argument is developed in the paper here:
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a thermodynamic impossibility!!
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I gotta tap out for a big I am fatigued and my brain hurts
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The detectors he introduces are not local operators, but "almost local operators." Possibly the way out of this mess is to suggest that no operation, performed in any bounded region U, is *exactly* capable of verifying an occupation number, but can do so approximately insofar as U is big (??)
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the probability or certainty that his detectors click), or if his definition of n-particle subspace differs from the standard notion. But, I think its the former. (Finding it difficult to internalize what he's saying in the lead-up to this paragraph.)
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By contrast, Haag says this in this text (pg 93) which seems to explicitly contradict what you've said. I need to read closer to determine if he has adopted a different measurement semantics (identifies a different mathematical expression or condition as
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Those occupation numbers do not simultaneously exist! We can only learn one of N(U) or N(V), and then we can't even partition the particle-count we found there into a cover of U by U', U''
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Ok, so c.f. Duncan the situation is far worse than I realized. If N(U) and N(V) do not commute, then it's not just that a "single particle" detected in U can also be detected in V. Rather, experiments to learn the occupation number both of U and of V *cannot even be designed.*
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oh yeah i don't deserve a cent I've been paid lmao
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same
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I simply don't believe this. It undermines either the idea of a single-particle space or a particle detector if a single-particle state can make two remote detectors click. Why call either of them those things?
There must be something wrong about the measurement semantics you have in mind.
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Awful, hate it
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Anyway I gotta read all the sources recommended to me and regroup.
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Exactly because of the issues I'm worrying about, I cannot make sense of "the subspace of states supported in U" or something, and an obvious guess immediately fails by Reeg-Schleider.
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I'd repeat the story about partial trace, but idk how to regard the total hilbert space as factorizing into one which pertains to spacetime region U and another which pertains to V. Partly this is why I'm reading that Witten paper.
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The status of those probabilities while they refer to an event of no temporal ordering to my own is fascinating.
Anyway, yeah, this should generically be the situation in QFT since operating within U will only ever tell me a little bit about the whole state.
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The question about QM entanglement is also something I've been thinking about lately. What I should do if I have only one of an entangled pair is form the partial trace of the overall ρ, which can be read as a mixture of my particle's "real" state weighted by the frequency with which they obtain
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Maybe conflating two issues by talking about points. A weaker interpretation assigns "prob. to encounter particle" only to regions, possibly even of some minimum size. If these are given by int_U《ψ|a*(x)|0》and if encounters in spacelike U,V are exclusive (for a 1particle ψ), we have a problem right?
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Yes, about the norm-square.
What's confusing if the events are non-exclusive is that I can't set the system into post-state a*(x)0 as well as a*(y)0. So it cannot be that I project onto a*(x)0 when I have some sort of experience at x.
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arxiv.org/abs/1803.04993
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Witten proves R-S in this source, proving that an inner product like the one above cannot be identically zero unless |ψ⟩ = 0, but with hermitian Φ in place of non-hermitian a*. Does that change the conclusion? After all, a* is a complex-linear comb of hermitian operators Φ, Π.
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But this contradicts Reeh-Schleider, right? And would do so even if we only quantified the xi over an arbitrarily small, arbitrarily remote region V?
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Another wishlist item is that states |ψ⟩ localized in U can be unambiguously discerned from those localized elsewhere. This would require ⟨ψ|a*(x1)a*(x2)...a*(xn)|0⟩ = 0 for every tuple (x1,x2,...,xn) of points outside U.
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What page?
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Earlier I was worried that my questions are pedantic are stupid. I've regained confidence that there is something seriously odd being glossed over.
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But I'd say there's worse issues if it doesn't even hold on one slice. What kind of probabilistic interpretation is that!!
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I elided that because I don't know, haha. I imagined a (x,0) slice for some inertial frame but idk if I should expect the integral to remain 1 under changes of slice. If we cannot expect that, then yeah I've got serious issues.
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Anyway, I *knew* I wasn't being crazy. Something is seriously wrong here!!
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Are there any such states |ψ⟩? Hopefully that integral doesn't do something dumb like diverge for every |ψ⟩. Something tells me, regardless, that physicists do not actually take this approach to localized states.
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You could restrict to states |ψ⟩ such that ∫dx ⟨ψ|Φ(x)|0⟩ = 1, but this would preclude outright the situation where a particle is certainly at x, or certainly within any overly-small ball. Maybe I've recovered the fact that relativistic particles can only be so localized?
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What you're getting at is that, if overlap with Φ(x)|0⟩ is taken to indicate probability of detection at x, then those probabilities will not sum to 1 -- right?
That's another great way of getting at why I wanted them to be orthogonal. How can they sustain probabilistic interpretation otherwise.
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this is what I'm trying to get at it when I say the entire interpretational strategy is derailed
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[1]: Yes, this just pushes back the issue of how to operationally identify quantum states onto the issue of how to identify operations with self-adjoint operators. But its how I think of it. Of course, quantum metrology is a whole field and presumably my idea is too simplistic.
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In QFT, without an X to accompany your proposed multi-localized states, how can I ever ID that my system is instantiating one of them? Maybe we don't? Maybe those states serve only theoretical purposes?
Which states do I take as the end-states of a scattering event and how do I ID them in practice?
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There's one other reason I really wanted a position or multi-position operator, and that's:
How do we ID that a system is in a given state, |x⟩? In my story-book understanding, it's cause we received value x from an X-measurement, so we projected the system into post-state |x⟩. [1]
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Thank you for talking with me at great length about this, by the way. Same to @valkyrie.hacker.gf and @timhenke.bsky.social, of course.
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I've heard of but have no familiarity with the Cluster Decomp principle. I will become acquainted.
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Assume both are number-operator eigenstates
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For consistency of not worrying about the whole universe, I think we need: when |ψ⟩, |ξ⟩ are localized in U, V the time evolution of |ψ⟩|ξ⟩ factorizes over the tensor. Is this true? It's tricky cause you didn't provide an exact criterion ("high overlap") so we haven't a definite U-localized subspace
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Like: when |ψ⟩ is localized to U, it doesn't impact the dynamics of states localized outside U.
So that quantum optics experiments in two countries can ignore each other. And even different arms of the same experiment can ignore each other (you often hear "photon went down this arm of the device")
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No, but.. without an X operator the high overlap of |ψ⟩ with Φ(x)|0⟩ doesn't translate into any statement about likelihood to detect the particle ψ near x..
I do agree that existence of an X is too much to ask in QFT. But we need something, and I'm trying to formulate it properly..
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let history sleep!!
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i can copy text on mobile it turns out
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www.reddit.com/r/AskReddit/...
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drag is already a perfecrly adequate way to insult u
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coulda said drag-hon
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(it was my best 😔)