> On 6 Jul 2021, at 09:21, smitra <[email protected]> wrote: > > On 05-07-2021 12:18, Bruce Kellett wrote: >> On Mon, Jul 5, 2021 at 7:39 PM smitra <[email protected]> wrote: >>> On 05-07-2021 09:00, Bruce Kellett wrote: >>>> On Mon, Jul 5, 2021 at 2:23 PM smitra <[email protected]> wrote: >>>> I don't think this is actually done in the experiment. What is >>>> observed is the presence or absence of the interference pattern on >>> the >>>> screen where the balls hit. The photons are not detected. But if, >>> in >>>> principle, they are of suitable wavelength to resolve the slit >>>> difference, then the interference pattern vanishes. The experiment >>> is >>>> convincing in that they start wil cold buckyballs which show a >>> clear >>>> interference pattern. They then gradually heat the balls so that >>> the >>>> typical wavelength of the photons decreases. This gradually washes >>> out >>>> the interference pattern. (Because at lower temperatures, the >>>> wavelength distribution of the IR photons is such that a few of >>> them >>>> have shorter wavelengths.) As the temperature is increased so that >>>> most IR photons have short enough wavelengths, the interference >>>> pattern disappears completely. The paper by Hornberger et al. is >>> at >>>> arXiv:quant-ph/0412003v2 >>> This is then what I said previously, what you denied, i.e. that you >>> are >>> only considering part of the system which is defined by the reduced >>> density matrix. The complete system of buckyball plus photons will >>> show >>> interference, even if the wavelength is small enough to resolve the >>> slits provided you perform the right sort of measurement on the >>> balls >>> and photons. >> That is false. > > This is easy to see. Denote the buckyball state of a buckball moving through > the left slit by |L> and moving through the right slit by |R>. Suppose that a > photon is emitted by the by the buckyballs such that the ball moving through > the left slit emits a photon in a state |PL> that will be orthogonal to the > state |PR> of the photon emitted by the ball moving through the right slit . > The state of the system after the ball passes the slits is then: > > |psi> = 1/sqrt(2) [|L>|PL> + |R>|PR>] > > This state then evolves under unitary time evolution, we can write the state > just before the ball hits the screen as: > > |psi_s> = 1/sqrt(2) [|L_s>|PL_s> + |R_s>|PR_s>] > > There is then no interference patter on the screen for the buckyballs because > |PL_s> and |PR_s> are orthogonal, the unitary time evolution preserves the > orthogonality of the initial states. The probability to observe a buckyball > on position x on the screen is: > > P(x) = ||<x|psi_s>||^2 = 1/2 [|<x|L_s>|^2 + |<x|R_s>|^2] + Re[<x|L_s> > <x|R_s>* <PR_s|PL_s>] > > And the last interference term is zero because <PR_s|PL_s> = 0 > > But if we also observe the photon on another screen and keep the joint count > for buckyballs landing on spot x on the buckyball screen and for photons > landing on spot y on the photon screen as a function of x and y, then we do > have an interference pattern as a function of x for fixed y. If we de note by > U the unitary time evolution for the photons until they hit their screen, and > put |PL_t> =U|PL_s> and |PR_t> = U|PR_s>, then the probability distribution > is: > > P(x,y) = |<x,y|U|psi_s>|^2 = 1/2 [|<x|L_s>|^2|<y|PL_t>|^2 + > |<x|R_s>|^2|<y|PR_t>|^2] +Re[<x|L_s> <x|R_s>* <y|PL_t><y|PR_t>*] > > The interference term Re[<x|L_s> <x|R_s>* <y|PL_t><y|PR_t>*] does not vanish > as it involves evaluating the components of the buckyball and photon states > in the position basis and so there is no inner product involved anymore. For > fixed y the quantity <y|PL_t><y|PR_t>* will have some value that will be > nonzero in general, so if we keep y fixed then there will be an interference > term. > > So, we can conclude that invoking escaping IR photons does not male any sense > in this discussion because all it does is it scrambles the interference > pattern to make it invisible in a way that allows it to be recovered in > principle using measurements on those IR photons. You can, of course, erase > the interference patter by measuring the observable for the photons that has > |PR> and |PL> as its eigenstates. But even in that case the information will > still be there in the state of all the atoms of the measurement apparatus for > the photons. But if you don't perform any measurement then the information > will simply continue to exists in the escaping photons. > > So, in general we can conclude by generalizing this to any large number of > particles that even with what we consider to be permanent records, you don't > get rid of the theoretical possibility of interference between the sectors > where those records are different. So, the existence of parallel worlds > cannot be made fully 100% irrelevant if QM is rigorously correct, and we > cannot therefore argue that QM is exactly equivalent to an alternative theory > that leaves out parallel worlds. Even though the difference may be almost > 100% insignificant FAPP, it's not exactly 100% even in the macroscopic realm. > > The argument against the existence of parallel worlds by invoking decoherence > that makes superposition hard to detect for complex systems is thus analogous > to the defense of creationists when they invoke a God of ever smaller gaps of > things that have not yet been fully explained.
