# [time-nuts] NPR Story I heard this morning

Tom Van Baak tvb at LeapSecond.com
Mon Nov 3 15:54:38 EST 2014

```> Yes,  A story about time and frequency standards.  They actually used
> numbers like 10E16 in the story.  Apparently at that level your clock can
> measure a change in elevation of a few centimeters because of the
> relativistic effects of the reduced gravity field in just a few cm.

Hi Chris,

That's correct. When it comes to frequency standards the official SI second is defined only for sea level. We know time and frequency are "bent" by speed or gravity; time is the integral of frequency; and frequency is a function of height (h) by approximately gh/c². It's that simple. But it's a very tiny effect.

Planet gravity fields decrease quadratically over large distances (1/R²) but approximately linearly near the surface. So here on Earth, with g = ~9.8 m/s² and c = ~300,000 km/s, frequency increases by about 1e-18/cm, or 1e-16/m, or 1e-13/km. This is called gravitational time dilation, or blueshift.

Now, for amateurs like us who just make things at home or buy and repair atomic clocks on eBay, numbers like 1e-18 and 1e-16 are completely out of range: that's what government labs are for. But the 1e-13 number is interesting, and approachable -- especially if you live near a tall mountain.

If you take a 1e-14 stable cesium clock up 1 km, it will run fast by about 1e-13 (in frequency) and thus it will gain about 10 ± 1 ns per day (in time, or phase) compared to a clock left down at home. These days, time differences at the nanosecond level are easily measurable -- so that's what I did with http://leapsecond.com/great2005/

Of course, NIST & USNO always have much better clocks than we do, so they can measure the effect of smaller elevation changes, over smaller time scales. Just amazing. Maybe we'll be able to buy an optical clock on eBay 20 years from now.

Note that their clocks are not (yet) portable and consequently you can make a more accurate gravitational time dilation / general relativity measurement at home by taking vintage hp 5071A cesium beam microwave clocks up a tall mountain than they can with record-setting strontium optical clocks inside a NIST building.

Essentially, if you take a clock to high altitude for a weekend you create a super-duper blueshift "microscope". Instead of unimaginably small numbers like 1e-18, I went up about 1340 meters (instead of just 1 cm) and I stayed up there about 42 hours (instead of one second). Thus my cm-second "magnification factor" was 1340 * 100 * 42 * 3600 = 20 billion! That reduces a crazy tiny number like 1e-18 to a real, tangible, measurable, fun-with-family, DIY time dilation number like 2e-8, or 20 ns.

/tvb

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