1. Gravitational experiments testing Lorentz symmetry Quentin G. Bailey Physics Department Embry-Riddle Aeronautical University Prescott, AZ From Quantum to Cosmos: Fundamental Physics in Space for the Next Decade, Arlie Center, VA, July 6-10, 2008 From Quantum to Cosmos: Fundamental Physics in Space for the Next Decade, Arlie Center, VA, July 6-10, 2008

2. Outline Background, motivation The Standard-Model Extension (SME) Gravity and Lorentz violation Gravitational sector of the SME Experiments –Overview –Lunar laser ranging –Gravity Probe B Summary

3. Motivation: There could be Lorentz violation coming from a fundamental theory Lorentz symmetry – the symmetry of Special Relativity Two kinds of transformations: Rotations and Boosts Background and Motivation General Relativity Fundamental theory (strings?, noncommutative spacetime?, quantum gravity?, …) Lorentz symmetry Standard Model Lorentz-symmetry breaking (spontaneous Lorentz-symmetry breaking?) Lorentz symmetry Standard Model General Relativity A signal for Lorentz violation would be a signal of Planck-scale physics!

4. Standard-Model Extension (SME) Idea (qualitative): General framework for studying Lorentz violation + + All possible forms of Lorentz violation Background fields interacting with known matter General Relativity Standard Model Idea (technical details): SME – effective field theory with lagrangian: Usual SM fieldsAll possible Lorentz-violating terms constructed from SM & GR fields and background coefficients Usual GR lagrangian (Kostelecký & Potting PRD 1995; Colladay & Kostelecký PRD 97, 98; Kostelecký PRD 04)

5. Subset - “Minimal SME” coefficients for Lorentz violation (a μ, b μν, c μν, k μν,… ) – controls the degree of Lorentz violation for each species (photons, electrons, higgs, …) - these are the quantities to hunt in experiments! Advantages of the SME –independent of underlying theory (general Lorentz violation) -can match any Lorentz violation model to the SME -many new effects predicted for experimental searches Disadvantages -substantially complex (requires lots of time) -few terms in the expansion=PhD thesis

6. Lunar laser ranging (Battat, Stubbs, Chandler) Harvard atom interferometric gravimeters (Chu, Mueller, …) Stanford cosmological birefringence (Carroll, Jackiw, Mewes, Kostelecky) MIT, IU pulsar timing (Altschul) South Carolina synchrotron radiation (Altschul) South Carolina Cosmic Microwave Background (Mewes, Kostelecky) Marquette U., IU meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …) neutrino oscillations (MiniBooNE, LSND, MINOS, Super K,… ) muon tests (Hughes, BNL g-2) Yale, … spin-polarized torsion pendulum tests (Adelberger, Hou, …) U. of Washington tests with resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …) Stanford, Institut fur Physik, Univ. West. Aust. clock-comparison tests (Hunter, Walsworth, Wolf, …) Harvard-Smithsonian Penning-trap tests (Dehmelt, Gabrielse, …) U. of Washington Minimal SME experiments (to date) SME Theory 1000+ papers topics include: classical electrodynamics QED: stability, causality, renormalizability gravitational couplings connection to NCQFT, SUSY, … spontaneous Lorentz-symmetry breaking Torsion couplings Only ~1/2 of minimal SME possibilities explored N Russell (NMU), “Constraining spacetime torsion” (makes use of SME results), Tuesday, 18:00

7. Spacetime described by metric curvature SME geometrical framework: Riemann-Cartan spacetime (generalization of the spacetime of General Relativity) For simplicity, focus on Riemann spacetime (no Torsion) Foundation: local Lorentz symmetry –Around each point in spacetime is a local inertial frame where the laws of physics are that of Special Relativity Also: diffeomorphism symmetry –mapping spacetime points → spacetime points “local translations”

8. Result 2: Explicit Lorentz/diffeo breaking is in general incompatible with Riemann geometry* *Kostelecký PRD 04 Explicit Lorentz breaking – prescribed, nondynamical coefficients Conflicts with geometric identities i.e., conflicts with Riemann geometry –Produces modified conservation laws Bianchi identities (boundary of a boundary is zero) angular momentum energy & momentum Gravity and Lorentz violation Result 1: Lorentz breaking  diffeomorphism breaking* Coefficients control Lorentz and diffeomorphism breaking

9. Tensor fields acquire vacuum expectation values Spontaneous Lorentz-symmetry breaking E.g., vector field Potential Expand about minimum Fluctuations, includes Nambu- Goldstone modes V vev Key feature: Lorentz violation is dynamical → Conservation laws are unaffected Bianchi identities are safe Result 3: Spontaneous symmetry breaking saves geometry! However … (Kostelecký PRD 04)

