1. Fundamental Physics Research in Space International Workshop Washington DC 22-24 May 2006 Probing Relativity using Space-Based Experiments Neil Russell Northern Michigan University, USA The Standard-Model Extension (SME): a tool to search for signals of quantum gravity at accessible energies Clock-Comparison Tests Optical and Microwave cavities

2. Standard ModelGeneral Relativity Studying Quantum Gravity at sub-Planck Energies SM + GR  highly successful description of observed phenomena What should go into an effective QFT for Lorentz violation? These two field theories are expected to merge at the Planck scale 10 19 GeV Any observable signals of Lorentz violation can be described using effective field theory Kostelecký, Potting PRD 51 3923 (1995) Suppressed effects of the fundamental quantum-gravity theory may be observable in sensitive experiments Relativity violation is a possible Planck-scale signal Quantum Gravity EPEP Energy Curvature / torsion  Minkowski limit

3. Standard Model with Gravity Coordinate-independent Lorentz violation Standard-Model Extension “SME” Kostelecký, PRD 69 105009 (2004) Colladay, Kostelecký, PRD 55 6760 (1997) PRD 58 116002 (1998) SME contains Minimally-coupled SM action Pure-gravity action Leading-order terms for Lorentz violation constructed from gravitational and SM fields Minimal SME: SME operators restricted to mass dimension 3 and 4

4. Special case: the Minimal SME The minimal SME has been used as the basis for a variety of investigations: (*) : bounds already existing Neutral meson oscillations (*) Neutrino oscillations Clock-comparison tests – ground (*) Clock-comparison tests -- space Spin-polarized torsion pendulum (*) Penning-trap tests of QED (*) H (*) and anti H spectroscopy Muon properties (*) Cosmological birefringence (*) Optical and microwave cavities (*) Baryon asymmetry Post-newtonian gravity New Scientist 16 August, 2003 http://physics.indiana.edu/ ~kostelec/faq.html There are now more than 500 papers on the SME

5. Sidereal variations Kostelecký, PRL 80 1818 (1998)

6. Clock-comparison tests Kostelecký, Lane, PRD 60, 116010 (1999) Bluhm, Kostelecký, Lane, Russell PRL 88, 090801 (2002) PRD 68, 125008 (2003)

7. Stable clock 9.1 GHz time Lorentz-violation signal could occur as minuscule variation in clock frequency To detect signal, compare two clocks: one sensitive, one inert or differently affected Line from atomic transition sensitive inert frequency Clock-comparison tests

8. To search for Lorentz and CPT violation in SME context, perturbation is… (Details of multiparticle aspects etc omitted) Clock-comparison tests Kostelecký, Lane, PRD 60, 116010 (1999) Accessing coefficients without suppression: Need change in z component of angular momentum Eg, for Hydrogen maser, is suppressed, making a good reference clock; is sensitive at leading order, making a good signal clock.

9. Possible advantages of space include: greater boosts greater fountain free-fall time choice of orbital plane

10. Clock-comparison analyses considering rotational effects: Kostelecký,Lane PRD 60 116010 (1999) Can consider also boosted trajectories of clocks in space. Bluhm, Kostelecký, Lane, Russell, PRL 2002 & PRD 2003 Issues: 1. A changing velocity is useful for improved sensitivity  satellite in orbit is a good candidate 2. A standard inertial reference frame must be selected Good candidates are centered on the Sun, the galaxy, and the CMB. Earth-centered frame is not suitable.  Choose Sun-centered frame, T starting at vernal equinox in 2000 Boosted clocks

11. Laboratory choices Speedv/cperiod ground 0.4 km/s (wrt Earth) 10 -6 24 h ISS 8 km/s (wrt Earth) 10 -5 92 min Earth 30 km/s (wrt Sun) 10 -4 365 d Sun 200 km/s (wrt galaxy) 10 -3 Dedicated experiment 300 km/s (wrt Sun) 10 -3 ~10 sec Wanted: fast-moving, rotating laboratory SpaceTime?

