1 / 22

The problem with cats lessons in quantum collapse

The problem with cats lessons in quantum collapse. hair balls, litter boxes, decapitated birds Schroedinger s Cat & Wigners Friend the parts of collapse contributions of decoherence the remaining options (choose your weirdness). hair balls, litter boxes, decapitated birds

flo
Download Presentation

The problem with cats lessons in quantum collapse

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The problem with catslessons in quantum collapse • hair balls, litter boxes, decapitated birds • Schroedingers Cat & Wigners Friend • the parts of collapse • contributions of decoherence • the remaining options (choose your weirdness) • hair balls, litter boxes, decapitated birds • Schroedingers Cat & Wigners Friend • the parts of collapse • contributions of decoherence • the remaining options (choose your weirdness) Blaylock - UMass seminar 3/4/11

  2. Shroedinger’s Cat The Measurement Problem I Until the box is opened and examined by the researcher, the cat is in a super-position of being alive and dead. with apologies to Berk Breathed Blaylock - UMass seminar 3/4/11

  3. Wigner’s Friend The Measurement Problem II When and how does collapse occur? Wigner’s press agent Wigner’s friend Wigner Blaylock - UMass seminar 3/4/11

  4. Rather like voodoo. This is a very particular, very restricted form of nonlocality. We still can’t make anything travel faster than the speed of light, or send a signal faster than the speed of light. Collapse is no use for intergalactic telephone calls. Collapse is nonlocal Collapse changes a wave function that is spread out over a region to a wave function that is localized in one spot. This is a nonlocal process! Blaylock - UMass seminar 3/4/11

  5. From Bob’s perspective in his relativistic space ship, Alice’s photon collapses after the other photon. Collapse is not Lorentz invariant In what reference frame is the collapse simultaneous, and why that frame? Consider two photons produced in an entangled state: Convention says when Alice measures one photon, both collapse simultaneously. A single complete collapse can only be specified by an arbitrary rule. Blaylock - UMass seminar 3/4/11

  6. Not Even Wrong The idea of collapse was an ill-defined ad hoc addition to the (very well defined) evolution described by the Schroedinger equation. Wolfgang Pauli, when shown the paper of a colleague, once said: “Not only is that not right, it’s not even wrong!” Blaylock - UMass seminar 3/4/11

  7. three parts to “collapse” • Disappearance of interference • The rules of probability change from those of a superposition to those of a mixture. • Choice of a basis • Only certain observations are possible (e.g. alive or dead); combinations of those observations are not. • Choice of a single outcome (a.k.a. projection) • Only one outcome is observed; the superposition has projected out a single component. Blaylock - UMass seminar 3/4/11

  8. decoherence decoherence A quantum system is never isolated in practice. It interacts with its environment, evolving into something that behaves like an incoherent mixture of states. Not really a new idea. Just a way of understanding how QM describes interactions between system and environment. • Accomplishments of decoherence: • Explains disappearance of interference • Explains choice of basis Blaylock - UMass seminar 3/4/11

  9. Double slit In an undisturbed single-electron double slit experiment two electron waves combine destructively in the center of the screen, giving minimum probability of detecting an electron at that location. phosphor screen mask with 2 slits electron gun Blaylock - UMass seminar 3/4/11

  10. Scattering shift What if a photon hits the electron on its way to the screen? The interaction will change the direction and the momentum of the electron. new original n.b.If the frequency has changed, the interference pattern will change as a function of time. If the wave has shifted by half a wavelength, there will be maximum probability of detecting an electron in the center of the screen. Blaylock - UMass seminar 3/4/11

  11. Scattering uncertainty There are many possibilities for where the interaction takes place, and what momentum is transferred. Many possibilities for interaction form many superposing interference patterns. new original If the photon is low energy and doesn’t disturb the electron too much, the interference pattern is smeared out just a bit. If the interaction is energetic enough, the pattern is completely smeared (an apparent mixture). Blaylock - UMass seminar 3/4/11

  12. The Essence of Decoherence Consider a system  in a superposition of two possibilities (complete basis): Let it interact with an environment  that has a large number of degrees of freedom: In the probability, the interference terms tend to zero; a superposition is turned into an approximate mixture. the phases of ai, bj tend to cancel Blaylock - UMass seminar 3/4/11

