Chin-Wen Chou, David Hume, Till P. Rosenband, David J. Wineland
Albert Einstein's theory of relativity forced us to alter our concepts of reality. One of the more startling outcomes of the theory is that we have to give up our notions of simultaneity. This is manifest in the so-called twin paradox in which a twin sibling who travels on a fast moving rocket ship returns home younger than the other twin. This time dilation can be quantified by comparing the tick-rates of identical clocks that accompany the traveler and the stationary observer. Another consequence of Einstein's theory is that time runs more slowly in a deeper gravitational potential. For example, if two identical clocks are separated vertically by 1 km near the surface of the earth, the higher clock emits about 3 more second-ticks than the lower one in a million years. These consequences of relativity have been observed with atomic clocks at high velocities and with large changes in elevation. Previously, smaller relativistic shifts could only be seen in short-distance γ-ray Mössbauer spectroscopy measurements. Here we compare two optical atomic clocks to observe time dilation from relative speeds of less than 10 m/s and changes in height of less than 1 m. This sensitivity to small relativistic clock shifts is enabled by recent accuracy improvements, as well as the high quality factor (Q = 4.2×1014) in the clock's observed atomic resonance. The clocks were compared through a 75 m length of optical fiber, and in the future this technique may be extended to the field of geodesy where measurement of the geoid-height with high spatial resolution is an area of active investigation with applications in geophysics and hydrology.