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Gravitational experiments testing Lorentz symmetry

Gravitational experiments testing Lorentz symmetry. Quentin G. Bailey Physics Department Embry-Riddle Aeronautical University Prescott, AZ.

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Gravitational experiments testing Lorentz symmetry

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  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

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

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

  5. Subset - “Minimal SME” coefficients for Lorentz violation (aμ, bμν, cμν, kμν ,… ) – 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. Minimal SME experiments (to date) 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 Only ~1/2 of minimal SME possibilities explored • SME Theory • 1000+ papers • topics include: • classical electrodynamics • QED: stability, causality, renormalizability • gravitational couplings • connection to NCQFT, SUSY, … • spontaneous Lorentz-symmetry breaking • Torsion couplings N Russell (NMU), “Constraining spacetime torsion” (makes use of SME results), Tuesday, 18:00

  7. 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 • Spacetime described by metric curvature • Also: diffeomorphism symmetry • mapping spacetime points → spacetime points “local translations”

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

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

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

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

  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. Gravitational experiments probing SME coefficients (Details: Bailey, Kostelecký PRD 06) • Celestial Mechanics • lunar/satellite ranging • (J. Battat, C. Stubbs, J. Chandler (Harvard), PRL 2007) • binary pulsar • perihelion shift of planets Today • 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)

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

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

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

  17. Gravity Probe B (GPB) (Image: http://einstein.stanford.edu/) • 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 GPB gyroscope (superconducting spinning sphere) (Image: http://einstein.stanford.edu/) (Schiff 1960) GPB collaboration: Everitt, Kaiser, Overduin, … (http://einstein.stanford.edu/) (Bailey, Kostelecký 06)

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

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

  20. Summary • Lorentz symmetry • foundation of our current fundamental theories General Relativity Standard Model Lorentz symmetry • Recent interest in testing Lorentz symmetry: • Signal of Lorentz violationnew 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

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