On Tue, Jul 6, 2021 at 5:21 PM 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: > > > >>> 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. >
It is a shame that your fancy analysis is contradicted by the actual experimental results. I leave it as an exercise for you to determine where your mistake is. But I suggest that you actually reads the paper quant-ph/0412003. 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. > My dear, you really have lost the plot, haven't you Saibal? -- 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/CAFxXSLRYic%2BvKTwuLp9waXoRjN-QOnkjY%2BLODX-y-ic_qq4T9A%40mail.gmail.com.
