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Matter-gravity couplings and Lorentz
breaking
Jay D. Tasson
Carleton College
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outline
• ‘basic’ symmetry violation example
• field redefinitions and the a coefficient
• what are matter gravity couplings?
• analysis of a laboratory experiment
• experimental opportunities past, present, future
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Is this obvious?
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Is this obvious?Jay’s answer is no… for 2 reasons:
1. It’s wrong2. Viable alternatives existed
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Q: Is there a ‘preferred frame’ in this model?
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Q: Is there a ‘preferred frame’ in this model?A1: It depends on your definition of apreferred frame.A2: Yes, the coordinates that diagonalize thismatrix
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an SME-style approach
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an SME-style approach
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example: block on inclined plane
Solving for the motion of the particle subject to the constraint
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example: block on inclined plane
Solving for the motion of the particle subject to the constraint
Why a normal m here?
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example: block on inclined plane
Solving for the motion of the particle subject to the constraint
Answers:
1. if anisotropy enters here in the same way,there will be no observable effects
2. inertial mass and gravitational mass areseparate concepts
3. anisotropy is observable only comparatively
4. anisotropy here is the role of the scoefficients in the gravity sector (see Q. Bailey’stalk), which are in general different from c
5. coordinate changes like the following canmove this sort of Lorentz violation around
Kostelecky, JT PRD ‘11, Sec. IIC2
6. existence of c and s destroys the notion of a‘preferred frame’
Why a normal m here?
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observer rotation
Solving for the motion subject to the constraint
Same acceleration down the ramp (magnitude of ) as before via therotation matrix acting on
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particle rotation
Solving for the motion subject to the constraint
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Spacetime Symmetries and Classical Mechanics,Bertschinger, … Tasson, Symmetry 11, 22 (2018)
K04Gravity, Lorentz Violation, and the Standard Model,Kostelecký, Phys. Rev. D 69, 105009 (2004)
BK06Signals for Lorentz Violation in Post-Newtonian Gravity, Bailey, Kostelecky, Phys. Rev. D 74, 045001 (2006).
KT11Matter-Gravity Couplings and Lorentz Violation,Kostelecký, Tasson, Phys. Rev. D 83, 016013 (2011)
FGT17Superconducting-Gravimeter Tests of Local Lorentz Invariance,Flowers, Goodge, Tasson, Phys. Rev. Lett. 119, 201101 (2017)
references
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field redefinition
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field redefinition
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field redefinition
If is constant removes it
If then removes it
If is spacetime dependent choosing egremoves one component
And it’s not a big surprise...
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relativistic gravity and fermion fields• fermions live on a Minkowski tangent space
linked via the vierbein
• gravitationally coupled Dirac Lagrangian
• covariant derivative for gravity as well a U1
general …
Lorentz a,b,c,…
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minimal gravity sector
conventionalpure-gravity
gravity sector: dynamics of gravitational field alone
● minimal post-Newtonian effects originate from● experiments that involve the gravitational field are relevant● particle species independent by definition
minimal Lorentz violation
source
source
BK06
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matter sector vs. gravity sector
conventional gravitationally coupled matter sector
matter sector: kinematics and interactions of particles
KT11
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matter sector vs. gravity sector
conventional gravitationally coupled matter sector
matter sector: kinematics and interactions of particles
● source-dependent field distortions● test-particle dependent responses● additional coefficient structures
Lorentz violation
KT 2011
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why constant coefficients in flat spacetime?• maintain energy and momentum conservation
(cf Kostelecký's Cutlass1)• could be leading term of a series expansion of some other function• could arise via explicit Lorentz breaking
– LV is a predetermined property of the spacetime
• be regarded as the vev of spontaneous breaking
– LV arises dynamically– fluctuations are not considered– unspecified dynamics coefficient field → general results
coefficient field
coefficient for Lorentz violation (vev)
fluctuations about vev
1) Tasson Rep. Prog. Phys. 2014
cf electroweak breaking
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why constant coefficients in flat spacetime?• maintain energy and momentum conservation
(cf Kostelecky's Cutlass)• could be leading term of a series expansion of some other function• could arise via explicit Lorentz breaking
– LV is a predetermined property of the spacetime
• be regarded as the vev of spontaneous breaking – LV arises dynamically– fluctuations are not considered– unspecified dynamics coefficient field → general results
coefficient field
coefficient for Lorentz violation (vev)
fluctuations about vev
Explicit Lorentz-symmetry breaking and/orignoring the fluctuations is typically in conflict withthe Riemann geometry on which our gravity theoryis based!
Explicit Lorentz-symmetry breaking and/orignoring the fluctuations is typically in conflict withthe Riemann geometry on which our gravity theoryis based!
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some simplifying procedures & assumption• write coefficient fields as vev (coefficient) + fluctuations
• notation warning: avoid things like (why?)