  13. Quantum Darwinism For a system that is frequently ‘measured’, the persistent states are (usually*) the eigenstates of the interaction Hamiltonian. n.b. Localized states are common because interactions often depend on direction and distance. Interaction with the environment will not change eigenstates of the interaction. These states are stable and persistent. Written in terms of these states, the wave function has no y1j2 or y2j1 cross terms, and the mathematics of the previous page is valid. Looked at from any other basis, the system does not evolve into an apparent mixture. *Assuming the self-Hamiltonian is negligible or absent. But if the difference in energy eigenstates is large compared to typical interaction energies, the persistent states are energy eigenstates, since these are the states that are time independent. (see esp. Zurek 99) Blaylock - UMass seminar 3/4/11

  14. Quantum Zeno Effect If we shine green polarized light through 6 cm of corn syrup, we get 90o rotation. No light gets through. The initial polarization evolves to something else… Shining the light through six 1 cm dishes of syrup (each rotating the light by 15o) followed by six polarizing filters, allows 66% of the light to get through. Blaylock - UMass seminar 3/4/11 … unless the environment is watching

  15. Projection • Projection must be: • nonlinear (linear evolution cannot evolve a superposition into a single outcome) • random and irreversible (there is no info in the wave function to choose a particular outcome) • gradual – fast but not all at once (otherwise microsystems would sometimes collapse too early, macro systems too late). An isolated cat is in a superposition of two possibilities until he is observed. Then very quickly, … Blaylock - UMass seminar 3/4/11

  16. potential solutions Specify the projection dynamical collapse Get rid of the projection multiple realities: Many Worlds one (nonlocal) reality: Hidden Variable Theory Sweep it under the rug shut up and calculate Blaylock - UMass seminar 3/4/11

  17. Dynamical Collapse Toy model: Ghirardi Rimini Weber (GRW) 1986 Each elementary component of the system is subjected at random times to spontaneous localizations (“hittings”). These hittings are mathematically represented by multiplying the wave function by a localized Gaussian. The hittings occur at locations given by the standard quantum probability (wave function amplitude squared). The time of the hits follows a random Poisson distribution. It has been an important proof of principle to show that one can choose a Gaussian spatial width (~10−7 m) and a Poisson time frequency (~108 yr) that is consistent with both micro and macro experience (i.e. micro states don’t collapse too fast and macro states collapse fast enough.) Blaylock - UMass seminar 3/4/11

  18. DC Observations GRW and offshoots are focused on spatial collapse (is this all that’s needed?). GRW is not Lorentz invariant, but Roderich Tumulka claims to have a relativistic version for non-interacting particles. Even these models do not provide complete projection in the sense of a single outcome. Alternatives still exist in tails of Gaussian distributions. Blaylock - UMass seminar 3/4/11

  19. Everettian Many Worlds Everett says even without projection, the experience of the MWI observer agrees with that of the orthodox ‘external observer’. Suppose an experimenter measures a spin. Two possibilities result (two branches). Moreover, repeated measurements of the same spin will yield identical results. It looks as if the particle spin has ‘collapsed’to a single outcome. Blaylock - UMass seminar 3/4/11

  20. MW Observations MW adds nothing beyond the unitary evolution of QM. It can be formulated as a local realist interpretation (taking the wave function to be the fundamental entity). There is great controversy over whether it explains the Born rule. Everett defined probability in terms of sequences of measurement results seen by observers along different branches, and claimed that the “relative frequencies” of different possible sequences is governed by the same amplitudes as in orthodox QM. But if all branches exist*, what does it mean to say that one branch is more probable than another? A rich literature surrounds this question, including many papers that claim MW is more appropriate for explaining probability than conventional QM (see esp. Deutsch 99, Wallace 03, Zurek 05). *n.b. the same question could be applied to GRW collapse! Blaylock - UMass seminar 3/4/11

  21. Bohmian QM (a.k.a. the de Broglie-Bohm interpretation of QM) A system of particles is described (only) in part by the wave function. The description is completed by the specification of the positions of the particles. Evolution of the system is determined by the Schroedinger equation for the wave function, and by a guide equation for the positions qk. Since the velocities depend on a wave function that samples all space, this is an explicitly non-local theory (as it must be to be consistent with Bell experiments). Also (irreparably?) non-relativistic. Bohmian trajectories for the 2-slit experiment. Blaylock - UMass seminar 3/4/11

  22. Cat in a Box There’s no comfortable solution. But it’s time to admit there’s a problem. Blaylock - UMass seminar 3/4/11

More Related