I had thought from earlier remarks that *you* believe there is an ultimate classical reality (which the QM formalism allows us to compute probabilities governing), etc. but apparently I was mistaken.

Cheers,

Steve

Wigner’s friend not only “can” say “Lubos thinks he has a definite outcome (saw spin up), but I can detect the other Lubos (saw spin down) who is just as sure about his result”?

He *must* say that, otherwise he is not doing a perfectly accurate (or at least more accurate than I can do) calculation (which is the point why he is inserted to the thought experiment at all). I am just another physical object so of course that as such, I do evolve to linear superpositions that include superpositions of macroscopically distinct states. If you have doubts about the superposition principle and linearity of QM evolution operators, you misunderstand lesson 2 of an undergraduate course. In that case, it’s nothing deep, it’s pure stupid.

Of course that it’s an isomorphic set of facts and different perspectives as we encounter with Alice in the black hole. How it could not be? Both discussions are about quantum mechanics, after all. Different observers may and often do measure observables that don’t commute with each other. In the black hole case, this becomes extremely natural, and not just Wigner’s friend academic discussion, because the “decoherence” operating from the viewpoint of the exterior and interior field mode operators are completely different, having different “preferred observables” and their eigenstates’ bases, and so on.

You ask: “Which of the various observers in the discussion actually transforms the unitary Schrodinger calculation into a “real”, “classical” outcome (or probabilities of outcomes)?”

I have answered this question about 180 times on 75 places already but you must have missed all of them. According to quantum mechanics, there is no “classical” or (in this sense) “real” i.e. objective reality. Quantum mechanics answers subjects’ questions and they may depend and generally do depend on the subject. There is no rule in QM that would objectively say which questions must be asked or how many questions should be asked. I can ask about something at the time when I observe something – and QM calculates the probability. But it’s not quite a set of perfectly consistent histories because Wigner’s friend may have a more consistent set of consistent histories in which he realizes that I also evolve into linear superpositions and they may recohere sometime in the future with a nonzero probability. So he will wisely avoid imagining that the objective single “classical” reality exists at the point of my measurement and will continue to work with superpositions of my brain in different states up to the moment of his, more accurate measurement, for which QM gives answers as well. No contradiction which would be “really weird” may ever occur in this setup because quantum mechanics predicts correlations between the answers to various questions – so whenever the “small picture” and “big picture” observers ask the same question, they get the same answers. But QM can’t say and doesn’t say that someone *must* treat the value of an observable at some moment as a classical fact. It never does it. On the contrary, QM always insists on summing over all histories, considering all possible superpositions as the intermediate states, when one wants to calculate the most accurate answer to a question. “Collapsing” the wave function or “truncating” the set of histories when in the intermediate states before the observation is always a mistake that may only be relatively harmless if classical physics is a good enough description for the collapsed degrees of freedom (whatever “good enough” is quantitatively). When it’s not, it’s just wrong to “collapse” premature. Always.

It’s sort of remarkable that you’re supposed to be on the side that *does* understand QM better than the other side but you too keep on emitting this breathtaking rubbish about “when quantum mechanics becomes classical”. It never becomes classical. Quantum mechanics fundamentally rejects the notion of objective reality seen in classical physics – because it is *not* classical physics – which emerges as an approximation, and only as an approximation to the laws of quantum mechanics. If I were your undergraduate or graduate QM instructor, I would probably give you the homework to write these elementary defining facts about QM 200 times on the blackboard or in a notebook. Quantum mechanics isn’t classical, stupid. Quantum mechanics isn’t classical, stupid. And so on.

“If you give a precise criterion for when FAPP applies…”

Haven’t I made it very clear that such a criterion doesn’t exist and all people who are looking for this criterion – for a moment when quantum mechanics becomes perfectly classical – are completely deluded? Quantum mechanics never becomes perfectly classical. What word do you need to be explained? Deluded?

