# Continued calibration of atomic clocks

First off I am not well versed in physics, but as I understand things the second is defined by the ceasium fountain clock which is calibrated as follows How was the first atomic clock calibrated?. Now my question relates to how that relates to time measured by the everyday person. Some background:

1. I am aware of GPS and the time dilation effect from geostationary orbit.
2. There are leap seconds as the earth's orbit around the sun is not constant.
3. Time measured in physics, for example the measurement in scientific experiments is different to the logging of time for financial transactions (for example stock trades), phone call logs etc. (or is it?)
4. That (in the UK) a radio signal is transmitted with the atomic time encoded in the signal.

My question is how is are the world's atomic clocks continually calibrated to compensate for the vagaries of the Earth's rotation and orbit around the sun?

How does the orbit of our solar system affect the calibration of these clocks? i.e. does the Doppler effect, affect the continual calibration?

• I think you are basically asking if there is something like a "clean absolute time standard". No, there is not. In a relativistic universe Doppler effect (time dilation plus change in distance plus gravitational effects) IS the "physics of time". We can not "calibrate it out". Nor do we have to because if we were to measure time in some form of absolute celestial standard time, then it would automatically be contaminated by our relative motion and gravitational potential to that standard and local physical data resynched to that clock would look very disturbing. Commented Jul 11 at 0:24
• @FlatterMann That is an interesting observation and yes, that is how I understood it. Commented Jul 12 at 7:12

My question is how is are the world's atomic clocks continually calibrated to compenstate for the vargaries of the Earth's rotation and orbit around the sun?

They aren't. The atomic timescale is independent of the current rotation or orbit of the earth. Instead multiple clocks are compared against each other (compensating for things like different gravitational field strength and different rotational speed due to latitude). Poorly performing clocks can be detected and excluded. The remaining ones are, in a sense, "averaged together" and produce TAI.

There are leap seconds as the earth's orbit around the sun is not constant

There are leap seconds as the earth's rotation on its axis is not constant and UTC currently ties together both the rotation of the earth and atomic time. Because of this, we cannot exactly predict when leap seconds will need to be added (or subtracted).

There are other proposals that would decouple rotation from UTC to avoid some of the problems with leap seconds.

The orbit of the earth around the sun doesn't vary as much. The problem there is we like to count (tropical) years in integer numbers of days, and there is no exact ratio between the two. Calendars need to compensate for that, but the discrepancies of calendars are different than the problems of atomic time and earth rotation.

• You suggest necessity of taking 'different rotational speed due to latitude' into account. However, whatever the latitude: for clocks located at sea level the same amount of proper time will elapse. On the rotating Earth: sea level is a gravitational equipotential. If you would split up in velocity time dilation and gravitational time dilation then at every equipotential the two drop away against each other. So there is no need to take latitude into account. The factor to take into account is the geopotential (height relative to sea level equipotential) of the location of the clock. Commented Aug 6 at 18:40

Modern metrology supports the issues you address by having multiple time systems, each with their own peculiarities. Any activity that needs a clock to measure time chooses a time system which meets their particular needs.

Each atomic clock produces its own time system. Technically any clock produces its own time system, but the atomic clocks are particularly precise so we draw extra attention to them. Each clock has some drift associated with the imperfections in the hardware. It also has predictable drift based on its environment. In particular, each clock is at a different altitude, and thus by general relativity has a different rate of time passing.

The major owners of high-precision clocks (such as NIST) work together to produce a calculated timescale called TAI. TAI was a weighted average of the clocks, but in 1970 they added a correction to the output of all of the clocks to correct for the effects of general relativity. Thus now TAI measures time "at sea level," by applying correction terms mathematically.

Another time system, UT1, follows the rotation of the Earth. This speeds up and slows down due to complicated mechanics inside the planet. UTC adds (or removes) leap seconds to try to stay within 0.9s of UT1, but otherwise stays in time with TAI (1 UTC second = 1 TAI second). TAI, on the other hand, just keeps ticking, 86400 seconds every day.

Beyond that we have additional calculated time systems. There's barycentric time systems, such as those which calculate the passage of time with some object staying some great fixed distance away from the sun (the great distance avoids more time dilation issues).

There's plenty more beyond that, but that should provide context for the answer: we use the atomic clocks to come up with a meaningful time in TAI, and then we apply correction factors to convert a time into a time system which is appropriate for the task at hand.