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

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

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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

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SLIDE 1

Quantum and Gravity Together: Cosmic, and Nano?

Lajos Di´

  • si

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´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 1 / 11

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SLIDE 2

Outline

1

Where do Quantum and Gravity meet?

2

Theories concerning QG?

3

Quantum Geometrodynamics

4

Bottle-neck of Quantum Gravity: Q OR G?

5

What’s wrong with Wheeler-DeWitt QG?

6

Newtonian G-related decoherence (hypothesis)

7

Proposed experimental tests

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 2 / 11

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SLIDE 3

Warning

In Quantum theory: “classical” means non-quantized. In Gravity theory: “classical” means non-relativistic.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 3 / 11

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SLIDE 4

Where do Quantum and Gravity meet?

Where do Quantum and Gravity meet?

Quantum theory = Schr¨

  • dinger eq. for Ψ:

dΨ(q, t) dt = − i H (q, −i∂/∂q) Ψ(q, t) plus von Neumann measurement theory. Gravity theory = Einstein eq. for gab (a, b = 0, 1, 2, 3): Rab − 1 2gabR = 8πG c4 Tab

gab: space-time metric, Rab, R: Ricci curvatures, Tab: energy-mom.

Quantum and Gravity meet at Planck scale: ℓP=

  • G/c3∼10−33cm, tP=
  • G/c5∼10−43s, mP=
  • c/G∼10−5g

Where Q and G meet: Cosmic Big Bang.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 4 / 11

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SLIDE 5

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´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 5 / 11

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SLIDE 6

Quantum Geometrodynamics

Quantum Geometrodynamics

Canonical quantization of (pure) Einstein eq. Rab − 1

2gabR = 0.

Canonical structure is well hidden, but it exists! Due to gauge invariance: canonical coordinates are fewer than gab, they are the spatial 3x3 metric ˜ gij; i, j = 1, 2, 3. Hamilton density: H(˜ g, ˜ π) = ˜ Gijkl ˜ πij ˜ πkl − (det ˜ g)1/2 ˜ R

˜ πij: conjugate momenta, ˜ Gijkl=1

2(det ˜

g)−1/2(˜ gik ˜ gjl + ˜ gil ˜ gjk − ˜ gij ˜ gkl).

Quantization via Schr¨

  • dinger eq. for wave functional Ψ[˜

g]: H(˜ g, −iδ/δ˜ g)Ψ[˜ g] = 0. That’s the Wheeler-DeWitt eq. of Quantum Geometrodynamics. Generic solutions: no time, no space-time!

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 6 / 11

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SLIDE 7

Bottle-neck of Quantum Gravity: Q OR G?

Bottle-neck of Quantum Gravity: Q OR G?

Mainstream blames G, sidestream blames Q.

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙ ❙

i ˙ Ψ = HΨ ∆Φ = 4πGf c2t2 − r 2 = invariant

  • G

c von Neumann Dirac positron Einstein black hole HΨ = 0 What’s wrong with Wheeler-DeWitt QG?

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 7 / 11

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What’s wrong with Wheeler-DeWitt QG?

What’s wrong with Wheeler-DeWitt QG?

H (˜ g, −iδ/δ˜ g) Ψ[˜ g] = 0 ˜ g = 3x3 metric tensor field of spatial geometry Problem: generic solution Ψ[˜ g] implies no time, no space-time Why? Because of ”Schr¨

  • dinger Cat” states:

Ψ[˜ g] = Ψ1[˜ g] + Ψ2[˜ g]; Ψ1, Ψ2 are peaked at ˜ g1, ˜ g2 A remedy: decoherence might kill “Schr¨

  • dinger Cat”.

Introduce a smart measure of “catness” of Ψ = Ψ1 + Ψ2. Modify Q theory to decohere Ψ = Ψ1 + Ψ2 if “catness” is big. Relativistic case is largely unexplored. Go Newtonian! Surprize: Q and G meet at nanoscales.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 8 / 11

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SLIDE 9

Newtonian G-related decoherence (hypothesis)

Newtonian G-related decoherence (hypothesis)

Rab − 1 2gabR = 8πG c4 Tab ⇒ ∆Φ = −4πGf

Φ: Newton potential, f : mass distribution

Schr¨

  • dinger Cat: superposition of “very” different f1 and f2.

Our choice of “catness” (D., Penrose): ∆EG = 2U(f1, f2) − U(f1, f1) − U(f2, f2) ≥ 0

U(f1, f2): Newton interaction potential between f1, f2.

Add universal decoherence to QM! Postulate decay time of catness: τd = /∆EG No effect for atomic systems but for massive ones (≥ 10−15g). Q and G meet already at “nano” scales.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 9 / 11

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SLIDE 10

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)

  • ptically levitated dielectric nano-sphere (Romero-Isart)

... y 2000-...: Laboratory race for a nanomechanical Schr¨

  • dinger Cat.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 10 / 11

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Nanomechanical Schr¨

  • dinger Cat

Nanomechanical Schr¨

  • dinger Cat
  • Nanommech. resonator (1mg,10kHz) cooled to ground state (µK)

Confirm Q theory for massive d.o.f. Confirm if “Schr¨

  • dinger 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´

  • si (Wigner Center, Budapest)

Quantum and Gravity Together: Cosmic, and Nano? July 8, 2012 11 / 11