What are we talking about? Naïve picture: Δx ↕ ~ external drive Ω fixed suspension mass M M ~ 10–18 kg (NEMS) ~ 10–21 kg (C nanotube) Ω ~ 2π ∙ 108 Hz Teq ≡  Ω / kB ~ 5 mK , x0 ~ 10–12 m rms groundstate displacement Actually:s ↕ Δ x d In practice, Δx « d.

DOES VANISHING OF EVIDENCE LEGITIMATE REINTERPRETATION OF MEANING? WHAT WILL WE LEARN? If QM predictions obeyed: check QM to “more macroscopic” scales?  learn mechanisms of decoherence?  “understand QM-classical transition”? NO! ______________ No doubt we will, eventually, see effects of decoherence in experiments. BUT: Decoherence does NOT solve the “measurement” (realization) problem! At micro-level: QM description α |1  + β |2  cannot be interpreted as “each microsystem is either |1  or |2 ” Evidence: interference At macro-level: QM description is still α |1  + β |2  (formalism is unchanged) but interference destroyed by decoherence. DOES VANISHING OF EVIDENCE LEGITIMATE REINTERPRETATION OF MEANING?

WHAT WILL WE LEARN? (cont.) (B) IF QM PREDICTIONS FAIL: (or we contemplate the possibility that they may fail) Test QM against — classical mechanics — specific theories of realization (e.g. GRWP, Penrose) — general class of macrorealistic (“MR”) theories. Some tests already done with other systems (fullerenes, quantum-optical systems, SQUIDS) in SQUID experiments, check QM predictions for superpositions of states in which large number N of microscopic entities (e–) behave differently (N~104–1010). What are advantages/disadvantages of MEMS vis-à-vis SQUIDS?

SIMPLE HARMONIC OSCILLATORS! MEMS vs SQUIDS SQUID: Ψ~ a|↺+ b|↻ I ~ 1-5 μA, N ~ 104–1010 (a) fidelity of readout quite poor (but rapidly improving) (b) states |↺, |↻ do not differ in distribution of center of mass (trigger for GRWP, Penrose . . .)  cannot discriminate between these particular MR theories and QM (but can test more general class of MR theories) In these respects MEMS much superior. But: major disadvantage of MEMS: to a first approximation, SIMPLE HARMONIC OSCILLATORS! Under driving force F(t), behavior of mean oscillator coordinate <x>(t) identical in QM and classical mechanics!

HOW TO GET AROUND QUANTUM-CLASSICAL CORRESPONDENCE FOR SHO? Couple to quantum-limit (2-state) system so as to generate strongly nonclassical states Ψ(x) = αΨ1(x)+ βΨ2(x) (2-state system: photon, trapped ion. . .) Introduce anharmonicity + external drive, study bistable behavior (R. Lifshitz) General problem in testing QM vs. “physical collapse” theories (e.g. GRWP, Penrose): DECOHERENCE MIMICS EFFECTS OF COLLAPSE! So, want simultaneously: “large” GRWP (etc.) collapse rate (coll) “small” decoherence rate (dec) ∆ : under experimentally realistic conditions (Δx « d) coll ~ Δx (GRWP), ~ (Δx)2 (Penrose) dec ~ (Δx)2  don’t gain by increasing Δx . –Ψ1 –Ψ2

HOW CONFIDENT ARE WE ABOUT (STANDARD QM’l) DECOHERENCE RATE? Theory: (a) model environment by oscillator bath (may be questionable) (b) Eliminate environment by standard Feynman-Vernon type calculation (seems foolproof) Result (for SHO): ARE WE SURE THIS IS RIGHT? Tested (to an extent) in cavity QED: never tested (?) on MEMS. Fairly urgent priority! provided kBT»Ω energy relaxation rate (Ω/Q) zero-point rms displacement