On Mon, Jul 12, 2021 at 8:43 AM Bruce Kellett <[email protected]> wrote:
> On Mon, Jul 12, 2021 at 3:44 AM smitra <[email protected]> wrote: > >> On 11-07-2021 02:46, Bruce Kellett wrote: >> > > >> > This is where you go seriously wrong. Simply recording where the >> > photons land does not quantum erase the information they carried. Once >> > the photons carry off the which way information, the interference >> > pattern is restored only if the information carried by the photons is >> > quantum erased. Simply running the photons into a screen (or the >> > wall), even if you record where they land, is not quantum erasure. >> > See, for example, the paper arXiv:1206.6578 on quantum erasure. In >> > this paper they say "the presence of path information anywhere in the >> > universe is sufficient to prohibit any possibility of interference. In >> > other words, the atoms' path states alone are not in a coherent >> > superposition due to the atom-photon entanglement." This transfers >> > directly to the buckyball experiment under discussion. Running the >> > photons into a screen, or the wall, does not destroy the ball-photon >> > entanglement. >> > >> >> Recording where the photons land on the screen is enough, this is very >> easy to see. Let's consider an interference experiment where the >> particle gets entangled with another particle that carries away the >> which way information. If we work in the position representation then we >> have a wavefunction: >> >> psi(x,y) = 1/sqrt(2) [psi_1(x,y) + psi_2(x,y)] (1) >> >> where x is the position of particle 1 just before it hits the screen and >> y the position of the other particle at that time, and psi_1(x,y) is the >> wavefunction when only slit 1 is open while psi_2(x,y) the wavefunction >> with only slit 2 open. We also assume that particle 2 carries the which >> way information, this means that psi_1(x,y) and psi_2(x,y) for x kept >> fixed and considered as a function of y are eigenfunctions with >> different eigenvalues of an observable that corresponds to extracting >> the which way information from the second particle. This then implies >> that psi_1(x,y) and psi_2(x,y) are orthogonal for every x: >> >> Integral psi_1(x,y)*psi_2(x,y)d^3y = 0 (2) >> > > > This is the same mistake that you have routinely made in all of these > discussions. You calculate for particles through each slit independently. > But if that is the case, then no interference can ever be seen. The > possibility of interference relies on coherence between the amplitudes at > the two slits. In your calculations, you have never allowed for this > coherence -- the amplitudes at the two slits are not independent. > To see this in more detail, we can go through your original argument. You write : denote the buckyball moving through the left slit by |L> and the right slit by |R> and the photons by |PL> and |PR>. Now the states |R> and |L> are coherent; thus correlated; and the overlap <L|R> does not vanish. Writing |psi> = (|L>|PL> + |R>|PR>) is the same as assuming that the photons are emitted from the slits if they detect a ball passing through that slit. This is a direct "which-way" measurement, and since the photon states are independent, they are, as you say, orthogonal, and there can be no interference if such measurements are made at the slits. This is the essential loss of coherence. Your claim then is that if we observe the photons on another screen and keep track of the ball positions on their screen for photons that arrive at the same point on this other screen, then the interference pattern is restored. This is wrong, because the photons emitted from the slits if and when they detect a ball passing through the corresponding slit are still independent. The fact that they might arrive at the same point on a further screen is irrelevant. The photon states are still independent. In fact, there can only ever be one photon for each buckyball, so there can be no case in which two photons arrive at the photon screen at the same time. So the photon states are necessarily always independent and orthogonal, and your overlap function <y|PL_t><y|PR_t> = 0, always. Consequently, your joint detection of photons does not restore the interference. Decoherence, once present, destroys coherence. And this coherence cannot be restored simply by observing the which-way photons. You have to quantum erase the which-way information. And this is not easy for this particular set-up. Quantum erasure essentially requires a measurement of a conjugate variable, measurement of which means that the original state cannot be recovered. For example, measurement of photon polarization at 45 degrees will quantum erase a horizontal/vertical polarization state. Going back to the original buckyball experiment, the balls are laser heated and this puts them in an excited state. The state then decays by IR emission. This happens after the balls have passed the initial slits, so it is not a direct which-way measurement. It is only as the temperature increases, and the emitted photons have shorter wavelengths, that the wavelength is such that the photon can discriminate between the slits, that which-way information can be recovered from the IR photons. Letting the photons go undisturbed to infinity, or detecting them on some other screen, does not destroy the which-way information that they carry. As long as these photons are created, the interference pattern of the balls is lost. The photon information could be quantum-erased, I suppose, but I have no idea how that might be achieved. Your analyses, neither the first nor subsequent analyses, come anywhere near explaining this observed behaviour. 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/CAFxXSLRJBsCtZxJfWFixRVKvVvfuknBdgue0s_r0fq1sBORcFA%40mail.gmail.com.
