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A Space-Based Optical Kennedy-ThorndikeExperiment Testing Special Relativity

Deborah N. Aguilera1, Alexander Milke2, Norman Gurlebeck2, Thilo Schuldt1,2,

Sven Herrmann2, Klaus Doringshoff3, Ruven Spannagel1,2,

Claus Lammerzahl2, Achim Peters3, Bernd Biering1, Hansjorg Dittus1, Claus Braxmaier1,2

1German Aerospace Center (DLR), Institute for Space Systems, Bremen, Germany2Center for Applied Space Technology and Microgravity (ZARM), University of Bremen, Germany

3Institute for Physics, Humboldt-University Berlin, Germanyemail: deborah.aguilera@dlr.de

Abstract

We propose a small satellite mission that aims for testing the foundations of special relativity by performing a Kennedy-Thorndike (KT) experiment. Apotential boost dependence of the velocity of light is measured by comparing a length reference (i.e. a highly stable optical resonator) with a molecularfrequency reference. By employing clocks with 10−16 frequency stability at orbit time (90 min) and by integration over 5000 orbits (2 years mission lifetimewith 50% duty cycle) a 1600-fold improvement in measuring the Kennedy-Thorndike coefficient is targeted, compared to the current best terrestrial test.

1. Test of special relativity

The Robertson-Mansouri-Sexl theory [6, 7] allows for deviations from the pre-dictions of special relativity, i.e., a speed of light that depends on the velocityof the frame, ~v, and the orientation of the frame, θ:

c(θ,~v)

c0= 1 + (β − α− 1)

~v 2

c 2︸ ︷︷ ︸

Kennedy−Thorndike

+

(1

2− β − δ

)~v 2

c 2sin2 θ

︸ ︷︷ ︸

Michelson−Morley

The Kennedy-Thorndike [5] and the Michelson-Morley experiment togetherwith the Ives-Stilwell experiment are sufficient to validate special relativity.

2. The Kennedy-Thorndike coefficient

The KT coefficient (β − α− 1) from above is obtained from data analysis thatcompares a rod length to the ticking rate of a clock as a function of velocity.The history of KT experiments on ground extends over 80 years and the pro-posed mission intends to lower δc/c down to 10−18.

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020

year

1e-18

1e-16

1e-14

1e-12

1e-10

1e-08

δ c

/c

Kennedy-Thorndike 1932

Hills & Halls 1990

proposed

Braxmaier et a

l. 2002

Tobar et a

l. 2010

Wolf et a

l. 2003

Figure 1: History of KT experiments performed on ground so far[4, 1, 3, 2].

3. Why to go to space?

The motivation of performing the experiment in space offers many advantagesover ground experiments

•Quiet environment: e.g. no acustic and seismic vibration

• Elimination of mechanical distortions due to gravity

•Higher orbital velocity: spacecraft moves 16 times faster than a groundlaboratory

•Faster orbital period → longer integration time: 90 vs 1440 min

Figure 2: Science case: change of satellite velocity relative to CMB inearthbound experiments

Improvement of KT experiment only possible in space!

4. Payload configuration

A modern KT experiment is based on a length based clock optical cavity, anatomic/molecular clock iodine spectroscopy, and a beat frequency what is acounter to measure with varying satellite velocity.

Figure 3: Schematic representation of a KT experiment

5. Length clock

Optical cavities made of Ultra Low Expansion (ULE) material are in use inmany laboratories worldwide. At the Humboldt University Berlin we havebeen working with such cavities to set up lasers with relative frequency sta-bilities in the low 10−15 range.

, 13

, 13

Figure 4: Optical cavities - Diagram and pictures

6. Atomic clock

The Iodine standard is an ultrastable molecular clock with 3×10−15 stabilityand using modulation transfer spectroscopy (MTS). It is currently operatedat 532 nm wavelength. By switching to a nearby line at 508 nm wavelengthwe expect an improvement of a factor of 10. Compact setup: 25 cm x 55 cmx 10 cm.

Schematic of the spectroscopy setup on EBB-Level

Figure 5: Iodine standard - Diagram and picture

7. Mission overview

The proposed mission has the following characteristics

• circular orbit, LEO, sun-synchronous (thermal)

• 650 km altitude & 90 min orbital period

• passively spin-stabilized

• small satellite technology (max. 60 kg payload, overall mass: 150 kg, maxpower: 1500 W)

• 2 years mission lifetime (longer → higher sensitivity)

• 10−16/orbit stability of both clocks

• Iodine-Reference compared with Cavity-Reference (Beat frequency 508nm/1016 nm)

8. Summary and Outlook

Proposed missions with KT experiment

• can test the symmetry of space-time comparing the relative variations oftime and length with velocity at orbital frequency

• can improve the KT coefficient 1600 times compared to ground

• can demonstrate technology first in space applicable to other missions (pre-cision laser with 10−16 stability, thermal control to 0.1 µK)

AcknowledgementsThe development of the iodine frequency references on EBB and EM levelis supported by the German Space Agency Deutsches Zentrum fr Luft- undRaumfahrt (DLR) with funds provided by the Federal Ministry of Economicsand Technology (BMWi) under grant numbers 50QT1102 and 50QT1201.

References

[1] C. Braxmaier et. al. Phys. Rev. Lett., 88(1):010401, 2002.

[2] M. E. Tobar et. al. Phys. Rev. D, 81(2):022003, 2010.

[3] P. Wolf et al. Phys. Rev. Lett., 90(6):060402, 2003.

[4] D. Hils and J. L. Hall. Phys. Rev. Lett., 64:1697–1700, 1990.

[5] R. J. Kennedy and E. M. Thorndike. Phys. Rev., 42:400–418, 1932.

[6] R. Mansouri and R. U. Sexl. Gen. Rel. and Grav., 8:497–513, 1977.

[7] H. P. Robertson. Rev. Mod. Phys., 21:378–382, 1949.