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Experimental Search for a Violation of Einstein’s Equivalence Principle
Michael D. Abercrombie, Adam Archibald, Tsitsi Madziwa-Nussinov, Kasey Wagoner, Ramanath Cowsik
Department of Physics & McDonnell Center for the Space Sciences, Washington University, St. Louis, MO 63130
[email protected], [email protected]
Introduction
Optical Lever
The Equivalence Principle (EP) states that a gravitational field is locally equivalent to a
uniformly accelerated reference frame[1]. The EP is a key component of Einstein’s
Theory of General Relativity (GR), however theoretical attempts to unify the Standard
Model and GR predict a violation of the EP at sensitivities beyond current experimental
results[2]. The discoveries of dark matter and dark energy further motivate investigations
of physics beyond the current framework.
Rotations of the balance are measured using a multi-slit optical lever in an autocollimating
arrangement. Angular resolution on the order of nanoradians. An illuminated array of 110 slits
produces an image with peaks spaced 182 μm apart. The image passes through a collimating field
lens and then reflects off the mirrored mass of the balance. The returning beam passes back through
the field lens and is focused on a linescan CCD camera. The centroid of the image, xc, is determined
and the angular displacement, θ = (xc)/2f between the optical axis and the normal of the balance
surface is calculated, where f = 100 cm is the focal length of the collimating lens[7].
In Newtonian terms, this principle requires the equivalence of inertial mass, mi, which
measures an object’s resistance to acceleration, and gravitational mass, mg, which is a
measure of the coupling of the object to an external gravitational field[3]. A result of the
EP is the universality of free fall; all objects fall with the same acceleration in a uniform
gravitational field, regardless of their mass or composition.


GM
F  mi a   2 mg rˆ
r

GM
a   2 rˆ
r
This statement can be tested precisely through torsion balance experiments. Using the
Sun as the attractor, as first performed by Dicke[3] and Braginsky[4], the orientation of a
balance composed as a composition dipole with an azimuthally symmetrical mass
distribution will undergo a diurnal modulation in the case of an EP violation.
A violation of the EP is quantified by the Eötvӧs parameter, η[3]
mg mi 1  mg mi 2
a1  a2
1, 2 

a1  a2  2 mg mi 1  mg mi 2 2


Remote Experimental Laboratory
Plots to the right show position and
temperature data for a fixed mirror test
of the autocollimator with polynomial
drift terms removed. The temperature
dependence illustrates the importance
of thermal stability, particularly at the
experiment signal frequency.
Experiment is located at the Tyson Research Center outside the city of St. Louis in a
bunker built into a hillside. Measurements of seismic and thermal noise in the bunker
interior indicate favorable conditions for sensitive experiments of this type.
Passive and active temperature
control will be implemented. Alternative
component materials may be explored
to increase the thermal inertia of the
autocollimator.
Current Progress
Glitches
• Until recently regularly occurring jolts to
the balance coinciding with chamber
pressure spikes slowed progress
• Pressure spikes found to occur at o-ring
seals where excessive vacuum grease
had been used, the problem has been
resolved
Expected Signal
Experimental Design
The Balance
Magnetic Shielding
• 2 Al disks, 2 SiO2 disks with mass of
10.3 grams, at the ends of a cross
• 4-fold symmetry in mass distribution,
composition dipole
• SiO2 disks mirrored on one side
• Diameter of 50.5 cm, moment of
inertia of ~26000 g cm2
Angular deflection of the balance shown
above. At t = 26.3 hours a ‘glitch’ occurs,
adding energy to the system and altering the
phase of oscillation.
• Balance non-magnetic by design
• Additional precaution to avoid signal
due to time varying magnetic fields
taken by installing mu-metal magnetic
shielding
• Shielding has been constructed and is
ready for installation
Torsion Fiber
Additional Modifications
• Balance suspended from grounded
tungsten fiber of length 115 cm,
diameter 25 μm
• Torsional rigidity of 5.4 10-2 dyne cm
• Natural period of 74 minutes
• Magnetic damping system to reduce
pendular motion
• Picomotor driven top rotary control
• Modifications including balance mass and radius, and fiber length, radius, and
material, can be easily implemented once initial results are obtained.
• Increasing intensity of autocollimator light source will improve image obtained
from the balance mirror
Vacuum Chamber
• Reduces noise due to collisions with
air molecules
• Ion pump maintains chamber
pressure at ~10-9 torr
The work shown here has been funded in part by the National Science Foundation.
The thermal noise amplitude spectral density of a
mechanical oscillator with the properties of our torsion
balance according to the fluctuation-dissipation theorem
is given by[8]:
 4k T

1

xTh     B
2
2
 Q 1   2 0  1 Q 2 

12

The readout level is given by the autocollimator viewing a fixed mirror. Diurnal peak attributed to daily
temperature variation, this limits the sensitivity of our measurement. The low frequency resolution of
a multi-slit autocollimator with an internal reference has recently been illustrated[9] , and
implementing such a design may improve the readout level at the expected signal frequency.
The expected signal shown is for an EP violation at the level of η = 10-12. The torque, τs, acting on
the balance due to such a signal varies with the azimuth, ϕ, and zenith, φ, angles of the sun.
 s  GM  mg r
s    2 
sin  sin 

 R  
References
[1] E. Adelberger et al., Progress in Part. And Nuc. Phys. 62, 102-134 (2009).
[2] T. Damour, Classical Quantum Gravity 13, A33 (1996).
[3] P. G. Roll, R. Krotkov, and R. H. Dicke, Ann. Phys. (N.Y.) 26, 442 (1964).
[4] V. B. Braginsky and V. I. Panov, Zh. Eksp. Teor. Fiz. 61, 873 (1971).
[5] S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, and E. G. Adelberger,
Phys. Rev. Lett. 100, 041101 (2008)
[6] T.A. Wagner, S. Schlamminger, J.H. Gundlach, and E.G. Adelberger, Class.
Quantum Grav. 29, 184002 (2012).
[7] R. Cowsik et al., Rev Sci Instrum. 78, (3):035105 (2007)
[8] P. R. Saulson, Phys. Rev. D, 42, 2437-45 (1990)
[9] T.B. Arp, C. A. Hagedorn, S. Schalamminger, and J. H. Gundlach. Rev. Sci. Instrum.
84, 095007 (2013)