Transcript Tests of Lorentz symmetry with gravitationally coupled atoms

Gravitational Experiments
and Lorentz Violation
Jay D. Tasson
V. Alan Kostelecký
Indiana University
outline
• introduction
– motivation
– Standard-Model Extension (SME)
• recent gravitational tests
• Lorentz violation
in matter-gravity couplings1,2
– theoretical analysis
– new sensitivities in gravitational experiments
1) Kostelecký, Tasson PRL ’09
2) Kostelecký, Tasson in preparation
motivation
• General Relativity and the Standard Model
describe known physics.
• new physics at the Planck scale (
)
• options for probing such high energies
– galaxy-sized accelerator
– suppressed effects
in sensitive experiments
Lorentz violation
• can arise in theories of new physics
• difficult to mimic with conventional effects
Standard-Model Extension (SME)
effective field theory which contains:
• General Relativity (GR)
• Standard Model (SM)
• arbitrary coordinate-independent Lorentz violation
L SME = L GR + L SM + L LV
• as a subset, other test frameworks
Lorentz-violating terms
• constructed from GR and SM fields
• parameterized
by coefficients for Lorentz violation
• samples
¹º
s R¹ º
¹
¹
Ãa¹ ° Ã
Colladay & Kostelecký PRD ’97, ’98 Kostelecký PRD ’04
What is Lorentz violation?
¹ ¹ ° 5° Ã
consider the flat spacetime example Ãb
under an observer Lorentz transformation (rotation)
¹
physics is unchanged
What is Lorentz violation?
¹ ¹ ° 5° Ã
consider the flat spacetime example Ãb
under a particle Lorentz transformation (rotation)
¹
Lorentz violation!
ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
Tests based on
ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
Tests based on
Results to date
ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
Tests based on
Results to date
Many more tests proposed.
ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
Tests based on
Results to date
Many more tests proposed. See Mike Seifert’s talk.
Ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
•
•
•
•
•
•
•
•
•
•
•
spin-polarized solids (Adelberger, Heckel, …)
clock comparisons (Gibble, Hunter, Romalis, Walsworth, …)
CMB analysis
astrophysical photon decay
cosmological birefringence
pulsar-timing observations
particle traps (Dehmelt,Gabrielse, …)
resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
neutrino oscillations (LSND, MINOS, Super K, …)
muons (Hughes, BNL g-2)
meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
Ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
•
•
•
•
•
•
•
•
•
•
•
spin-polarized solids (Adelberger, Heckel, …)
clock comparisons (Gibble, Hunter, Romalis, Walsworth, …)
CMB analysis
astrophysical photon decay
cosmological birefringence
pulsar-timing observations
particle traps (Dehmelt,Gabrielse, …)
resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
neutrino oscillations (LSND, MINOS, Super K, …)
muons (Hughes, BNL g-2)
meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
Ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
•
•
•
•
•
•
•
•
•
•
•
spin-polarized solids (Adelberger, Heckel, …)
clock comparisons (Gibble, Hunter, Romalis, Walsworth, …)
CMB analysis
astrophysical photon decay
cosmological birefringence
pulsar-timing observations
particle traps (Dehmelt,Gabrielse, …)
resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
neutrino oscillations (LSND, MINOS, Super K, …)
muons (Hughes, BNL g-2)
meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
Ongoing searches with...
L LV = L puregravit y + L fermion + L phot on + : : :
• spin-polarized solids (Adelberger, Heckel, …)
•• only
~1/2 of lowest order
couplings explored
clock-comparisons
(Gibble, Hunter, Romalis, Walsworth, …)
• use gravitational couplings and experiments to get more!
• CMB analysis
• astrophysical photon decay
• cosmological birefringence
• pulsar-timing observations
• particle traps (Dehmelt,Gabrielse, …)
• resonant cavities (Lipa, Mueller, Peters, Schiller, Wolf, …)
• neutrino oscillations (LSND, MINOS, Super K, …)
• muons (Hughes, BNL g-2)
• meson oscillations (BABAR, BELLE, DELPHI, FOCUS, KTeV, OPAL, …)
gravitationally coupled fermions1
= e¹ a eº b´ ab
Ã!
1 ¹
a
ºa ¸
b
= 2 i e a Ã(° ¡ cº ¸ e e b° : : : ) D ¹ Ã
¡ Ã(m+ a¹ e¹ a ° a + : : : )Ã
vierbein g¹ º
L fer mion
coefficients for Lorentz violation
• particle-species dependent
additional coefficients for LV,
non-minimal torsion, …
covariant derivative for spacetime as well as U(1)
Idea :
• new gravitational couplings provide new LV sensitivity
• explore a¹ coefficient unobservable in flat spacetime
Kostelecký, Tasson PRL ’09
1) Kostelecký PRD ’04
gravitationally coupled fermions1
= e¹ a eº b´ ab
Ã!
