Transcript Advances in Precision Tests of General Relativity

Recent Precision Tests of
General Relativity
Thomas P. Kling
Brown Astrophysics Journal Club
August 2008
Department of Physics
Brown APJC – August 2008
Weak Equivalence Principle
Some local frame
&
Should fall with the
same acceleration
Department of Physics
Brown APJC – August 2008
Strong or Einstein
Equivalence Principle
some local frame
in free fall
&
should fall freely
along straight lines,
or all observations
consistent with SR
Department of Physics
Brown APJC – August 2008
Implications for gravity
• Gravity is “curved space-time”
• Gravity is a metric theory
• Freely falling observers
= locally flat region
• Freely falling test bodies fall
along geodesics
Department of Physics
Brown APJC – August 2008
EEP + Ocham’s razor
leads directly to . . .
Rab
1
 R g ab   g ab  8 G Tab
2
Department of Physics
Brown APJC – August 2008
Schiff’s conjecture (1960):
“Any complete, self-consistent
theory of gravity that embodies
WEP necessarily embodies EEP.”
Department of Physics
Brown APJC – August 2008
Combine gravity with
standard model?
Violations of
•Equivalence Principle
•Inverse square law
Department of Physics
Brown APJC – August 2008
Two Projects
• Lunar ranging at
Apache Point
Observatory
Department of Physics
• Rotating Torsion
Balance of Univ.
of Washington
Brown APJC – August 2008
Eöt-Wash Group
Careful
Torsion Balance!
Department of Physics
Brown APJC – August 2008
aN  Be   aN  Ti    0.6  3.1 1015 m/s 2
aW  Be   aW  Ti    2.5  3.5  1015 m/s 2
Department of Physics
Brown APJC – August 2008
Yukawa Potential
< 100 m
– local hill
< 10 km
– bedrock
> 1000 km
– Earth
Department of Physics
Brown APJC – August 2008
Towards galactic center
Best fit (pink):
a   2.1  3.1 1015 m/s2
hypothetical (dashed):
a  20 1015 m/s 2
Department of Physics
Brown APJC – August 2008
Classical Equivalence
Parameter
  Be  Ti    0.3 1.8 10
13
DM ,BeTi   4  7 10
5
Department of Physics
Brown APJC – August 2008
APOLLO Lunar Ranging
A pache
P oint
O bservatory
L aser
L unar-ranging
O peration
Department of Physics
Brown APJC – August 2008
Department of Physics
Brown APJC – August 2008
Basics of LLR
• Apollo missions &
others left Moon
reflectors.
• Measure time of
flight.
• Past 15 years:
about 1-3 cm
precision.
Department of Physics
Brown APJC – August 2008
All about Numbers
• Previous return rates: 0.002 to
0.01 photons return per pulse . . .
Typically get 15 to 40 photons
return per pointing.
• To get mm precision, need about
225 to 1300 photons returning.
Department of Physics
Brown APJC – August 2008
Department of Physics
Brown APJC – August 2008
APOLLO Contributions
• Larger aperture (3.5 m), better
seeing (1.1 arcsecond) means
higher return rate.
• Higher energy laser:
–90 ps FWHM Nd:YAG
–20 Hz & 115 mJ/pulse
• Best return rate: Apollo 15 at
1.33 photons per shot
Department of Physics
Brown APJC – August 2008
Department of Physics
Brown APJC – August 2008
Stuff making you worry
• Tides change surface height ~ 350 mm
• Crustal loading from atmosphere,
ground water, etc. ~ 2-5 mm
• Atmospheric propagation delay must be
modeled
Department of Physics
Brown APJC – August 2008
Murphy et al. 0710.0890v2
Department of Physics
Brown APJC – August 2008
Department of Physics
Brown APJC – August 2008