DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? Lajos Di osi, Budapest - - PowerPoint PPT Presentation

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DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? Lajos Di osi, Budapest - - PowerPoint PPT Presentation

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DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? Lajos Di osi, Budapest Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute November 25, 2011 Lajos Di osi, Budapest (Research Institute for Particle

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SLIDE 1

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY?

Lajos Di´

  • si, Budapest

Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute

November 25, 2011

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 1 / 12

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SLIDE 2

Outline

1

Bottle-neck of Quantum Gravity: Q OR G?

2

What’s wrong with Wheeler-DeWitt Eq. HΨ = 0?

3

Newtonian decoherence distance

4

Newtonian decoherence/localization dynamics

5

Proposed tests

6

Gravity caused by wave function collapse?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 2 / 12

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SLIDE 3

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 Eq. HΨ = 0?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 3 / 12

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SLIDE 4

What’s wrong with Wheeler-DeWitt Eq. HΨ = 0?

What’s wrong with Wheeler-DeWitt Eq. HΨ = 0?

H

  • g, ∂

∂g , q, ∂ ∂q

  • Ψ(g, q) = 0

g = 3-geometry, q =matter fields Generic solution Ψ(g, q) implies no 4-geometry No room for von Neumann measurement theory ”Schr¨

  • dinger Cat” states

A remedy would be a certain (hypothetic) universal decoherence to forbid “Schr¨

  • dinger Cat” states, to enforce wave function collapse

into states localized in g. Ttechnical key-element is our smart choice for: Distance ℓ(g1,g2) between 3-geometries, to measure “catness” Modification of WDW Eq. to decohere Ψ for large ℓ Full relativistic option is largely unexplored. Go Newtonian! Decent models, exper’ proposals.

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 4 / 12

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SLIDE 5

Newtonian decoherence distance

Newtonian decoherence distance

Choice for the distance (to measure “catness”): ℓ2(g1, g2) = 1 4πG

  • |g1 − g2|2dV

g1, g2: Newtonian acceleration fields. In mass densities f1, f2: ℓ2(f1, f2) = G [f1(r) − f2(r)][f1(s) − f2(s)] drds |r − s| = 2U(f1, f2) − U(f1, f1) − U(f2, f2) Popular alternatives (Ghirardi et al, Pearle 1986-): ℓ2

GRW /CSL(f1, f2) = γGRW /CSL

  • [f ν

1 (r) − f ν 2 (r)]2dr

ν = 1/2 for GRW, ν = 1 for CSL. Add universal decoherence and quantum state collapse to QM!

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 5 / 12

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SLIDE 6

Newtonian decoherence/localization dynamics

Newtonian decoherence/localization dynamics

Decay time of catness (Penrose 1996, D. 1987) τd =

  • ℓ2(f , f ′) =
  • 2U(f , f ′) − U(f , f ) − U(f ′, f ′)

Master equation for the density matrix (D. 1987) d ˆ ρ dt = − i [ˆ H, ˆ ρ] − 1 2ℓ2(ˆ fL, ˆ fR)ˆ ρ = − i [ˆ H, ˆ ρ] − G 2 [ˆ f (r), [ˆ f (s), ˆ ρ]] drds |r − s| SSE=stochastic Schr¨

  • dinger Equation (D. 1986/89)

dψ dt = − i

  • ˆ

Hψ + non-linear stochastic term Do we have testable predictions?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 6 / 12

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SLIDE 7

Proposed tests

Proposed 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) nano-mechanical oscillator (Marshall & Simon & Penrose & Bouwmeester)

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

... Are there more characteristic effects than excess noise? There would be — in a more radical theory.

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 7 / 12

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SLIDE 8

Gravity caused by wave function collapse?

Gravity caused by wave function collapse?

◗ ◗ ◗ ◗ ◗ ◗ ❦ ✁ ✁ ✁ ✕

  • ✒❈

❈ ❈ ❈ ❈❈ ❲

  • ✒❇

❇ ❇ ❇ ❇ ◆✟✟ ✟ ✯

  • ✒

v v+∆v In the above Newtonian model decoherence/collapse superimposes ”Brownian” diffusion/jumps

  • n c.o.m. motion of massive objects.

