Einstein’s General Relativity Tested Again, Much More Stringently

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This time it was the gravitational redshift part of General Relativity; and the stringency? An astonishing better-than-one-part-in-100-million!

How did Steven Chu (US Secretary of Energy, though this work was done while he was at the University of California Berkeley), Holger Müler (Berkeley), and Achim Peters (Humboldt University in Berlin) beat the previous best gravitational redshift test (in 1976, using two atomic clocks – one on the surface of the Earth and the other sent up to an altitude of 10,000 km in a rocket) by a staggering 10,000 times?

By exploited wave-particle duality and superposition within an atom interferometer!

About this figure: Schematic of how the atom interferometer operates. The trajectories of the two atoms are plotted as functions of time. The atoms are accelerating due to gravity and the oscillatory lines depict the phase accumulation of the matter waves. Arrows indicate the times of the three laser pulses. (Courtesy: Nature).

Gravitational redshift is an inevitable consequence of the equivalence principle that underlies general relativity. The equivalence principle states that the local effects of gravity are the same as those of being in an accelerated frame of reference. So the downward force felt by someone in a lift could be equally due to an upward acceleration of the lift or to gravity. Pulses of light sent upwards from a clock on the lift floor will be redshifted when the lift is accelerating upwards, meaning that this clock will appear to tick more slowly when its flashes are compared at the ceiling of the lift to another clock. Because there is no way to tell gravity and acceleration apart, the same will hold true in a gravitational field; in other words the greater the gravitational pull experienced by a clock, or the closer it is to a massive body, the more slowly it will tick.

Confirmation of this effect supports the idea that gravity is geometry – a manifestation of spacetime curvature – because the flow of time is no longer constant throughout the universe but varies according to the distribution of massive bodies. Exploring the idea of spacetime curvature is important when distinguishing between different theories of quantum gravity because there are some versions of string theory in which matter can respond to something other than the geometry of spacetime.

Gravitational redshift, however, as a manifestation of local position invariance (the idea that the outcome of any non-gravitational experiment is independent of where and when in the universe it is carried out) is the least well confirmed of the three types of experiment that support the equivalence principle. The other two – the universality of freefall and local Lorentz invariance – have been verified with precisions of 10^-13 or better, whereas gravitational redshift had previously been confirmed only to a precision of 7×10^-5.

In 1997 Peters used laser trapping techniques developed by Chu to capture cesium atoms and cool them to a few millionths of a degree K (in order to reduce their velocity as much as possible), and then used a vertical laser beam to impart an upward kick to the atoms in order to measure gravitational freefall.

Now, Chu and Müller have re-interpreted the results of that experiment to give a measurement of the gravitational redshift.

In the experiment each of the atoms was exposed to three laser pulses. The first pulse placed the atom into a superposition of two equally probable states – either leaving it alone to decelerate and then fall back down to Earth under gravity’s pull, or giving it an extra kick so that it reached a greater height before descending. A second pulse was then applied at just the right moment so as to push the atom in the second state back faster toward Earth, causing the two superposition states to meet on the way down. At this point the third pulse measured the interference between these two states brought about by the atom’s existence as a wave, the idea being that any difference in gravitational redshift as experienced by the two states existing at difference heights above the Earth’s surface would be manifest as a change in the relative phase of the two states.

The virtue of this approach is the extremely high frequency of a cesium atom’s de Broglie wave – some 3×10²⁵Hz. Although during the 0.3 s of freefall the matter waves on the higher trajectory experienced an elapsed time of just 2×10^-20s more than the waves on the lower trajectory did, the enormous frequency of their oscillation, combined with the ability to measure amplitude differences of just one part in 1000, meant that the researchers were able to confirm gravitational redshift to a precision of 7×10^-9.

As Müller puts it, “If the time of freefall was extended to the age of the universe – 14 billion years – the time difference between the upper and lower routes would be a mere one thousandth of a second, and the accuracy of the measurement would be 60 ps, the time it takes for light to travel about a centimetre.”

Müller hopes to further improve the precision of the redshift measurements by increasing the distance between the two superposition states of the cesium atoms. The distance achieved in the current research was a mere 0.1 mm, but, he says, by increasing this to 1 m it should be possible to detect gravitational waves, predicted by general relativity but not yet directly observed.

Sources: Physics World; the paper is in the 18 February, 2010 issue of Nature