Equivalence Principle and Gravitational Redshift

Michael A. Hohensee,1,* Steven Chu,1,† Achim Peters,2 and Holger Mu¨ ller1

1Department of Physics, University of California, Berkeley, California 94720, USA

2Institut fu¨r Physik, Humboldt-Universita¨ t zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany

(Received 17 February 2011; published 11 April 2011)

We investigate leading order deviations from general relativity that violate the Einstein equivalence

principle in the gravitational standard model extension.We show that redshift experiments based on matter

waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along

with matter-wave, microwave, optical, and Mo¨ssbauer clock tests, yields comprehensive limits on spinindependent

Einstein equivalence principle-violating standard model extension terms at the 106 level.

Gravity makes time flow differently in different places.

This effect, known as the gravitational redshift, is the

original test of the Einstein equivalence principle (EEP)

[1] that underlies all of general relativity; its experimental

verification [2–6] is fundamental to our confidence in the

theory. Atom interferometer (AI) tests of the gravitational

redshift [4,6] have a precision 10 000 times better than tests

based on traditional clocks [3], but their status as redshift

tests has been controversial [7]. Here, we show that the

phase accumulated between two atomic wave packets in

any interferometer equals the phase between any two

clocks running at the atom’s Compton frequency following

the same paths, proving that atoms are clocks.

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes:

Visualizing the Curvature of Spacetime

Robert Owen,1 Jeandrew Brink,2 Yanbei Chen,3 Jerey D. Kaplan,3 Georey Lovelace,1 Keith D.

Matthews,3 David A. Nichols,3 Mark Scheel,3 Fan Zhang,3 Aaron Zimmerman,3 and Kip S. Thorne3, 4

1Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853

2National Institute of Theoretical Physics, Private Bag X1 Matieland, Stellenbosch, South Africa, 7602

3Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, CA 91125

4 Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research

Centre at Stellenbosch University, Marais Street, Stellenbosch 7600, South Africa

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split

into an "electric" part Ejk that describes tidal gravity and a \magnetic" part Bjk that describes

differential dragging of inertial frames. We introduce tools for visualizing Bjk (frame-drag vortex

lines, their vorticity, and vortexes) and Ejk (tidal tendex lines, their tendicity, and tendexes), and

also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to

elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.