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Superposition Censorship

AB, EPR and AC Conspiring to Preserve Causality Avshalom C. Elitzur avshalom.elitzur@weizmann.ac.il Shmuel Marcovitch shmuelma@post.tau.ac.il. Superposition Censorship. Bob. Alice. EPR source Which-path correlation. Interference in Terms of Spin Using Stern-Gehrlach Devices. SG (- x ).

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Superposition Censorship

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  1. AB, EPR and AC Conspiring to Preserve CausalityAvshalom C. Elitzuravshalom.elitzur@weizmann.ac.il Shmuel Marcovitchshmuelma@post.tau.ac.il

  2. Superposition Censorship Bob Alice EPR source Which-path correlation

  3. Interference in Terms of SpinUsing Stern-Gehrlach Devices SG (-x) Interference key: z-spin SG (x) C D Aharonov and Vardi, PRD 20, 3213 (1979) SG (z) (Erasure of the x-spin measurement) Eigenstate of z-spin enters

  4. SG (-x) SG (x) Superposition Censorship SG (z) SG (z) Bob Alice SG (x) EPR-Bohm source Spin correlation

  5. AB-MZI D C Click always in C Click in either C or D Current only on left (or right) Current superposed

  6. AB+EPR We neglect any phases due to interaction of the spin with the magnetic fields in the SG devices throughout D C Click in C Click in either C or D Current only on left (or right) Current superposed Bob Alice measures x spin does nothing EPR-Bohm source

  7. “Cat State” of a Current too gedankenly? C D

  8. Let’s Go 2-Dimensional Superconductor setting Quantum mechanical flux in discrete units

  9. Flux Interference Josephson Arrays, Elion et. al, PRL 71, 2311, 1993 = fluxon = electron does nothing measures spin x Alice Bob Particle acquires 0 or  AB phase, thus breaking the fluxon’s interference Particle does not measure the fluxon, which stays in superposition

  10. Resolution: Aharonov-Casher effect25 years retrodiction.. D C Aharonov and Casher, PRL 53, 319 (1984) AC effect: It is the fluxon interference which shifts! In any case, clicks may equally appear in D Alice Bob measures spin x Fluxon acquires 0 or  AC phase, in accordance with Bob’s particle’s location

  11. Superposition of Macroscopic Clockwise/Anticlockwise Currents Van der Wal el. al, Science, 206, 773 (2000) Friedman et. al. Nature, 406, 43 (2000) 2D: Solenoid  SQUID System is in ground state Josephson Junction removes degeneracy Macroscopic current ~A

  12. Superposition of Macroscopic Clockwise/Anticlockwise Currents Superconducting layer Induced magnetic field? topological effect – electron can be very far! superposition remains Alice Bob Particle acquires /2 or -/2 AB phase, breaking the fluxon’s superposition. Fluxon is not effected by the electron and stays in superposition. measures spin x does nothing

  13. AC cannot help ?

  14. electron near and fast Strong Impulsive Interaction → Back-reaction Furry and Ramsey, Phys. Rev. 118, 623 (1960) Bob’s particle changes the state of the flux even when not interfering Bob cannot distinguish between Alice’s two choices No paradox

  15. What if interaction is adiabatic?

  16. Enter Protective Measurement 16 years retrodiction..Aharonov, Anandan and Vaidman, PRA 47, 4616 (1993) Classic trajectory! Protective Measurement Strong measurement Electron in superposition e Measuring charge

  17. This is just what we have: Protective AB setting Flux remains superposed Even if Alice does nothing, Bob’s particle remains unentangled with flux, measuring the flux’s expectation value: 0  No AB phase  No paradox

  18. Conclusions AB bears on QM fundamentals: causality, nonlocality, adiabaticy Flux Interference: Causality protected by AB+AC electrons and fluxons interact topologically Flux Superposition: Causality protected by Back-reaction – when interaction is strong Flux expectation value – when measurement becomes protective

  19. 3Delectron spread in long wire Electron flux flux Electron

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