Transcript Testing Relativity in the 21st Century

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
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
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
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!
• General framework for studying Lorentz violation
Standard-Model Extension (SME)
(Kostelecký & Potting PRD 1995; Colladay & Kostelecký PRD 97, 98; Kostelecký PRD 04)
• Idea (qualitative):
General
Relativity
+
Standard Model
+
All possible forms of
Lorentz violation
Background fields
interacting with known
matter
• Idea (technical details):
SME – effective field theory with lagrangian:
Usual SM fields
Usual GR lagrangian
All possible Lorentz-violating terms
constructed from SM & GR fields
and background coefficients
Subset - “Minimal SME”
coefficients for Lorentz violation (aμ, bμν, cμν, kμν ,… )
– 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 expansion=PhD thesis
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
minimal
SME possibilities explored
SME Theory
• of
classical
electrodynamics
• 1000+ papers • QED: stability, causality, renormalizability
• topics include: • gravitational couplings
• connection to NCQFT, SUSY, …
N Russell (NMU),
“Constraining spacetime
torsion”
• spontaneous
Lorentz-symmetry
breaking
use of SME results), Tuesday, 18:00
• Torsion couplings
(makes
• 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”
Gravity and Lorentz violation
Result 1: Lorentz breaking  diffeomorphism breaking*
Coefficients control Lorentz and diffeomorphism breaking
Explicit Lorentz breaking
– prescribed, nondynamical coefficients
– Produces modified conservation laws
angular momentum
energy & momentum
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
However…
Result 3: Spontaneous symmetry breaking saves geometry!
(Kostelecký PRD 04)
Spontaneous Lorentz-symmetry breaking
• Tensor fields
acquire vacuum expectation values
• E.g., vector field
Potential
• Expand about minimum
vev
Fluctuations, includes NambuGoldstone modes
Key feature: Lorentz violation is dynamical
→ Conservation laws are unaffected
Bianchi identities are safe
V
Gravity sector of the SME
• Basic idea
General Relativity
+
All possible (pure-gravity)
Lorentz-violating terms
• Basic Riemann spacetime lagrangian
Ricci tensor
(Kostelecký PRD 04)
:
Weyl tensor
Einstein-Hilbert
term (GR)
Leading Lorentz-violating couplings
Contains ordinary matter,
dynamics for coefficient fields
• Leads to modified Einstein equations:
• 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
Comparison to well-known test models
• Parametrized Post-Newtonian (PPN) formalism
(Will, Nordtvedt APJ 70’s)
– 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
Gravitational experiments probing SME coefficients
• Celestial Mechanics
lunar/satellite ranging
(Details: Bailey, Kostelecký PRD 06)
(J. Battat, C. Stubbs, J. Chandler (Harvard), PRL 2007)
binary pulsar
perihelion shift of planets
• 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)
Today
Lunar laser ranging
• Idea: measure distance to Moon
by reflecting laser light off mirrors
• Many tests of gravity
(30+ years)
• Accuracy < 1 cm
• Basic observable:
oscillations in lunar distance r
r
Images: http://physics.ucsd.edu/~tmurphy/apollo/apollo.html
&
http://ilrs.gsfc.nasa.gov/
(LLR Review: Muller et al, gr-qc/0509114)
• 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
unmodified orbit
satellites
e.g.,
LAGEOS,
GALILEO, …
Dominant effects:
• Recent paper bounding SME gravity coefficients
(J. Battat, C. Stubbs, J. Chandler (Harvard), PRL 2007)
• Uses 35 years of data
T Murphy (UCSD), “APOLLO: A Comprehensive Test of
Gravity via Lunar Laser Ranging”, Monday, July 7, 16:00
• Ongoing APOLLO project (NM) (Murphy, Stubbs, Adelberger…)
– ongoing, achieves < 1 mm sensitivity
Gravity Probe B (GPB)
(Image: http://einstein.stanford.edu/)
(Image: http://einstein.stanford.edu/)
GPB gyroscope
(superconducting
spinning sphere)
• General Relativity predicts
– spin precession in curved spacetime (Schiff 1960)
• Idea of GPB: measure precession
1) geodetic precession
2) dragging of inertial frames (gravitomagnetic)
GPB collaboration: Everitt, Kaiser, Overduin, … (http://einstein.stanford.edu/)
• Also: Lorentz-violating precession
(Bailey, Kostelecký 06)
• 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
• Standard general relativity contributions
• Dominant SME contributions
Coefficients referred to standard SME Sun-centered frame
Along orbital angular momentum axis σ
Along Earth’s spin axis Z
Along perpendicular axis n
• Assuming GPB angular resolutions of order 10-4’’ C-1
can obtain 10-4 on
coeffs
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
• A recent New Scientist cover…
General info on Lorentz violation and the SME:
http://www.physics.indiana.edu/~kostelec/faq.html