Newtonian interaction potential is included by hand Can’t we turn it around? Attribute Brownian diffusion/jumps to emergent g gravity around the mass? What if collapse implies the Newtonian field?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 8 / 12

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SLIDE 9

Gravity caused by wave function collapse?

Excursion: Ambient pressure from ’Brownian’ trajectory I

Motivation: For a single free mass M, one might like to derive the presence of an average attractive Newtonian field g = −GM/r 2 from the features of the random path of the c.o.m., broken by the repeated collapses. Exercise: In a non-standard ‘Brownian’ motion model the presence and the average value of a central compressing force can exactly be derived from the ‘Brownian’ motion.

◗ ◗ ◗ ◗ ◗ ◗ ❦ ✁ ✁ ✁ ✕

  • ✒❈

❈ ❈ ❈ ❈❈ ❲

  • ✒❇

❇ ❇ ❇ ❇ ◆✟✟ ✟ ✯

  • ✒

v v+∆v

◗ ◗ ◗ ◗ ◗ ◗ ❦ ✁ ✁ ✁ ✕

  • ✒❈

❈ ❈ ❈ ❈❈ ❲

  • ✒❇

❇ ❇ ❇ ❇ ◆ ✫✪ ✬✩ s ❅ ❅ ❅ ❅ ■ ✟ ✟ ✟ ✟ ✟ ✟ ✙ ✟✟ ✟ ✯

  • ✒

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 9 / 12

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SLIDE 10

Gravity caused by wave function collapse?

Excursion: ... pressure from trajectory II

Classical rigid ball of radius R, mass M, in thin gas of small rigid ball molecules that hit the ”Brownian” ball. Brownian trajectory becomes a random broken line which encodes the ambient pressure P! Imagine you sit inside the Brownian mass, experience the sequence ∆v1, ∆v2, . . . , ∆vk, . . . of velocity jumps. You shall conclude that there must be and average compressing force acting on the surface of the Brownian Mass (a hydrodamic pressure, this time): P = M surface x time

n

  • k=1

|∆vk|

◗ ◗ ◗ ◗ ◗ ◗ ❦ ✁ ✁ ✁ ✕

  • ✒❈

❈ ❈ ❈ ❈❈ ❲

  • ✒❇

❇ ❇ ❇ ❇ ◆✟✟ ✟ ✯

  • ✒

v v+∆v

◗ ◗ ◗ ◗ ◗ ◗ ❦ ✁ ✁ ✁ ✕

  • ✒❈

❈ ❈ ❈ ❈❈ ❲

  • ✒❇

❇ ❇ ❇ ❇ ◆ ✫✪ ✬✩ s ❅ ❅ ❅ ❅ ■ ✟ ✟ ✟ ✟ ✟ ✟ ✙ ✟✟ ✟ ✯

  • ✒

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 10 / 12

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SLIDE 11

Gravity caused by wave function collapse?

Back to collapse induced gravity

G-related wave function collapse ⇒ ”Browinian” c.o.m. motion Newton interaction put by hand Einstein equivalence (Newton Law ∆Mv = F∆t) violated Can ”Brownian” motion be attributed to emergent −G/r Newton field? Would restore Einstein equivalence (Newton’s Law) Analogue: Ambient Pressure Very preliminary calculations G ⇒ Gr ∼collapse intensity at length scales r Are there more characteristic effects than excess noise? Short distance drop of G?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 11 / 12

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SLIDE 12

Gravity caused by wave function collapse?

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 von Neumann → von Neumann + emergent gravity?

Lajos Di´

  • si, Budapest (Research Institute for Particle and Nuclear Physics (transforms in 2012 into: Wigner Institute)

DOES WAVE FUNCTION COLLAPSE CAUSE GRAVITY? November 25, 2011 12 / 12