You are right. Some people invoke their personal ontological commitment, which is invalid in this setting. To make a parallel world disappearing is impossible as long as 2+2=4. Bruno > > Saibal > > >>>> This is not what happens. Read the paper referenced above. >>> It's not what happens in that experiment, but you can in principle >>> demostrate an interference pattern also when photons are emitted by >>> the >>> balls. >> Provided the wavelength of the IR photons is too large to resolve the >> inter-slit distance. When you heat the balls further, the interference >> disappears. >>>> This is all totally irrelevant to the actual experiment in >>> question. >>> And that experiment is in turn irrelevant to the question of whether >>> or >>> not a real superposition actually exist. You can always perform a >>> measurement involving more particles where an interference has >>> vanished, >>> that only demonstrates that the reduced density matrix described a >>> mixed >>> state, the entire system is still in a pure state. >> Of course real superpositions exist. The experiment shows that >> decoherence need not involve large numbers of degrees of freedom. >>>> These considerations do apply to each and every case. I mentioned >>> the >>>> buckyball experiment because it makes things obvious. But the >>> general >>>> principle is always true. Experiments that produced recorded >>> results >>>> are not reversible. Because, for example, they are not thermally >>>> isolated, and IR photons can always escape to infinity and be >>>> irretrievable. >>> Even if IR photons always escape to infinity, the complete quantum >>> state >>> of the entire system is still a pure state. There is still a >>> superposition between the balls going through one and the other >>> slit. >> Maybe that is not what is observed. That superpostion has decohered. >>>>> For example, one may object by invoking that the universe is >>>>> filled with a plasma and that the IR photons travel at a speed >>>>> slightly below the true vacuum speed of light. >>>> What difference would that make. The IR photons are still faster >>> than >>>> any material object sent after them to capture them. They will >>> always >>>> escape. And because the universe is expanding, they will >>> eventually >>>> pass over the Hubble horizon and be forever lost from sight! >>> But the observations on the balls will be completed long before >>> that, so >>> how is this relevant for the existence of parallel worlds? >> I think it is relevant to the question of reversibility. >>>> Whether this means that the off-diagonal terms of the density >>> matrix >>>> (in the appropriate basis) do actually vanish, or if this is >>> achieved >>>> by some other means, your theory has to adapt to the reality of >>>> irreversibility or your theory does not describe the real world. >>> It is >>>> clear that for many reasons, pure Everettian QM, based solely on >>> the >>>> Schrodinger equation, fails to explain many important features of >>> the >>>> world we observe. >>> Which would mean that QM cannot be correct as a fundamental theory. >> It is very probable the QM, in its current form, is not the correct >> fundamental theory. In the history of science it is never the case >> that the dominant theory at one time survives unaltered into the >> future. The negative induction against scientific realism is that all >> scientific theories are ultimately shown to be false. >> Bruce >> -- >> You received this message because you are subscribed to the Google >> Groups "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send >> an email to [email protected]. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/CAFxXSLR%3De%2BDdQHS_QCECFsf-Yt2NbFQw7gUPf7tpVpLjTB%2B_QQ%40mail.gmail.com >> [1]. >> Links: >> ------ >> [1] >> https://groups.google.com/d/msgid/everything-list/CAFxXSLR%3De%2BDdQHS_QCECFsf-Yt2NbFQw7gUPf7tpVpLjTB%2B_QQ%40mail.gmail.com?utm_medium=email&utm_source=footer > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/68ed0f821281a93b3044ee78e31a5c89%40zonnet.nl. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/9CE20F6E-076E-4530-8EA5-E6F4A43923FB%40ulb.ac.be.
