Pop quiz, hotshot: Your really long optical fiber isn’t letting (much) light through, so there’s obviously a break in it somewhere. You need to fix the fiber. What do you do? What…do…you…do?
Obviously, shooting the hostage is not an option here. The fiber is probably buried underground, so it would be really helpful to know where the break is, to a resolution of at least the location of the nearest manhole, so you can go in, find the fault and splice the fiber. The solution is an optical time-domain reflectometer (OTDR). You send a pulse of light down the fiber and measure the delay of any reflection, because breaks (and other faults) tend to reflect the light, as any change in index of refraction causes a reflection. Since the speed of light transmission in a medium is simply c/n, if you can measure the return time of the pulse you can figure out how far way the fault is.
To do this in a helpful way, though, one needs to locate the fault to within a few meters, and light in a fiber will be traveling at around 200,000 km/sec, or 5 nanoseconds per meter, which means we need timing at a level at around the 10 nanosecond level. That sounds like the precision realm of commercial atomic clocks, and that sounds expensive — that kind of clock can run you several tens of thousands of dollars. But there’s an important distinction: an atomic clock gives precision long-term timing, and we don’t need that. If our optical fiber is 100 km long, a round-trip signal will take no longer than a millisecond. In other words, we don’t need a clock that will add fewer than 10 nanoseconds in a day, we just need one that won’t add more than 10 nanoseconds in a millisecond. There is almost 8 orders of magnitude difference in performance in those two systems. Put another way, we don’t want to measure the time, we want to measure a short time interval. A timing error of 10 nanoseconds in a millisecond is 10 parts-per-million, a performance that is easily reached by a cheap quartz oscillator (Here’s a cheap system that does 2 parts per million along with some extra functions we wouldn’t need). As long as the oscillator is calibrated, such a device would be just fine for this task.
Another example of this time interval application is a GPS receiver. These receivers compute your location based on the time difference between signals from multiple satellites, but since the satellites have precise clocks on them and broadcast that information, the receiver only has to measure the difference in those time tags. GPS satellites orbit at altitudes of around 20,000 km, but it’s the differences in the distances that are important to us. Overhead satellites are closest, while ones nearer the horizon are farther away, by a few thousand km. That’s a factor of ~10 greater distance than our OTDR signal (though our speed is very close to c), and we want somewhat better timing, so that puts our needs closer to 0.1 ppm, but this is also achievable, though undoubtedly a little more expensive. The great part about GPS receivers, though, is that you can actually use the timing signals to synchronize a local clock, and gain the benefit of the atomic time on the satellites, which is synchronized to the earth’s atomic time, UTC. (You might recall that such synchronization was initially — and incorrectly — blamed for timing errors in the superluminal neutrino story a little over a year ago. It’s actually quite good.)
