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Climbing with Atomic Clocks

16-Nov-2006

A century ago Einstein predicted that clocks run slower the faster their speed. Another prediction from his general theory of relativity is that clocks run slower the stronger the gravity.

It follows then that clocks run a tiny bit faster the higher they are above the earth (as gravity weakens). You could prove this relativistic time dilation effect for yourself by taking a sufficiently accurate clock to a high altitude for a long duration and precisely measuring to see if it gains a tiny bit of time. Don't laugh; it's been done and the theory works.

Now there are several ways to take an atomic clock to high altitude: airplane, rocket, satellite, and mountain. Over the decades scientists have performed wonderful relativity experiments using each of these methods. Planes are rather expensive and a rocket or satellite is out of the question. So that leaves me with the mountain. Fortunately, there are many high mountains near Seattle.

I can think of two ways to carry an atomic clock up a mountain: climb or drive. After trying for a few minutes, I'd say climbing is out of the question. But I had to be sure. Time for plan B.

Tom checks if climbing with an atomic clock is possible:

Yes, but is that a grin or a grimace?

Hewlett Packard model 5071A:

Rear and side views (cesium beam tube visible inside):

Two more shots while we're at it:

Oh, and for long trips remember to carry external power; lots of power:

Footnotes:

• [1] speed: The time dilation is approximately -½v²/c² according to the special theory of relativity.
• [2] gravity: For low altitudes the general relativistic effect is approximately +gh/c².
• [3] weakens: The force is inverse squared so the acceleration of gravity is ¼ as much 2x away. A one meter change in altitude changes the frequency of a clock by approximately 10-16 (a ratio equivalent to one second in 300 million years or about 9 ps/day).
• [4] tiny: This key sentence contains five unknowns: how accurate, how high, how long, how precise, and how much. How much depends on how high and how long. The quality of your experiment depends on how accurate the clock is and how precise you can measure.
• [5] works: Relativistic time dilation has been demonstrated with clever physics experiments to varying degrees of accuracy from the 1960's to the present.
• [6] mountain: Mt Rainier is just 100 miles away; the summit is 14410 ft (4392 m).
• [7] airplane: The two classic examples of this are the 1971 Hafele-Keating round-the-world experiment and the 1975 flying clock experiments by C.O. Alley.
• [8] rocket: The best example is Gravity Probe A, the 1976 Scout D rocket experiment by R.F.C. Vessot.
• [9] satellite: An early example is the 1977 NTS-2 pre-GPS satellite experiment.
• [10] plan: Project GREAT: General Relativity Einstein/Essen Anniversary Test.
• [11] power: A 5071A uses about 50 W at 24 VDC (~2 A). The internal 2.5 Ah battery is guaranteed for 45 minutes. A pair of external 90 Ah batteries as shown should keep the clock running for ~40 hours. Three sleds are for 3 clocks; or one clock for five days. On belay!