Quantum and Gravity Together: Cosmic, and Nano? Lajos Di osi - PowerPoint PPT Presentation

Quantum and Gravity Together: Cosmic, and Nano? Lajos Di´ osi Wigner Center, Budapest July 8, 2012 Acknowledgements go to: Hungarian Scientific Research Fund under Grant No. 75129 EU COST Action MP1006 ‘Fundamental Problems in Quantum Physics’ Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 1 / 11

Outline Where do Quantum and Gravity meet? 1 Theories concerning QG? 2 Quantum Geometrodynamics 3 Bottle-neck of Quantum Gravity: Q OR G? 4 What’s wrong with Wheeler-DeWitt QG? 5 Newtonian G-related decoherence (hypothesis) 6 Proposed experimental tests 7 Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 2 / 11

Warning In Quantum theory: “classical” means non-quantized. In Gravity theory: “classical” means non-relativistic. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 3 / 11

Where do Quantum and Gravity meet? Where do Quantum and Gravity meet? Quantum theory = Schr¨ odinger eq. for Ψ: d Ψ( q , t ) = − i � H ( q , − i � ∂/∂ q ) Ψ( q , t ) dt plus von Neumann measurement theory. Gravity theory = Einstein eq. for g ab ( a , b = 0 , 1 , 2 , 3): R ab − 1 2 g ab R = 8 π G c 4 T ab g ab : space-time metric, R ab , R : Ricci curvatures, T ab : energy-mom. Quantum and Gravity meet at Planck scale: � � � � G / c 3 ∼ 10 − 33 cm , t P = � G / c 5 ∼ 10 − 43 s , m P = � c / G ∼ 10 − 5 g ℓ P = Where Q and G meet: Cosmic Big Bang. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 4 / 11

Theories concerning QG? Theories concerning QG? No experimental evidence at all! You are free to speculate! Main stream: Apply Q to G! Canonical quantization of Einstein eq. Quantum-field theory for Einstein eq. String theory approach (I won’t adress it.) Side stream: Revise Q first! Hybrid dynamics: Q plus classical d.o.f. Decoherent Histories Add (tiny) decoherence to Q theory Be main stream conservative, see canonical quantization first! Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 5 / 11

Quantum Geometrodynamics Quantum Geometrodynamics Canonical quantization of (pure) Einstein eq. R ab − 1 2 g ab R = 0 . Canonical structure is well hidden, but it exists! Due to gauge invariance: canonical coordinates are fewer than g ab , they are the spatial 3x3 metric ˜ g ij ; i , j = 1 , 2 , 3. Hamilton density: π ij ˜ g ) 1 / 2 ˜ π kl − (det ˜ π ) = ˜ H (˜ g , ˜ G ijkl ˜ R π ij : conjugate momenta, ˜ G ijkl = 1 g ) − 1 / 2 (˜ ˜ 2 (det ˜ g ik ˜ g jl + ˜ g il ˜ g jk − ˜ g ij ˜ g kl ). Quantization via Schr¨ odinger eq. for wave functional Ψ[˜ g ]: H (˜ g , − i � δ/δ ˜ g )Ψ[˜ g ] = 0 . That’s the Wheeler-DeWitt eq. of Quantum Geometrodynamics. Generic solutions: no time, no space-time! Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 6 / 11

Bottle-neck of Quantum Gravity: Q OR G? Bottle-neck of Quantum Gravity: Q OR G? Mainstream blames G, sidestream blames Q. c 2 t 2 − r 2 = invariant ✓ ❙ ✓ ❙ c ✓ ❙ ✓ ❙ ✓ ❙ ✓ ❙ Dirac Einstein ✓ ❙ positron black hole ✓ ❙ ✓ ❙ H Ψ = 0 ✓ ❙ ✓ ❙ ✓ ❙ ✓ ❙ ✓ ❙ � G i � ˙ ✓ ❙ Ψ = H Ψ ∆Φ = 4 π Gf von Neumann What’s wrong with Wheeler-DeWitt QG? Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 7 / 11

What’s wrong with Wheeler-DeWitt QG? What’s wrong with Wheeler-DeWitt QG? H (˜ g , − i � δ/δ ˜ g ) Ψ[˜ g ] = 0 g = 3 x 3 metric tensor field of spatial geometry ˜ Problem: generic solution Ψ[˜ g ] implies no time, no space-time Why? Because of ”Schr¨ odinger Cat” states: Ψ[˜ g ] = Ψ 1 [˜ g ] + Ψ 2 [˜ g ]; Ψ 1 , Ψ 2 are peaked at ˜ g 1 , ˜ g 2 A remedy: decoherence might kill “Schr¨ odinger Cat”. Introduce a smart measure of “catness” of Ψ = Ψ 1 + Ψ 2 . Modify Q theory to decohere Ψ = Ψ 1 + Ψ 2 if “catness” is big. Relativistic case is largely unexplored. Go Newtonian! Surprize: Q and G meet at nanoscales. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 8 / 11

Newtonian G-related decoherence (hypothesis) Newtonian G-related decoherence (hypothesis) R ab − 1 2 g ab R = 8 π G c 4 T ab ∆Φ = − 4 π Gf ⇒ Φ: Newton potential, f : mass distribution Schr¨ odinger Cat: superposition of “very” different f 1 and f 2 . Our choice of “catness” (D., Penrose): ∆ E G = 2 U ( f 1 , f 2 ) − U ( f 1 , f 1 ) − U ( f 2 , f 2 ) ≥ 0 U ( f 1 , f 2 ): Newton interaction potential between f 1 , f 2 . Add universal decoherence to QM! Postulate decay time of catness: τ d = � / ∆ E G No effect for atomic systems but for massive ones ( ≥ 10 − 15 g). Q and G meet already at “nano” scales. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 9 / 11

Proposed experimental tests Proposed experimental tests Detecting Newton-G-related loss of coherence in: nucleon decay (Pearle & Squires) flavor oscillations of neutrinos from distant cosmic sources (Christian) light propagation from distant stars (Christiansen & Ng & vanDam) gravity wave interferometer LIGO/VIRGO (Amelino-Camelia) seeds of cosmic structure (Sudarsky) nano-mechanical oscillator (Marshall & Simon & Penrose & Bouwmeester) optically levitated dielectric nano-sphere (Romero-Isart) ... y 2000-...: Laboratory race for a nanomechanical Schr¨ odinger Cat. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 10 / 11

Nanomechanical Schr¨ odinger Cat Nanomechanical Schr¨ odinger Cat Nanommech. resonator (1mg,10kHz) cooled to ground state ( µ K) Confirm Q theory for massive d.o.f. Confirm if “Schr¨ odinger Cats” exist at all. Confirm G-related (or other) models of their decay Experiments: nano-mirror coupled to single photon, nano-resonator coupled to single-electron-transistor, or to single-electron-spin, to Cooper-pair-box Possible relevance: Extension of Q superposition Extension of Q-coherent control Extension of Q-information technology New physics: discovery of Newtonian (non-Cosmic) QG. Lajos Di´ osi (Wigner Center, Budapest) Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 11 / 11