1. Introduction Motivation (i): philosophical necessity physics is an experimental science → solid experimental confirmation of foundations of physics is crucial

2. Pre-Relativity Situation Galilean symmetry believed valid for over 200 years agreement with observs. incl. planetary motion: v ~ 30 km/s ~ 10 -4 c extrapolation of validity by 3-4 orders of magnitude fails conceptual difficulties with Maxwell’s electrodynamics Present Situation Lorentz symmetry believed valid for about 100 years agreement with observations to E ~ 10 12 GeV ~ 10 -8 E Planck extrapolate validity of Lorentz symmetry to E Planck and far beyond conceptual difficulties with Quantum Gravity

3. Motivation (ii): discovery potential various approaches to physics beyond the Standard Model („quantum gravity“) can accomodate tiny violations of Relativity

4. common approach (top-down): scan predictions of a given theory for sub-Planck effects accessible with near-future technology, e.g., - novel particles (SuSy) - large extra dimensions & microscopic black holes - gravitational-wave background … Issue: attainable E << quantum-gravity (QG) scale  Planck suppression of QG observables

5. bottom-up motivation: What can be measured with Planck precision? Is there a corresponding quantum-gravity effect? Symmetries: - allow exact theoretical prediction - are typically amenable to ultrahigh-precision (null) tests Quantum gravity: likely to affect spacetime structure - More than 4 dimensions? - Non-commuting coordinates? - Discreteness? - “Foamy” structure? - … Tests of spacetime symmetries could probe Planck-scale physics

6. Sec A: Construction of general test framework (SME) for violations of Lorentz and CPT symmetry Outline Sec B: Mechanisms for Lorentz- and CPT breakdown Strings? Topology? Noncomm. geometry? Loop quantum gravity? Varying Scalars? Other? Sec C: Phenomenology and exp. tests astrophysics Penning traps other quantum optics satellites

7. A. The Standard-Model Extension (SME) A test framework that allows for deviation from exact Lorentz symmetry is desirable: - to identify suitable tests - to interpret and analyze experimental observations - to compare tests in different physical systems - to study the theoretical consistency Example: CPT symmetry - if CPT holds  particle mass m 1 = antiparticle mass m 2 - if CPT is broken  ??? (in SME, m 1 = m 2 is still OK ) - usual CPT test for Kaons uses model only valid for Kaon interferometry  precludes comparison with other tests

8. How can one get a test framework for Lorentz violation? underlying physics (strings, loop gravity, noncommutative geometry, SUGRA,...) effective theory (SME test model) E ~E Planck ~E LHC Problem 1: many theory approaches Problem 2: low-E limit can be unclear ? SME must be constructed by hand guided by gen. principles Advantage: generality; independence of underlying physics

9. How can Lorentz violation be implemented? But:- relatively simple - purely kinematical - phenomenological DSR:- conceptual issues (Unruh, Ahluwalia, Grumiller, …) New Lorentz transformts. e.g., Robertson’s framework, Mansouri-Sexl, doubly special relativity (DSR) deformed lightcone  no Lorentzian spacetime vacuum is empty Preferred vacuum directions usual lightcone  Lorentzian spacetime nontrivial vacuum - motivated by theory (Sec B) - fully dynamical & microscopic description possible (Sec A) - incorporates kinemat. models  focus on Lorentz violation via non-dynamical background vectors or tensors

11. Construction of the SME - k , s ,... coefficients for Lorentz violation - minimal SME  fermion 44, photon 23,... - generated by underlying physics (Sec B) - amenable to ultrahigh-precision tests (Sec C) Colladay, Kostelecký ‘97;’98; Kostelecký ‘04; Coleman, Glashow ‘99 Remarks: - can consider operators of higher mass dimension (Myers, Pospelov ‘03; Anselmi, Halat ’07; …) - in gravity context, the above explicit Lorentz breaking is typically inconsistent  spont. Lorentz violation needed (Kostelecký ‘03; Jacobson, Mattingly ‘04)

12. Is Lorentz breakdown consistent with causality? SME fermions (m  0): - no problems for SME operators of dimension 3 - otherwise (dim>3): look at group velocity non-local corrections (e.g., strings) can avoid causality and unitarity violations at high energies Kostelecký, R.L. ‘01 causality (and unitarity) can be violated, but only at ~E Planck  SME remains causal within its range of validity superluminal

13. sample theoretical investigations of the SME - radiative corrections (Jackiw, Kostelecký '99; Y.-L. Wu’s talk?) - causality and stability (Kostelecký, R.L. '01) - gravity: LV must be dynamical (e.g., spontaneous) (Kostelecký '04) - supersymmetry (Berger, Kostelecký '02) - "Anti-CPT Theorem" (Greenberg '02) - one-loop renormalizability (Kostelecký, Lane, Pickering '02) - dispersion relations and kinematical analyses (R.L. '03) - generalization of conventional math. formulas (R.L. '04; '06) - symmetry studies (Cohen, Glashow '06; Hariton, R.L. '07) -...

14. (1) Spontaneous Lorentz breaking in string theory conventional case: gauge symmet. B. Mechanisms for Lorentz breakdown string theory: Lorentz symmetry Kostelecký, Perry, Potting, Samuel ’89; ’90; ’91; ’95; '00

15. (2) Cosmol. varying scalars (e.g., fine-structure parameter) intuitive argument: spacetime small scalar large scalar gradient of the scalar selects pref. direction mathematical argument:  =  (x)... varying coupling , ... dynamical fields Integration by parts: slow variation of  : Kostelecký, R.L., Perry '03; Arkani-Hamed et al. '03; X. Zhang’s talk?