• work to first order in the coefficients
• work at linear order in the fluctuations
• assume the vevs are constant in asymptotically inertialCartesian coordinates
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proceeding generally with the matter sector• fluctuation problems in 2 places
• vary with respect to x
• vary with respect to the metric
• if minimal gravity couplings:― Bianchi satisfied to post newtonian order 3 w/o fluctuations― to find to order 3 impose on system―match gravity sector via field redefinition
• if nonminimal couplings:― impose diffeomorphism invariance on general― use to get
KT11
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acceleration of a test particle T
Play
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lab testsacceleration of a test particle T
• monitor acceleration of
one particle over time
→ gravimeter
• monitor relative behavior
of particles → EP test
• frequency and phase
distinguish from other
effects
• monitor acceleration of
one particle over time
→ gravimeter
• monitor relative behavior
of particles → EP test
• frequency and phase
distinguish from other
effects
annual variations
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• species dependence
species dependence
Multiple experiments needed for a maximum
number of independent sensitivities.
Multiple experiments needed for a maximum
number of independent sensitivities.
S and T denote
composite coefficients
for source and test
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experiments
• lab tests (Earth source)
- gravimeter
force comparison
free fall
- Weak Equivalence Principle (WEP)
force comparison
free fall
• space-based WEP
• exotic tests
- charged matter
- antimatter
- higher-generation matter
• solar-system tests
- laser ranging
- perihelion precession• pulsar tests
• light-travel tests
- time delay
- Doppler shift
- red shift• clock tests
- null redshift
- comagnetometers• ...
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Experiment list
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Warning: theorist doing experiments ahead
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overview of Lorentz violation/SMETasson, Rep. Prog. Phys. 77, 062901 (2014), arXiv:1403.7785
http://iopscience.iop.org/0034-4885/77/6/062901/
– simple examples
– general overview
– video abstract
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Drew Down sets up an experiment by hanging a pair of masses
from identical springs in his lab in Springville IA. While the springs
are identical the masses are not. One is niobium while the other is
polypropylene. The springs are initially drawn down the same
distance meaning they have the same conventional mass to zeroth
order in Lorentz violation. He plans to monitor their relative stretch
as a function of time to achieve constraints on Lorentz violation.
hypothetical experiment
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Drew Down sets up an experiment by hanging a pair of masses
from identical springs in his lab. While the springs are identical the
masses are not. One is niobium while the other is polypropylene.
The springs are initially drawn down the same distance meaning the
bobs have the same conventional mass to zeroth order in Lorentz
violation. He plans to monitor their relative stretch as a function of
time to achieve constraints on Lorentz violation.
hypothetical experiment
Notes: - with LV stretch varies annually/sidereally - acceleration is approximately 0- one of these would be a force comparisongravimeter- if he compares one to the other, it’s a forcecomparison WEP test
Where could we find a relevant theoryanalysis?
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Drew Down sets up an experiment by hanging a pair of masses
from identical springs in his lab. While the springs are identical the
masses are not. One is niobium while the other is polypropylene.
The springs are initially drawn down the same distance meaning the
bobs have the same conventional mass to zeroth order in Lorentz
violation. He plans to monitor their relative stretch as a function of
time to achieve constraints on Lorentz violation.
hypothetical experiment
Notes: - with LV stretch varies annually/sidereally - acceleration is approximately 0- one of these would be a force comparisongravimeter- if he compares one to the other, it’s a forcecomparison WEP test- KT11 Sec. VIIE says“The predicted motion depends on thedetails of the configuration, so a unifiedanalysis for all force-comparison WEP testsis impractical...”
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Solution: difference of 2 force
comparison gravimeter results from
Sec. VIIC, or Flowers, Goodge,
Tasson PRL ‘17 (FGT17)
hypothetical experiment
FGT Eq. 3
FGT Eq. 5
annualsidereal
Take data, Fourier transform (or fit etc.) at these frequencies → measure these amplitudes
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Solution: difference of 2 force
comparison gravimeter results from
Sec. VIIC, or Flowers, Goodge,
Tasson PRL ‘17 (FGT).
hypothetical experiment
FGT Eq. 3
FGT Eq. 5
annualsidereal
Take data, Fourier transform (or fit etc.) at these frequencies → measure these amplitudes
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connection to SME coefficients
gravity-sector LV (KT Eq. 142)
FGT Eq. 4
matter LV associated with Earth (KT table IV)
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connection to SME coefficients
gravity-sector LV (KT Eq. 142)
FGT Eq. 4
matter LV associated with Earth (KT table IV)
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some numbers
Springville 42 degrees North→
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phase
T=0 at 07:35 (Universal Time Coordinate) UTC Mar 20, 2000 … at least according to NOAA
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phase
Springville 91.44 West or
to Sun
noon
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results
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results
Where would we look to find out if wehave interesting sensitivity?
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results
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results
Thinker Education
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results
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a more likely result
1. ‘max reach analysis’: let one coefficient be nonzero at a time
2. report all of the raw bounds
3. ‘coefficient separation’: obtain independent sensitivities to individual coefficients by combining measurements of several different linear combinations
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Cute Newtonian SME examples can be constructed
Lorentz violation in matter-gravity couplings introduces qualitatively
new signals in a wide variety of gravitational experiments
a considerable space of experiments can/have been done
analogies with matter-sector Lorentz violation can be used to test
additional physics
Summary