introduction motivation (i): philosophical necessity physics is an experimental science → solid...
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Introduction
Motivation (i): philosophical necessity
physics is an experimental science
→ solid experimental confirmation of foundations of physics is crucial
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Motivation (ii): discovery potential
various approaches to physics beyond theStandard Model („quantum gravity“) canaccomodate tiny violations of Relativity
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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
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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
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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
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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
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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
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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)
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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)
- . . .
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(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
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(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?
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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...
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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
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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
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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?)
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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
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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)
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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
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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
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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
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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
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Bounds on SME coeff. for matter”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4
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Bounds on photon SME coeff.”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4