10. Gravity sector of the SME Basic idea General Relativity + All possible (pure-gravity) Lorentz-violating terms Basic Riemann spacetime lagrangian (Kostelecký PRD 04) : Einstein-Hilbert term (GR) Leading Lorentz-violating couplings Contains ordinary matter, dynamics for coefficient fields Ricci tensor Weyl tensor Leads to modified Einstein equations:

11. Ordinary matterLorentz-violating corrections Upshot: can calculate observables, compare specific models 9 coeffs, controls the dominant Lorentz violation Challenging theoretical task: construct the effective Einstein equations Assume spontaneous Lorentz-symmetry breaking –Ensures consistency with Riemann geometry Details: Bailey, Kostelecký PRD 06 Final result in weak-field limit effective linearized field equations Remaining quantities:,,

12. Parametrized Post-Newtonian (PPN) formalism (Will, Nordtvedt APJ 70’s) –General post-newtonian metric expansion –Isotropic parameters in the Universe Rest Frame –Compare alternate theories to PPN SME – general action-based expansion Partial match of PPN with SME possible SME isotropic limit → 18 coefficients outside PPN Comparison to well-known test models

13. Celestial Mechanics lunar/satellite ranging (J. Battat, C. Stubbs, J. Chandler (Harvard), PRL 2007) binary pulsar perihelion shift of planets Tests of spacetime geometry geodesics: gyroscope experiment light propagation (Time-delay effect,...) accelerated/rotating: gravimeter tests (H. Mueller, S. Chu, … (Stanford) PRL 2008) torsion-pendulum tests short-range tests of gravity (J. Long etal, (Indiana), in progress) Today Gravitational experiments probing SME coefficients (Details: Bailey, Kostelecký PRD 06)

14. Idea: measure distance to Moon by reflecting laser light off mirrors Lunar laser ranging r Many tests of gravity (30+ years) Accuracy < 1 cm Basic observable: oscillations in lunar distance r (LLR Review: Muller et al, gr-qc/0509114) Images: http://physics.ucsd.edu/~tmurphy/apollo/apollo.htmlhttp://physics.ucsd.edu/~tmurphy/apollo/apollo.html & http://ilrs.gsfc.nasa.gov/

15. One primary oscillation, from Lorentz violation, is at twice the orbital frequency Lorentz-violating background (Represent heuristically as red arrows) unmodified orbit (Bailey, Kostelecký PRD 06) Dominant effects: Analysis also exists for satellites e.g., LAGEOS, GALILEO, …

16. Recent paper bounding SME gravity coefficients Uses 35 years of data (J. Battat, C. Stubbs, J. Chandler (Harvard), PRL 2007) Ongoing APOLLO project (NM) ( Murphy, Stubbs, Adelberger … ) –ongoing, achieves < 1 mm sensitivity T Murphy (UCSD), “APOLLO: A Comprehensive Test of Gravity via Lunar Laser Ranging”, Monday, July 7, 16:00

17. General Relativity predicts –spin precession in curved spacetime Idea of GPB: measure precession 1) geodetic precession 2) dragging of inertial frames (gravitomagnetic) Also: Lorentz-violating precession Gravity Probe B (GPB) (Schiff 1960) GPB collaboration: Everitt, Kaiser, Overduin, … (http://einstein.stanford.edu/) GPB gyroscope (superconducting spinning sphere) (Bailey, Kostelecký 06) (Image: http://einstein.stanford.edu/)

18. Spin precession for gyroscope in Earth orbit Lorentz-violating precession Mean orbital velocity Value of g for orbit Gravitomagnetic precession Conventional geodetic precession Polar GPB orbit

19. Standard general relativity contributions Dominant SME contributions Assuming GPB angular resolutions of order 10 -4 ’’ C -1 can obtain 10 -4 on coeffs Along orbital angular momentum axis σ Along Earth’s spin axis Z Along perpendicular axis n Coefficients referred to standard SME Sun-centered frame

20. Summary Lorentz symmetry –foundation of our current fundamental theories Lorentz symmetry General RelativityStandard Model Recent interest in testing Lorentz symmetry: –Signal of Lorentz violation new physics (beyond Standard Model and General Relativity) Space-based tests - Lunar Laser Ranging, Gravity Probe B, Time-delay effect, Binary pulsars

21. A recent New Scientist cover… General info on Lorentz violation and the SME: http://www.physics.indiana.edu/~kostelec/faq.html