Last week I gave a seminar at Augusta State University called “It’s About Time” and promised to write up a summary of the talk, so here it is (sans a few cartoons and some data I don’t have permission to show). Some of the material I have discussed before, and some has been covered recently at the Virtuosi and, previously, at Uncertain Principles. Both discussions are good, but as I had noted for the former post, there are some subtleties to the discussion that one might not be expected to know if one isn’t exposed to timekeeping on a semi-regular basis.
The Chicago Way
I raised the questions asked in Chicago’s 1969/1970 song “Does Anybody Really Know What Time It Is?” the lyrics to which includes the followup question, “Does Anybody Really Care?”
Does Anybody Really Know What Time It Is? No.
Does Anybody Really Care? Yes.
(at which point I paused for comedic effect, as if this were the end of the talk. I crack myself up sometimes)
The basic point of the first answer is that there is no predefined “truth” for what time it is. There are choices/decisions that go into that determination, so the time is a voted quantity in addition to being a measured quantity — measurement limitations are not the only reason the answer is “no”.
For the second question, which is the whole motivation for precision timekeeping, the answer had better be “yes” or else there is no justification for performing the task. The motivation for the navy (both here and abroad) for timekeeping is navigation, and this dates back to Harrison and the “longitude problem”. To know your latitude it’s fairly straightforward — the north star is almost due north, so finding its angle in the sky relative to the horizon gives you that information, or you can get the information from the declination of the sun at noon. But the longitude isn’t so easy; for a long time navigation was done by dead reckoning, but with increased ocean travel and the reach of the British Empire there was too much “dead” in dead reckoning, and so the British navy sought a way to improve navigation.
If you know your longitude and the time, you can watch stars as they transit a line passing overhead, north-to-south, i.e. a meridian (the act of which is called a transit in astronomy) and make a log of this, noting the time. A ship captain with such an almanac can make a similar measurement aboard a ship. If a star is overhead at a certain time on land, and the ship’s captain sees this occurring an hour earlier onboard his ship, he knows his longitude is 15º west of that fixed point, because the earth rotates 15º per hour (approximately), and the limitation here is how well you can keep time. Each minute you are off translates to 15 nautical miles at the equator; this gives you an idea of what “precise time” meant back in the 1700’s.
Today precise navigation is also driven by precise time, in the form of the Global Positioning System. Signals from GPS satellites are received and the time differences measured; if you have 4 signals you can solve for your 4 unknowns (your three spatial and your time coordinate). Since these are EM signals and for light a nanosecond is a foot (or 3 nanoseconds is a meter), precise time at the nanosecond-ish level is required for meter-ish level geolocation.
There are other applications as well: various people want to time-tag events, from commerce to people doing Very-Long-Baseline Interferometry; you have communications efforts — sending ones and zeroes requires having synchronized clocks to properly measure the ones and zeroes, and secure communication with frequency-hopping requires good clocks so that sender and receiver “hop” at the same time. So many have timing needs at assorted levels of precision and accuracy.
What do we mean by time
When people ask what is time they are often asking a philosophical question; time is an abstraction rather than a thing, so a standard physics answer is time is what is measured by a clock. The way we measure this is by measuring the phase of an oscillator, i.e. we count ticks.
\(omega = frac{dphi}{dt} \) or in integral form, \(phi = int_{} {omega} dt \)
The first clock we have is the earth rotation coupled with measuring the position of the sun, often by the shadow it casts. There is an immediately obvious problem with this: the analemma, the figure-8-ish figure we get if we note the sun’s position at the same time every day. The sun isn’t overhead at noon each day by the way we currently tell time. The sun’s apparent travel through the sky isn’t at a constant east-west rate because of the tilt of the earth, and the rotation angle to where the sun would be overhead isn’t the same because we travel an ellipse and out speed is greater when we are closer to the sun. These effects accumulate, increasing and decreasing, over the course of the year, and are summed up in the equation of time.
But the sun could be overhead each day at noon, if we chose to define time that way — this is our first example of “what time is it” being a subject to a vote. We have the option of having the sun be overhead and a day that is not 86,400 seconds long (varying by up to ~30 seconds) or we can have a nominally constant length of day, in which case the sun can be up to ~15 minutes on either side of being overhead. We have chosen the latter.
Even with that choice, though, we have the problem with variations in the earth’s rotation rate, so that even with our definitions of time interval, then length of a day varies by a few milliseconds, and when the accumulated phase difference gets near a second, we add a leap second to our clocks. The rotation rate varies because of changes to the earth’s moment of inertia (i.e mass moves around — e.g. snowpack in the mountains vs water in the ocean) or issues of angular momentum (weather systems rotate, and that angular momentum is traded with the earth), and an overall tidal braking from the moon. But many of these effects are unpredictable, so we can’t schedule leap seconds very far in advance.
Next up: Building a Better Clock