1 ¹
a
ºa ¸
b
= 2 i e a Ã(° ¡ cº ¸ e e b° : : : ) D ¹ Ã
¡ Ã(m+ a¹ e¹ a ° a + : : : )Ã
vierbein g¹ º
L fer mion
coefficients for Lorentz violation
• particle-species dependent
additional coefficients for LV,
non-minimal torsion, …
covariant derivative for spacetime as well as U(1)
Idea :
• new gravitational couplings provide new LV sensitivity
• explore a¹ coefficient unobservable in flat spacetime
Kostelecký, Tasson PRL ’09
What is the form of
a¹ ?
Where does it come from?
1) Kostelecký PRD ’04
Lorentz-symmetry breaking
• explicit
– Lorentz violation is a predetermined property
of the spacetime
– inconsistent with Riemannian geometry
• spontaneous
– LV arises dynamically
– consistent with geometry
– possible in numerous underlying theories:
string theory, quantum gravity …
• upon investigating spontaneous breaking we find
Minkowski-spacetime coefficients
a¹ = a¹ +
1
º
2®a h¹ º
¡
1
º
4®a¹ h º
characterize couplings
in dynamical theories
countershaded Lorentz violation
a¹ = a¹ +
unobservable shift
in fermion phase
•
1
º
®a
h
¹º
2
¡
1
º
®a
h
¹
º
4
observable effects
via gravity coupling
a¹ for matter is unobservable in flat-spacetime tests
• observable a¹ effects are suppressed
by the gravitational field
•
a¹ could be large (~ 1eV)
relative to existing matter-sector bounds
c.f. b¹ < 10¡ 30 GeV
path to experimental analysis
Lfermion
expand to desired order in LV and gravity
field redefinition
L’fermion
Euler-Lagrange eq.
HRelativistic
relativistic quantum experiments
Foldy-Wouthuysen expansion
HNonRel
non-relativistic quantum experiments
inspection
LClassical
non-relativistic quantum experiments
classical experiments
relativistic hamiltonian
Hrel=
H ( 0 ; 0 ) + 1 i ( h j k + h 0 0 ´ j k ) ° 0 ° k @j + i h j 0 @j ¡ 1 m h 0 0 ° 0 + 1 T ® ¯ ° ² ® ¯ ° ± ° 5 ° 0 ° ± + 1 @j h 0 k ² j k l ° 5 ° 0 ° l + 1 i @j h j 0
2
2
8
4
2
+ 1 i [ @j h 0 0 + @k h j k ] ° 0 ° j + a 0 ¡ m e 0 + 2 i c ( j 0 ) @j ¡ [m c 0 0 ¡ i e j @j ] ° 0 ¡ f j @j ° 0 ° 5 + [ a j + i ( c 0 0 ´ j k + c j k ) @k ] ° 0 ° j
4
+ [ ¡ b0 ¡
2 i d ( j 0 ) @j ] ° 5 + [ i H 0 j + 2 g j ( k 0 ) @k ] ° j ¡
[ b j + i ( d j k @k + d 0 0 @j ) ¡
0 j
1 m gk l 0²
j k l ]° 5 ° °
2
( 1; 1) j
( 1; 1) 0
) @k ° 5 ° j + i h
@ ¡ 1 m h 00
°
j 0
2
i
h
i
( 1; 1)
( 1; 1)
0° j +
j h
1a h
1 ak h
~
+ 1 i (h
+ h 00
´j
¡
°
¡
b
+
b
0
0
0
j 0 °5
j k
2
2 j
2
j k
h
³
´
1c
+ ~
bj ¡ 1 bj h 0 0 ¡ 1 bk
h 00 ´ j k ¡ h j k + 2c ( l 0) h l 0 ´ j k + 1 ck 0 h j 0 ¡ 1 cj 0 h k 0
0
0
2
2
2
4
4
³
´
i
h
i
h
i
¡ 1 c l j h 0 0 ´ l k + h l k ¡ c k l h l j ° 0 ° k @j ¡ 2 i c~( j 0 ) + c ( k 0 ) h j k + c j k h k 0 @j ¡ m c~0 0 + 1 c 0 0 h 0 0 + 2 c ( j 0 ) h j 0 ° 0
2
2
h
i
h
i
2 i d~( j 0 ) + d ( k 0 ) h j k + d ( j k ) h k 0 ° 5 @j + i d~0 0 + 1 d 0 0 h 0 0 + 2 d ( k 0 ) h k 0 ° 0 ° 5 ° j @j
2
h
³
´
i
+ i d~k j + 1 d k 0 h j 0 ¡ 1 d j 0 h k 0 ¡ 1 d 0 0 h j k ¡ 1 d l j h 0 0 ´ l k + h l k ¡ d k l h l j ° 0 ° 5 ° k @j
4
4
2
2
h
i
h
i
+ m d~j 0 ´ j k ¡ 1 d j 0 h j k ¡ d k j h j 0 ° 5 ° k ¡ 1 i m d j 0 h k 0 ² j k l ° l i e~j + 1 e 0 h j 0 ¡ 1 e j h 0 0 ¡ e k h j k ° 0 @j
2
4
4
2
h
i
¡ m e~0 + m e j h j 0 + 1 m e 0 h j 0 ° 0 ° j + ¡ f~j + 1 f 0 h j 0 ¡ 1 f j h 0 0 ¡ f k h j k ° 0 ° 5 @j
