The Quantum Dynamics of Shape A New Starting Point for Quantum Gravity

Sean Gryb OAPT Workshop

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May 1, 2010 What do we really know about reality?

How can our physical theories reflect that? Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Outline

1 Introduction

2 Backgrounds Newton’s Bucket and Symmetries

3 Einstein’s Gravity Newton vs Einstein How General Relativity Works

4 Shape Dynamics Geometry vs Shape

5 ∞’s in Quantum Gravity Smoothing out the Micro

6 Quantum Shape Dynamics Phase Transitions

7 Conclusions 1 2 3 4 Relative Motion NO YES NO YES Absolute Motion of H2O NO NO YES YES Shape of H2O FLAT FLAT CURVED CURVED

Proof of Absolute Space!!

Relational/Absolute ⇒ Different Predictions

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Newton’s Bucket Proof of Absolute Space!!

Relational/Absolute ⇒ Different Predictions

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Newton’s Bucket

1 2 3 4 Relative Motion NO YES NO YES Absolute Motion of H2O NO NO YES YES Shape of H2O FLAT FLAT CURVED CURVED Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Newton’s Bucket

1 2 3 4 Relative Motion NO YES NO YES Absolute Motion of H2O NO NO YES YES Shape of H2O FLAT FLAT CURVED CURVED

Proof of Absolute Space!!

Relational/Absolute ⇒ Different Predictions Mach’s Argument Backgrounds emerge when many heavy objects (eg, galaxies) are present. → Related to Hilbert spaces of quantum theories!

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Symmetries vs Backgrounds

Definitions Symmetry ≡ Equations are invariant. Relational ≡ Physical Laws are invariant. Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Symmetries vs Backgrounds

Definitions Symmetry ≡ Equations are invariant. Relational ≡ Physical Laws are invariant.

Mach’s Argument Backgrounds emerge when many heavy objects (eg, galaxies) are present. → Related to Hilbert spaces of quantum theories! ∵ Parallel straight lines converge ⇒ spactime is curved!

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Equivalence Principle and Curvature Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Equivalence Principle and Curvature

∵ Parallel straight lines converge ⇒ spactime is curved! 2 Spin 2 particle Mercury’s Orbit Gravity wave polarization

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Newton vs Einstein

Two key OBSERVED differences: 1 Special Relativity No action at a distance. Lorentz transformations Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Newton vs Einstein

Two key OBSERVED differences: 1 Special Relativity No action at a distance. Lorentz transformations

2 Spin 2 particle Mercury’s Orbit Gravity wave polarization Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 1: The Variables (Kinematics)

Rules for painting lines: 1 number of dim = number of lines 2 No lines of the same color can cross 3 Draw enough for desired resolution

metric vs geometry Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 2: Symmetry

Variables are painted lines! Key Idea Symmetry: eq’ns → independent of how you paint. (Need differential geometry) Relational: physics → independent of how you paint. (Need best matching)

True degree of freedom: geometry! 2 ∆g K ≡ Rate of change of geometry (K ∼ v , where v = ∆t ) V ≡ P local curvature (= 1/R) E ≡ cosmological constant

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 3: Dynamics

“Conservation of Energy” ⇒ K + V = E

Geometry Dynamics (Geometrodynamics) V ≡ P local curvature (= 1/R) E ≡ cosmological constant

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 3: Dynamics

“Conservation of Energy” ⇒ K + V = E

Geometry Dynamics (Geometrodynamics) 2 ∆g K ≡ Rate of change of geometry (K ∼ v , where v = ∆t ) E ≡ cosmological constant

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 3: Dynamics

“Conservation of Energy” ⇒ K + V = E

Geometry Dynamics (Geometrodynamics) 2 ∆g K ≡ Rate of change of geometry (K ∼ v , where v = ∆t ) V ≡ P local curvature (= 1/R) Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Part 3: Dynamics

“Conservation of Energy” ⇒ K + V = E

Geometry Dynamics (Geometrodynamics) 2 ∆g K ≡ Rate of change of geometry (K ∼ v , where v = ∆t ) V ≡ P local curvature (= 1/R) E ≡ cosmological constant Angles:

1 d2 + d2 − d2 cos θ = 2 3 1 2 d2d3 1 (Ωd )2 + (Ωd )2 − (Ωd )2 = 2 3 1 (2) 2 (Ωd2)(Ωd3)

∴ d1/d2, θ, etc... are unchanged!

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Geometry vs Shape Part 1: Size

Rescale: Only angles and ratios of lengths are measurable. Ratios of Lengths: d Ωd 1 = 1 , etc... (1) d2 Ωd2 Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Geometry vs Shape Part 1: Size

Rescale: Only angles and ratios of lengths are measurable. Ratios of Lengths: d Ωd 1 = 1 , etc... (1) d2 Ωd2

Angles:

1 d2 + d2 − d2 cos θ = 2 3 1 2 d2d3 1 (Ωd )2 + (Ωd )2 − (Ωd )2 = 2 3 1 (2) 2 (Ωd2)(Ωd3)

∴ d1/d2, θ, etc... are unchanged! Solution? Find a local scale independent theory (using best matching).

