Improved Tests of the Equivalence Principle

...Using TorsionBalances

Frank Fleischer,University of Washington

11 May 2011

The Equivalence Principle (EP)

Fundamental assumption of general relativity

locally a homogenous gravitational field looks the same as a uniform acceleration of the frame

usually tested via the universality of free fall (UFF)

Motivation: Why Test It?

Test the foundation of general relativity

More interesting: assume that classical gravity obeys the EP, then

use EP tests as extremely sensitive probes for new scalar or vector interactions!

Many ideas for physics beyond the standard model introduce such interactions.

Torsion balance experiments provide stringent limits on such models!

New Forces?

Examples for possible couplings: to baryon number B, B – L (L being the lepton number) ...

parameterization:

with a hypothetical ”charge”

B - L is especially interesting – conserved in GUTs

Testing the EP with Torsion Balances

To test the equivalence principle with a torsion balance, a couple things are needed:

a torsion balance with a composition dipole an attractor producing a force with a horizontal

component modulation of the signal

Eötvös parameter

Possible Attractors

nearby attractor

earth

sun

center of galaxy

need to providerotation

use theearth'srotation

Also important: these attractors differ in composition!

Using the Earth as a Source Mass

If the EP is violated, ”down” is not a unique direction

➔ depends on the ratio of gravitational and inertial mass!

Using the Earth as Source Mass

fiber Simplified model of a

pendulum for EP tests

➔ Balance twists if the two force vectors are not parallel, i.e. if EP is violated or gravitational field is not uniform.

Choice of Test Body Materials

Obvious constraints: solid, non-magnetic

For complete coverage of the parameter space, more than one test-body pair / attractor combination is necessary.

Large differences in number of neutrons and nuclear binding energy give greater sensitivity.

x10-2 Be PE Al Ti Cu Pt

Be -12.65 -3.80 -1.58 -1.25 4.40

PE -12.63 8.85 11.07 11.40 17.05

Al -3.59 9.03 2.22 2.54 8.20

Ti -1.33 11.29 2.26 0.32 5.98

Cu -1.01 11.62 2.59 0.33 5.65

Pt 4.55 17.18 8.15 5.89 5.56

Early Torsion Balance Experiments

Loránd Eötvös (1922):

various test-body pairs in the field of the earth

e.g. Roll, Krotkov, Dicke (1964):

sun as attractor, feedback

Braginsky, Panov (1972):

sun as attractor, no feedback

Reminder:

State of the Art

Our group at UW started looking for EP violations after a reanalysis of the Eötvös data by Fischbach et al., claiming evidence of a ”fifth force” with finite range.

Most recent published experiment*:

rotating torsion balance employing different source masses

local topography earth sun galaxy

sensitive to forces with λ from ~1m upward * Schlamminger et al. 2009

State of the Art

5 cm

70g pendulum,suspended by a 20μm thick, 1.08 m long tungsten fiber

Screws to reduce residual coupling to gravitational gradients

Eight test bodies(4 Be & 4 Ti) or (4 Be & 4 Al)4.84g each

Design minimizes coupling to gravitational gradients:4-fold azimuthal symmetry and top-bottom reflection symmetry

State of the Art

High precision turn table for continuous smooth rotation.

State of the Art

Reminder:

EotWash group (2009):

Next Generation EP Tests

Two possibilities to push the limits of torsion balance experiments for EP tests:

Increase the signal by using more sensitive test body material pairs

Reduce the noise floor

Combine both? Would be ideal, of course - but difficult.

