Sunday, May 20, 2012

What is time ?

There is an anecdote about a foreigner visiting London asking a man on the street “what is time?” and receiving the answer “I’m sorry, but I am not a philosopher”.

I don’t want to discuss here the philosophical or physical questions of what time is, but rather what we mean by time in telecommunications applications. In particular, we frequently hear the terms “UTC”, “GPS time”, “NTP time”, and “1588 time”, and I would like to clarify what these terms mean.

Everything starts with the question “what is a second?”. Until 1960 the second’s duration was based on the rotation of Earth. Specifically, the second was defined as the unit of time of which there are precisely 24*60*60 =86,400 of them in a mean solar day. Unfortunately, the Earth’s rotation is slowing down due to tidal friction, and so between 1960 and 1967 the second was redefined as a particular fraction of the duration of the year 1900. Since it is hard to reproduce the year 1900 in the lab, the second was finally linked to a stable, reproducible, physical phenomenon, namely the radiation emitted when an electron transitions between the two hyperfine levels of the ground state of the cesium 133 atom. Cesium atomic clocks need only count 9,192,631,770 oscillations and declare that a second has passed. (Cesium is chosen because all of its 55 electrons except the outermost one are in stable shells, minimizing their effect on the outermost electron.)

Even such a stable phenomenon as the hyperfine transition is somewhat subject to variability (due to contaminants, undesired fields, and General Theory of Relativity corrections due to height above sea level) leading to variability on the order of a nanosecond or two per day. In order to remove even this small variability the TAI international time scale (TAI stands for “Temps Atomique International” or International Atomic Time) maintained by the International Bureau of Weights and Measures (BIPM) in Paris, is defined as the weighted average of over 300 atomic clocks located around the world (the higher weightings going to the more stable clocks).

TAI is precisely defined, but has become entirely divorced from the Earth’s rotation. Were we to adopt only TAI the time of day would slowly lose connection with the position of the sun in the sky, and after a long enough time we would be having breakfast at 12 noon. IN order to resynchronize the two definitions of the second UTC is defined. UTC stands for Coordinated Universal Time (the order of letters is a compromise between several languages), and it replaced older time standards such as “GMT”. It is defined in ITU-R Recommendation TF.460-6 to be TAI adjusted by leap seconds introduced to compensate for the changing of Earth’s rotational velocity. When to introduce leap seconds is now determined by the International Earth Rotation and Reference Systems Service (IERS). While leap seconds can be either positive or negative, and can be introduced at the end of any month, there have only been positive ones (corresponding to slowing down of Earth’s rotation) and they have only been introduced on the last day of June or December. There are presently proposals to eliminate leap seconds entirely (in which case TAI would be abolished), and perhaps introduce leap hours should the need arise.

UTC is now exactly 34 seconds behind TAI, because of a 10 second introduced in 1972 when the present system was adopted, and 24 positive leap seconds that have been declared since then. The next leap second will be at the end of June 2012, increasing the difference to 35 seconds.

Actually there are several versions of Universal Time. UT0 and UT1 are found by observing the motion of stars (UT0) or distant quasars (UT1), as well as from laser ranging of the Moon and artificial Earth satellites (such as GPS satellites). UT1R and UT2R are smoothed versions of UT1, filtered to remove periodic and stochastic variations in the Earth’s rotation. UT2R is smoother than UT1, and any variations left in it are because of erratic changes in the Earth’s rotation, due to plate tectonics and climate change.

So, what kind of time do we use in GPS and our time distribution protocols ?

The time of day reported by GPS, which is often called “GPS time”, is not UTC. Every GPS satellite has several on-board atomic clocks, and these clocks are set according to the master clock at the US Naval Observatory in Boulder Colorado. “GPS time” does not include leap seconds, but GPS satellites periodically transmit a UTC offset message for this purpose (the GPS-UTC offset field is 8 bits and can thus accommodate 255 leap seconds, which should be sufficient for several hundred years). Once thus compensated, USNO time is within tens of nanoseconds of UTC. However, it can take over 10 minutes until you receive an offset message.

It is interesting that the on-board atomic clocks must be corrected for relativistic effects. Since the satellites are moving at high speeds with respect to an observer on the ground, the Special Theory of Relativity predicts that the on-board clocks will seem to be running about 7 microseconds per day slower than were they stationary with respect to the observer. On the other hand, the General Theory of Relativity predicts that because the satellite is high above the Earth, and thus experiences a weaker gravitational field, the on-board clocks will seem to be running faster by about 45 microseconds per day. The net relativistic correction is about 38 microseconds per day. After compensating for relativistic effects, the accuracy of time derived from a good GPS receiver is about 50 nanoseconds.

NTP (and that included SNTP) distributes UTC (i.e., it does takes leap seconds into account) and specifies UTC in seconds since Jan 1, 1900. The NTP 64-bit timestamp consists of 32 bits of whole seconds (about 136 years until roll-over) and 32 bits of fractional seconds (about 233 picoseconds of resolution). However, any specific NTP server distributes time according to the stratum of its reference clock. Of course, the time a particular NTP client obtains depends on the network between the client and the NTP server. You can expect an NTP client to be within tens of milliseconds of its server on a LAN, but only 100s of milliseconds of error over the Internet. However, NTP allows a client to track several servers, and thus improve its accuracy.

IEEE 1588 distributes TAI according to UNIX epochs. Since the UNIX time epoch started Jan 1, 1970, 1588 time is now ahead of UTC by 24 seconds (soon to be 25). The 1588v2 10-byte timestamp consists of 48 bits of whole seconds, and 32-bits of nanoseconds. Once again, the precise time accuracy depends on the type of grand master to which the 1588 master is synchronized. The big difference between 1588 and NTP is the possibility of on-path support in the network. If you have Boundary Clocks (BCs) or Transparent Clocks (TCs) in your network, the time error should be very small (perhaps a microsecond or less). 1588 can't simultaneously track multiple masters, but it can choose the best one from a list.

So that's what we mean by time.