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@DavidHammen's answer got me thinking.

GPS time "comes from" (US Naval Observatory) a whole bunch of atomic clocks, in space and on Earth. TAI or International Atomic Time also comes from a whole bunch of atomic clocks, distributed around the Earth.

I'm guessing they are not strictly coupled, but are they "really close" to each other, say on the order of microseconds?

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TL;DR: For all practical purposes except milliarcsecond radio astronomy, TAI and GPS time are separated by exactly 19 seconds.

TAI and GPS time both attempt to represent time as ticked by an ideal clock at mean sea level on the surface of the Earth. Both differ from UT1, time as ticked by the Earth's rotation (this is the source of leap seconds), and because of how they represent time, they also differ very slightly from one another.

GPS time is an operational time scale. Each GPS satellite contains an atomic clock, but with a tick rate that deviates slightly from the standard definition of "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom".

The atomic clocks on GPS satellites are subject to both special relativistic and gravitational effects. The special relativistic effects result from the relative motion of the GPS satellites and a clock on the surface of the Earth. The gravitational (general relativistic) effects result from the altitude at which GPS satellites orbit. To compensate for these effects, the GPS satellites' atomic clocks are intentionally made to tick at a slightly slower rate than is standard (the standard being "9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom").

The goal is to have the tick rate of a GPS satellite as observed from a receiver at sea level be equal to the tick rate of the best atomic clocks, adjusted to sea level. While this is the goal, it is not the reality. The smallish atomic clocks on the GPS satellites aren't as accurate as are the very large atomic clocks maintained by the US Naval Observatory. The GPS satellite atomic clocks are updated regularly, roughly once per day, to satisfy the promised accuracy of GPS receivers.

TAI is an ideal time scale as opposed to an operational time scale. To best represent this ideal, time as ticked by atomic clocks worldwide are averaged over the course of a year, weighted by the accuracies of those clocks. This addresses issues such as tidal effects and subtle changes in elevation. As the most accurate atomic clocks currently are those maintained by the US Naval Observatory, those clocks get more weight as to what constitutes TAI.

The end result is that GPS time and TAI are not separated by exactly 19 seconds. However, except for those who need milliarcsecond pointing accuracy, treating GPS time as being offset from TAI by exactly 19 seconds is more than good enough.

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  • $\begingroup$ There's always more than I expected in your answers, and it's all fascinating! About the "..made to tick at a slightly slower rate than is standard..." to mince words, slower means while they are on the ground, before launch, right? Is this de-tuning of the cesium atoms with some fields, or by heterodyning with an offset oscillator, or the removal of one out of every $n$ ticks? $\endgroup$
    – uhoh
    Commented Jul 9, 2017 at 13:13
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    $\begingroup$ The GPS satellites use a master clock frequency of 10.23 MHz, this is derived from the 9,192,631,770 periods. To compensate the relativistic effects, 10.229999995453 MHz is generated instead. But when the GPS signal is received by a receiver on earth at mean sea level, the signal looks like being based on 10.23 MHz as desired. I think a PLL system is used for generation of that master clock from that atomic clock. See en.wikipedia.org/wiki/Phase-locked_loop $\endgroup$
    – Uwe
    Commented Jul 9, 2017 at 13:53
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From the book GPS Satellitennavigation by Frank Schröder ISBN 3-7723-6692-1: "GPS has it own time scale, it starts with the week 0 at 6th January of 1980. The long term difference between GPS and UTC time should be held less than 1 microsecond (disregarding leap seconds). To acheive this, the atomic clocks of GPS satellites and ground stations are synchronized to less than 20 nanoseconds and the GPS time to UTC time to less than 100 nanoseconds. The GPS ground stations monitors all atomic clocks of the GPS system and UTC for that purpose." "Atomic clocks on earth could be synchronized using GPS to less than 10 nanoseconds difference."
So GPS and TIA clocks are not strictly coupled, but the differences are kept very small.

The differences between atomic clocks on earth on different gravitational potentials are compensated since 1977. After that TAI corresponds to the time at mean sea level. "Due to several relativistic effects, the atomic clocks in the GPS satellites run a little faster, they gain 445 picoseconds per second. To compensate this a master clock frequency of nominal 10.23 MHz has actual 10.229999995453 MHz"
GPS: https://en.wikipedia.org/wiki/Global_Positioning_System#Timekeeping
TIA or TAI: https://en.wikipedia.org/wiki/International_Atomic_Time
UTC: https://en.wikipedia.org/wiki/Coordinated_Universal_Time
Atomic clocks: https://en.wikipedia.org/wiki/Atomic_clock

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  • $\begingroup$ Please add some verifiable links to these statements, otherwise they are completely unsupported. If you got this information from somewhere, you should add a link or reference to its source. If you didn't get this information from anywhere, then... that's not a good way to provide factual statements either! $\endgroup$
    – uhoh
    Commented Jul 9, 2017 at 10:53
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    $\begingroup$ The links are all in the wikipedia articles you mentioned in your question. Regard also the links within the articles itself. $\endgroup$
    – Uwe
    Commented Jul 9, 2017 at 11:07
  • $\begingroup$ OK thanks, it's good to make your answer stand alone, so even if the links are deleted from the question, they can still be found in your answer. So you are saying that the two are within a microsecond of each other only because they both have precisions well below a microsecond? That doesn't rule out another offset, and it doesn't really rule out a slow drift, if for example they are calculated for different gravitational potentials (don't forget general relativity). So an argument based only on precision alone is not "proof" they are the same within a microsecond. It may be true, but... $\endgroup$
    – uhoh
    Commented Jul 9, 2017 at 11:18
  • $\begingroup$ @uhoh The differences between atomic clocks on different gravitational potentials are compensated since 1977. After that TAI corresponds to the time at mean sea level. $\endgroup$
    – Uwe
    Commented Jul 9, 2017 at 11:35
  • $\begingroup$ So both GPS and TAI represent time at mean sea level? Please put all relevant information into the answer, not in comments. Comments should be considered temporary; The information in the answer should stand by itself. Also don't forget the link where the mean sea level information comes from! $\endgroup$
    – uhoh
    Commented Jul 9, 2017 at 11:42

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