Tests of the Equivalence Principle · 2016-07-27 · Eöt-Wash Gravity Workshop for the American Association of Physics Teacher Meeting in Seattle 2007 3 The Equivalence Principle

Eöt-Wash Gravity Workshop for the American Association of Physics Teacher Meeting in Seattle 2007

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Tests of theEquivalence

PrincipleStephan Schlamminger

with Todd Wagner, Ki-Young Choi, Jens Gundlach and Eric AdelbergerFriday 1/5/2007

AAPT-Visit


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Outline• What is the Equivalence Principle?

• Why do we want to test it?

• How has it been tested?

• The principle of our Apparatus

• What will you see in the lab tour?

• Results


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The Equivalence Principle

Our Current theory of gravity, General Relativity,is based on the Equivalence Principle:

All bodies fall in a gravitational field with the same acceleration regardless of their mass or internal structure.

Einstein realized, that:

A uniform gravitational field is the same as an accelerated reference frame.


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-a

F=-ma

The Equivalence Principle

g

F=mg

Gravitational field g Acceleration a

Inertial mass = gravitational mass, mI=mG for all bodies


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General Relativity and the EPThree classical tests:ØPerihelion shift of MercuryØDeflection of light by the SunØGravitational red shift of light

The last two can be explained and calculated with the EP alone!


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MotivationGR is one of the most essential pillars of modern physics.Ø We should continue to test it.

GR should be combined with quantum mechanics for a full description of Nature.

Ø New theories like string theory, quantum gravity, etc., most of which violate the equivalence principle at small level

Tests like this can be used to find new interactions (“fifth force”)

Tests of the equivalence principle are the most

sensitive probes of fundamental physics.


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Historical overview

Galileo

Newton

Bessel

Potter

EötvösDicke

BraginskyUW

)( 2121

21

aaaa

+−

=η

drop

pendula

Type of experiment

torsionbalance

modulatedtorsionbalance


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1st Tests of the Equivalence Principle

gmF G=

gmma

I

G=

gmma

I

G=

a2a1

gmm

ht

I

G

2=

gmma

I

G=amF I=

h

Time t to fall from h:

1600 Galileo: 1.0)( 212

121 ≈

+−

=aa

aaη


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2nd Generation Tests

G

I

mm

gLT π2=l

Measurement of the swing periods of pendula:

Newton (1686), Bessel (183), Porter (1923)

5102 −≈ xη


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Eötvös Experiments

θω cos2rmF II =

ω

θ

ε

r

)2sin(2

2

θω

εgr

mm

G

I=gmF GG =


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Why a torsion balance?• A violation of the EP would yield to different plumb-line for different materials.

•A torsion balance can be used to measure the difference in plumb-lines:

Torsion fiber hangs like the average plumb line.

Difference in plumb lines produces a torque on the beam.

Eötvös (1922) 9105 −≈ xη


12 Principle of our Experiment

Source Mass

EP-Violating signal

Composition dipole pendulum(Be-Ti)

Rotation1 rev./ 20min

Autocollimator (=optical readout)

1020 - ∞1011 - ∞106 - 107

1 - 104

λ (m)source mass

Milky Way (incl. DM)Sunentire earthlocal masses (hill)

aBe

aTi

13.3min


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20 µm diameter tungsten fiber(length: 108 cm)

tuning screws for adjustingtiny asymmetries

8 test masses (4 Be & 4 Ti )4.84 g each (within 0.1 mg)

5 cm

4 mirrors

EP Torsion Pendulum

frequency: 1.261 mHzquality factor: 4000decay time: 11d 6.5 hrsmachining tolerance: 5 µmtotal mass : 70 g


14 The Apparatus

upper part of the apparatus

on a concrete bridge (not shown)

turntable on air bearing& angle encoder

electrical feedthrough

thermal legs to adjust tilt

rotating adapter pieces

lower part of theapparatus

fiber positioner (x,y,z,φ)rotating vacuum vessel

autocollimatorion pump

(10-5 Pa)

thermal & magnetic shield(non rotating)

pendulummagnetic shield (rotating)


15 The Upper Part of the Apparatus

thermal expansion feet

to level turntable

air bearing turntable

electronics of angle encoder

feedthrough for electric signals

thermal insulation


16 The Lower Part of the Apparatus

vacuum chamber

ion pump

autocollimator

support structure forgravity gradient compensators

gravity gradient compensators


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Systematic Effects

0.3 × 10 -13Tilt

0.3 × 10 -13Magnetic

0.9 × 10 -13Gravitational Coupling

1.7 × 10 -13Temperature

2.2 × 10 -13Total Systematic

3.6 × 10 -13Statistical Uncertainty

0.6 × 10 -13Turntable Rate

(cm/s2)


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Range of a hypothetical “fifth” force (m)

Stre

ngth

rel

ativ

e to

gra

vity

ResultsExcluded

with

95 % confidence


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THE END

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Tests of the Equivalence Principle · 2016-07-27 · Eöt-Wash Gravity Workshop for the American Association of Physics Teacher Meeting in Seattle 2007 3 The Equivalence Principle