Gravitational experiments testing Lorentz symmetry

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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
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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

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Background and Motivation

• Lorentz symmetry the symmetry of Special
  Relativity
• Two kinds of transformations Rotations and
  Boosts

• Motivation
• There could be Lorentz violation coming from a
  fundamental theory

General Relativity
Standard Model
Standard Model
General Relativity
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!
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Standard-Model Extension (SME)

• General framework for studying Lorentz violation

(Kostelecký Potting PRD 1995 Colladay
Kostelecký PRD 97, 98 Kostelecký PRD 04)

• Idea (qualitative)

All possible forms of Lorentz violation
Background fields interacting with known matter
Standard Model
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
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Subset - Minimal SME
coefficients for Lorentz violation (aµ, bµ?, cµ?,
kµ? , )
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
expansionPhD thesis
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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, 1800
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• 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

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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
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Spontaneous Lorentz-symmetry breaking
However
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

Fluctuations, includes Nambu-Goldstone modes
vev
Key feature Lorentz violation is dynamical ?
Conservation laws are unaffected
Bianchi identities are safe
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Gravity sector of the SME

• Basic idea

General Relativity

All possible (pure-gravity) Lorentz-violating
terms

• 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

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• Assume spontaneous Lorentz-symmetry breaking
• Ensures consistency with Riemann geometry

• Challenging theoretical task
  construct the effective Einstein
  equations

Details Bailey, Kostelecký PRD 06

• Final result in weak-field limit
  effective
  linearized field equations
• Remaining quantities , ,

Ordinary matter
Lorentz-violating corrections
9 coeffs, controls the dominant Lorentz violation
Upshot can calculate observables, compare
specific models
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Comparison to well-known test models

• Parametrized Post-Newtonian (PPN) formalism
  (Will, Nordtvedt APJ 70s)
• 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

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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)

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Lunar laser ranging

• Idea measure distance to Moon
  by reflecting laser light off
  mirrors
  

• Many tests of gravity
  (30 years)
• Accuracy lt 1 cm
• Basic observable
  oscillations in lunar distance r

r
Images http//physics.ucsd.edu/tmurphy/apollo/ap
ollo.html http//ilrs.gsfc.nasa.gov/
(LLR Review Muller et al, gr-qc/0509114)
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• One primary oscillation, from Lorentz violation,
  is at twice the orbital frequency

(Bailey, Kostelecký PRD 06)
Lorentz-violating background (Represent
heuristically as red arrows)
Analysis also exists for satellites e.g., LAGEOS,
GALILEO,
unmodified orbit
Dominant effects
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• Recent paper bounding SME gravity coefficients
• Uses 35 years of data

(J. Battat, C. Stubbs, J. Chandler (Harvard), PRL
2007)
T Murphy (UCSD), APOLLO A Comprehensive Test of
Gravity via Lunar Laser Ranging, Monday, July 7,
1600

• Ongoing APOLLO project (NM) (Murphy, Stubbs,
  Adelberger)
• ongoing, achieves lt 1 mm sensitivity

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Gravity Probe B (GPB)
(Image http//einstein.stanford.edu/)
GPB gyroscope (superconducting spinning sphere)
(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

(Schiff 1960)
GPB collaboration Everitt, Kaiser, Overduin,
(http//einstein.stanford.edu/)
(Bailey, Kostelecký 06)
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• 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
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• 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 s
Along Earths spin axis Z
Along perpendicular axis n
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Summary

• Lorentz symmetry
• foundation of our current fundamental theories

General Relativity
Standard Model
Lorentz symmetry

• Recent interest in testing Lorentz symmetry
• Signal of Lorentz violation new physics
  (beyond Standard Model and
  General Relativity)

• Space-based tests
• - Lunar Laser Ranging, Gravity Probe B,
  Time-delay effect, Binary pulsars

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• A recent New Scientist cover

General info on Lorentz violation and the SME
http//www.physics.indiana.edu/kostelec/faq.html