⇒ Shape Dynamics

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Geometry vs Shape Part 2: LOCAL Size

Only LOCAL shapes are measured! Problem Local size not measurable. GR depends on scale. Why? Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Geometry vs Shape Part 2: LOCAL Size

Only LOCAL shapes are measured! Problem Local size not measurable. GR depends on scale. Why?

Solution? Find a local scale independent theory (using best matching).

⇒ Shape Dynamics GR is Bad and Ugly!!

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Statistical Smoothing

Physics is possible because we can “smooth–out” fine details.

The Good, the Bad, and the Ugly Good: micro–physics averages out. Bad: micro destroys macro. Ugly: averaging doesn’t work. Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Statistical Smoothing

Physics is possible because we can “smooth–out” fine details.

The Good, the Bad, and the Ugly Good: micro–physics averages out. Bad: micro destroys macro. Ugly: averaging doesn’t work. GR is Bad and Ugly!! Quantum: hc E = hf ⇒ E = (4) 2∆x Gravity: (Black hole radius)

2mG 2EG R = = (5) BH c2 c4 q ~G If ∆x ∼ RBH then ∆x = c3 ≡ Plank length.

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Why GR is bad: A Particle in the Smallest Box

Longest wavelength photon: c λ = 2∆x ⇒ f = (3) 2∆x Gravity: (Black hole radius)

2mG 2EG R = = (5) BH c2 c4 q ~G If ∆x ∼ RBH then ∆x = c3 ≡ Plank length.

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Why GR is bad: A Particle in the Smallest Box

Longest wavelength photon: c λ = 2∆x ⇒ f = (3) 2∆x Quantum: hc E = hf ⇒ E = (4) 2∆x q ~G If ∆x ∼ RBH then ∆x = c3 ≡ Plank length.

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Why GR is bad: A Particle in the Smallest Box

Longest wavelength photon: c λ = 2∆x ⇒ f = (3) 2∆x Quantum: hc E = hf ⇒ E = (4) 2∆x Gravity: (Black hole radius)

2mG 2EG R = = (5) BH c2 c4 Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Why GR is bad: A Particle in the Smallest Box

Longest wavelength photon: c λ = 2∆x ⇒ f = (3) 2∆x Quantum: hc E = hf ⇒ E = (4) 2∆x Gravity: (Black hole radius)

2mG 2EG R = = (5) BH c2 c4 q ~G If ∆x ∼ RBH then ∆x = c3 ≡ Plank length. Local scale invariance:

Plank length is meaningless!

Alternatives: string theory, LQG, etc...

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Local Scale Symmetry Saves the Day

Waves with λ < Plank length create black holes! ⇒ micro destroys macro!! Alternatives: string theory, LQG, etc...

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Local Scale Symmetry Saves the Day

Waves with λ < Plank length create black holes! ⇒ micro destroys macro!! Local scale invariance:

Plank length is meaningless! Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Local Scale Symmetry Saves the Day

Waves with λ < Plank length create black holes! ⇒ micro destroys macro!! Local scale invariance:

Plank length is meaningless!

Alternatives: string theory, LQG, etc... Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Phase Transitions: Water

Symmetries can be “broken” at low energy!

High Energy (Liquid)

Low Energy (Solid)

Latice → broken symmetry Uniform Distribution → symmetry Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Phase Transitions: Geometry

In Quantum Shape Dynamics, I expect scale symmetry will be broken.

High Energy Low Energy

Gravity → QSD Gravity → GR Disclaimer Shape dynamics is not yet a complete theory! There are still many unresolved question. If we knew what we were doing, it wouldn’t be called research!

Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Conclusions

Summary: Symmetry 6= Relational (Background Independence) Equivalence Principle → curved spacetime Gravity = dynamic geometry (energy balance) Coordinate dependence is relational Scale dependence is NOT! Shape Dynamics might tame ∞’s?! Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Conclusions

Summary: Symmetry 6= Relational (Background Independence) Equivalence Principle → curved spacetime Gravity = dynamic geometry (energy balance) Coordinate dependence is relational Scale dependence is NOT! Shape Dynamics might tame ∞’s?!

Disclaimer Shape dynamics is not yet a complete theory! There are still many unresolved question. If we knew what we were doing, it wouldn’t be called research! Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Bonus Slides: Best Matching – The Idea

What is the “difference” between 2 shapes?

X ∆S2 = (∆x)2 (6) I Or, X (∆S0)2 = (∆x0)2? I (7)

Ambiguity in coordinates? Intro Backgrounds Gravity Shape Dynamics ∞’s in QG QSD Conclusions Bonus Slides: Best Matching

Solution: minimize ∆S by shifting coordinates! ⇒ Best Matching

y y 5 5 à 2 à 2 4 4

3 3 à 3 à 3 ì 2 2 æ 2 æ 2 1 1 à 1 à 1 ì x' x' -2 3 æ 2 4 6 -2 3 æ 2 4 6 1 æ -1 1 æ -1 ì -2 -2 Newton’s Laws (F (= ∇V ) = ma) → min(V · ∆S) for all t.