Cheers

LM

Thanks for taking the time to read what Bell wrote. Apologies if it was painful 🙁 At the risk of subjecting you to more pain I will write some more below, but feel free to ignore and end the discussion if you are getting bored 🙂

I’m still not exactly sure what your position is on all this. If standard QM is just an algorithm for computing probabilities, do you agree that (at least in principle, if not in practical situations) Wigner’s friend, watching you compute your probabilities, might say “Lubos thinks he has a definite outcome (saw spin up), but I can detect the other Lubos (saw spin down) who is just as sure about his result”? Because what you regard as a “normal measurement … loss of coherence … etc.” is described by Wigner’s friend as just a part of the overall unitary evolution in his description of the system. Sort of like comparing the various Alices’ experiences in the BH context. (Ordinarily one can just refuse to consider a Wigner friend watching a human experimenter, because it’s so far from practical. But in the BH information context you can’t punt on this question without getting the “wrong” answer — i.e., dropping some of Alice’s decoherent histories from the calculation.)

Which of the various observers in the discussion actually transforms the unitary Schrodinger calculation into a “real”, “classical” outcome (or probabilities of outcomes)? Can an observer be *mistaken* about having done this (as Alice might be)? Sometimes largely decohered branches can be re-interfered, in the lab, through exquisite control.

Bell’s discussion focuses on the “split” or “when pure becomes mixed (and probability enters)” or exactly when “FAPP” should be imposed. This is an old question which I feel has never been answered and is being pushed on all the time as lab experiments get better at controlling decoherence. If you give a precise criterion for when FAPP applies (e.g., “when overlap of decohered branches is less than exp(-1000)”), then, FAPP, you’ll conclude (sufficiently big) BH evaporation lets pure –> mixed (i.e., is non-unitary).

Thanks for your patience! 🙂

]]>A normal measurement anywhere in this quantum world does involve a loss of coherence – decoherence – caused by tracing over many degrees of freedom that reinforce the classical character of the measured information. So it’s completely correct to describe a measurement in this way.

But there’s no contradiction. Once you measure something and “annihilate” all the non-realized parts of the wave function, of course that you perform an operation that kills the unitarity. Unitarity refers to the unitarity of the evolution operator whose matrix elements can’t be directly measured – they have a probabilistic interpretation. If someone is trying to squeeze some approximations such as tracing over some degrees of freedom (e.g. decoherence) or collapses into the evolution, the state vector castrated in this way is of course not related to the initial state vector by the universal unitary transformation anymore. It’s not even related by any universal transformation because the result of the measurement is random. But that’s true not only in black holes. It’s true everywhere in quantum mechanics. So if you insanely decided that this means that the unitarity is broken, the conclusion would apply to any quantum system, not just black holes.

But all of this would be an artifact of a wrong interpretation of WHAT should be unitary.

]]>Bell: https://docs.google.com/file/d/0ByYDxaP-OyVjVXAtV2VqQlVNMTg/edit?usp=sharing

http://motls.blogspot.cz/2013/09/an-apologia-for-ideas-from-hawkings-bh.html?m=1

]]>if the state is a*psi1+b*psi2 and you describe it by a “larger state” with many Motls, well, then your description will be easily falsified because the right state is a*psi1+b*psi2 and it says that I am unique, among many other things it says. 😉

I never said that I was OK with a pure state evolving to a mixed state. I only wrote that a*psi1+b*psi2 allows you to calculate the probabilities of having properties indicated by eigenstates psi1, psi2. These probabilities are |a|^2 and |b|^2, respectively, even in the pure state. The pure state also allows one to compute the probabilities of other observables that don’t commute with this one – and the relative phase of a,b will influence this probability – but I didn’t write anything that would contradict that fact, either.

“If you demand pure-to-pure in spin measurements, you get many worlds.”

I definitely don’t get many worlds. You don’t get them, either. Only if you’re drunk, you may *think* that you see any evidence for many worlds.

Cheers

LM

http://infoproc.blogspot.com/2009/03/black-holes-and-decoherence.html

]]>I think even you sometimes refer to the subjective experience of one of the (many) Alices described by the wave function. Once you appreciate that Psi describes many possible experiences (“decoherent histories” or whatever), then it raises the question of whether you might be one of many Motls within a larger quantum state.

If you are comfortable with a pure state (single spin + Stern-Gerlach device) evolving into a mixed state — Prob 1/2 (“spin up” + “device registers spin up”) and Prob 1/2 (down outcome) — then why be worried about a pure state of dust evolving into a mixed state of Hawking radiation? (Please don’t reply Banks, Peskin, Susskind … 🙂

In the BH case you demand that pure –> pure, but if you demand that in the spin measurement you get many worlds 😉

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