4
4
2
h
i
h
³
´
+ 2 g~ k ( j 0 ) ¡ 1 g l 0 0 h l 0 ´ j k ¡ g l ( j 0 ) h l k ¡ 2 g k ( l 0 ) h l j + 2 g k ( j l ) h l 0 ° k @j + i g~ l 0 0 ´ j k ¡ 1 g~ k l j ¡ 1 g k 0 0 h 0 0 ´ j l ¡ h j l
4
2
2
¡ ( 1 H k l ² j k l + m dj 0)° 5° j ¡
2
i ² j l m ( g l 00 ´ k m + 1 g l m k
2
h
0 ° k @j + a~ ¡ a j h
)
°
+
a~ j ¡
0
j 0
k
i
h
h j k ° 0 ° 5 ° k + i c~0 0 ´ j k + c~k j +
¡ 1 g n 00 h l n ´ j k ¡ 1 g j k 0 h l 0 + 2g l ( n 0) h n 0 ´ j k ¡ 1 g k l 0 h j 0 + 1 g k l j h 00 + 1 m i g j k 0 h k 0 ° 0 ° j + 1 m g j k 0 h l 0 ² j k l ° 5
2
4
8
4
2
8
i
h
i
j
j
+ 1 gk l n h
¡ 1 g k n j h l n ² k l m ° 5 ° m @j ¡ 1 m g~ j k 0 + g k m 0 h
+ gj k m h m 0 ² j k l ° 0° 5° l
n
m
2
2
2
h
i
h
i
¡ 1 H~ j k ¡ H j m h k n ¡ 1 H j k h 0 0 ² j k l ° 5 ° l ¡ i H~ j 0 + 1 H k 0 h j k + H j k h k 0 ° j
2
2
2
h
i
h
i
i 1 h 0 0 h 0 0 ´ j k + 1 h l 0 h l 0 ´ j k ¡ 1 h 0 0 h j k ¡ 3 h j l h l k ° 0 ° k @j ¡ i h k 0 h j k @j ¡ m 1 h 0 0 h 0 0 + 1 h j 0 h j 0 ° 0
8
2
4
8
8
2
experimental implications
³
´
T
S
F3 = ¡ mT g ¡ 2g® aTt + m
a
+ :::
mS t
P
T
S and T denote
a¹ = w= p;n;e N waw
¹
composite coefficients
for source and test respectively
• gravimeter tests
• exotic tests
– charged matter
• tests of Weak Equivalence
– antimatter
– laboratory
– higher generation matter
– space based
• light-travel tests
• Lunar laser ranging
• …
experimental implications
³
´
T
S
F3 = ¡ mT g ¡ 2g® aTt + m
a
+ :::
mS t
P
T
S and T denote
a¹ = w= p;n;e N waw
¹
composite coefficients
for source and test respectively
• gravimeter tests
• exotic tests
– charged matter
• tests of Weak Equivalence
– antimatter
– laboratory
– higher generation matter
– space based
• light-travel experiments
• Lunar laser ranging
• …
Sun-centered frame
• standard frame
for reporting SME bounds
V© = 10¡
• boost and rotation of test
4
annual & sidereal variations
lab tests
differential acceleration for test-particles A and B
• monitor acceleration
of one particle
over time
gravimeter
• monitor relative
behavior of particles
- EP test
• frequency and phase
distinguish from other
effects
experimental sensitivities
• one bound1 based on torsion-pendulum data2
• excellent prospects for remaining 11 coefficients
in current and future experiments
[] = crude estimate for existing experiment
{} = crude estimate for future experiment
1) Kostelecký, Tasson PRL ’09 2) Schlamminger et al. PRL ’08
experimental sensitivities
• one bound1 based on torsion-pendulum data2
• excellent prospects for remaining 11 coefficients
in current and future experiments
• multiple experiments needed for
maximum number of sensitivities
• other coefficients yield additional effects1,3
[] = crude estimate for existing experiment
{} = crude estimate for future experiment
1) Kostelecký, Tasson PRL ’09 2) Schlamminger et al. PRL ’08 3) Kostelecký, Tasson in prep.
Summary
Lorentz violation introduces qualitatively new signals in
gravitational experiments
– several experiments performed
– much remains unexplored
– comparatively large
– detectable in current and planned tests
– multiple tests needed for maximum independent
sensitivities