12.   ssss X Y Z Equatorial plane Spring equinox Satellite orbit Bluhm, Kostelecký, Lane, Russell, PRL 88, 090801 (2002); PRD 68, 125008 (2003)

14. Need the inertial-frame quantities in terms of the lab-frame quantities… Bluhm, Kostelecký, Lane, Russell, PRL 88, 090801 (2002); PRD 68, 125008 (2003)

15.  s = speed of satellite relative to the Earth = 8 km/s Without boosts, recover rotation dependence equivalent to result in Lane, Kostelecky PRD 1999 General form of boost and rotation dependence for b 3 tilde  = speed of Earth relative to the Sun = 10  4 c = 30 km/s

16. Optical and Microwave cavities Kostelecký and Mewes PRL 87, 251304 (2001) PRD 66, 056005 (2002)

17. Lorentz-violating photon sector (dimensionless) Parity odd Parity even 1 3x3, traceless, symmetric 3x3, antisymmetric 3 Total coefficients: 19 5 5 5 Kostelecký and Mewes, PRL 87 251304 (2001); PRD 66 056005 (2002) These 19 coefficients describe all dimensionless photon-sector observer-independent Lorentz violations

18. SME Birefringence Tests 10 relevant coefficients: The vacuum is found to be birefringent 10 particular combinations: Comparison of polarization for different wavelengths Analysis based on data for 16 sources Kostelecký and Mewes, PRL 87 251304 (2001); PRD 66 056005 (2002)

19. Cavity Oscillators optical: microwave, T 010 cylindrical mode: Fractional frequency shifts for cavity Kostelecký and Mewes, PRL 87 251304 (2001); PRD 66 056005 (2002)

20. Tests with Optical and Microwave cavities Each experiment bounds different SME coefficient combinations Lipa et al. (PRL 90 060403, 2003) 4 combs. of coeffs <10 -13 ; 5 comb. of coeffs <10 -9 Brillet,Hall (PRL 1979) Michelson-Morley type 1 combination of coeffs < 10 -15 Hils,Hall (PRL 1990) Kennedy-Thorndike type 1 comb. of coeffs < 10 -13 Müller, Herrmann, Braxmaier, Schiller, Peters, (PRL 91 020401, 2003) 4 combs. of kappa coeffs <10 -15 ; 5 comb. of kappa coeffs < 10 -11 Müller, Herrmann, Saenz, Peters, Lämmerzahl, (PRD 68 116006, 2003) 2 combs. of electron coeffs <10 -14 ; 1 comb. of electron coeffs < 10 -12 Wolf, Tobar, et al, (GRG 36 2352, 2004); and (PRD 70 051902, 2004) combs. of kappa coefficients <10 -15 Müller, (PRD 71 045004, 2005) kappa coeffs <10 -15 ; electron coeffs < 10 -16 Herrmann, Peters et al, (PRL 95 150401, 2005) 5.2 < 10 -15 ; … Antonini, Okhapin, Göklü, Schiller (PRA 72 66102, 2005) 2.2 < 10 -14 ; … Stanwix, Tobar, Wolf et al (PRL 95 040404, 2005) kappa e minus, ZZ component: 5.7 < 10 -14 ; …

21. “SuperSUMO” Planned or proposed space tests include: Lipa, Wang, Nissen, Kasevich, Mester : (see poster)  possible in principle to resolve  c/c at 10 –20  STEP orbiter platform (for example) OPTIS Optical cavities and atomic clocks  photon and fermion sectors of SME See talk by Laemmerzahl, poster by H. Dittus ACES Cs Atomic clock (PHARAO) and space H maser (SHM) see talk by C. Salomon

22. SpaceTime  three ion clocks, trajectory close to Sun  higher boost factor than Earth satellites  see talk by Maleki PARCS  PARCS Primary atomic reference clock in space, on ISS Gravitational tests : see talk by Kostelecky  Rubidium atomic clock experiment on ISS RACE SUMO  Superconducting microwave oscillator on ISS

23. Transition changes the z component of angular momentum eg: 4,4  4,3 Proton and electron parameters: For sensitivity of 100  Hz, bounded terms include: Proton parameters: 10 -27 GeV on b Z 10 -25 GeV on d Z 10 -23 GeV on b T, d ±, d Q, d JK, H JT ~ ~ ~ ~ ~ ~ ~ 10 -25 GeV on c Q from single and double frequencies ~ Hydrogen maser 10 -27 GeV on b Z 10 -23 GeV on b T, d ±, d Q, d JK, H JT ~ ~ ~ ~ ~ ~ Hyperfine transition: 1,1  1,0 Proton and electron parameters: Estimate, using 400  Hz variation limit: Cesium and Rubidium Examples: ACES, PARCS, RACE:

24. The Standard-Model Extension (SME) Allows study of all possible Lorentz violations in context of Standard Model and General Relativity Limit of underlying Quantum-Gravity models The SME predicts signals at the orbital and double-orbital frequencies signals at the frequency of the Earth’s orbital motion Summary Specific calculations for Cs 133, Rb 87, and H clocks are available and include relativistic effects at first order in the boost Estimates for attainable sensitivities for space have been obtained 10 of the 19 dimensionless photon coefficients are strongly constrained by birefringence The remaining ones have been vigorously pursued in cavity experiments; space tests hold the potential for even higher resolutions