Increasing the Sensitivity

Significant gain in sensitivity possible with a ”hydrogen-rich” test body

Promising material: UHMWPE – Ultra-High Molecular Weight PolyEthylene

x10-2 Be PE Al Ti Cu Pt

Be -12.65 -3.80 -1.58 -1.25 4.40

PE -12.63 8.85 11.07 11.40 17.05

Al -3.59 9.03 2.22 2.54 8.20

Ti -1.33 11.29 2.26 0.32 5.98

Cu -1.01 11.62 2.59 0.33 5.65

Pt 4.55 17.18 8.15 5.89 5.56

Increasing the Sensitivity

Significant gain in sensitivity possible with a ”hydrogen-rich” test body

Promising material: UHMWPE – Ultra-High Molecular Weight PolyEthylene

Problems / challenges:

Precision in machining Low density (0.94 g/cm3) Large thermal expansion coefficient Dimensional stability when ”baking”? Gold coating?

Increasing the Sensitivity

Will Terrano designed and built a test pendulum to learn about the specific problems of this choice of material:

”test bodies” mounted near their center of mass to avoid big moment changes by thermal expansion

completely encapsulated in aluminum

First test planned: investigate the dimensional stability – determine moments, bake out and check for changes.

Reducing the Noise

An inherent limitation for torsion balance experiments is thermal noise

Cooling helps in two respects:

lower temperature T Higher values of Q possible at low temperatures:

values of order 105 reported with metal fibers at 4.2K

Reducing the Noise

An inherent limitation for torsion balance experiments is thermal noise

Cooling helps in two respects:

lower temperature T Higher values of Q possible at low temperatures:

values of order 105 reported with metal fibers at 4.2K

Build a cryogenic torsion balance toinvestigate operation at low temperature!

cooling to 4K: factor ~60

factor ~100

A Cryogenic Torsion Balance

Use a pulse tube cooler for cooling to cryogenic temperatures

Problem: vibrations!

Isolate the cold head vibrationally from the cryostat:

Separate wall mount Only flexible connections

(edge-welded bellows, flexible copper heat links)

Air springs for vibrational isolation

cold head

fiber

magneticdamper

aut

oco

llim

ato

rla

ser

bea

m

thermalshields

flexibleheatlinks

pump portsuperinsulation

Some Pictures...

cold headsupport

openedcryostat(without thermalshields)

Current Status – Cooling

By now, several thermal cycles.

Min. temperature: ~5.5K

Cool-down time: ~2 days

Warming up takes a similar amount of time.

Even slightly exceeds design values!

Current Status – Noise

Designed and built test pendulums to explore the noise spectrum.

small gravitational multipole moments mass similar to our latest EP test

pendulum explore cryo-compatible design – lots of

engineering challenges

Current Status – Noise

Current noise level slightly above thermal noise.

Excess noise due to magnetic effects?

At current level at least, no extra noise from cold head visible!

RT thermalnoise for Q=3000

6K thermalnoise for Q=200000

What About Q?

Even if without having reached thermal noise yet, it is possible to check the quality factor Q.

A lot of the improvement in thermal noise level is expected to come from a better Q!

➔ Measure Q at room temperature and when cold.

Much of the expectedimprovement comes from Q

Measuring Q

At room temperature:

Q as expected, ~3000

Still the same at 5K!

Possible limiting factor: eddy current damping?

Applying an additional magnetic field (a few times the earth's field):

Q ~ 1100

t [s]

angl

e [m

rad]

Need magnetic shielding!

Record free oscillation, fit exp. decaying sine wave:

Next Steps

Magnetic shield has just been completed and installed.

Should hopefully open the way to higher Q and bring down the noise.

With substantially improved noise, will need to develop more sensitive optical readout.

Physics with ColdWash

Current setup has potential for an order of magnitude improvement in limits on long-range EP violations.

Design a EP test pendulum for operation at low temperature.

Implement a tilt monitoring (and, if necessary stabilization) system – very important systematic!

More magnetic shielding?

Study other possible systematics.

Physics with the current setup:

Summary and outlook

Significant (order of magnitude) improvements over our current limits are possible.

We are following a two-fold approach to achieve higher sensitivity to EP violating forces:

increase signal (choice of test body materials) reduce noise (operation at low temperature)

Both paths are being pursued – hydrogen-rich test bodies and a cryogenic torsion balance under development.