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Indeterminism and Decoherence in Standard Quantum Theory

Indeterminism and Decoherence in Standard Quantum Theory. Christian Schilling. together with: Jürg Fröhlich. Cambridge, 25.11.2009. Overview. Indeterminism in Standard QT Standard QT Problem of Indeterminism Famous Example Proof of Indeterminism 2. Decoherence

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Indeterminism and Decoherence in Standard Quantum Theory

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  1. Indeterminism and Decoherence in Standard Quantum Theory Christian Schilling together with: Jürg Fröhlich Cambridge, 25.11.2009

  2. Overview • Indeterminism in Standard QT • Standard QT • Problem of Indeterminism • Famous Example • Proof of Indeterminism 2. Decoherence • What is Decoherence? • Decoherence Parameter • Intuitive Understanding • Doubleslit Experiment

  3. 1. Indeterminism i. standard QT Hilbert space states observables (non-relativ.) measurement object matter : (measurement) events role of ? how to predict events ?

  4. iii. famous example restricted to assumption : area of

  5. ii. problem of indeterminism init. state „ „ can prepare experiment: macr. property of M ( unknown) different outcomes example : determined outcome ?

  6. Theorem:

  7. iv. proof of indeterminism assume determinism: assume:

  8. theorem but determinism: no determinism

  9. 2. Decoherence i. what is decoherence ? mechanism: „cohererent superposition incoherent“ more precise: due to a second (larger) system E

  10. ii. decoherence parameter special form:

  11. iii. intuitive understanding = N interaction processes:

  12. iv. doubleslit experiment coherent state (Pauli-Fierz Hamiltonian) too difficult approximations why decoherence?: „laser observes, which slit has been passed“

  13. universal decoherence: Kramer‘s approximation: electron not accelerated electron does not emit photons calculations decoherence parameter small (< 1/100) : independent of laser wave! universal decoherence

  14. nonuniversal decoherence: consider recoil of laser on electron (semiclassical) strategy: Newton‘s equation of motion:

  15. initial incoherence decoherence

  16. results: no resolution of slits photon number good resolution of slits , but decreasing photon number

  17. Summary standard QT is indeterministic with respect to measurements (quantum state of measurement device does not determine the outcome) standard QT makes only probabilistic predictions laser waves can destroy interference pattern in double slit experiment (cause decoherence) • high laser intensities condition: • long interaction time • laser wave length slit distance D caused by acceleration (its origin is unimportant)

  18. thank you

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