Introduction

Motivation (i): philosophical necessity

physics is an experimental science

→ solid experimental confirmation of foundations of physics is crucial

Motivation (ii): discovery potential

various approaches to physics beyond theStandard Model („quantum gravity“) canaccomodate tiny violations of Relativity

common approach (top-down):

scan predictions of a given theory for sub-Planckeffects 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

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

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?

VaryingScalars?

Other?

Sec C:Phenomenologyand exp. tests astrophysics

Penning traps

other

quantum optics

satellites

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 m1 = antiparticle mass

m2

- if CPT is broken ??? (in SME, m1 = m2 is still OK)- usual CPT test for Kaons uses model only valid for Kaon interferometry precludes comparison with other tests

How can one get a test framework for Lorentz violation?

underlying physics (strings, loop gravity,noncommutative geometry, SUGRA, ...)

effective theory (SME test model)

E

~EPlanck

~ELHC

Problem 1: many theory approachesProblem 2: low-E limit can be unclear?

SME must be constructed by hand guided by gen. principlesAdvantage: generality; independence of underlying physics

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)

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)

- . . .

(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

(2) Cosmol. varying scalars (e.g., fine-structure parameter)

intuitiveargument:

spacetime

small scalar

large scalar

gradient of thescalar selectspref. 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?

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...

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

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

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?)

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

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)

Hydrogen and Antihydrogen spectroscopyBluhm, Kostelecký, Russell '99Phillips et al. '01

Penning-Trap experimentsBluhm, Kostelecký, Russell '97; '98Gabrielse et al. '99Mittelman et al. '99Dehmelt et al. '99

Studies of muonsBluhm, Kostelecký, Lane '99Hughes et al. '00(g-2) collaboration ‘08

Clock-comparison testsKostelecký, Lane '99Hunter et al. '99Stoner '99Bear et al. '00Cane et al. ‘04

Other phenomenological studies performed within SME

Satellite-based testsKostelecký et al. '02; '03ACESPARCS?RACE?SUMO?OPTIS

Tests involving photons and radiative effectsCarroll, Field, Jackiw '90Colladay, Kostelecký '98Kostelecký, Mewes '01; '02; ‘06; ‘07Lämmerzahl et al. '03Lipa et al. '03Stanwix et al. '05Klinkhamer et al. '07

GravityBailey, Kostelecký '06Battat et al. ‘07Müller et al. ‘08

Studies of baryogenesisBertolami et al. '97

Studies of neutrinosBarger, Pakvasa, Weiler, Whisnant '00Kostelecký et al. '03; '04Katori et al. '06Barger, Marfatia, Whisnant ‘07

Kinematical studies of cosmic rays (see many talks at this meeting)Coleman, Glashow '99Bertolami, Carvalho '00R.L. '03Altschul ‘06; ‘07

Studies of neutral-meson systemsKostelecký et al. '95; '96; '98; '00KTeV Collaboration, Hsiung et al. '99FOCUS Collaboration, Link et al. '03OPAL Collaboration, Ackerstaff et al. '97DELPHI Collaboration, Feindt et al. '97BELLE CollaborationBaBar Collaboration ‘08

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

Bounds on SME coeff. for matter”Data Tables for Lorentz and CPT Violation”

arXiv: 0801.0287v4

Bounds on photon SME coeff.”Data Tables for Lorentz and CPT Violation”

arXiv: 0801.0287v4