16. Example: Supergravity cosmology N = 4 supergravity in 4 dims. (Cremmer, Julia ’79 ) - unrealistic in detail - but: limit of N = 1 supergravity in 11 dims. - contained in M-theory  can illuminate general features of a promising approach to quantum gravity Bosonic action (one graviphoton excited): explicit form of the functions M and N is known

17. Remark: Kostelecký, R.L., Perry '03; Bertolami, R.L., Potting, Ribeiro '04 global: (k=0) FRW universe (isotropic, homogeneous) - only time dependence, no spatial dependence - F  =0 no e.m. fields, g   S (t ) only scale factor result: analytic solutions for “background” a (t ), b (t ), S (t ) local: excitations of F  on this cosmological background SUGRA modelconventional case compare  time-dependent coupling

18. Other mechanisms for Lorentz violation Noncommutative geometry (QM of spacetime points) Seiberg-Witten:  usual Minkowski coordinates x   SME terms emerge: e.g., Carroll et al. ‘01 Topology (1 spatial dim. is compact: large radius R) Vacuum fluctuations along this dim. have periodic boundary conditions  preferred direction in vacuum  calculation: Klinkhamer ‘00...

19. Example (1): free particles E dispersion relation now contains Lorentz-violating terms:  usual 4-fold degeneracy for is lifted Sample effect: threshold modification in particle reactions C. Phenomenology and Tests

20. kinematical changes in particle collisions: p dependence of E is modified: Energy-momentum conservation:  thresholds may be shifted  decays/reactions normally allowed may now be forbidden  decays/reactions normally forbidden may now be allowed  kinematical modifications in existing effects

21. Vacuum Cherenkov radiation: e  e +   (D. Anselmi’s talk?) - not seen for 104.5 GeV electrons at LEP  can extract bound: certain LV < 10 -11 (Hohensee, R.L., Phillips, Walsworth, PRL ’09) Sidereal variations of the Compton edge:  + e -   + e - - not seen at ESRF’s GRAAL facility  can extract bound: certain LV < 10 -13 (Bocquet et al., PRL ’10; Bo-Qiang Ma’s talk?) GBR measurements (Zi-Gao Dai’s and Xue-Feng Wu’s talks?) UHECR anisotropies (Xiao-Bo Qu’s talk?) GZK cut-off modifications (Xiao-Jun Bi’s talk?) Photon birefringence (Ming-Zhe Li’s and Lijing Shao’s talks?)

22. Conventional electrodynamics: in QED Lagrangian, coupling of E, B fields to electrons is: nontrivial potential A affects, e.g., atomic spectra: - Stark effect - Zeeman effect -... Example (2): corrections to bound-state levels How can Lorentz/CPT breakdown affect matter? SME Lagrangian contains Expect: Lorentz/CPT violation shifts energy levels

23. Antihydrogen spectroscopy: - ALPHA, ASACUSA, ATRAP will trap & study anti H  projected bound: certain LV < 10 -26 GeV (Bluhm, Kostelecký, Russell, PRL ‘99) Clock-comparison type tests: - clock = atomic/nuclear transition  many bounds: certain LV < 10 -20…-30 GeV (many papers; e.g., nEDM, PRL ‘09, EPL ‘10) Muonic Hydrogen/Helium spectrum: - What are the level shifts?  What (muon) bounds can be extracted? (R.L., work in progress)

24. Hydrogen and Antihydrogen spectroscopy Bluhm, Kostelecký, Russell '99 Phillips et al. '01 Penning-Trap experiments Bluhm, Kostelecký, Russell '97; '98 Gabrielse et al. '99 Mittelman et al. '99 Dehmelt et al. '99 Studies of muons Bluhm, Kostelecký, Lane '99 Hughes et al. '00 (g-2) collaboration ‘08 Clock-comparison tests Kostelecký, Lane '99 Hunter et al. '99 Stoner '99 Bear et al. '00 Cane et al. ‘04 Other phenomenological studies performed within SME

25. Satellite-based tests Kostelecký et al. '02; '03 ACES PARCS? RACE? SUMO? OPTIS Tests involving photons and radiative effects Carroll, Field, Jackiw '90 Colladay, Kostelecký '98 Kostelecký, Mewes '01; '02; ‘06; ‘07 Lämmerzahl et al. '03 Lipa et al. '03 Stanwix et al. '05 Klinkhamer et al. '07 Gravity Bailey, Kostelecký '06 Battat et al. ‘07 Müller et al. ‘08

26. Studies of baryogenesis Bertolami et al. '97 Studies of neutrinos Barger, Pakvasa, Weiler, Whisnant '00 Kostelecký et al. '03; '04 Katori et al. '06 Barger, Marfatia, Whisnant ‘07 Kinematical studies of cosmic rays (see many talks at this meeting) Coleman, Glashow '99 Bertolami, Carvalho '00 R.L. '03 Altschul ‘06; ‘07 Studies of neutral-meson systems Kostelecký et al. '95; '96; '98; '00 KTeV Collaboration, Hsiung et al. '99 FOCUS Collaboration, Link et al. '03 OPAL Collaboration, Ackerstaff et al. '97 DELPHI Collaboration, Feindt et al. '97 BELLE Collaboration BaBar Collaboration ‘08

27. Summary presently no credible exp. evidence for Relativity violations, but: (1) various theoretical approaches to quantum gravity can cause such violations ? (2) at low E, such violations are described by SME test framework (eff. field theory + background fields)  (3) high-precision tests (gravity waves, astrophysical studies, satellite missions, atomic clocks, interferometry,...) possible

28. Bounds on SME coeff. for matter ”Data Tables for Lorentz and CPT Violation” arXiv: 0801.0287v4

29. Bounds on photon SME coeff. ”Data Tables for Lorentz and CPT Violation” arXiv: 0801.0287v4