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Transcript
(=“PB”) (=“PC”) (=“PB or C”) NEITHER B NOR C “SELECTED”…. BY EACH INDIVIDUAL ATOM ! “SUPERPOSITION” “interference term” In quantum mechanics, if state 1 → state 1’ and state 2 → 2’, then superposition of 1 and 2 → superposition of 1’ and 2’ . Here, B → cat alive C → cat dead superposition of B and C → superposition of “alive” and “dead”! i.e. ampl. (cat alive) ≠ 0 ampl. (cat dead) ≠ 0 “interference” term averages to zero Is quantum mechanics the whole truth? How do we tell? If all “everyday-scale” bodies have the property that the interference term is randomized (“decoherence”), then all experimental results will be “as if” one path or the other were followed. cannot tell. So: must find “everyday-scale” object where decoherence is not effective. Does any such exist? Essential: -- difference of two states is at “everyday” level -- nevertheless, relevant energies at “atomic” level -- extreme degree of isolation from outside world -- very low intrinsic dissipation QM CALCULATIONS HARD! BASE ON: a) A PRIORI “MICROSCOPIC” DESCRIPTION b) EXPTL. BEHAVIOR IN “CLASSICAL” LIMIT X PHYSICS OF SUPERCONDUCTIVITY bosons fermions “Bose condensate” Fermi energy “Fermi sea” ↔ kT even Pairing of electrons: “di-electronic molecules” Cooper Pairs In simplest (“BCS”) theory, Cooper pairs, once formed, must automatically Undergo Bose condensation! must all do exactly the same thing at the same time (also in non-equilibrium situation) SUPERCONDUCTING RING IN EXTERNAL MAGNETIC FLUX: integer “flux quantum” h/2e Either all pairs rotate clockwise Or all pairs rotate anticlockwise Note: state with 50% and 50% strongly forbidden by energy considerations The experimental system of choice: Superconducting quantum interference device (SQUID) “CIRCUMSTANTIAL” TESTS OF QM ALREADY DONE The two states of interest correspond to current of ~1 microamp clockwise (state +) or anticlockwise (state -) ti tint tf If we “look” at times tint we always find either + or – (experiment already done). In we don’t look, quantum mechanics predicts interference effects in the probability of getting (say) “+” at a later time tf. Trapped flux Φext Josephson circuits Bulk superconducting ring Josephson junction ΔE Φext Other systems where Quantum Mechanics has been tested in direction of “Everyday World” ~1200 ~5000 ~106 ~1010 Where to go next? (?)
